Making apples from oranges: Comparing noncollapsible effect estimators and their standard errors after adjustment for different covariate sets.

Rhian Daniel,Daniel Farewell,Jingjing Zhang

doi:10.1002/bimj.201900297

Rhian Daniel, Daniel Farewell + Show 1 more

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https://doi.org/10.1002/bimj.201900297

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Abstract

We revisit the well‐known but often misunderstood issue of (non)collapsibility of effect measures in regression models for binary and time‐to‐event outcomes. We describe an existing simple but largely ignored procedure for marginalizing estimates of conditional odds ratios and propose a similar procedure for marginalizing estimates of conditional hazard ratios (allowing for right censoring), demonstrating its performance in simulation studies and in a reanalysis of data from a small randomized trial in primary biliary cirrhosis patients. In addition, we aim to provide an educational summary of issues surrounding (non)collapsibility from a causal inference perspective and to promote the idea that the words conditional and adjusted (likewise marginal and unadjusted) should not be used interchangeably.

Highlights

1.1 Noncollapsibility An overviewIt is well known that two of the statistical models most often used in medical research, namely, logistic regression and Cox proportional hazards (PH) regression, involve parameters of interest that are noncollapsible
Even in an ideal randomized controlled trial (RCT) with a binary or rightcensored time-to-event outcome, no matter how large the sample size, the odds ratio or hazard ratio comparing treated and untreated individuals will change upon including a baseline covariate in the model, whenever that covariate is associated with the outcome
The following methods are compared: (A) an unadjusted logistic or Cox model, (B) the same unadjusted model as in (A) but including inverse probability of treatment weighting (IPTW) (Hernan, 2006), where the model for the treatment weights is a logistic regression for treatment/exposure given the baseline covariate/confounder, (C) Zhang’s method or our proposal, (D) an adjusted logistic or Cox model including the baseline covariate/confounder where we are interested in the estimator of the conditional log OR or log HR from these models

Summary

Introduction

1.1 Noncollapsibility An overviewIt is well known that two of the statistical models most often used in medical research, namely, logistic regression and Cox proportional hazards (PH) regression, involve parameters of interest that are noncollapsible. Even in an ideal randomized controlled trial (RCT) (i.e., no dropout, non-adherence or other complicating structural features) with a binary or rightcensored time-to-event outcome, no matter how large the sample size, the odds ratio or hazard ratio comparing treated and untreated individuals will change upon including a baseline covariate in the model, whenever that covariate is associated with the outcome. Conditioning on a covariate changes the very nature of the treatment effect we are estimating. This difference (between a conditional and marginal odds/hazard ratio) is not explained by sampling variation, and is what is referred to when it is said that odds/hazard ratios are noncollapsible

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