Table 1.
Characteristics of 5 Missing-Data Methods for Partially Observed Time-Varying Confounders
| Method | Missing Data on… | Assumptions | Unbiased in MSMs When… | Advantages | Limitations |
|---|---|---|---|---|---|
| Complete-case analysis | Covariates Treatment Outcome |
Missing data are MCAR. | MCAR | Straightforward | May be inefficient because of the loss in sample size |
| Last observation carried forward | Covariates Treatment Outcome (except at baseline) |
The true, but missing, value is the same as the last available measurement or the treatment decision depends on the previous available measurement rather than the true (unobserved) one. |
Constant | Straightforward Discards fewer patients than complete-case analysis |
Can lead to confidence intervals that are too narrow Patients are discarded if baseline measurements are missing. |
| Multiple imputation | Covariates Treatment Outcome |
Missing data are MAR.a The imputation model is correctly specified. |
MCAR MAR|A, L MAR|A, L, Y MAR|A, L, V |
Maintains the original sample size | May be computationally intensive Challenging for a large number of time points |
| Inverse-probability-of-missingness weighting | Covariates Treatment Outcome |
Missing data are MAR given the treatment and the covariates, but not the outcome. The weight model is correctly specified. |
MCAR MAR|A, L MAR|A, L, V Constant |
Faster than multiple imputation for large data setsWeights simultaneously address confounding and missing data. | May be inefficient for small and moderate sample sizes |
| Missingness pattern approach | Covariates | The partially observed covariate is no longer a confounder once missing (e.g., the treatment decision depends on the confounder value only when a measurement is available). | Differential | Relatively simple to implement Assumptions do not relate to Rubin’s taxonomy, so this method may work when standard methods do not. |
Does not handle missing data on the exposure or outcome Challenging when the number of missingness patterns is large |
Abbreviations: MAR, missing at random; MCAR, missing completely at random; MSM, marginal structural model.
a Extensions with which to accommodate data that are missing not at random exist but are challenging to apply in practice.