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Vaccines Sub-Committee of the International Society for Clinical Biostatistics |
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New Publications
New books and articles related to the statistics of vaccines research are summarized in the sub-committee's quarterly newsletter.
If you know of a recent publication in the field of statistics of vaccines research or have recently had an article or book published and would like it included in the newsletter and on this page, email newpublications@iscb-vaccines.info.
Rolland M, Gilbert P. Evaluating Immune Correlates in HIV Type 1 Vaccine Efficacy Trials: What RV144 May Provide. AIDS Res Hum Retroviruses. 2011.
Describes how researchers can determine correlates of immune protection for an HIV/AIDS vaccine and the terminology used to describe correlates and surrogates.
Huang Y, Gilbert PB. Comparing biomarkers as principal surrogate endpoints. Biometrics. 2011. 67(4):1442-51.
Proposes the characterization of a marker or risk model’s principal surrogate value based on the distribution of risk difference between interventions. Also proposes a new summary measure for comparing markers and assessing the incremental value of a new marker. The joint surrogate value of multiple markers is estimated by a semi-parametric estimated-likelihood method that can accommodate two-phase sampling.
Ganju J, Zhou K. The benefit of stratification in clinical trials revisited. Statistics in Medicine 2011 30 (24): 2881-2889.
Examines the effect of stratification on variance when stratum sizes are allowed to vary but total sample size is fixed. The relationship between the stratified and unstratified variances is established and shown to be approximately the same for prestratified and post-stratified trials. They demonstrate why stratification may increase the variance compared with no stratification even when the mean square error is reduced on account of stratification.
Aiello F, Attanasio M, Tine F. Assessing covariate imbalance in meta-analysis studies. Statistics in Medicine 2011 30(22): 2671–2682.
Proposes a statistical tool to assess possible covariate imbalance in baseline variables to investigate similarity of trials. Provides a quantitative method to assess combinability of studies for meta-analysis, focusing primarily on RCTs but with possible extension to other settings.
Bacchetti P, Deeks S, McCune J. Breaking free of sample size dogma to perform innovative translational research. Sci Transl Med. 2011 3(87):87ps24.
Argues that studies of new ideas must often have small sample sizes due to cost and feasibility issues and that innovative clinical and translational research can still be attained. Recent statistical work shows that small sized studies can produce more projected scientific value per dollar spent than larger sized studies.
O’Hagan JJ, Hernan MA, Walensky RP, Lipsitch M. Apparent declining efficacy in randomized trials: examples of the Thai RV144 HIV vaccine and South African CAPRISA 004 microbicide trials. AIDS. 2012 Jan 14;26(2):123-6.
Discuss possible explanations for the apparent waning efficacy, positing that selection bias due to heterogeneity in infection risk may be in part responsible. Such bias occurs when study participants have different susceptibility to infection, which can lead to increasing differences in the composition of the study arms over time as those at highest risk become infected and can occur despite arms being similar at baseline. Also discuss methods to improve understanding the effects of infectious disease interventions and risk factors by assessing the impact of frailty on the results.
Statistical Considerations in Determining HIV Incidence from Changes in HIV Prevalence, Ron Brookmeyer and Jacob Konikoff. Statistical Communications in Infectious Diseases, Volume 3(2011)/ Issue 1.
The authors show that the incidence estimator depends on the relative survival rate. They evaluate the sensitivity of estimates to incorrect assumptions about the relative survival rate, and show that small errors in the relative survival can, in some situations, create large biases in HIV incidence. They based prevalence surveys with a mortality follow-up sub-study. We determine sample sizes of the prevalence surveys and mortality sub-studies for this augmented design and provide the necessary R code (version 2.13.0) for sample size determinations. http://www.bepress.com/scid/vol3/iss1/art9/
Sample Size for a Binomial Proportion with
Autocorrelation,
Amalia S. Magaret and Jeffrey Stanaway.
Statistical Communications in Infectious Diseases, Volume 3(2011)/ Issue 1
The authors determine a sample size computation that accounts for: (1) participant-level differences in outcome frequency, (2) autocorrelation in time between samples, and (3) varying number of samples per participant. They developed a computation appropriate for crossover designs that accounts for the dependence of the investigational treatment effect on the pre-treatment detection frequency. http://www.bepress.com/scid/vol3/iss1/art8/
Using HIV Diagnostic Data to Estimate HIV Incidence: Method and Simulation, Yan, Ping; Zhang, Fan; and Wand, Handan. Statistical Communications in Infectious Diseases: Vol. 3 (2011)/ Issue 1, Article 6.
The authors propose a new approach to estimate the number of new infections with the human immunodeficiency virus (HIV), by integrating the back-calculation method based on HIV diagnostic data with proportions of recent infections among newly diagnosed individuals. http://www.bepress.com/scid/vol3/iss1/art6/
A Sequential Phase 2b Trial Design for Evaluating Vaccine Efficacy and Immune Correlates for Multiple HIV Vaccine Regimens, Peter B. Gilbert, Douglas Grove, Erin Gabriel, Ying Huang, Glenda Gray, Scott M. Hammer, Susan P. Buchbinder, James Kublin, Lawrence Corey, and Steven G. Self. Statistical Communications in Infectious Diseases, Volume 3(2011)/ Issue 1.
The article proposes a design, which has main objectives (1) to evaluate VE of each regimen versus placebo against HIV exposures occurring near the time of the immunizations; (2) to evaluate durability of VE for each vaccine regimen showing reliable evidence for positive VE; (3) to expeditiously evaluate the immune correlates of protection if any vaccine regimen shows reliable evidence for positive VE; and (4) to compare VE among the vaccine regimens. The design uses sequential monitoring for the events of vaccine harm, non-efficacy, and high efficacy, selected to weed out poor vaccines as rapidly as possible while guarding against prematurely weeding out a vaccine that does not confer efficacy until most of the immunizations are received. http://www.bepress.com/scid/vol3/iss1/art4/
Identifying Adverse Events of Vaccines Using a Bayesian Method of Medically Guided Information Sharing. Crooks, Colin John, Prieto-Merino, David, Evans, Stephen J.W. Drug Safety. 35(1):61-78, January 1, 2012.
The authors demonstrate a method of medically guided Bayesian information sharing that avoids grouping or splitting the data, and they further combine this with the standard epidemiological tools of stratification and multivariate regression. This study demonstrated a sequence of methods for routinely analyzing spontaneous report databases that was easily understandable and reproducible. The combination of classical and Bayesian methods in this study help to focus the limited resources for hypothesis testing studies towards adverse events with the strongest support from the data.
Assessment of varicella vaccine effectiveness in Germany: A time-series approach, Höhle M., Siedler A., Bader H.-M., Ludwig M., Heininger U. and Von Kries R. Epidemiology and Infection 2011 139:11 (1710-1719).
A multivariate time-series regression model was developed in order to describe the 2005 - 2008 age-specific time-course of varicella sentinel surveillance data following the introduction of a varicella childhood vaccination programme in Germany.
Modeling competing infectious pathogens from a Bayesian perspective: Application to influenza studies with incomplete laboratory results. Yang Yang, M. Elizabeth Halloran, Michael J. Daniels, Ira M. Longini, Jr., Donald S. Burke, and Derek A. T. Cummings. J Am Stat Assoc. 2010; 105(492):1310-1322.
A Bayesian competing-risk model for multiple cocirculating pathogens is proposed for inference on transmissibility and intervention efficacies under the assumption that missingness in the biological confirmation of the pathogen is ignorable. Using the proposed model, it was found that a nonpharmaceutical intervention is marginally protective against transmission of influenza A in a study conducted in elementary schools. http://www.ncbi.nlm.nih.gov/pubmed/21472041
Statistical efficiency in multiple-to-one comparison trials with optimal allocation ratio. Zhang J., Zhang J.J. J. Biopharm. Stat. 2011; 21:1(125-135).
This paper discusses multiple-to-one comparison trials testing a multivalent vaccine product against multiple comparators with respect to immunologic responses. An optimal subject allocation ratio between the multivalent vaccine group and any of the comparators is introduced. http://www.informaworld.com/smpp/content~db=all~content=a931668485
Handling missing data in vaccine clinical trials for immunogenicity and safety evaluation. Li X., Wang W.W.B., Liu G.F., Chan I.S.F. Journal of Biopharmaceutical Statistics 2011; 21:2 (294-310)
This report presents a variety of statistical approaches for analyses of vaccine immunogenicity and safety trials in the presence of missing data. The methods are illustrated with numerical simulations and vaccine trial examples. http://www.ncbi.nlm.nih.gov/pubmed/21391003
Statistical interpretation of the RV144 HIV vaccine efficacy trial in Thailand: A case study for statistical issues in efficacy trials. Peter B. Gilbert, James O. Berger, Donald Stablein, Stephen Becker, Max Essex, Scott M. Hammer, Jerome H. Kim, and Victor G. DeGruttola. The Journal of Infectious Diseases 2011; 203:969–75.
