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A Causal Proportional Hazards Estimator for the Effect of Treatment Actually Received in a Randomized Trial with All‐or‐Nothing Compliance
Author(s) -
Loeys T.,
Goetghebeur E.
Publication year - 2003
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/1541-0420.00012
Subject(s) - jackknife resampling , estimator , randomized controlled trial , proportional hazards model , variance (accounting) , econometrics , causal inference , average treatment effect , statistics , medicine , delta method , treatment effect , selection bias , mathematics , economics , accounting , traditional medicine
Summary . Survival data from randomized trials are most often analyzed in a proportional hazards (PH) framework that follows the intention‐to‐treat (ITT) principle. When not all the patients on the experimental arm actually receive the assigned treatment, the ITT‐estimator mixes its effect on treatment compliers with its absence of effect on noncompliers. The structural accelerated failure time (SAFT) models of Robins and Tsiatis are designed to consistently estimate causal effects on the treated, without direct assumptions about the compliance selection mechanism. The traditional PH‐model, however, has not yet led to such causal interpretation. In this article, we examine a PH‐model of treatment effect on the treated subgroup. While potential treatment compliance is unobserved in the control arm, we derive an estimating equation for the Compliers PROPortional Hazards Effect of Treatment (C‐PROPHET). The jackknife is used for bias correction and variance estimation. The method is applied to data from a recently finished clinical trial in cancer patients with liver metastases.