Proportional hazards models with continuous marks

For time-to-event data with finitely many competing risks, the proportional hazards model has been a popular tool for relating the cause-specific outcomes to covariates [Prentice et al. Biometrics 34 (1978) 541--554]. This article studies an extension of this approach to allow a continuum of competing risks, in which the cause of failure is replaced by a continuous mark only observed at the failure time. We develop inference for the proportional hazards model in which the regression parameters depend nonparametrically on the mark and the baseline hazard depends nonparametrically on both time and mark. This work is motivated by the need to assess HIV vaccine efficacy, while taking into account the genetic divergence of infecting HIV viruses in trial participants from the HIV strain that is contained in the vaccine, and adjusting for covariate effects. Mark-specific vaccine efficacy is expressed in terms of one of the regression functions in the mark-specific proportional hazards model. The new approach is evaluated in simulations and applied to the first HIV vaccine efficacy trial.Comment: Published in at http://dx.doi.org/10.1214/07-AOS554 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Evaluating Causal Effect Predictiveness of Candidate Surrogate Endpoints

Most methods for evaluating surrogate endpoints measure validity in terms of net effects (i.e., treatment effects adjusted for the biomarker measured after randomization). Frangakis and Rubin (2002, Biometrics) criticized these approaches because net effects may reflect selection bias, and suggested an alternative definition of a surrogate endpoint (a principal surrogate) based on causal effects. For evaluating principal surrogates we introduce a causal effect predictiveness (CEP) surface, which quantifies how well causal treatment effects on the biomarker predict causal treatment effects on the clinical endpoint. The CEP surface is not identifiable in general due to missing potential outcomes. However, by incorporating baseline covariates that predict the biomarker, the CEP surface is identified under relatively weak assumptions in the important special case that the biomarker has no variability in one treatment arm. For this setting we develop an estimated likelihood method for estimating the CEP surface. The approach is illustrated by the problem of assessing an immune response to a vaccine as a surrogate endpoint for infection

Genome Scanning Methods for Comparing Sequences Between Groups, with Application to HIV Vaccine Trials

Consider a placebo-controlled preventive HIV vaccine efficacy trial. An HIV amino acid sequence is measured from each volunteer who acquires HIV, and these sequences are aligned together with the reference HIV sequence represented in the vaccine. We develop genome scanning methods to identify HIV positions at which the amino acids in sequences from infected vaccine recipients tend to be more divergent from the corresponding reference amino acid than the amino acids in sequences from infected placebo recipients. We consider five two-sample test statistics, based on Euclidean, Mahalanobis, and Kullback-Leibler divergence measures. Weights are incorporated to reflect biological information contained in diverent amino acid positions and substitutions. Position-wise p-values are obtained by approximating the null distribution of the statistics either by a permutation procedure or by nonparametric estimation. Modified Bonferroni and false discovery rate procedures that exploit the discrete nature of the genetic data are used to infer statistically significant signature positions. The methods are examined in simulations and are applied to data from a vaccine trial. More broadly, these methods address the general problem of comparing discrete frequency distributions between groups in a high-dimensional data setting

Nonparametric Bounds and Sensitivity Analysis of Treatment Effects

This paper considers conducting inference about the effect of a treatment (or exposure) on an outcome of interest. In the ideal setting where treatment is assigned randomly, under certain assumptions the treatment effect is identifiable from the observable data and inference is straightforward. However, in other settings such as observational studies or randomized trials with noncompliance, the treatment effect is no longer identifiable without relying on untestable assumptions. Nonetheless, the observable data often do provide some information about the effect of treatment, that is, the parameter of interest is partially identifiable. Two approaches are often employed in this setting: (i) bounds are derived for the treatment effect under minimal assumptions, or (ii) additional untestable assumptions are invoked that render the treatment effect identifiable and then sensitivity analysis is conducted to assess how inference about the treatment effect changes as the untestable assumptions are varied. Approaches (i) and (ii) are considered in various settings, including assessing principal strata effects, direct and indirect effects and effects of time-varying exposures. Methods for drawing formal inference about partially identified parameters are also discussed.Comment: Published in at http://dx.doi.org/10.1214/14-STS499 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Centrally Acting Perindopril Attenuates the Exercise Induced Increase in Muscle Sympathetic Nerve Activity during Heavy Dynamic Exercise