Different analyses of the RV144 HIV vaccine efficacy trial seemed to give conflicting results, and a heated debate ensued as scientists and the broader public struggled with their interpretation. First the interpretation of frequentist results is addressed. Second the paper addresses how Bayesian statistics, which provide clearly interpretable statements about probabilities that the vaccine efficacy takes certain values, provide more information for weighing the evidence about efficacy than do frequentist statistics alone. http://jid.oxfordjournals.org/content/203/7/969.short
An extension of the single threshold design for monitoring efficacy and safety in phase II clinical trials. Brutti, P., Gubbiotti, S. and Sambucini, V. Statistics in Medicine, 2011, 30: 1648–1664. doi: 10.1002/sim.4229
An extension of a Bayesian two-stage design for treatment efficacy is proposed to incorporate safety considerations by using a criterion based on the joint posterior probability that the true overall toxicity rate and the true efficacy-and-safety rate are, respectively, smaller and larger than conveniently pre-specified target values. http://onlinelibrary.wiley.com/doi/10.1002/sim.4229/abstract
HIV-1 vaccine and adaptive trial designs. Lawrence Corey, Gary J. Nabel, Carl Dieffenbach, Peter Gilbert, Barton F. Haynes, Margaret Johnston, James Kublin, H. Clifford Lane, Giuseppe Pantaleo, Louis J. Picker and Anthony S. Fauci. Science Translational Medicine 2011, Vol. 3, Issue 79, p. 79ps13.
A discussion of how adaptive clinical trial designs can accelerate vaccine development by rapidly screening out poor vaccines while extending the evaluation of efficacious ones, improving characterization of promising vaccine candidates and the identification of correlates of immune protection. http://stm.sciencemag.org/content/3/79/79ps13.abstract
A modified self-controlled case series method to examine association between multidose vaccinations and death. Kuhnert R, Hecker H, Poethko-Muller C, Schlaud M, Vennemann M, Whitaker HJ, Farrington CP. Stat. Med. 2011; 30:6(666-677)
The self-controlled case series method (SCCS) was developed to analyze the association between a time-varying exposure and an outcome event. We consider penta- or hexavalent vaccination as the exposure and unexplained sudden unexpected death (uSUD) as the event. The special situation of multiple exposures and a terminal event requires adaptation of the standard SCCS method. This paper proposes a new adaptation, in which observation periods are truncated according to the vaccination schedule. The new method exploits known minimum spacings between successive vaccine doses. Its advantage is that it is very much simpler to apply than the method for censored, perturbed or curtailed post-event exposures recently introduced. This paper presents a comparison of these two SCCS methods by simulation studies and an application to a real data set. In the simulation studies, the age distribution and the assumed vaccination schedule were based on real data. Only small differences between the two SCCS methods were observed, although 50 per cent of cases could not be included in the analysis with the SCCS method with truncated observation periods. By means of a study including 300 uSUD, a 16-fold risk increase after the 4th dose could be detected with a power of at least 90 per cent. A general 2-fold risk increase after vaccination could be detected with a power of 80 per cent. Reanalysis of data from cases of the German case-control study on sudden infant death (GeSID) resulted in slightly higher point estimates using the SCCS methods than the odds ratio obtained by the case-control analysis.
Power of tests for comparing trend curves with application to national immunization survey (NIS). Zhao Z. Stat. Med. 2011; 30:5(531-540)
To develop statistical tests for comparing trend curves of study outcomes between two socio-demographic strata across consecutive time points, and compare statistical power of the proposed tests under different trend curves data, three statistical tests were proposed. For large sample size with independent normal assumption among strata and across consecutive time points, the Z and Chi-square test statistics were developed, which are functions of outcome estimates and the standard errors at each of the study time points for the two strata. For small sample size with independent normal assumption, the F-test statistic was generated, which is a function of sample size of the two strata and estimated parameters across study period. If two trend curves are approximately parallel, the power of Z-test is consistently higher than that of both Chi-square and F-test. If two trend curves cross at low interaction, the power of Z-test is higher than or equal to the power of both Chi-square and F-test; however, at high interaction, the powers of Chi-square and F-test are higher than that of Z-test. The measurement of interaction of two trend curves was defined. These tests were applied to the comparison of trend curves of vaccination coverage estimates of standard vaccine series with National Immunization Survey (NIS) 2000-2007 data. © 2011 John Wiley & Sons, Ltd.
Quantifying bias in a health survey: Modeling total survey error in the National Immunization Survey. Molinari NM, Wolter KM, Skalland B, Montgomery R, Khare M, Smith PJ, Barron ML, Copeland K, Santos K, Singleton JA. Stat. Med. 2011; 30:5(505-514)
Random-digit-dial telephone surveys are experiencing both declining response rates and increasing under-coverage due to the prevalence of households that substitute a wireless telephone for their residential landline telephone.
These changes increase the potential for bias in survey estimates and heighten the need for survey researchers to evaluate the sources and magnitudes of potential bias. We apply a Monte Carlo simulation-based approach to assess bias in the NIS, a land-line telephone survey of 19-35 month-old children used to obtain national vaccination coverage estimates. We develop a model describing the survey stages at which component nonsampling error may be introduced due to nonresponse and under-coverage. We use that model and components of error estimated in special studies to quantify the extent to which noncoverage and nonresponse may bias the vaccination coverage estimates obtained from the NIS and present a distribution of the total survey error.
Results indicated that the total error followed a normal distribution with mean of 1.72 per cent (95 per cent CI: 1.71, 1.74 per cent) and final adjusted survey weights corrected for this error. Although small, the largest contributor to error in terms of magnitude was nonresponse of immunization providers. The total error was most sensitive to declines in coverage due to cell phone only households. These results indicate that, while response rates and coverage may be declining, total survey error is quite small. Since response rates have historically been used to proxy for total survey error, the finding that these rates do not accurately reflect bias is important for evaluation of survey data.
Identifying optimal risk windows for self-controlled case series studies of vaccine safety. Stanley Xu, Lijing Zhang, Jennifer C. Nelson, Chan Zeng, John Mullooly, David McClure, Jason Glanz. Stat in Med. Volume 30, Issue 7, pages 742–752, 30 March 2011
In vaccine safety studies, subjects are considered at increased risk for adverse events for a period of time after vaccination known as risk window. To our knowledge, risk windows for vaccine safety studies have tended to be pre-defined and not to use information from the current study. Inaccurate specification of the risk window can result in either including the true control period in the risk window or including some of the risk window in the control period, which can introduce bias. We propose a data-based approach for identifying the optimal risk windows for self-controlled case series studies of vaccine safety. The approach involves fitting conditional Poisson regression models to obtain incidence rate ratio estimates for different risk window lengths. For a specified risk window length (L), the average time at risk, T(L), is calculated. When the specified risk window is shorter than the true, the incidence rate ratio decreases with 1/T(L) increasing but there is no explicit relationship. When the specified risk window is longer than the true, the incidence rate ratio increases linearly with 1/T(L) increasing. Theoretically, the risk window with the maximum incidence ratio is the optimal risk window. Because of sparse data problem, we recommend using both the maximum incidence rate ratio and the linear relationship when the specified risk window is longer than the true to identify the optimal risk windows. Both simulation studies and vaccine safety data applications show that our proposed approach is effective in identifying medium and long-risk windows.
Model structure analysis to estimate basic immunological processes and maternal risk for parvovirus B19. Goeyvaerts N. Hens N, Aerts M. and Beutels Ph. Biostat kxq059 first published online September 14, 2010 doi:10.1093/biostatistics/kxq059
After a steep monotone rise with age, the seroprevalence profiles for human parvovirus B19 (PVB19) display a decrease or plateau between the ages of 20 and 40, in each of 5 European countries. We investigate whether this phenomenon is induced by waning antibodies for PVB19 and, if this is the case, whether secondary infections are plausible, or whether boosting may occur. Several immunological scenarios are tested for PVB19 by fitting different compartmental dynamic transmission models to serological data using data on social contact patterns. The social contact approach has already been shown informative to estimate transmission rates and the basic reproduction number for infections transmitted predominantly through nonsexual social contacts. Our results show that for 4 countries, model selection criteria favor the scenarios allowing for waning immunity at an age-specific rate over the assumption of lifelong immunity, assuming that the transmission rates are directly proportional to the contact rates. Different views on the evolution of the immune response to PVB19 infection lead to altered estimates of the age-specific force of infection and the basic reproduction number. The scenarios which allow for multiple infections during one lifetime predict a higher frequency of PVB19 infection in pregnant women and of associated fetal deaths. When prevaccination serological data are available, the framework developed in this paper could prove worthwhile to investigate these different scenarios for other infections as well, such as cytomegalovirus.
Estimating the distribution of the window period for recent HIV infections: A comparison of statistical methods. Sweeting MJ, De Angelis D, Parry J, Suligoi B. Stat Med. 2010; 29(30)3194-3202.
