Table 4 Points to consider on properties of each approach

Estimand for non-collapsible summary measures

Conditional

Marginal

Marginal

For non-collapsible summary measures, true β depends on…

Covariates conditioned on in outcome model

In-trial distribution of covariates

In-trial distribution of covariates

Misspecification of covariate effects

Loses efficiency vs. correctly specified model but expected to gain vs. no adjustment. True β changes under non-collapsibility

Loses efficiency vs. correctly specified model but expected to gain vs. no adjustment

Loses efficiency vs. correctly specified model but expected to gain vs. no adjustment

Convergence

Vulnerable

Reasonable (but see GetTested experience)

Solid

Stratification/minimisation handled by variance estimator

Yes

Yes

Yes

Efficiency

Asymptotically optimal

Asymptotically optimal

Asymptotically optimal

Standard error calculation

Direct

Delta method

Robust, accounting for estimation of weights via joint estimating equations. Standard error can be biased downwards in small samples [38]

Treatment–covariate interactions

Can be fitted but does not produce an estimate of an average treatment effect

Naturally handled this and produces an estimate of the average treatment effect

Does not handle

Handling of missing covariate data in order to target all-randomised population

Missing indicator or single mean imputation (though neither is suitable with non-collapsible population summary measures)

Missing indicator or single mean imputation

Missing indicator or single mean imputation

Handling of missing outcome data in order to target all-randomised population

Multiple imputation by-arm (or inverse probability of missingness weighting)

Standardisation to all-randomised rather than complete-case sample; alternatively multiple imputation by-arm or inverse probability of missingness weighting

Inverse probability of missingness weighting (or multiple imputation by-arm)