Statistics_in_Clinical_Vaccine trials.pdf

Statistics in Clinical Vaccine TrialsJozef NautaStatisticsin ClinicalVaccine Trials123Jozef NautaSolvay PharmaceuticalsGlobal StatisticsC.J.van Houtenlaan 361381 CP WeespNetherlandsj.nautaekimpworldonline.nlISBN 978-3-642-14690-9e-ISBN 978-3-642-14691-6DOI 10.1007/978-3-642-14691-6Springer Heidelberg Dordrecht London New YorkcThis work is subject to copyright.All rights are reserved,whether the whole or part of the material isconcerned,specifically the rights of translation,reprinting,reuse of illustrations,recitation,broadcasting,reproduction on microfilm or in any other way,and storage in data banks.Duplication of this publicationor parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965,in its current version,and permission for use must always be obtained from Springer.Violations areliable to prosecution under the German Copyright Law.Theuse of general descriptive names,registered names,trademarks,etc.in this publication does not imply,even in the absence of a specific statement,that such names are exempt from the relevant protective lawsand regulations and therefore free for general use.Cover design:WMXDesign GmbH,HeidelbergPrinted on acid-free paperSpringer is part of Springer Science+Business Media()Library of Congress Control Number:2010937985?Springer-Verlag Berlin Heidelberg 2011To my wife Erna Kimp,and our son Izaak.PrefaceThisbookisintendedforstatisticians workinginclinicalvaccinedevelopmentinthepharmaceutical industry,at universities,at national vaccines institutes,etc.Statisti-cians already involved in clinical vaccinetrials may find some interesting new ideasin it,while colleagues who are new to vaccines will be able to familiarize them-selves quickly with the statistical methodology.A good knowledge of statistics is assumed.The reader should be familiar withhypothesis testing,point and confidence interval estimation,likelihood methods,regression,mathematical and statistical notation,etc.A book that would providethe necessary background is:Armitage P.,Berry G.and Matthews J.N.S.StatisticalMethods in Medical Research,4th edition,Blackwell Science,New York,2001.Thescopeofthebookispracticalratherthantheoretical.Manyreal-lifeexamplesare given,and SAS codes are provided,making application of the methods straight-forward.SAS codes are also given for accurate sample size estimation,includingcodes for the estimation of required sample sizes for equivalence and noninferiorityvaccine trials.The first two chapters are introductionsto the immunology of vaccines,and theywill provide the reader with the necessary background knowledge.In Chap.1,thefundamentals of vaccination,the immune system and vaccines are presented.Theprinciple of vaccination is explained,and the major infectious microorganisms areintroduced.The primary defence mechanism of microorganisms antigenic vari-ation is discussed.A sketch of the immune system is given so that the readerwill understand roughly how it works,including the distinction between the innateand the adaptive immune system.The chapter proceeds with a short section on thebasics of tumour immunology.An overview of the several types of vaccines forviruses and bacteria,from the first generation live-attenuated vaccines to third gen-eration vaccines such as recombinant vector vaccines,DNA vaccines and virus-likeparticles vaccines is given.As an example of a parasite vaccine,a summary of thestate of affairs of malaria vaccine development is given.Therapeutic vaccines fornoninfectiousdiseases are briefly touched upon.Humoral immunity,the componentof the immune system involving antibodies that circulate in the humor,and cellularimmunity,the component that provides immunity by action of cells,are explained.Antibodytitres andantibodyconcentrationsare introduced,and two standardassaysfor humoral immunity,the haemagglutination inhibition test and ELISA,are dis-viiviiiPrefacecussed.The distinction between T helper cells and T killer cells and their differentrolesareexplained.A numberofassays forcellularimmunityare brieflyintroduced,including the ELISPOT assay.Chapter3 is thecentraloneofthebook.Thefourstandardstatistics to summarizehumoraland cellular immunogenicitydata are introduced,and in the sections on thestatistical analysis of proportionsthe use of Wilson-type confidenceintervals is pro-moted rather than the more familiar Wald-type intervals.It is explained how exactconfidence intervals for the risk difference and the relative risk can be obtained.In Chap.4,two types of possible bias for antibody titres are discussed.The firsttypeofbias is duetohowantibodytitres are defined.Analternativedefinitionis pro-posed,the mid-value definition.With this definition,the bias is properly corrected.This type of bias is largely of theoretical interest only.That cannot be said of thesecond type of bias,which is of major practical importance.It occurs when titresabove(or below)a certain level are not determined.If this