Conditional average treatment effect estimation with marginally constrained models

TL;DR

This paper proposes a constrained modeling approach to improve the estimation of conditional average treatment effects (CATE) using marginal odds-ratios from randomized trials, addressing limitations of existing offset methods especially under unobserved confounding.

Contribution

It introduces a novel regularizer that leverages marginal odds-ratios for more accurate CATE estimation and analyzes its validity under different confounding scenarios.

Findings

The constrained approach provides closer CATE approximations when variation is sufficient.

Offset methods are invalid for CATE estimation with unobserved confounding.

The proposed method offers consistent CATE estimates under standard causal assumptions.

Abstract

Treatment effect estimates are often available from randomized controlled trials as a single average treatment effect for a certain patient population. Estimates of the conditional average treatment effect (CATE) are more useful for individualized treatment decision making, but randomized trials are often too small to estimate the CATE. Examples in medical literature make use of the relative treatment effect (e.g. an odds-ratio) reported by randomized trials to estimate the CATE using large observational datasets. One approach to estimating these CATE models is by using the relative treatment effect as an offset, while estimating the covariate-specific untreated risk. We observe that the odds-ratios reported in randomized controlled trials are not the odds-ratios that are needed in offset models because trials often report the marginal odds-ratio. We introduce a constraint or regularizer to better use marginal odds-ratios from randomized controlled trials and find that under the standard observational causal inference assumptions this approach provides a consistent estimate of the CATE. Next, we show that the offset approach is not valid for CATE estimation in the presence of unobserved confounding. We study if the offset assumption and the marginal constraint lead to better approximations of the CATE relative to the alternative of using the average treatment effect estimate from the randomized trial. We empirically show that when the underlying CATE has sufficient variation, the constraint and offset approaches lead to closer approximations to the CATE.