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Randomization in clinical trials minimizes differences between treatment arms, allowing observed treatment differences to be attributable to an intervention. For prospective clinical trials, we examine the effects on inference when other specified treatment arm differences are also present. These differences are imposed using three measures: time between the unobserved failure event (e.g., HIV infection) and its detection, visit schedule adherence and dropout. Our context of interest is trials with non-recurrent time-to-event outcomes and fixed visit intervals, where treatment efficacy is measured either by a hazard ratio or by a ratio of cumulative incidence functions. Moderate treatment differences in visit adherence, either through missed visits or additional unscheduled visits, were not found to cause substantial bias or to reduce power. However, both differential loss to follow-up (when coincidentally dependent on risk of failure) and differential time between event and detection should be of concern in designing clinical trials. Efforts to re-capture subjects at the end of study for failure assessment are helpful in some contexts, and may be considered in study planning.

The world's first efficacy trial of a preventive HIV vaccine was completed in 2003. Study participants who became HIV infected were followed for 2 years and monitored for HIV viral load and initiation of antiretroviral therapy (ART). In order to determine if vaccination may have altered HIV progression in persons who acquired HIV, a pre-specified objective was to compare the time until a composite endpoint between the vaccine and placebo arms, where the composite endpoint is the first event of ART initiation or viral failure (HIV viral load exceeds a threshold x(vl) copies/ml). Specifically, with vaccine efficacy, VE(tau, x(vl)), defined as one minus the ratio (vaccine/placebo) of the cumulative probability of the composite endpoint (with failure threshold x(vl)) occurring by tau months, the aim was to estimate the four parameters {VE(tau, x(vl)): x(vl) is an element of {1500, 10,000, 20,000, 55,000} copies/ml} with simultaneous 95% confidence bands. A Gaussian multipliers simulation method is devised for constructing confidence bands for VE(tau, x(vl)) with x(vl) spanning multiple discrete values or a continuous range. The new method is evaluated in simulations and is applied to the vaccine trial data set.

Consider a study of two groups of individuals infected with a population of a genetically related heterogeneous mixture of viruses, and multiple viral sequences are sampled from each person. Based on estimates of genetic distances between pairs of aligned viral sequences within individuals, we develop four new tests to compare intra-individual genetic sequence diversity between the two groups. This problem is complicated by two levels of dependency in the data structure: (i) Within an individual, any pairwise distances that share a common sequence are positively correlated; and (ii) for any two pairings of individuals which share a person, the two differences in intra-individual distances between the paired individuals are positively correlated. The first proposed test is based on the difference in mean intra-individual pairwise distances pooled over all individuals in each group, standardized by a variance estimate that corrects for the correlation structure using U-statistic theory. The second procedure is a nonparametric rank-based analog of the first test, and the third test contrasts the set of subject-specific average intra-individual pairwise distances between the groups. These tests are very easy to use and solve correlation problem (i). The fourth procedure is based on a linear combination of all possible U-statistics calculated on independent, identically distributed sequence subdatasets, over the two levels (i) and (ii) of dependencies in the data, and is more complicated than the other tests but can be more powerful. Although the proposed methods are empirical and do not fully utilize knowledge from population genetics, the tests reflect biology through the evolutionary models used to derive the pairwise sequence distances. The new tests are evaluated theoretically and in a simulation study, and are applied to a dataset of 200 HIV sequences sampled from 21 children.

