Hazard Ratio Estimation in Small Samples

<p>When comparing survival times between groups in the setting of proportional hazards, the Cox model is typically used for estimation and inference, the latter based on large sample considerations. Mehrotra and Roth introduced a generalized log-rank (GLR) method for better statistical efficiency in estimating relative risk in small samples. In this article, we propose a refined GLR (RGLR) statistic by eliminating an unnecessary approximation in the development of the original GLR approach, and provide further insights into the performance of GLR and RGLR statistics. We also extend RGLR to allow for tied event times. We show across a variety of simulated scenarios that RGLR provides a smaller bias than commonly used Cox model, parametric models and GLR in small samples (up to 40 subjects per group), and has notably better efficiency relative to Cox and parametric models in terms of mean squared error. The RGLR method also consistently delivers adequate confidence interval coverage and Type I error control, while parametric methods and the Cox model tend to under-perform on that front in small samples. We further show that while the performance of the parametric model can be significantly influenced by misspecification of the true underlying survival distribution, the RGLR approach provides a consistently low bias and high relative efficiency. We apply all competing methods to data from two clinical trials. Supplementary materials for this article are available online.</p

Effect of rAd5-Vector HIV-1 Preventive Vaccines on HIV-1 Acquisition: A Participant-Level Meta-Analysis of Randomized Trials

<div><p>Background</p><p>Three phase 2b, double-blind, placebo-controlled, randomized efficacy trials have tested recombinant Adenovirus serotype-5 (rAd5)-vector preventive HIV-1 vaccines: MRKAd5 HIV-1 <i>gag/pol/nef</i> in Step and Phambili, and DNA/rAd5 HIV-1 <i>env/gag/pol</i> in HVTN505. Due to efficacy futility observed at the first interim analysis in Step and HVTN505, participants of all three studies were unblinded to their vaccination assignments during the study but continued follow–up. Rigorous meta-analysis can provide crucial information to advise the future utility of rAd5-vector vaccines.</p><p>Methods</p><p>We included participant-level data from all three efficacy trials, and three Phase 1–2 trials evaluating the HVTN505 vaccine regimen. We predefined two co-primary analysis cohorts for assessing the vaccine effect on HIV-1 acquisition. The modified-intention-to-treat (MITT) cohort included all randomly assigned participants HIV-1 uninfected at study entry, who received at least the first vaccine/placebo, and the Ad5 cohort included MITT participants who received at least one dose of rAd5-HIV vaccine or rAd5-placebo. Multivariable Cox regression models were used to estimate hazard ratios (HRs) of HIV-1 infection (vaccine vs. placebo) and evaluate HR variation across vaccine regimens, time since vaccination, and subgroups using interaction tests.</p><p>Findings</p><p>Results are similar for the MITT and Ad5 cohorts; we summarize MITT cohort results. Pooled across the efficacy trials, over all follow-up time 403 (n = 224 vaccine; n = 179 placebo) of 6266 MITT participants acquired HIV-1, with a non-significantly higher incidence in vaccine recipients (HR 1.21, 95% CI 0.99–1.48, P = 0.06). The HRs significantly differed by vaccine regimen (interaction <i>P</i> = 0.03; MRKAd5 HR 1.41, 95% CI 1.11–1.78, <i>P</i> = 0.005 vs. DNA/rAd5 HR 0.88, 95% CI 0.61–1.26, <i>P</i> = 0.48). Results were similar when including the Phase 1–2 trials. Exploratory analyses based on the efficacy trials supported that the MRKAd5 vaccine-increased risk was concentrated in Ad5-positive or uncircumcised men early in follow-up, and in Ad5-negative or circumcised men later. Overall, MRKAd5 vaccine-increased risk was evident across subgroups except in circumcised Ad5-negative men (HR 0.97, 95% CI 0.58−1.63, <i>P</i> = 0.91); there was little evidence that the DNA/rAd5 vaccine, that was tested in this subgroup, increased risk (HR 0.88, 95% CI 0.61–1.26, <i>P</i> = 0.48). When restricting the analysis of Step and Phambili to follow-up time before unblinding, 114 (n = 65 vaccine; n = 49 placebo) of 3770 MITT participants acquired HIV-1, with a non-significantly higher incidence in MRKAd5 vaccine recipients (HR 1.30, 95% CI 0.89–1.14, P = 0.18).</p><p>Interpretation and Significance</p><p>The data support increased risk of HIV-1 infection by MRKAd5 over all follow-up time, but do not support increased risk of HIV-1 infection by DNA/rAd5. This study provides a rationale for including monitoring plans enabling detection of increased susceptibility to infection in HIV-1 at-risk populations.</p></div

Estimated Covariate-Adjusted HRs of HIV-1 Infection (Vaccine vs Placebo) Based on Step, Phambili and HVTN505 Combined.

<p>Panel A is for the MITT Cohort, Panel B is for the Ad5 cohort, and Panel C is for circumcised Ad5-negative men in the Ad5 Cohort. The MITT cohort included all randomly assigned participants HIV-1 uninfected at study entry, who received at least one dose of vaccine or placebo; the Ad5 cohort included MITT participants who received at least one dose of rAd5-HIV vaccine or rAd5-placebo. Red lines are 95% confidence intervals indicating HRs significantly different from 1.0; blue lines are 95% confidence intervals indicating HRs not significantly different from 1.0. Shaded rows indicate significantly different HRs within subgroups.</p

Key Data Summary of Individual Studies Included in the Meta-analysis.

<p>Key Data Summary of Individual Studies Included in the Meta-analysis.</p

Enrollment and Follow-up in Step, Phambili and HVTN505.

<p>Indicated are dates of unblinding when data were frozen for pre-unblinding analyses, and the percent of person-years (% pyrs) occurring during the blinded period. HVTN505 is still in active follow-up; HVTN505 data included in the meta-analysis are as of July 9, 2014.</p

Kaplan-Meier Curves and Their Difference (Vaccine vs Placebo) of Cumulative Incidence of HIV-1 Infection.

<p><b>These incidence estimates were not adjusted for covariates.</b> Panel A is for the MITT cohort and Panel B is for the Ad5 cohort based on Step, Phambili and HVTN505 combined using all follow-up time; Panel C is for the Ad5 Cohort based on HVTN505 alone using follow-up time before unblinding, and Panel D is based on Step and Phambili combined using follow-up time before unblinding. The MITT cohort included all randomly assigned participants HIV-1 uninfected at study entry, who received at least one dose of vaccine or placebo; the Ad5 cohort included MITT participants who received at least one dose of rAd5-HIV vaccine or rAd5-placebo.</p

Study Flow Diagram.

<p>Study Flow Diagram.</p

Estimated HRs in the MITT Cohort (Panel A) and Ad5 Cohort (Panel B) Using Follow-up Time before Unblinding Based on Step, Phambili and HVTN505.

<p>The MITT cohort included all randomly assigned participants HIV uninfected at study entry, who received at least one dose of vaccine or placebo; the Ad5 cohort included MITT participants who received at least one dose of rAd5-HIV vaccine or rAd5-placebo. Blue lines are 95% confidence intervals indicating HRs not significantly different from 1.0.</p

Key Features of Individual Studies Included in the Meta-analysis.

<p>Key Features of Individual Studies Included in the Meta-analysis.</p