In the past few years a number of antibody biomarkers have been developed to distinguish between recent and established Human Immunodeficiency Virus (HIV) infection. Typically, a specific threshold/cut-off of the biomarker is chosen, values below which are indicative of recent infections. Such biomarkers have attracted considerable interest as the basis for incidence estimation using a cross-sectional sample. An estimate of HIV incidence can be obtained from the prevalence of recent infection, as measured in the sample, and knowledge of the time spent in the recent infection state, known as the window period. However, such calculations are based on a number of assumptions concerning the distribution of the window period. We compare two statistical methods for estimating the mean and distribution of a window period using data on repeated measurements of an antibody biomarker from a cohort of HIV seroconverters. The methods account for the interval-censored nature of both the date of seroconversion and the date of crossing a specific threshold. We illustrate the methods using repeated measurements of the Avidity Index (AI) and make recommendations about the choice of threshold for this biomarker so that the resulting window period satisfies the assumptions for incidence estimation.
Estimation of overall survival in an 'illness-death' model with application to the vertical transmission of HIV-1. Frydman H and Szarek M. Stat Med. 2010; 29(19):2045-2054.
We derive a nonparametric maximum likelihood estimate of the overall survival distribution in an illness-death model from interval censored observations with unknown status of the nonfatal event. This expanded model is applied to the re-analysis of data from a randomized trial where infants, born to women infected with HIV-1 that were randomly assigned to breastfeeding or counseling for formula feeding, were followed for 24 months for HIV-1 positivity, HIV-1-free survival, and overall survival. HIV-1 positivity, assessed by postpartum venous blood tests, is the interval censored nonfatal event, and HIV-1 positivity status is unknown for a subset of infants due to periodic assessment. The analysis demonstrates that estimation of the overall and the pre- and post-nonfatal event survival distributions with the proposed methods provide novel insights into how overall survival is influenced by the occurrence of the nonfatal event. More generally, it suggests the usefulness of this expanded illness-death model when evaluating composite endpoints as potential surrogates for overall survival in a given disease setting.
Estimating time since infection in early homogeneous HIV-1 samples using a Poisson model. Giorgi EE, Funkhouser B, Athreya G, Perelson AS, Korber BT and Bhattacharya T. BMC Bioinformatics 2010; 11(1):532.
BACKGROUND: The occurrence of a genetic bottleneck in HIV sexual or mother-to-infant transmission has been well documented. This results in a majority of new infections being homogeneous, i.e., initiated by a single genetic strain. Early after infection, prior to the onset of the host immune response, the viral population grows exponentially. In this simple setting, an approach for estimating evolutionary and demographic parameters based on comparison of diversity measures is a feasible alternative to the existing Bayesian methods (e.g. BEAST), which are instead based on the simulation of genealogies. RESULTS: We have devised a web tool that analyzes genetic diversity in acutely infected HIV-1 patients by comparing it to a model of neutral growth. More specifically, we consider a homogeneous infection (i.e. initiated by a unique genetic strain) prior to the onset of host-induced selection, where we can assume a random accumulation of mutations. Previously, we have shown that such a model successfully describes about 80 of sexual HIV-1 transmissions provided the samples are drawn early enough in the infection. Violation of the model is an indicator of either heterogeneous infections or the initiation of selection. CONCLUSIONS: When the underlying assumptions of our model (homogeneous infection prior to selection and fast exponential growth) are met, we are under a very particular scenario for which we can use a forward approach (instead of backwards in time as provided by coalescent methods). This allows for more computationally efficient methods to derive the time since the most recent common ancestor. Furthermore, the tool performs statistical tests on the Hamming distance frequency distribution, and outputs summary statistics (mean of the best fitting Poisson distribution, goodness of fit p-value, etc). The tool runs within minutes and can readily accommodate the tens of thousands of sequences generated through new ultradeep pyrosequencing technologies. The tool is available on the LANL website
The evaluation of vaccine safety involves pre-clinical animal studies, pre-licensure randomized clinical trials, and post-licensure safety studies. Sequential design and analysis are of particular interest because they allow early termination of the trial or quick detection that the vaccine exceeds a prescribed bound on the adverse event rate. After a review of the recent developments in this area, we propose a new class of sequential generalized likelihood ratio tests for evaluating adverse event rates in two-armed pre-licensure clinical trials and single-armed post-licensure studies. The proposed approach is illustrated using data from the Rotavirus Efficacy and Safety Trial. Simulation studies of the performance of the proposed approach and other methods are also given.
The development of a new pneumococcal conjugate vaccine involves assessing the responses of the new serotypes included in the vaccine. The World Health Organization guidance states that the response from each new serotype in the new vaccine should be compared with the aggregate response from the existing vaccine to evaluate non-inferiority. However, no details are provided on how to define and estimate the aggregate response and what methods to use for non-inferiority comparisons. We investigate several methods to estimate the aggregate response based on binary data including simple average, model-based, and lowest response methods. The response of each new serotype is then compared with the estimated aggregate response for non-inferiority. The non-inferiority test p-value and confidence interval are obtained from Miettinen and Nurminen's method, using an effective sample size. The methods are evaluated using simulations and demonstrated with a real clinical trial example.
This article describes various empirical and statistical approaches to defining a positive response in the ELISPOT assay, a cellular assay commonly used in HIV vaccine trials as well as in cancer immunotherapy applications. A bootstrap approach is advocated to account for the inherent assay variability and to allow for multiplicity adjustment across multiple antigen stimulation conditions. A web-based user interface was developed to allow easy access to the recommended statistical methods, allowing the user to upload data from an ELISPOT assay and obtain an output file of the binary responses. R code is also provided to implement the proposed methods.
Recent innovative statistical approaches for phase I/II clinical trials allow one to jointly model the toxicity and efficacy of a new treatment, taking into account the information gathered during the trial. Prior probabilities are then updated with interim data and thus predictive probabilities become more accurate as the trial progresses. In this study, prior distribution elicited from a physician's opinion on the available dose levels planned for a vaccination dose-finding trial, with human DNA in patients with HER2-positive tumours in terms of toxicity and therapeutic response is presented and discussed. A simulation study was conducted in order to quantify the impact of the choice of prior on study results, i.e. the recommended dose level at the end of the trial.
Increasing the Efficiency of Prevention Trials by Incorporating Baseline Covariates. Zhang, Min and Gilbert, Peter B. (2010) Statistical Communications in Infectious Diseases: Vol. 2: Iss. 1, Article 1. Available at: http://www.bepress.com/scid/vol2/iss1/art1
Most randomized efficacy trials of interventions to prevent HIV or other infectious diseases have assessed intervention efficacy by a method that either does not incorporate baseline covariates, or that incorporates them in a non-robust or inefficient way. Yet, it has long been known that randomized treatment effects can be assessed with greater efficiency by incorporating baseline covariates that predict the response variable. Tsiatis et al. (2007) and Zhang et al. (2008) advocated a semiparametric efficient approach, based on the theory of Robins et al. (1994), for consistently estimating randomized treatment effects that optimally incorporates predictive baseline covariates, without any parametric assumptions. They stressed the objectivity of the approach, which is achieved by separating the modeling of baseline predictors from the estimation of the treatment effect. While their work adequately justifies implementation of the method for large Phase 3 trials (because its optimality is in terms of asymptotic properties), its performance for intermediate-sized screening Phase 2b efficacy trials, which are increasing in frequency, is unknown. Furthermore, the past work did not consider a right-censored time-to-event endpoint, which is the usual primary endpoint for a prevention trial. For Phase 2b HIV vaccine efficacy trials, we study finite-sample performance of Zhang et al.'s (2008) method for a dichotomous endpoint, and develop and study an adaptation of this method to a discrete right-censored time-to-event endpoint. We show that, given the predictive capacity of baseline covariates collected in real HIV prevention trials, the methods achieve 5-15% gains in efficiency compared to methods in current use. We apply the methods to the first HIV vaccine efficacy trial. This work supports implementation of the discrete failure time method for prevention trials.
Given a randomized treatment Z, a clinical outcome Y, and a biomarker S measured some fixed time after Z is administered, we may be interested in addressing the surrogate endpoint problem by evaluating whether S can be used to reliably predict the effect of Z on Y. Several recent proposals for the statistical evaluation of surrogate value have been based on the framework of principal stratification. In this article, we consider two principal stratification estimands: joint risks and marginal risks. Joint risks measure causal associations (CAs) of treatment effects on S and Y, providing insight into the surrogate value of the biomarker, but are not statistically identifiable from vaccine trial data. Although marginal risks do not measure CAs of treatment effects, they nevertheless provide guidance for future research, and we describe a data collection scheme and assumptions under which the marginal risks are statistically identifiable. We show how different sets of assumptions affect the identifiability of these estimands; in particular, we depart from previous work by considering the consequences of relaxing the assumption of no individual treatment effects on Y before S is measured. Based on algebraic relationships between joint and marginal risks, we propose a sensitivity analysis approach for assessment of surrogate value, and show that in many cases the surrogate value of a biomarker may be hard to establish, even when the sample size is large.
Statistics in Clinical Vaccine Trials. Jozef Nauta. Springer. ISBN: 978-3-642-14690-9. Due: November 2010.
