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

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.