FIVE AUTHORS REPLY

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Abstract
We thank Dijkzeul and Labrecque for their letter ( 1) on our recent missing outcome data paper ( 2). Regarding their first point on homogeneity constraints, it might be helpful to consider our scenario B (i.e., missing at random with positivity). Here, both g-computation (stratified by treatment) and multiple imputation (including treatment-covariate product term) models were saturated, and therefore asymptotically equivalent. Neither estimator makes a homogeneity assumption with respect to completing the missing data. And both estimators make marginal comparisons of the mean outcomes between completed treated and untreated data (which is reasonable because this is a randomized trial). Here, g-computation is a nonparametric maximum likelihood estimator, and multiple imputation approaches maximum likelihood as the number of imputations tends towards infinity. Some discussion of how g-computation and multiple imputation relate is provided in Westreich et al. ( 3). Now, in our scenario C (i.e., missing at random without positivity), all the same above points hold, except, as noted by Dijkzeul and Labrecque, all women with 17α-hydroxyprogesterone caproate (17p) treatment and short cervix are missing outcomes. The imputed outcomes, whether by g-computation or multiple imputation, can depend on 17p or short cervix but cannot depend on their product (because no such outcome data is observed). Both g-computation and multiple imputation make this same homogeneity assumption, with the differences in performance most likely attributable to random error. In scenario C, the standard errors for g-computation (500 bootstrap samples) and multiple imputation (50 imputations) were 0.340 and 0.274 (see Cole et al. ( 2), Table 2 and Web Table 1). However, with 10,000 bootstrap samples and 5,000 imputations, the standard errors were instead 0.328 and 0.355.
Funding Information
  • National Institutes of Health (R01AI157758)

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