This book is intended for statisticians working in clinical vaccine development in the pharmaceutical industry, at universities, at national vaccines institutes, etc. A good knowledge of statistics is assumed, but the scope of the book is practical rather than theoretical. Many real-life examples are given, and SAS codes are provided. SAS codes are also given for accurate sample size estimation, including codes for the estimation of required sample sizes for equivalence and non-inferiority vaccine trials. The book opens with two introductory chapters on the immunology of vaccines to provide the reader with the necessary background knowledge. Chapter 3 is the central one of the book. The four standard statistics to summarize humoral and cellular immunogenicity data are introduced. In Chapter 4 two types of possible bias for antibody titers are discussed. The first type of bias is due to how antibody titers are defined. An alternative definition is proposed, the mid-value definition. The second type of bias occurs when titers above (or below) a certain level are not determined. If this bias is ignored the geometric mean titer will be underestimated. It is shown how the method of maximum likelihood estimation for censored observation can be applied to eliminate this bias. A standard approach to baseline imbalance is ANCOVA. In case of antibody values the assumption of homoscedasticity is not met, the larger the baseline value the smaller the standard deviation of the error term. In Chapter 5 a solution to this problem is offered. It is shown that the heteroscedasticity can be modeled. A variance model is derived, and it is demonstrated how this model can be fitted with SAS. In Chapter 6 the statistical analysis of equivalence or non-inferiority trials is explained. The standard analysis of lot consistency data is known to be conservative, but a simple formula is presented which can be used to decide if the lot sample sizes guarantee that the actual type I error rate of the trial is sufficiently close to the nominal level. The chapter is concluded with a discussion of sample size estimation for vaccine equivalence and non-inferiority trials, including lot consistency trials. Recommendations are given how to avoid that the statistical power is overestimated. Chapter 7 considers vaccine field efficacy trials. The three incidence measures for infection are introduced: the attack rate, the infection rate and the force of infection. The statistical analysis of field efficacy trials using these estimators is explained. The chapter then continues with the statistical analysis of recurrent infection data, which is known to be complex. The chapter is concluded with a discussion of sample size estimation for vaccine field efficacy trial. It is shown that the standard method to estimate the sample size for a trial comparing two attack rates and with the aim to demonstrate super efficacy is highly conservative. A SAS code to compute sample sizes for trials comparing two infection rates is presented. The topic of Chapter 8 is correlates of protection. It is demonstrated how the parameters of the protection curve can be estimated from challenge study data and vaccine field efficacy data. Also explained is how a threshold of protection can be estimated from the protection curve. The final chapter, Chapter 9, addresses vaccine safety. Vaccine safety surveillance is briefly discussed, and some recent controversies are recalled. The notorious problem of vaccine safety and multiplicity is discussed at great length. Four different methods to handle this problem are presented, including the recently proposed double false discovery method. The performance of the different methods is illustrated with the help of simulation results. The second part of the chapter is dedicated to the analysis of reactogenicity data. In the appendices a generalized worst-case sensitivity analysis for a single seroresponse rate for which the confidence interval must fall above a pre-specified bound is presented.
Relationship between haemagglutination-inhibiting antibody titres and clinical protection against influenza: development and application of a bayesian random-effects model. Coudeville L, Bailleux F, Riche B, Megas F, André P, Ecochard R. BMC Medical Research Methodology 2010; 10(1):18
Background: Antibodies directed against haemagglutinin, measured by the haemagglutination inhibition (HI) assay are essential to protective immunity against influenza infection. An HI titre of 1:40 is generally accepted to correspond to a 50% reduction in the risk of contracting influenza in a susceptible population, but limited attempts have been made to further quantify the association between HI titre and protective efficacy.
Methods: We present a model, using a meta-analytical approach, that estimates the level of clinical protection against influenza at any HI titre level. Source data were derived from a systematic literature review that identified 15 studies, representing a total of 5899 adult subjects and 1304 influenza cases with interval-censored information on HI titre. The parameters of the relationship between HI titre and clinical protection were estimated using Bayesian inference with a consideration of random effects and censorship in the available information.
Results: A significant and positive relationship between HI titre and clinical protection against influenza was observed in all tested models. This relationship was found to be similar irrespective of the type of viral strain (A or B) and the vaccination status of the individuals.
Conclusion: Although limitations in the data used should not be overlooked, the relationship derived in this analysis provides a means to predict the efficacy of inactivated influenza vaccines when only immunogenicity data are available. This relationship can also be useful for comparing the efficacy of different influenza vaccines based on their immunological profile.
Some design issues in phase 2B vs phase 3 prevention trials for testing efficacy of products or concepts. Gilbert P.B. Statistics in Medicine 2010 29:10 (1061-1071)
After one or more Phase 2 trials show that a candidate preventive vaccine induces immune responses that putatively protect against an infectious disease for which there is no licensed vaccine, the next step is to evaluate the efficacy of the candidate. The trial-designer faces the question of what is the optimal size of the initial efficacy trial? Part of the answer will entail deciding between a large Phase 3 licensure trial or an intermediate-sized Phase 2b screening trial, the latter of which may be designed to directly contribute to the evidence-base for licensing the candidate, or, to test a scientific concept for moving the vaccine field forward, acknowledging that the particular candidate will never be licensable. Using the HIV vaccine field as a case study, we describe distinguishing marks of Phase 2b and Phase 3 prevention efficacy trials, and compare the expected utility of these trial types using Pascal's decision-theoretic framework. By integrating values/utilities on (1) correct or incorrect conclusions resulting from the trial; (2) timeliness of obtaining the trial results; (3) precision for estimating the intervention effect; and (4) resources expended; this decision framework provides a more complete approach to selecting the optimal efficacy trial size than a traditional approach that is based primarily on power calculations. Our objective is to help inform the decision-process for planning an initial efficacy trial design.
Estimating Influenza vaccine effectiveness using routinely collected laboratory data. Fleming DM, Andrews NJ, Elllis JS, Bermingham A, Sebastianpillai P, Elliot AJ, Miller E, Zambon M. J Epidemiol Community Health. 2009 Nov 12.
BACKGROUND: There is a need for real-time, within season, estimation of influenza vaccine effectiveness (V/E) in order to optimize management of circulating influenza; a need which will be even greater in a pandemic situation. OBJECTIVE: To examine the potential of using routinely collected national virological surveillance data to generate estimates of V/E in real-time. METHODS: Information collected in the integrated clinical and virological community influenza surveillance program of the Royal College of General Practitioners and Health Protection Agency over three winters 2004/5-2006/7 was used. From vaccination and clinical data entered on the investigation request form and the influenza virology detection result, we calculated the odds of vaccination in virus positive and in virus negative persons. One minus the ratio of these odds provided crude estimates of V/E, which were adjusted for confounding using logistic regression. RESULTS: Multivariate analysis suggested that adjustments were necessary for patient age and month of sampling. The annual adjusted V/E was 2005/6, 67% (95% confidence intervals 41-82); 2006/7 55% (26-73) and 2007/8 67% (41-82); and in persons <65 years, 70% (57-78) and 65 years and over 46% (-17-75). Estimates derived separately for influenza A and B, for interval between illness onset and swab sample, for early and late winter periods, and according to viral load did not differ significantly in each comparison. CONCLUSION: We have demonstrated the potential of using routine management data to provide estimates of V/E in real-time. We recommend this approach to V/E measurement in the evaluation of national influenza vaccination programmes.
New Journal: Statistical Communications in Infectious Diseases
Berkeley Electronic Press has launched a new peer-reviewed journal: Statistical Communications in Infectious Diseases. The journal is edited by Victor De Gruttola (Harvard University), Christl Donnelly (Imperial College London) and Gavin Gibson (Heriot-Watt University).
The journal takes a broad perspective, both theoretical and policy-oriented, on the role of statistics in infectious disease control efforts. It aims to foster much-needed rapid communication among statisticians on the best approaches to increasingly complex data on infectious diseases. The hope is that it will be a venue for statisticians to enter a dialogue with other scientists and with policy makers on the strengths and limitations of methods for analysis in this important area.
The editors of the journal invite your submissions on topics germane to the mission of the journal, including: randomized interventional trials, the history of past epidemics, infectious disease control policy, statistical methodology related to infectious disease epidemiology, modeling of infectious diseases - deterministic and stochastic, vaccine development and testing, Other types of 'infection’, such as network theory and social and cultural spread. The website is at http://www.bepress.com/scid/
New Book: An Introduction to Infectious Disease Modelling, by E Vynnycky and RG White [with an introduction by PEM Fine]. Oxford University Press, 2010
Mathematical models are increasingly being used to examine questions in infectious disease control. Written for readers without advanced mathematical skills, this book provides an excellent introduction to this exciting and growing area. Drawing on examples from many diverse infections (e.g. influenza, rubella, tuberculosis, HIV, gonorrhoea, varicella), the book guides readers step-by-step through the different types of models and the methods and data needed to set them up. It also covers the applications of modelling and the important insights that it has provided into the transmission and control of infections.
The chapters include easy-to-follow worked examples, together with exercises based on real data and real-life problems. Understanding is further enhanced by downloadable models, enabling readers to gain practical experience of modelling. The book also includes a chapter revising basic mathematical concepts which are relevant for the text, as well as Appendices with proofs for any readers wishing to learn more than just the basics.
