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Failure time data subject to various types of censoring commonly arise in epidemiological and biomedical studies. Motivated by an AIDS clinical trial, we consider regression analysis of failure time data that include exact and left-, interval-, and/or right-censored observations, which are often referred to as partly interval-censored failure time data. We study the effects of potentially time-dependent covariates on partly interval-censored failure time via a class of semiparametric transformation models that includes the widely used proportional hazards model and the proportional odds model as special cases. We propose an EM algorithm for the nonparametric maximum likelihood estimation and show that it unifies some existing approaches developed for traditional right-censored data or purely interval-censored data. In particular, the proposed method reduces to the partial likelihood approach in the case of right-censored data under the proportional hazards model. We establish that the resulting estimator is consistent and asymptotically normal. In addition, we investigate the proposed method via simulation studies and apply it to the motivating AIDS clinical trial.

Studying the incidence of rare events is both scientifically important and statistically challenging. When few events are observed, standard survival analysis estimators behave erratically, particularly if covariate adjustment is necessary. In these settings, it is possible to improve upon existing estimators by considering estimation in a bounded statistical model. This bounded model incorporates existing scientific knowledge about the incidence of an event in the population. Estimators that are guaranteed to agree with existing scientific knowledge on event incidence may exhibit superior behavior relative to estimators that ignore this knowledge. Focusing on the setting of competing risks, we propose estimators of cumulative incidence that are guaranteed to respect a bounded model and show that when few events are observed, the proposed estimators offer improvements over existing estimators in bias and variance. We illustrate the proposed estimators using data from a recent preventive HIV vaccine efficacy trial. Copyright © 2017 John Wiley & Sons, Ltd.

Two-phase designs are commonly used to subsample subjects from a cohort in order to study covariates that are too expensive to ascertain for everyone in the cohort. This is particularly true for the study of immune response biomarkers in vaccine immunology, where new, elaborate assays are constantly being developed to improve our understanding of the human immune responses to vaccines and how the immune response may protect humans from virus infection. It has long being recognized that if there exist variables that are correlated with expensive variables and can be measured for every subject in the cohort, they can be leveraged to improve the estimation efficiency for the effects of the expensive variables. In this research article, we developed an improved inverse probability weighted estimation approach for semiparametric transformation models with a two-phase study design. Semiparametric transformation models are a class of models that include the Cox PH and proportional odds models. They provide an attractive way to model the effects of immune response biomarkers as human immune responses generally wane over time. Our approach is based on weights calibration, which has its origin in survey statistics and was used by Breslow et al. to improve inverse probability weighted estimation of the Cox regression model. We develop asymptotic theory for our estimator and examine its performance through simulation studies. We illustrate the proposed method with application to two HIV-1 vaccine efficacy trials.

Principal surrogate endpoints are useful as targets for Phase I and II trials. In many recent trials, multiple post-randomization biomarkers are measured. However, few statistical methods exist for comparison of or combination of biomarkers as principal surrogates and none of these methods to our knowledge utilize time-to-event clinical endpoint information. We propose a Weibull model extension of the semi-parametric estimated maximum likelihood method of Huang and Gilbert [1] that allows for the inclusion of multiple biomarkers in the same risk model as multivariate candidate principal surrogates. We propose several methods for comparing candidate principal surrogates and evaluating multivariate principal surrogates. These include the time-dependent and surrogate-dependent true and false positive fraction, the time-dependent and the integrated standardized total gain and the cumulative distribution function of the risk difference. We illustrate the operating characteristics of our proposed methods in simulations and outline how these statistics can be used to evaluate and compare candidate principal surrogates. We use these methods to investigate candidate surrogates in the Diabetes Control and Complications Trial.

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.

In replying to Andrew Dunning’s helpful letter, we endeavor to clarify the value of incorporating baseline participant predictors of the potential surrogate endpoint and of the clinical endpoint into the evaluation of a surrogate endpoint. Such baseline predictors are useful for the evaluation of surrogates defined within each of the statistical and principal surrogate frameworks, which are complementary.

In a randomized controlled clinical trial that assesses treatment efficacy, a common objective is to assess the association of a measured biomarker response endpoint with the primary study endpoint in the active treatment group, using a case-cohort, case-control, or two-phase sampling design. Methods for power and sample size calculations for such biomarker association analyses typically do not account for the level of treatment efficacy, precluding interpretation of the biomarker association results in terms of biomarker effect modification of treatment efficacy, with detriment that the power calculations may tacitly and inadvertently assume that the treatment harms some study participants. We develop power and sample size methods accounting for this issue, and the methods also account for inter-individual variability of the biomarker that is not biologically relevant (e.g., due to technical measurement error). We focus on a binary study endpoint and on a biomarker subject to measurement error that is normally distributed or categorical with two or three levels. We illustrate the methods with preventive HIV vaccine efficacy trials and include an R package implementing the methods. Copyright © 2016 John WileySons, Ltd.

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.

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.

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.

Principal surrogate endpoints are useful as targets for Phase I and II trials. In many recent trials, multiple post-randomization biomarkers are measured. However, few statistical methods exist for comparison of or combination of biomarkers as principal surrogates and none of these methods to our knowledge utilize time-to-event clinical endpoint information. We propose a Weibull model extension of the semi-parametric estimated maximum likelihood method of Huang and Gilbert [1] that allows for the inclusion of multiple biomarkers in the same risk model as multivariate candidate principal surrogates. We propose several methods for comparing candidate principal surrogates and evaluating multivariate principal surrogates. These include the time-dependent and surrogate-dependent true and false positive fraction, the time-dependent and the integrated standardized total gain and the cumulative distribution function of the risk difference. We illustrate the operating characteristics of our proposed methods in simulations and outline how these statistics can be used to evaluate and compare candidate principal surrogates. We use these methods to investigate candidate surrogates in the Diabetes Control and Complications Trial.

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 (P0.001). 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.