bias is ignored,the geo-metric mean titre will be underestimated.It is shown how the method of maximumlikelihood estimation for censored observation can be applied to eliminate this bias.Pre-vaccination or baseline antibody levels need not to be zero.Examples ofinfectious diseases for which this can be the case are tetanus,diphtheria,pertus-sis and tick borne encephalitis.Imbalance in pre-vaccination state,i.e.,a differencein baseline antibody levels between vaccine groups,can complicate the interpreta-tion of a difference in post-vaccinationantibody values.A standard approach to thisproblemis analysis of covariance.But in case of antibodyvalues one of the assump-tions underlying this analysis,homoscedasticity,is not met.The larger the baselinevalue the smaller the standard deviation of the error term.In Chap.5,a solutionto 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 fittedwith SAS.Many vaccine immunogenicity trials are conducted in an equivalence or nonin-feriority framework.The objective of such trials is to demonstrate that the immuno-genicity of an investigationalvaccine is comparableor not less than that of a controlvaccine.In Chap.6,the statistical analysis of such trials is explained,both for trialswith an antibody response as endpoint and trials with seroprotection or serocon-version as endpoint.The standard analysis of lot consistency data is known to beconservative,but a simple formula is presented which can be used to decide if thelot sample sizes guarantee that the actual type I error rate of the trial is sufficientlyclose to the nominal level.The chapter is concluded with a discussion of samplesize estimation for vaccine equivalence and noninferiority trials,including lot con-sistency trials.Recommendations are given how to avoid that the statistical poweris overestimated.Chapter 7 considers vaccine field efficacy trial.The aim of a field efficacy trial isto demonstratethat avaccineprotectsagainstinfectionordisease.First,an overviewof the different effects vaccines can produce is given.Next,some critical aspectsof such field efficacy trials are discussed.The three most common incidence mea-sures for infection are presented:the attack rate,the infection rate and the forceof infection.The statistical analysis of field efficacy trials using these estimators isPrefaceixexplained.The chapterthencontinueswith the statistical analysis of recurrentinfec-tion data,which is knownto be complex.Thechapteris concludedwith a discussionof sample size estimation for vaccine field efficacy trial.It is shown that the stan-dard method to estimate the sample size for a trial comparing two attack rates andwith the aim to demonstrate super efficacy is highly conservative.An SAS code tocompute sample sizes for trials comparing two infection rates is presented.A correlate of protection is an immunological assay that predicts protectionagainst infection.The concept is the topic of Chap.8.In clinical vaccine,trials cor-relates of protection are widely used as surrogate endpoints for vaccine efficacy.The function specifying the relationship between log-transformed immunogenicityvalues and the probability of protection against infection,conditional on exposureto the pathogen,is called the protection curve.It is demonstrated how the parame-ters of the protection curve can be estimated from challenge study data and vaccinefield efficacy data.Also explained is how a threshold of protection can be estimatedfrom the protection curve.The generalizability of estimated protection curves isdiscussed.The final chapter,Chap.9,addresses vaccine safety.To proof the safety of a vac-cine is much more difficult than proving its efficacy.Of many vaccines millions ofdoses are administered,which canbringveryrare butserious adversevaccineeventsto light.In this chapter,some statistical aspects of vaccine safety are addressed.Vaccine safety surveillance is briefly discussed,and some recent controversies arerecalled.The notorious problem of vaccine safety and multiplicity is discussed atgreat length.Four different methods to handle this problem are presented,includingthe recently proposed double false discovery method.The performance of the dif-ferent methods is illustrated with the help of simulation results.The second part ofthe chapter is dedicated to the analysis of reactogenicity data.AmsterdamJos NautaDecember 2009AcknowledgementI would like to acknowledge my colleague and good friend Dr Walter Beyer of theDepartment of Virology,Erasmus Medical Centre,Rotterdam,the Netherlands,forhis generous advice on Chaps.1 and 2.Jos NautaxiContents1Basic Concepts of Vaccine Immunology.11.1Vaccination and Preventing Infectious Diseases.11.2Microorganisms:Bacteria,Yeasts,Protozoa and Viruses.21.3The Immune System.31.3.1Basics.31.3.2Microbial Clearance.41.3.3Active and Passive Protection from Infectious Diseases.51.3.4Antigenic Variation.51.3.5Tumour Immunology.61.4Prevention of Infectious Diseases by