The book is based on material from popular courses developed by the authors over many years. It will be of interest to epidemiologists, public health researchers, policy makers, veterinary scientists, medical statisticians, health economists, infectious disease researchers, applied mathematicians, and those generally interested in mathematical modelling or infectious diseases. Tutors and students of courses on epidemiology or infectious diseases will also find the book helpful.
For further details see www.anintroductiontoinfectiousdiseasemodelling.com
New Articles:
Assessing association in a stratified experiment. Jason J.Z. Liao, Daniel J. Holder. Statistics in Biopharmaceutical Research. May 1, 2009, 1(2): 170-175.
Pearson’s correlation coefficient has been widely used to measure the association of two variables in an unstratified experiment. In practice, however, experiments are often stratified based on factors. In this article, a common correlation coefficient is derived to estimate the common association when the association at each level of a stratified experiment is the same. Our estimator of the common correlation coefficient has a better small-sample performance than the commonly used sample size weighted estimator in terms of bias and mean squared error. The proposed statistics are demonstrated using data from a vaccine potency assay in mice.
Optimal two-stage designs to evaluate a series of new agents or treatments. Vandana Mukhi, Yongzhao Shao. Statistics in Biopharmaceutical Research. November 1, 2009, 1(4): 377-387.
Recent developments in cancer vaccines and other research programs have prompted the need for screening a large number of agents (or treatments) to identify promising ones for further clinical investigation. This article proposes optimal two-stage group sequential designs that minimize the expected number of patients exposed to inactive agents. The proposed three-outcome, two-stage designs include some region of uncertainty which enables factors such as cost of the agent and convenience of administration to be used in the decision making when the observed response rate falls into the uncertainty region. In the special case of two-outcome designs, our proposal extends Simon’s optimal two-stage design and other existing screening trial designs that use available distributional information on response rates. It does so by allowing early termination of the trial when the observed response rate is below a certain threshold and by providing more choices of error rates to control. A computer algorithm was developed to effectively calculate the three-outcome and/or two-outcome optimal designs. It is demonstrated via numerical studies and a cancer vaccine trial.
Stratified Wilson and Newcombe confidence intervals for multiple binomial proportions. Xin Yan, Xiao Gang Su. Statistics in Biopharmaceutical Research: 1-7. Posted online on 25 Aug 2009.
This article proposes the stratified Wilson confidence interval for multiple binomial proportions and the stratified Newcombe confidence intervals for multiple binomial proportion differences. Both confidence intervals are presented in closed forms to facilitate easy calculations. The confidence levels of the proposed intervals are theoretically justified and demonstrated through extensive simulations. The coverage rates are found to be rather satisfactory. When the Wilson and Newcombe methods are used in unstratified analysis, the proposed methods may serve as the counterparts for stratified analysis. The proposed methods are applied to a vaccine trial to compute the stratified sero-conversion rate and rate difference over multiple clinical centers.
The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross-sectional serological data. N. Hens, A. Wienke, M. Aerts, G. Molenberghs. Statistics in Medicine. Volume 28, Issue 22, Date: 30 September 2009, Pages: 2785-2800
Frailty models are often used to study the individual heterogeneity in multivariate survival analysis. Whereas the shared frailty model is widely applied, the correlated frailty model has gained attention because it elevates the restriction of unobserved factors to act similar within clusters. Estimating frailty models is not straightforward due to various types of censoring. In this paper, we study the behavior of the bivariate-correlated gamma frailty model for type I interval-censored data, better known as current status data. We show that applying a shared rather than a correlated frailty model to cross-sectionally collected serological data on hepatitis A and B leads to biased estimates for the baseline hazard and variance parameters.
Transfer of methods supporting biologics and vaccines. Rong Liu, Timothy L. Schofield, Jason J.Z. Liao. Statistics in Biopharmaceutical Research. November 1, 2009, 1(4): 450-456. doi:10.1198/sbr.2009.0045.
The transfer of analytical methods supporting biologics and vaccines is complicated by the complexity and variability of biological systems. Many of these assays may be linked to clinical performance, and thus subject to specifications established from materials that were tested in the development laboratory. Thus, transfer must account for the risk that the method characteristics have changed, and may generate results for commercial lots that either earmarks a satisfactory lot as failing, or an unsatisfactory lot as passing specification. Transfer study strategies have been proposed based on method parameters or on tolerance intervals. This article describes a framework for establishing the equivalence between two laboratories with emphasis on the associated risks, and compares and contrasts the parametric and tolerance approaches.
New strategies are needed to improve the accuracy of influenza vaccine effectiveness estimates among seniors. Nelson JC, Jackson ML, Weiss NS, Jackson LA. Journal of Clinical Epidemiology 2009; 62(7):687-94.
Objective: The magnitude of the benefit of influenza vaccine among elderly individuals has been recently debated. Existing vaccine effectiveness estimates derive primarily from observational studies, which may be biased. In this paper, we provide a methodological examination f the potential sources of bias in observational studies of influenza vaccine effectiveness in seniors and propose design and analysis strategies to reduce bias in future studies.
Study Design and Setting: We draw parallels to bias documented in observational studies of therapies in other areas of medical research including pharmacoepidemiology, discuss reasons why existing adjustment methods in influenza studies may not adequately control or the bias, and evaluate statistical approaches that may yield more accurate estimation of influenza vaccine effectiveness.
Results: There is strong evidence for the presence of bias in existing observational estimates of influenza vaccine effectiveness in the elderly and the failure of current adjustment methods to reduce bias.
Conclusion: Promising approaches for reducing bias include obtaining more accurate information on confounders, such as functional status, avoiding all-cause death in favor of outcomes, such as pneumonia or influenza-related pneumonia, and evaluating the extent to which bias is reduced by these and other methods using the ‘control’ period before influenza season.
The methodology of self-controlled case series studies. Whitaker HJ, Hocine MN, Farrington CP. Statistical Methods in Medical Research 2009; 18(1):7-26.
The self-controlled case series method is increasingly being used in pharmacoepidemiology, particularly in vaccine safety studies. This method is typically used to evaluate the association between a transient exposure and an acute event, using only cases. We present both parametric and semiparametric models using a motivating example on MMR vaccine and bleeding disorders. We briefly describe approaches for interferent events and a sequential version of the method for prospective surveillance of drug safety. The efficiency of the self-controlled case series method is compared to the that of cohort and case control studies. Some further extensions, to long or indefinite exposures and to bivariate counts, are described.
Nonclinical testing of vaccines: Report from a workshop. van der Laan JW, Forster R, Ledwith B, Gruber M, Gould S, Segal L, Penninks A. Drug Information Journal 2009; 43(1):97-107.
Vaccine research and development is a heterogeneous and intensely active area, encompassing the development of many different kinds of novel preventive and therapeutic vaccines (e.g. against infectious, allergic, and autoimmune diseases, cancer, etc). Included in this is the development of different types of vaccines (e.g. DNA vaccines, novel routes of administration, novel adjuvants, and immune system modulation). This poses challenges regarding approaches to preclinical evaluation of these products. Published regulatory guidance has not always kept up with scientific advances and innovation in this area and, at the same time, many vaccine developers are interested in better understanding and meeting regulatory expectations. It was in this context that in June 2007 a workshop was organized and held in Amsterdam (DIA International Workshop on Nonclinical Testing of Vaccines) to discuss the nonclinical aspects of vaccine development. This article provides a short historical overview of preclinical testing of vaccines and reviews and summarizes the discussions held during the June 2007 meeting.
Evaluation of serological trials submitted for annual re-licensure of influenza vaccines to regulatory authorities between 1992 and 2002. A.C.G. Voordouw, W.E.P. Beyer, D.J. Smith, M.C.J.M. Sturkenboom, B.H.Ch. Stricker. Vaccine Volume 28, Issue 2, 11 December 2009, Pages 392-397
Background: As part of the regulatory requirements, serological evaluation of trivalent inactivated influenza vaccines must be performed before annual re-licensure in the European Union. These studies are typically set up as uncontrolled, open label trials including 2 groups of at least 50 healthy adults and healthy elderly.
Methods: The serological data submitted to the Dutch Medicines Evaluation Board (MEB) for annual re-licensure purposes between 1992 and 2002, were analysed with respect to their ability to assess the immunogenic properties of the vaccines. The trials in this meta-analysis were selected by strictly applying the inclusion and exclusion criteria described in the Committee of Human Medicinal Products (CHMP) Note for Guidance on harmonisation of requirements for influenza vaccines. To select the final dataset additional exclusion criteria were defined: age outside the inclusion criterion of the trial, incomplete demographics, co-morbid conditions, antibody determination by SRH assay, incomplete dataset and sample size smaller than 50 subjects.
Results: Out of 51 trials retrieved from the archives, 48 age-defined trials including 2510 adults and 2008 elderly fulfilled all the in- and exclusion criteria. A large proportion of vaccinees already met the threshold for seroprotection at baseline. Post-vaccination, the serological response was shown to be age dependent. Previous influenza vaccinations significantly affected pre-vaccination but not post-vaccination titres.