The progression of colorectal cancer is a multistage process associated with specific molecular alterations. The stepwise accumulation of these multiple genetic mutations progressively results in the acquisition of neoplastic cell behavior. The genetic abnormalities associated with the expression of metastatic phenotype, therefore, may be of prognostic significance in the clinical treatment of colorectal cancer patients. In this study, the immunohistochemical expression of the deleted in colorectal cancer gene (DCC) and p27Kip1 was assessed in 168 paraffin-embedded, formalin-fixed tumors of patients with stage II and III colorectal cancer. Kaplan-Meier survival curves and log-rank statistics were used to analyze survival times after curative primary tumor resection, and Cox proportional hazards models were used to adjust the assessment of demographic and clinical covariates. Loss of DCC or p27Kip1 expression had no influence on survival in patients with stage II or III colorectal cancer. The 5-year survival rates of DCC-positive and DCC-negative tumors were 51.8% and 35.7% (P=0.40), respectively. The 5-year survival rate of patients with p27Kip1-positive tumors was 47.9%, whereas the rate for patients with p27Kip1-negative tumors was 38.8% (P=0.68). After adjustment for all evaluated variables, neither DCC or p27Kip1 was found to be a predictor of survival (risk ratio for DCC, 0.98; 95% confidence interval, 0.66-1.56; P=0.92; risk ratio for p27Kip1, 0.87; 95% confidence interval, 0.58-1.29; P=0.49). The present study demonstrated that the expression of neither DCC nor p27Kip1 was predictive in poor survival outcome in patients with stage II or III colorectal cancer.

Background: An objective of the first efficacy trial of a candidate vaccine containing recombinant human immunodeficiency virus (HIV) type 1 envelope glycoprotein 120 (rgp120) antigens was to assess correlations between antibody responses to rgp120 and the incidence of HIV-1 infection., Methods: Within the randomized trial (for vaccinees, n=3598; for placebo recipients, n=1805), binding and neutralizing antibody responses to rgp120 were quantitated. A case-cohort design was used to study correlations between antibody levels and HIV-1 incidence., Results: Peak antibody levels were significantly inversely correlated with HIV-1 incidence. The relative risk (RR) of infection was 0.63 (95% confidence interval, 0.45-0.89) per log(10) higher neutralization titer against HIV-1(MN), and the RRs of infection for second-, third-, and fourth-quartile responses of antibody blocking of gp120 binding to soluble CD4 versus first-quartile responses (the lowest responses) were 0.35, 0.28, and 0.22, respectively., Conclusions: Despite inducing a complex, robust immune response, the vaccine was unable to reduce the incidence of HIV-1. Two interpretations of the correlative results are that the levels of antibodies (i) caused both an increased (low responders) and decreased (high responders) risk of HIV-1 acquisition or (ii) represented a correlate of susceptibility to HIV-1 but had no causal effect on susceptibility. Although the data cannot definitively discriminate between these 2 explanations, (ii) appears to be more likely.

Candidate human immunodeficiency virus (HIV)-1 vaccines that elicit cytotoxic T lymphocytes may modulate HIV infection, requiring a prototype evaluation to assess participants who become infected with HIV. Of 1497 participants in canarypox HIV-1 vaccine prime-boost trials, 28 (1.9%) acquired HIV-1 infection after vaccination. Median plasma HIV-1 RNA levels (vaccinees, 4.78 log10 copies/mL; placebo recipients, 4.27 log10 copies/mL) and CD4 cell counts (vaccinees, 552 cells/mm3; placebo recipients, 657 cells/mm3) before administration of antiretroviral therapy (ART) and time to a composite end point (plasma HIV-1 RNA level >55,000 copies/mL, CD4 cell count <350 cells/mm3, or initiation of ART) did not differ significantly between vaccinees and placebo recipients (P =.4, P =.1, and P =.7, respectively). Persons who acquire HIV-1 infection while enrolled in HIV-1 vaccine trials can be successfully followed after infection, to determine whether vaccines alter the course of HIV-1 infection.

In this paper we discuss statistical considerations regarding endpoints in preventive vaccine trials. Brief discussion is given to preclinical, Phase I, and Phase II trials, with the bulk of attention paid to endpoint choice and analysis in Phase III efficacy trials. In addition to traditional efficacy measures of vaccine effects for immunized individuals, consideration is given to waning, strain specific efficacy, correlates of protective immunity, postinfection endpoints, and cluster randomized trials.