Vaccination.61.4.1Viral and Bacterial Vaccines Currently in Use.81.4.2Routes of Administration.101.4.3Malaria Vaccines.111.4.4Experimental Prophylactic and Therapeutic Vaccines.112Humoral and Cellular Immunity.132.1Humoral Immunity.132.1.1Antibody Titres and Antibody Concentrations.142.1.2Two Assays for Humoral Immunity.142.2Cellular Immunity.152.2.1Assays for Cellular Immunity.163Standard Statistical Methods for the Analysisof Immunogenicity Data.193.1Introduction.193.2Geometric Mean Titres and Concentrations.203.2.1Single Vaccine Group.223.2.2Two Vaccine Groups.233.3Geometric Mean Fold Increase.243.3.1Analysis of a Single Geometric Mean Fold Increase.253.3.2Analysis of Two Geometric Mean Fold Increases.253.3.3A Misconception about Fold Increasesand Baseline Imbalance.27xiiixivContents3.4Two Seroresponse Rates.283.4.1Seroprotection Rate.283.4.2SeroconversionRate.283.5Analysis of Proportions.293.5.1Analysis of a Single Proportion.293.5.2Comparing Two Proportions.333.5.3The Suissa and Shuster Exact Test for ComparingTwo Proportions.363.6Multiple Co-Primary Endpoints and the IntersectionUnionTest.393.7The Reverse Cumulative Distribution Plot.393.8Discussion.413.9Sample Size Estimation.423.9.1Comparing Two Geometric Mean Responses.423.9.2Comparing Two Proportions.433.9.3Sample Size Estimation for Trialswith Multiple Co-Primary Endpoints.444Antibody Titres and Two Types of Bias.474.1Standard Antibody Titres versus Mid-Value Titres.474.2Censored Antibody Titres and Maximum Likelihood Estimation.494.2.1ML Estimation for Censored Normal Data.504.2.2ML Estimation for Censored Antibody Titres.525Adjusting for Imbalance in Pre-Vaccination State.575.1Imbalance in Pre-Vaccination State.575.2Adjusting for Baseline Imbalance.585.3Analysis of Covariance for Antibody Values.595.3.1A Solution to the Problem of Heteroscedasticity.605.3.2Fitting the Variance Model for Heteroscedasticity.605.3.3ANCOVA for Comparative Clinical Vaccine Trials.626Vaccine Equivalence and Noninferiority Immunogenicity Trials.676.1Equivalence and Noninferiority.676.2Equivalence and Noninferiority Testing.686.2.1Basic Concepts.686.2.2Equivalence and Noninferiority Testing for Normal Data.696.2.3The ConfidenceIntervalApproachto Equivalenceand Noninferiority Testing.706.3Equivalence and Noninferiority Vaccine Trialswith a Geometric Mean Response as Outcome.706.4Equivalence and Noninferiority Trailswith a Seroresponse Rate as Outcome.736.5Vaccine Lot Consistency Trials.746.5.1Lot Consistency and the Confidence Interval Method.74Contentsxv6.5.2The Wiens and Iglewicz Test to Inspectthe Consistency of Three Vaccine Lots.756.6Discussion.786.7Sample Size Estimation.796.7.1Comparing Two Geometric Mean Responses.796.7.2Comparing Two Seroresponse Rates.826.7.3Lot Consistency Trials.827Vaccine Field Efficacy Trials.857.1Introduction.857.2Some Critical Aspects of Vaccine Field Trials.867.2.1Efficacy versus Effectiveness.867.2.2The Influence of the Sensitivity and Specificityof the Diagnostic Test on the Vaccine Efficacy Estimate.877.2.3Surveillance Period.907.3Incidence Measures for Infection.907.3.1Attack Rate.907.3.2Infection Rate.917.3.3Force of Infection.927.4Statistical Analysis of Vaccine Efficacy Data.937.4.1Comparing Two Attack Rates.947.4.2Comparing Two Infection Rates.957.4.3Comparing Two Force of Infection Functions.977.5Recurrent Infections.997.5.1Average Number of Episodes Experienced by a Subject.997.6Sample Size Estimation.1037.6.1Trials Comparing Two Attack Rates.1037.6.2Trials Comparing Two Infection Rates.1057.6.3Trials Comparing Two Forces of Infection.1068Correlates of Protection.1078.1Introduction.1078.2The Protection Curve.1088.3Estimating the Protection Curve.1088.3.1Estimating the Protection Curve from ChallengeStudy Data.1088.3.2Estimating a Protection Curve from Vaccine FieldEfficacy Study Data.1118.3.3Predicting Vaccine Efficacy.1138.4Threshold of Protection.1138.5Discussion.115xviContents9Safety of Vaccines.1179.1Ensuring Vaccine Safety.1179.2Vaccine Safety Surveillance.1189.3Safety Data and the Problem of Multiplicity.1209.4Vaccine Reactogenicity.1249.4.1Local and Systemic Reactions.1249.4.2Statistical Analysis of Local and Systemic Reactions.125ASAS and Floating Point Format for Calculated Variables.131BClosed-Form Solutions for the ConstrainedML EstimatorsQR0.133CSimulation Results on Jewells Correctionfor the Rate Ratio.135DEA Generalized Worst-Case Sensitivity Analysis for a SingleSeroresponse Rate for Which the Confidence Interval MustFall Above a Pre-Specified Bound.139E.1Introduction.139E.2Motivating Example.140E.3Complete-Case and Worst-Case Maximum Likelihood Analyses.140E.4Maximum Likelihood Analysis with Missing Data.142E.5Generalized Sensitivity Analysis.142E.6Concluding Remarks.143E.7Technical Notes.144References.145Index.149Proof of Inequality(3.16).137AcronymsAAPAmerican academy of pediatricsAIDSAcquired immune deficiency syndromeANCOVAAnalysis of covarianceAOMAcute otitis mediaARAttack rateCBERCen