Conclusions: The annual update trials performed for regulatory purposes have serious methodological limitations, which affect their ability to identify influenza vaccines with low immunogenicity. To establish clinical (protective) efficacy different trials and different assessment criteria are needed.
Assessing Vaccine Effects in Repeated Low-Dose Challenge Experiments. Michael G. Hudgens, Peter B. Gilbert. Biometrics Volume 65, Issue 4, December 2009, Pages 1223-1232
Evaluation of HIV vaccine candidates in nonhuman primates (NHPs) is a critical step toward developing a successful vaccine to control the HIV pandemic. Historically, HIV vaccine regimens have been tested in NHPs by administering a single high dose of the challenge virus. More recently, evaluation of candidate HIV vaccines has entailed repeated low-dose challenges, which more closely mimic typical exposure in natural transmission settings. In this article, we consider evaluation of the type and magnitude of vaccine efficacy from such experiments. Based on the principal stratification framework, we also address evaluation of potential immunological surrogate endpoints for infection.
Predicted long-term persistence of pertussis antibodies in adolescents after an adolescent and adult formulation combined tetanus, diphtheria, and 5-component acellular pertussis vaccine, based on mathematical modeling and 5-year observed data. Bailleux F, Coudeville L, Kolenc-Saban A, Bevilacqua J, Barreto L, Andre P. Vaccine 2008; 26(31):3903-8.
Several random effect models were applied to data on the persistence of pertussis antigens observed in clinical trials over a 5-year period to predict further antibody decay. LR tests were used to compare models and the model providing the best fit was used to make further predictions. Predictions were notably used to determine the time during which the antibody titers of each subject remains superior to a predefined threshold. This analysis confirmed 10 years as a adequate interval for a pertussis booster vaccination.
A conditional maximized sequential probability ratio test for Pharmacovigilance. Lingling Li, Martin Kulldorff. Statistics in Medicine Volume 29, Issue 2, 30 January 2010, Pages 284-295
The importance of post-marketing surveillance for drug and vaccine safety is well recognized as rare but serious adverse events may not be detected in pre-approval clinical trials. In such surveillance, a sequential test is preferable, in order to detect potential problems as soon as possible. Various sequential probability ratio tests (SPRT) have been applied in near real-time vaccine and drug safety surveillance, including Wald's classical SPRT with a single alternative and the Poisson-based maximized SPRT (MaxSPRT) with a composite alternative. These methods require that the expected number of events under the null hypothesis is known as a function of time t. In practice, the expected counts are usually estimated from historical data. When a large sample size from the historical data is lacking, the SPRTs are biased due to the variance in the estimate of the expected number of events. We present a conditional maximized sequential probability ratio test (CMaxSPRT), which adjusts for the uncertainty in the expected counts. Our test incorporates the randomness and variability from both the historical data and the surveillance population. Evaluations of the statistical power for CMaxSPRT are presented under different scenarios. Copyright © 2009 John Wiley & Sons, Ltd.
ME Halloran, IM Longini Jr, CJ Struchiner. Design and Analysis of Vaccine Studies, Springer 2009
Phases III and IV studies are the main focus of the book, in that its focus is on field studies. In defining the various effects of vaccination and their relation to one another, they implicitly assume a randomized study, with observational studies being departures from the randomized study. Departures from the randomized study can result in confounding and types of biases. Their general paradigm is that of causal inference. Aspects of the book are largely conceptual, showing the interface among study design, statistical analysis, and epidemic theory, and implications for interpretation. After giving an overview of the book, in the remainder of Chapter 1, some key definitions in infectious disease research and causal inference are introduced.
Chapter 2 presents a systematic framework for thinking about many of the different types of vaccination effects and the study designs and estimators used to evaluate them. This chapter is based on a paper by Halloran et al (1997), called the Table Paper because it lays out a two-dimensional table showing several of the main vaccine efficacy and effectiveness estimators. The book then covers four basic study designs for dependent happenings for differentiating and evaluating direct effects and indirect, total, and overall population-level effects of vaccination. Motivated by the malaria vaccine discussions of the 1980s, Struchiner, Halloran and colleagues differentiated the efficacies of vaccines against infection, disease, and transmission. Much of the book expands those aspects presented within this framework. At the conceptual level, the emphasis is on the many different measures of vaccine efficacy and how they relate to each other.
Chapter 3 provides a brief introduction to the immune response to infection, the basis for the idea of prophylatic immunization, and a brief chronicle of the development of vaccines. This is intended to help the reader who does not know immunology and vaccines to be able to read the rest of the book. Vaccine safety is of key importance in vaccine studies. Preclinical animal studies and Phase I and II clinical trials are designed to evaluate immunogenicity and safety, thus are also included in Chapter 3. The idea of herd immunity, the level of immunity to an infectious agent in a population, in contrast to the immune response within an individual, is presented.
Chapter 4 introduces dynamic models and assumptions about mixing patterns in a population. The chapter focuses on the Reed--Frost model and stochastic, discrete-time methods. The chapter demonstrates randomness and the use of stochastic models to investigate direct, indirect, total, and overall effects of vaccination programs. The Reed--Frost model is the basis of estimation procedures in later chapters. Chapter 5 focuses on the basic reproductive number Ro and the role of vaccination. A simple deterministic differential equation is presented, but such models do not play a large role in this book. These two chapters can be read on their own as an introduction to dynamic infectious disease models. Chapters 6 through 8 focus on studies for evaluating the direct protective effects of vaccination. Chapter 6 presents the estimands and estimators for the measures of protective efficacy that do not condition on exposure to infection. Specifically, these include the most common estimators of vaccine efficacy based on the incidence rate, hazard rate, and cumulative incidence. Cumulative incidence is often called the attack rate in infectious diseases. Several examples of field studies are presented. The chapter covers general considerations of designing a study, including choice of populations and comparison populations, choice of outcomes, sample size determination, and randomized versus observational studies.
Chapter 7 discusses different distributions of protection in a population and the implications for study design. The problems of estimating vaccine efficacy in the presence of heterogeneity in protection or exposure to infection or if efficacy wanes are considered. Chapter 8 considers case-control studies in vaccine evaluation. The choice of outcome measures and the use of validation sets for nonspecific outcomes are presented. Chapter 9 presents the evaluation of the effects of vaccination on post-infection outcomes, such as whether vaccination reduces the probability of clinical illness if a person becomes infected.
Chapters 10 through 12 present studies in households and other small transmission units and methods for their analysis. In particular, the chapters present methods for estimating vaccine efficacy for infectiousness and direct protective effects of vaccination when exposure to infection information is available. Chapter 10 presents several examples of studies in households and other small transmission units and discusses considerations of study design. Chapter 11 presents statistical analyses that assume the households or other transmission units are nested within a community. Chapter 12 presents methods of analysis assuming the households or transmission units are independent of each other, including the conventional secondary attack rate analysis.
Chapter 13 focuses on estimation of the indirect, total, and overall effects of widespread vaccination. The framework is the study designs for dependent happenings. The first part presents approaches comparing incidence before and after implementing a vaccination strategy in a population. The second part presents cluster-randomized designs in which several communities are compared. Chapter 14 discusses issues related to the limitations of randomization to control for confounding and interpretation of estimates when baseline transmission, pre-existing immunity, and vaccine-induced protection interact to produce apparently different efficacy of vaccination in different populations. Chapter 15 focuses on evaluating immunological correlates and surrogates of protection.
Dean Follmann, Michael P. Fay, Michael Proschan. Chop-Lump Tests for Vaccine Trials, Biometrics Volume 65, Issue 3, Date: September 2009, Pages: 885-893
This article proposes new tests to compare the vaccine and placebo groups in randomized vaccine trials when a small fraction of volunteers become infected. A simple approach that is consistent with the intent-to-treat principle is to assign a score, say W, equal to 0 for the uninfecteds and some postinfection outcome X > 0 for the infecteds. One can then test the equality of this skewed distribution of W between the two groups. This burden of illness (BOI) test was introduced by Chang, Guess, and Heyse (1994, Statistics in Medicine 13, 1807-1814). If infections are rare, the massive number of 0s in each group tends to dilute the vaccine effect and this test can have poor power, particularly if the X's are not close to zero. Comparing X in just the infecteds is no longer a comparison of randomized groups and can produce misleading conclusions. Gilbert, Bosch, and Hudgens (2003, Biometrics 59, 531-541) and Hudgens, Hoering, and Self (2003, Statistics in Medicine 22, 2281-2298) introduced tests of the equality of X in a subgroup - the principal stratum of those "doomed" to be infected under either randomization assignment. This can be more powerful than the BOI approach, but requires unexaminable assumptions. We suggest new "chop-lump" Wilcoxon and t-tests (CLW and CLT) that can be more powerful than the BOI tests in certain situations. When the number of volunteers in each group are equal, the chop-lump tests remove an equal number of zeros from both groups and then perform a test on the remaining W's, which are mostly >0. A permutation approach provides a null distribution. We show that under local alternatives, the CLW test is always more powerful than the usual Wilcoxon test provided the true vaccine and placebo infection rates are the same. We also identify the crucial role of the "gap" between 0 and the X's on power for the t-tests. The chop-lump tests are compared to established tests via simulation for planned HIV and malaria vaccine trials. A reanalysis of the first phase III HIV vaccine trial is used to illustrate the method.