It is of interest in some applications to determine whether there is a relationship between a hazard rate function (or a cumulative incidence function) and a mark variable which is only observed at uncensored failure times. We develop nonparametric tests for this problem when the mark variable is continuous. Tests are developed for the null hypothesis that the mark-specific hazard rate is independent of the mark versus ordered and two-sided alternatives expressed in terms of mark-specific hazard functions and mark-specific cumulative incidence functions. The test statistics are based on functionals of a bivariate test process equal to a weighted average of differences between a Nelson-Aalen-type estimator of the mark-specific cumulative hazard function and a nonparametric estimator of this function under the null hypothesis. The weight function in the test process can be chosen so that the test statistics are asymptotically distribution-free. Asymptotically correct critical values are obtained through a simple simulation procedure. The testing procedures are shown to perform well in numerical studies, and are illustrated with an AIDS clinical trial example. Specifically, the tests are used to assess if the instantaneous or absolute risk of treatment failure depends on the amount of accumulation of drug resistance mutations in a subject's HIV virus. This assessment helps guide development of anti-HIV therapies that surmount the problem of drug resistance.

Vaccines with limited ability to prevent HIV infection may positively impact the HIV/AIDS pandemic by preventing secondary transmission and disease in vaccine recipients who become infected. To evaluate the impact of vaccination on secondary transmission and disease, efficacy trials assess vaccine effects on HIV viral load and other surrogate endpoints measured after infection. A standard test that compares the distribution of viral load between the infected subgroups of vaccine and placebo recipients does not assess a causal effect of vaccine, because the comparison groups are selected after randomization. To address this problem, we formulate clinically relevant causal estimands using the principal stratification framework developed by Frangakis and Rubin (2002, Biometrics 58, 21-29), and propose a class of logistic selection bias models whose members identify the estimands. Given a selection model in the class, procedures are developed for testing and estimation of the causal effect of vaccination on viral load in the principal stratum of subjects who would be infected regardless of randomization assignment. We show how the procedures can be used for a sensitivity analysis that quantifies how the causal effect of vaccination varies with the presumed magnitude of selection bias.

Initial human immunodeficiency virus (HIV) vaccines are unlikely to prevent acquisition of HIV in all recipients. Moreover, several HIV vaccines are under evaluation that are designed to reduce viremia after acquisition of infection. Such vaccines could provide important benefits to delay HIV progression and to reduce transmission. The decision to license a vaccine on the basis of observed effects on virus load and other postinfection surrogate end points in an efficacy trial is complicated by uncertainty about whether the vaccine effects will persist and reliably predict clinical effects, and by the challenge in interpreting the data posed by treatment of some seroconverters with antiretroviral drugs. Here, we evaluate how analyses of certain surrogate end points can be used for inferring clinically significant vaccine effects and propose end points that could be evaluated in efficacy trials to support licensure. The assessment suggests that a vaccine demonstrating moderately durable effects to delay therapy and to ameliorate viremia merits consideration for licensure.

This report evaluates long-term safety data from 3189 human immunodeficiency virus type 1 (HIV-1) uninfected, healthy volunteers who were enrolled into 51 National Institute of Allergy and Infectious Diseases (NIAID)-sponsored Phase I and II multicentred, randomized, double-blind trials of recombinant HIV-1 subunit vaccines (23 studies), synthetic peptide vaccines (7 studies), live vaccinia-vector recombinant envelope vaccines (7 studies), canarypox vector recombinant vaccines (13 studies), a DNA vaccine (1 study), and a Salmonella-vector vaccine (1 study). During the 12,340 person-years of follow-up, participants were monitored for adverse events including immune dysfunction/autoimmunity, anaphylaxis, cancer, death, and vaccine allergy. The analysis provides evidence that a preparation of a C4-V3 polypeptide vaccine emulsified in incomplete Freund's caused serious toxicity, but otherwise no safety problems considered serious were identified for any of the vaccines and adjuvants studied. These data serve to solidify the growing safety base of current vaccine technologies utilized in candidate vaccines for HIV-1 infection.

