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

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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.

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