Yunda Huang, Peter B. Gilbert, David C. Montefiori, Steve G. Self. Simultaneous Evaluation of the Magnitude and Breadth of a Left- and Right-Censored Multivariate Response, With Application to HIV Vaccine Development. Statistics in Biopharmaceutical Research; February 1, 2009, 1(1): 81-91.
To compare antibody-based HIV-1 vaccine candidates in Phase I and II trials, both the magnitude and breadth of neutralization against multiple strains of virus are main endpoints. These also are key markers to be evaluated in vaccine efficacy trials as immune correlates of protection against HIV-1 infection. More generally, magnitude and breadth are considered when there is interest in comparing quantitative multivariate response data between groups. In this article, we discuss two approaches to simultaneously evaluating the magnitude and breadth of a multivariate response. We suggest methods for the summarization and group comparison of multivariate response data that are subject to left and/or right censoring. We discuss applications to data from a phase III clinical trial (Vax004). We also present simulation-based sample size calculations and power analyses of the described methods.
J. Simonsen, K. Molbak, G. Falkenhorst, K. A. Krogfelt, A. Linneberg, P. F. M. Teunis. Estimation of incidences of infectious diseases based on antibody measurements. Statistics in Medicine Volume 28, Issue 14, Date: 30 June 2009, Pages: 1882-1895
Owing to underascertainment it is difficult if not impossible to determine the incidence of a given disease based on cases notified to routine public health surveillance. This is especially true for diseases that are often present in mild forms as for example diarrhoea caused by foodborne bacterial infections. This study presents a Bayesian approach for obtaining incidence estimates by use of measurements of serum antibodies against Salmonella from a cross-sectional study. By comparing these measurements with antibody measurements from a follow-up study of infected individuals it was possible to estimate the time since last infection for each individual in the cross-sectional study. These time estimates were then converted into incidence estimates. Information about the incidence of Salmonella infections in Denmark was obtained by using blood samples from 1780 persons. The estimated incidence was about 0.094 infections per person year. This number corresponds to 325 infections per culture-confirmed case captured in the Danish national surveillance system. We present a novel approach, termed as seroincidence, that has potentials to compare the sensitivity of public health surveillance between different populations, countries and over time. Copyright 2009 John Wiley & Sons, Ltd.
Hayes RJ & Moulton LH. Cluster Randomized Trials: A Practical Approach. Chapman & Hall/CRC, 2009.
The book discusses the design, analysis and conduct of trials of health interventions in which groups or clusters of individuals are randomized to different conditions. It is for statisticians, epidemiologists, and public health specialists, and is at the academic level of a Master's course in Biostatistics or Epidemiology. The emphasis is on the understanding of key concepts rather than on mathematical detail. The book is designed to be accessible to quantitatively-minded clinicians and public health specialists as well as statisticians. Compared to other books on cluster randomized trials, there is relatively more material on study design. There is extensive use of case studies from developed and developing countries to illustrate key concepts and methods, with a focus on infectious diseases, including examples of Phase III vaccine trials. Simple computer code for the Stata software package, based on the illustrative, downloadable datasets, demonstrates how the recommended analytical methods are carried out and interpreted.
Richard Hayes is Professor of Epidemiology & International Health in the Department of Infectious & Tropical Diseases at the London School of Hygiene & Tropical Medicine. He has designed and coordinated cluster-randomized trials of preventive interventions against HIV and malaria in Africa. With Lawrence Moulton he directs the Biostatistics Core of the CREATE consortium which is carrying out several clinic and community randomized TB intervention trials in Africa and South America. Lawrence Moulton is a Professor in the Departments of International Health and Biostatistics at the Johns Hopkins Bloomberg School of Public Health. He has served as the principal statistician on large pneumococcal and Hib vaccine community-randomized trials.
Both authors have carried out methodological research on the design and analysis of cluster randomized trials.
Nauta JJP, Beyer WEP, Osterhaus ADME. On the relationship between mean antibody level, seroprotection. Biologicals 2009; 37: 216-21.
The
relationship between mean antibody level, seroprotection and clinical
protection from influenza is explored, using a simple statistical model. The
model reveals that the relationship is more complex than perhaps thought,
and depends not only on the mean but also on the standard deviation of the
antibody values, the threshold for clinical protection and the clinical
protection curve. This dependency on the standard deviation of the antibody
values has been
largely overlooked until now. The authors find that mean antibody levels
cannot be compared between randomized populations in terms of the fraction
clinically protected subjects without considering standard deviations as
well. Their model further predicts that differences in the fraction
seroprotected subjects cannot be interpreted without taking into account the
mean antibody levels and standard deviations, which limits the usefulness of
the concept of
seroprotection.
Gilbert PG, Sato A, Sun X, Mehrotra DV. Efficient and robust method for comparing the immunogenicity of candidate vaccines in randomized clinical trials. Vaccine 2009, 27: 396-401.
In randomized clinical trials designed to compare the magnitude of vaccine-induced immune responses between vaccination regimens, the statistical method used for the analysis typically does not account for baseline participant characteristics. The article shows that incorporating baseline variables predictive of the immunogenicity study endpoint can provide large gains in precision and power for estimation and testing of the group mean difference compared to conventional methods, and recommends the 'semiparametric efficient' method described in paper by Tsiatis et al. As such, vaccine clinical trial programs can be improved (1) by investigating baseline predictors (e.g., readouts from laboratory assays) of vaccine-induced immune responses, and (2) by implementing the proposed semiparametric efficient method in trials where baseline predictors are available.
Charvat B, Brookmeyer R, and Herson J. The effects of herd immunity on the power of vaccine trials. Statistics in Biopharmaceutical Research 2009; 9(1): 108-17.
The authors of the report evaluated the effects of herd immunity (referring to incidence reduction due to removal of would-be infectious individuals from the pool of infectious carriers) on the power of vaccine trials, specifically considering large-scale trials in which persons are individually randomized to either placebo or vaccine. The authors evaluate the adequacy of naive power calculations that ignore the effects of herd immunity such as those based on the comparison of two independent binomials. The authors developed a simulation design to evaluate the quantitative effects of herd immunity on power, accounting for non-homogeneous mixing. The authors have found that naive power calculations that ignore the effect of herd immunity can seriously overestimate power; in fact, as sample size increases it is possible for the power to actually decrease, due to herd immunity reducing the overall number of infections. In the situations the authors considered, power may eventually begin to decrease once the proportion of the population enrolled in the trial exceeds about 25%. The findings are discussed in the context of a pneumococcal vaccine trial for children, and serve as a cautionary note that naive sample size calculations for larger scale vaccine trials that ignore herd immunity can yield underpowered studies. Simulations as discussed in the article can help alert investigators to situations where significant dilution of power could result.
Summary contributed by Aaron Galluzzi, Sanofi Pasteur.
Dunning AJ. Comment on 'Evaluating a surrogate endpoint at three levels, with application to vaccine development' by Peter B. Gilbert, Li Qin and Steven G. Self. Statistics in Medicine 2008; 27(29): 6268-70
It is suggested that the authors might also have included the condition that the surrogate of protection quantitatively predicts the efficacy of the vaccine, and proposes that with such a condition the criteria for a statistical surrogate and a principal surrogate are substantially equivalent. The method for finding the threshold level of an immunological assay that quantitatively predicts the efficacy of the vaccine, developed by the statisticians Chang and Kohberger in the 7-valent pneumococcal conjugate vaccine efficacy trial, is described.
Gilbert PB, Qin L, Self SG. Response to Andrew Dunning's comment on 'Evaluating a surrogate endpoint at three levels, with application to vaccine development'. Statistics in Medicine 2009; 28(4): 716-9
The authors' response confirms the importance of the condition that the surrogate quantitatively predicts efficacy and points to the inclusion of the condition in the subject paper and other related papers. Further, they show that the statistical surrogate criterion and principal surrogate criterion are equivalent only if a certain strong assumption holds, namely that there are no unaccounted for baseline simultaneous predictors of the biomarker and the clinical endpoint. The authors also welcome the suggestion of Sadoff and Wittes (Journal of Infectious Diseases; 196:1279-1281) to rename the proposed second and third tiers of immune correlates of protection to a 'specific surrogate of protection' and a 'general surrogate of protection', respectively.
Kohberger RC. Comments on 'Sample size for equivalence trials: A case study from a vaccine lot consistency trial' by J. Ganju, A. Izu & A. Anemona. Statistics in Medicine 2009; 28(1): 177-8.