From a prospective cohort study of 1948 initially human immunodeficiency virus (HIV) uninfected female commercial sex workers followed between 1985 and 1999 in Dakar, Senegal, the authors compared the male to female per infectious sexual exposure transmission probability of HIV types one (HIV-1) and two (HIV-2). New non-parametric competing risks failure time methods were used, which minimized modelling assumptions and controlled for risk factors for HIV infection. The HIV-1 versus HIV-2 infectivity ratio over time was estimated by the ratio of smoothed non-parametric kernel estimates of the HIV-1 and HIV-2 infection hazard functions in sex workers, adjusted by an estimate of the relative HIV-1 versus HIV-2 prevalence in the partner population. HIV-1 was found to be significantly more infectious than HIV-2 throughout the follow-up period (P < 0.001). The HIV-1/HIV-2 infectivity ratio was inferred to be approximately constant over time, with estimated common value 3.55. The finding of greater HIV-1 infectivity persisted in sensitivity analyses and in covariate-adjusted analyses, with adjusted infectivity ratio estimates ranging between 3.40 and 3.86. Understanding the mechanisms by which HIV-1 infects more efficiently than HIV-2 may be useful in the development of HIV-1 vaccines. Additionally, the methodology developed here may be useful for analysing other data sets., (Copyright 2003 John Wiley & Sons, Ltd.)

At the present time, many AIDS clinical trials compare drug therapies by a time-to-event primary endpoint that measures the durability of suppression of HIV replication. For such studies, survival differences tend to occur early and/or late in the follow-up period due to drug differences in initial potency and/or durability of efficacy, and detecting these differences is of primary interest. We propose a weighted log-rank statistic that emphasizes early and/or late survival differences. We also consider some versatile tests that also emphasize these differences but are sensitive to a wider range of alternatives. The performances of the new tests are evaluated in numerical studies. For the alternatives of interest, the new tests show greater power and flexibility than commonly used weighted log-rank tests and related versatile tests. When the main interest is in detecting early and/or late survival differences, these tests may be preferable to the other versatile and weighted log-rank tests that have been studied.

In survival analysis, often times the pattern of instantaneous risk over time is more interesting than that of the cumulative risk. For this case, a nonparametric hazard function estimate is more appropriate for summarizing the risk experience of a group of patients than the corresponding Kaplan-Meier estimate. In comparing a new treatment with a standard therapy, it is important to know if the treatment loses it potency during the follow-up period, and if it does, one would like to know when it becomes ineffective. Unfortunately, with a plot of the differences of two Kaplan-Meier curves, it is rather difficult to capture such temporal trends. In this article, we propose simple procedures for constructing confidence bands for the contrast of two hazard functions with censored data. The simultaneous interval estimates are quite useful for identifying possible values of the contrast over time with a certain degree of confidence. The new proposals are illustrated with an example and a small simulation study.

This article develops omnibus tests for comparing cause-specific hazard rates and cumulative incidence functions at specified covariate levels. Confidence bands for the difference and the ratio of two conditional cumulative incidence functions are also constructed. The omnibus test is formulated in terms of a test process given by a weighted difference of estimates of cumulative cause-specific hazard rates under Cox proportional hazards models. A simulation procedure is devised for sampling from the null distribution of the test process, leading to graphical and numerical technques for detecting significant differences in the risks. The approach is applied to a cohort study of type-specific HIV infection rates.