Central angiotensin II (Ang II) linked free radical (FR) production scavenges nitric oxide (NO) enabling an increased central sympathetic neural outflow (SNA). The pathophysiological increase in Ang II linked FR production is recognized as a major mechanism involved in neurogenic hypertension. During exercise, there is a physiological increase in Ang II and muscle sympathetic nerve activity (MSNA) in direct relation to increasing exercise intensity. We tested the hypothesis that the exercise induced increase in Ang II linked FR production and MSNA activity during exercise is located within the brain. Six healthy subjects performed three randomly ordered trials of 70° upright back-supported dynamic leg cycling after ingestion of two different lipid soluble Angiotensin converting enzyme inhibitors ((ACEi) Perindopril (PER) - highly lipid soluble; Captopril (CAP) non-lipid soluble)) and/or placebo (PL). Repeated measurements of whole venous blood, MSNA, and mean arterial pressures (MAP) were obtained at rest and during steady-state heavy intensity exercise at heart rates (HR) of 120 bpm (e120). Peripheral venous superoxide concentrations as measured by electron paramagnetic resonance (EPR) were not significantly altered at rest (P≥0.4) and during E120 by the ACE inhibitors (P≥0.07). Likewise, baseline MSNA (PL, 25 ± 1.5 bust/min; CAP, 21 ± 0.7 bust/min; PER, 25 ± 0.7 bust/min) and MAP (PL, 86 ± 2.8 mmHg vs. CAP, 84 ± 2.6 mmHg; PER, 84 ± 0.7 mmHg) were unchanged at rest (P≥0.1; P≥0.8 respectively). However, during E120 central acting PER attenuated the increases in MSNA and MAP, increasing only 15±6% for MAP and 24±8% for MSNA when compared to PL (26 ± 6% MAP; 57±16% MSNA; P\u3c0.05) and CAP (26±4%MAP; 69±13%MSNA P\u3c0.05). From these data we conclude that centrally acting PER attenuated the central increase in the exercise induced Ang II linked free radical production resulting in an increased central NO activity induced reduction in MSNA during heavy intensity dynamic exercise

The Two-sample Problem for Failure Rates Depending on a Continuous Mark: An Application to Vaccine Efficacy

The efficacy of an HIV vaccine to prevent infection is likely to depend on the genetic variation of the exposing virus. This paper addresses the problem of using data on the HIV sequences that infect vaccine efficacy trial participants to 1) test for vaccine efficacy more powerfully than procedures that ignore the sequence data; and 2) evaluate the dependence of vaccine efficacy on the divergence of infecting HIV strains from the HIV strain that is contained in the vaccine. Because hundreds of amino acid sites in each HIV genome are sequenced, it is natural to treat the divergence (defined in terms of Hamming distance say) as a continuous mark variable that accompanies each failure (infection) time. Problems 1) and 2) can then be approached by testing whether the ratio of the mark-specific hazard functions for the vaccine and placebo groups is unity or independent of the mark, respectively. We develop nonparametric and semiparametric tests for these null hypotheses, based on contrasts of Nelson–Aalen-type estimates of cumulative mark-specific hazard functions for the two groups. Techniques for nonparametric estimation of mark-specific vaccine efficacy based on the cumulative mark-specific incidence functions are also developed. Numerical studies show satisfactory performance of the procedures. The methods are illustrated with application to HIV genetic sequence data collected in the first HIV vaccine efficacy trial. The methodology applies generally to the study of relative risks of failure wherein a continuous mark variable accompanies each failure event

Sensitivity Analysis for the Assessment of Causal Vaccine Effects on Viral Load in HIV Vaccine Trials

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), 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