Four comments are made. First, a reference is made to previous, similar work by Wiens and Iglewicz. Second, it is stressed that a posteriori analysis of the power of the case study should be viewed with caution. Third, the authors estimated the between-lot variance of the case study from only three observations, and it is doubted if in practice it is possible to estimate the variance with sufficient precision. It might therefore be better to use the conservative approach suggested by Wiens and Iglewicz, which provides an upper bound on the required sample size of the trial. Fourth, the authors' recommendation to loosen the equivalence range (0.67,1.5) to (0.5,2.0) is objected to, because any loosening would need to take into account the strength of the immune correlate.
Ganju J, Izu A, & Anemona A. Author's Reply. Statistics in Medicine 2009; 28(1): 178-9.
The
authors reply that the key messages are:
1. For those involved in lot consistency trials (e.g., trial designers and
regulators) to recognize that inherently lots will not be identical (The
availability of pre- and post-vaccination GMTs afforded the opportunity to
communicate and illustrate the point of variation between lots in excess of
random noise far more effectively than making a statement to that effect.)
2. Assuming equality between lots in the planning stage leads to an
underpowered trial, and sometimes, a grossly underpowered trial. Sample size
calculations need to explicitly recognize some variation between lots.
3. Large within-lot variability and acceptable between-lot variability may
mean a prohibitively large trial powered for the (0.67, 1.5) interval after
adjustment for multiple seropgroups. If the (0.67, 1.5) interval was
predicted in part on the (incorrect) equality of lots assumption, then a
wider interval deserves considerations.
The authors then proceed to reply to his specific comments. For example,
regarding the clinical relevance for proposing the (0.5, 2) interval, note
the following and see item 3 above: Our point is that the interval (0.5 - 2)
deserves consideration and may well be justifiable. This is also what
Kohberger alludes to when he says that "the clinical relevance of the
differences [between lot means] ... were deemed not important". Thus, the
wider interval was implicitly considered after looking at the data. Indeed,
at the VRBPAC meeting, the GMT ratio of < 2 (rather than < 1.5) was used as
a criterion by the FDA reviewer for judging consistency. Our rationale for a
wider interval was proposed for consideration before looking at the data.
EMEA Guidance for Industry: European Medicines Agency Evaluation of Medicines for Human Use (EMEA). Guideline on Dossier Structure and Content for Pandemic Influenza Vaccine Marketing Authorisation Application. The guidance is available online at: http://www.emea.europa.eu/pdfs/human/vwp/471703enfin.pdf
Rhorer J, Ambrose CS, Dickinson S, et al. Efficacy of Live Attenuated Influenza Vaccine in Children: A Meta-analysis of nine randomized clinical trials. Vaccine 2009; 27(7): 1101-1110.
Summary: Nine randomized clinical trials, including approximately 25,000 children aged 6-71 months and 2000 children aged 6-17 years, have evaluated the efficacy of live attenuated influenza vaccine (LAIV) against culture-confirmed influenza as compared to placebo or trivalent inactivated vaccine (TIV). We conducted meta-analyses, based on Mantel-Haenszel relative risks from fixed effect models, to provide an estimate of vaccine efficacy (VE). Relative to placebo, year 1 VE for two doses in vaccine-naive young children was 77% (95% CI: 72%, 80%; P < 0.001) against antigenically similar strains and 72% against strains regardless of antigenic similarity. Efficacy was 85%, 76%, and 73% against antigenically similar A/H1N1, A/H3N2, and B, respectively. Year 1 VE of one dose against antigenically similar strains in vaccine-naive children was 60%; efficacy of one dose in previously vaccinated children in year 2 of the various studies was 87%. In head-to-head trials comparing two doses of TIV and LAIV, vaccine-naive children who received two doses of LAIV experienced 46% fewer cases of influenza illness caused by antigenically similar strains. Similarly, for studies including older children who had been previously vaccinated, those receiving one LAIV dose experienced 35% fewer cases of influenza illness than those receiving one TIV dose. LAIV showed high VE versus placebo with no evidence of difference by age or by circulating subtype. In these studies, LAIV was more effective than TIV.
Volume 26, Supplement 4, of Vaccine is a special issue: Influenza Vaccines: Research, Development and Public Health Challenges.
FDA Guidance for Industry: General Principles for the Development of Vaccines to Protect Against Global Infectious Diseases, September 2008.
Summary: The guidance provides information to assist sponsors in developing vaccines to protect against global infectious diseases. It focuses on the development and licensure of vaccines targeted against infectious diseases or conditions endemic in areas outside the United States, and clarifies regulations, statutes and guidances applicable to the development of these products. General recommendations for regulatory pathways to use in the development of vaccines to protect against global infectious diseases for U.S. licensure are provided and several misconceptions surrounding the development of vaccines to protect against global infectious diseases in regard to U.S. regulatory requirements are clarified. The clarifications are intended to ensure that potential sponsors and vaccine manufacturers understand that a) FDA can license vaccines to protect against infectious diseases or conditions not endemic in the United States; b) the regulatory pathways to U.S. licensure for the development of vaccines to protect against infectious diseases not endemic in the U.S. are the same as for vaccines to protect against diseases that are endemic in the United States; and c) sponsors may submit data from clinical trials conducted outside the United States to support product licensure. The guidance is available online at http://www.fda.gov/BiologicsBloodVaccines/GuidanceCompliance RegulatoryInformation/Guidances/Vaccines/ucm074762.htm
Forrest BD, Pride MW, Dunning AJ, Capeding MRZ, Chotpitayasunondh T, Tam JS, Rappaport R, Eldridge J, and Gruber WC. Correlation of Cellular Immune Responses with Protection Against Culture-Confirmed Influenza in Young Children. Clinical and Vaccine Immunology; 15(7):1042-53.
Summary: 2172 children aged 6 to <36 months of age were randomized 1:1:1:1 to receive one of three dose levels of live attenuated trivalent influenza vaccine or placebo. Blood samples taken after vaccination were assayed for enumeration of IFN-γ spot-forming cells by ELISPOT. The occurrence of laboratory confirmed influenza illness in the subsequent influenza season was determined for each subject.
A scaled logit model was used to assess the relationship between assay values and protection; the exposure parameter and protection curve was first estimated for all subjects taken together. The consistency of the exposure parameters and protection curves was then examined when separate models were fitted for males and females, for each of the two countries, and for each of the four treatment groups. 95% confidence intervals for exposure parameters and protection curves were based on the observed Fisher information and the asymptotic normality of maximum likelihood estimators. The goodness-of-fit of the models was compared with likelihood ratio chi-squared tests. The consistency of exposure parameters and protection curves was evaluated with Wald-type F tests.
McClure DL, Glanz JM, Xu S, Hambidge SJ, Mullooly JP, Baggs J. Comparison of epidemiologic methods for active surveillance of vaccine safety. Vaccine (2008); 26:3341-3345
Summary: We performed a simulation study to compare four study designs [matched-cohort, vaccinated-only (risk-interval) cohort, case-control, and self-controlled case-series (SCCS)] in the context of vaccine safety active surveillance. Methods: For each combination of various incidence levels (3, 30, 300 per 105 person-years) and relative risks (RR 1.5-18), 100 case sets were infused into the cohort, matching 105 vaccinated to 105 unvaccinated on age and gender. The matched-cohort was converted into weekly accumulated data intervals with the other three study design samples drawn from each. Analyses were with appropriate regression models. The signal detection time was the first week where the log likelihood ratio (LLR) exceeded the upper boundary from the MaxSPRT sequential analysis method. Empirical type I (false positive) and type II (power) error rates and risk estimate bias were also calculated. Results: The matched-cohort design exhibited the shortest detection time, lowest false positive rate and highest empirical power followed by the risk-interval cohort, SCCS, and case-control. In most monitoring weeks, the risk estimate bias was smallest for the cohort, followed by the risk-interval, SCCS and case-control designs. Conclusions: The cohort study design performed the best in the sequential analysis of active surveillance for vaccine safety. The risk-interval cohort and SCCS designs offer reasonable and efficient alternatives, especially if selection bias is a concern. Future research should address seasonality or age effects. Copyright 2008 Elsevier Ltd.
Ganju J, Izu A, Anemona A. Sample size for equivalence trials: A case study from a vaccine lot consistency trail. Statistics in Medicine 2008; 27(19):3743-54.
Summary: For some trials, simple but subtle assumptions can have a profound impact on the size of the trail. A case in point is a vaccine lot consistency (or equivalence) trial. Standard sample size formulas used for designing lot consistency trials rely on only one component of variation, namely, the variation in antibody titers within lots. The other component, the variation in the means of titers between lots, is assumed to be equal to zero. In reality, some amount of variation between lots, however small, will be present even under the best manufacturing practices. Using data from a published lot consistency trial, we demonstrate that when the between-lot variation is only 0.5 per cent of the total variation, the increase in the sample size is nearly 300 per cent when compared with the size assuming that the lots are identical. The increase in the sample size is so pronounced that in order to maintain power one is led to consider a less stringent criterion for demonstration of lot consistency. The appropriate sample size formula that is a function of both components of variation is provided. We also discuss the increase in the sample size due to correlated comparisons arising from three pairs of lots as a function of the between-lot variance. Copyright 2008 John Wiley & Sons, Ltd.