Background: Virologic rebound can result from suboptimal antiviral potency in combination antiretroviral therapy., Design: Multicenter, partially blinded, prospective, randomized study of 202 HIV-infected subjects to determine whether therapy intensification improves long-term rates of virologic suppression., Methods: Subjects had plasma HIV RNA < 200 copies/ml, CD4 cell count of > 200 x 10(6) cells/l, and treatment with indinavir (IDV) + zidovudine (ZDV) + lamivudine (3TC) for at least 6 months before randomization to stay on this regimen or to receive IDV + didanosine (ddI) + stavudine (d4T) plus or minus hydroxyurea (HU) (600 mg twice daily). Treatment failure was defined as either confirmed rebound of HIV RNA level to > 200 copies/ml or a drug toxicity necessitating treatment discontinuation., Results: Treatment failure occurred more frequently in subjects randomized to the HU-containing arm (32.4%), than in those taking IDV + ddI + d4T (17.6%) or IDV + ZDV + 3TC (7.6%). The time to treatment failure was shorter for the HU-containing arm compared with the IDV + ZDV + 3TC (P < 0.0001) or IDV + ddI + d4T arms (P = 0.032). Dose-limiting toxicities rather than virologic rebound accounted for the differences between treatment failure among the study arms. Pancreatitis led to treatment discontinuation in 4% of subjects in treatment arms containing ddI + d4T. Three subjects with pancreatitis died, all randomized to the HU-containing arm., Conclusions: Switching to IDV + ddI + d4T + HU in patients treated with IDV + ZDV + 3TC was associated with a worse outcome, principally because of drug toxicity.

Suppression of plasma human immunodeficiency virus (HIV) RNA levels has been widely accepted as an appropriate surrogate end point for HIV disease progression, and it is currently used as the primary end point to determine efficacy in many antiretroviral trials. However, this end point does not always measure other important effects of treatment, such as inducement of multidrug resistance, which depletes future therapy options, and toxic effects. An alternative that directly factors in these treatment costs is a composite regimen termination end point, defined as a protocol-determined change in regimen due to either virologic failure or treatment-related toxic effects. Pros and cons for using purely virologic vs various composite primary end points are discussed. Conclusions include (1) a trial's clinical objective guides the choice of primary end point, (2) a purely virologic end point is often preferable, (3) it may be important to analyze both end point types in interpreting study results, and (4) long-term clinical outcome studies are needed for identifying the most predictive surrogate end points.

From data on HIV-1 characteristics measured on viruses isolated from vaccinated and unvaccinated persons infected while enrolled in preventive HIV-1 vaccine trials, interpretable inferences into strain variations of vaccine efficacy can be made with recently developed sieve analysis models. Four assumptions are needed for the parameters in these models to have meaningful interpretations in terms of vaccine-induced reductions in strain-specific per-contact transmission probabilities: (A1) vaccination impacts each strain-specific transmission probability homogeneously in vaccinated persons (leaky vaccine effect); (A2) for each strain biological susceptibility to infection given exposure is homogeneous among vaccinated trial participants and among unvaccinated trial participants; (A3) the distribution of exposure is equal in vaccinated and unvaccinated trial participants; (A4) the relative prevalence of circulating HIV-1 strains during the trial follow-up period is constant. Through theoretical considerations and simulations of an ongoing phase III HIV-1 vaccine efficacy trial in Bangkok, we evaluate the importance and necessity of these assumptions. We show that the models still provide estimates of biologically interpretable parameters when A1 is violated, but with bias the extent to which vaccine protection is heterogeneous. We also show that the models are highly robust to departures from A4, with implication that the time-independent models are adequate for applications. In addition, we suggest extensions of the sieve analysis models which incorporate random effects that account for unmeasured heterogeneity in infection risk. With these mixed models, usefully interpretable strain-specific vaccine efficacy parameters can be estimated without requiring A2. The conclusion is that A3, which is justified by randomization and blinding, is the essential assumption for the sieve models to provide reliable interpretable inferences into strain variations in vaccine efficacy., (Copyright 2001 John Wiley & Sons, Ltd.)

