A class of nonparametric methods for evaluating the effect of continuous treatments on survival outcomes

TL;DR

This paper develops nonparametric methods to evaluate how continuous treatments influence survival outcomes, addressing challenges with non-pathwise differentiability and applying the approach to HIV trial data.

Contribution

It introduces novel nonparametric inference techniques for continuous treatments affecting survival, extending existing methods beyond multi-level interventions.

Findings

Methods successfully test for constant survival probabilities across treatment levels.

Application to HIV trials demonstrates practical utility.

Numerical studies show good performance of proposed estimators.

Abstract

In randomized trials and observational studies, it is often necessary to evaluate the extent to which an intervention affects a time-to-event outcome, which is only partially observed due to right censoring. For instance, in infectious disease studies, it is frequently of interest to characterize the relationship between risk of acquisition of infection with a pathogen and a biomarker previously measuring for an immune response against that pathogen induced by prior infection and/or vaccination. It is common to conduct inference within a causal framework, wherein we desire to make inferences about the counterfactual probability of survival through a given time point, at any given exposure level. To determine whether a causal effect is present, one can assess if this quantity differs by exposure level. Recent work shows that, under typical causal assumptions, summaries of the counterfactual survival distribution are identifiable. Moreover, when the treatment is multi-level, these summaries are also pathwise differentiable in a nonparametric probability model, making it possible to construct estimators thereof that are unbiased and approximately normal. In cases where the treatment is continuous, the target estimand is no longer pathwise differentiable, rendering it difficult to construct well-behaved estimators without strong parametric assumptions. In this work, we extend beyond the traditional setting with multilevel interventions to develop approaches to nonparametric inference with a continuous exposure. We introduce methods for testing whether the counterfactual probability of survival time by a given time-point remains constant across the range of the continuous exposure levels. The performance of our proposed methods is evaluated via numerical studies, and we apply our method to data from a recent pair of efficacy trials of an HIV monoclonal antibody.