We address the problem of comparing interindividual genomic sequence diversity between two populations. Although the methods are general, for concreteness we focus on comparing two human immunodeficiency virus (HIV) infected populations. From a viral isolate(s) taken from each individual in a sample of persons from each population, suppose one or multiple measurements are made on the genetic sequence of a coding region of HIV. Given a definition of genetic distance between sequences, the goal is to test if the distribution of interindividual distances differs between populations. If distances between all pairs of sequences within each group are used, then data-dependencies arising from the use of multiple sequences from individuals invalidates the use of a standard two-sample test such as the t-test. Where this problem has been recognized, a typical solution has been to apply a standard test to a reduced dataset comprised of one sequence or a consensus sequence from each patient. Disadvantages of this procedure are that the conclusion of the test depends on the choice of utilized sequences, often an arbitrary decision, and exclusion of replicate sequences from the analysis may needlessly sacrifice statistical power. We present a new test free of these drawbacks, which is based on a statistic that linearly combines all possible standard test statistics calculated from independent sequence subsamples. We describe statistical power advantages of the test and illustrate its use by application to nucleotide sequence distances measured from HIV-1 infected populations in southern Africa (GenBank accession numbers AF110959--AF110981) and North America/Europe. The test makes minimal assumptions, is maximally efficient and objective, and is broadly applicable.

In a preventive vaccine efficacy trial of a vaccine for a genotypically and phenotypically diverse pathogen, it is important to assess if and how vaccine protection against infection or disease varies with characteristics of the exposing pathogen. Gilbert, Self and Ashby developed statistical methods for this problem when the outcome data are counts of the number of vaccinated and unvaccinated trial participants infected by each pathogen strain. However, in many vaccine trials time-to-case information is available, and the extent to which this information improves investigation of differential vaccine protection is unclear. We describe how cause-specific proportional hazards models and other popular competing risks failure time techniques can be applied to this problem. This includes new results on the assumptions required for these methods to give valid inferences about strain-specific vaccine efficacy, and a comparison of theoretical and finite-sample properties between these methods and the time-independent methods. Theoretical considerations, a cholera vaccine trial example, and an extensive simulation study of a human immunodeficiency virus type 1 (HIV-1) vaccine trial show that information about failure times does not appreciably improve estimation or testing unless the pathogen has a high attack rate and the relative prevalence of pathogen strains shifts substantially during the trial follow-up period. An important implication is that practically optimal evaluation of strain-specific vaccine efficacy in HIV-1 vaccine trials will not require knowledge of infection times., (Copyright 2000 John Wiley & Sons, Ltd.)

From data on HIV-1 genotypes collected from antiretroviral trial participants who fail virologically, we describe methods for comparing distributions of acquired HIV-1 mutations across different treatment regimens. Given a definition of a "mutational distance" that summarizes the genetic change of a subject's virus in a way that captures the resistance cost of exposure to an antiretroviral regimen, these comparative analyses inform about the relative treatability of emergent virus by next-line therapy directed to the same viral target. The utility of the methods is illustrated by application to data from AIDS Clinical Trials Group (ACTG) Study 241. We find that patients failing zidovudine/didanosine/nevirapine accumulated a 2.41-fold greater nonnucleoside reverse transcriptase inhibitor (RTI) mutational distance than patients failing zidovudine/didanosine [95% confidence interval (1.55, 5.26), p < 0.000001], quantitating expectations that adding a nonnucleoside RTI to a double nucleoside regimen may attenuate future effectiveness of nonnucleoside RTI therapy for nucleoside-experienced patients if viremia is not suppressed. We also find that persons with extensive prior experience with suboptimal nucleoside therapy who were virologically failing zidovudine/didanosine/nevirapine or zidovudine/didanosine accumulated a similar nucleoside RTI mutational distance, implying that the addition of the nonnucleoside RTI did not preserve future nucleoside options.

Objectives: At present, many clinical trials of anti-HIV-1 therapies compare treatments by a primary endpoint that measures the durability of suppression of HIV-1 replication. Several durability endpoints are compared., Design: Endpoints are compared by their implicit assumptions regarding surrogacy for clinical outcomes, sample size requirements, and accommodations for inter-patient differences in baseline plasma HIV-1-RNA levels and in initial treatment response., Methods: Virological failure is defined by the non-suppression of virus levels at a prespecified follow-up time T(early virological failure), or by relapse. A binary virological failure endpoint is compared with three time-to-virological failure endpoints: time from (i) randomization that assigns early failures a failure time of T weeks; (ii) randomization that extends the early failure time T for slowly responding subjects; and (iii) virological response that assigns non-responders a failure time of 0 weeks. Endpoint differences are illustrated with Agouron's trial 511., Results: In comparing high with low-dose nelfinavir (NFV) regimens in Agouron 511, the difference in Kaplan-Meier estimates of the proportion not failing by 24 weeks is 16.7% (P = 0.048), 6.5% (P = 0.29) and 22.9% (P = 0.0030) for endpoints (i), (ii) and (iii), respectively. The results differ because NFV suppresses virus more quickly at the higher dose, and the endpoints weigh this treatment difference differently. This illustrates that careful consideration needs to be given to choosing a primary endpoint that will detect treatment differences of interest., Conclusion: A time from randomization endpoint is usually recommended because of its advantages in flexibility and sample size, especially at interim analyses, and for its interpretation for patient management.

This article summarizes material on statistical issues in the design of HIV-1 preventive vaccine trials and antiretroviral HIV-1 treatment trials that was presented at the first school on Modern Statistical Methods in Medical Research, held at the International Centre for Theoretical Physics in Trieste, in September 1999. Design issues for the two trial types are discussed separately and are compared, which highlights the relative complexity of vaccine trials. Vaccine trial designs for assessing various vaccine effects are considered, including classical double-blind individual-randomized designs for evaluating biological vaccine effects on susceptibility to infection, and augmented partners, cluster-randomized, and infant designs for evaluating biological vaccine effects on infectiousness as well as on susceptibility. Within these designs, covered topics include surrogate endpoints for measuring vaccine effects on secondary transmission and on HIV-1 disease progression, and exploratory and confirmatory methods for assessing host immune and viral genotypic or phenotypic correlates of vaccine protection against infection or disease. For antiretroviral trials, covered topics include endpoint selection and structured designs such as fractional factorial and Latin square designs for rapidly screening combination drug regimens and for identifying patterns of HIV-1 genomic evolution that predict loss of drug efficacy.

The human immunodeficiency virus type 1 (HIV-1) is extremely diverse. In assessing the utility of an HIV-1 vaccine, an important issue is the possibility of differential protection. We discuss statistical methods of inferring how the vaccine efficacy may vary with viral type from data that would be collected from a randomized, double-blind, placebo-controlled preventive vaccine efficacy trial. Detailed characterization of virus isolated from individuals infected during the trial will be available. We focus on the highly simplified case in which the viral characteristics are summarized by a single feature, which may be nominal, or a scalar quantity that represents distance between the isolate and the prototype virus or viruses used in the vaccine preparation. We consider discrete categorical and continuous response models for this quantity and identify models whose parameters can be interpreted as log ratios of strain-specific relative risks of infection in a prospective model for HIV-1 exposure and transmission. Methods of inference are described for the multinomial logistic regression (MLR) model for discrete categorical response, and a new semiparametric model which can be viewed as a continuous analog of the MLR model is introduced. The methods are illustrated by application to HIV-1 and hepatitis B vaccine trial data.

The generalized odds-rate class of regression models for time to event data is indexed by a non-negative constant rho and assumes that [formula: see text] where g: rho(s) = log(rho-1(s-rho - 1)) for rho > 0, g0(s) = log(-logs), S(t[symbol: see text]Z) is the survival function of the time to event for an individual with q x 1 covariate vector Z, beta is a q x 1 vector of unknown regression parameters, and alpha(t) is some arbitrary increasing function of t. When rho = 0, this model is equivalent to the proportional hazards model and when rho = 1, this model reduces to the proportional odds model. In the presence of right censoring, we construct estimators for beta and exp(alpha(t)) and show that they are consistent and asymptotically normal. In addition, we show that the estimator for beta is semiparametric efficient in the sense that it attains the semiparametric variance bound.