Pattern-Mixture Models as Linear Combinations of Least Squares Means from MMRM with Delta Method Variance Estimation

For studies with missing data, it is being increasingly recommended to provide sensitivity analyses that assume data are Missing Not at Random (MNAR). In certain therapeutic areas, MNAR assumptions about the missingness mechanism are even recommended for the primary analysis. MNAR assumptions can be modeled within several statistical frameworks, one of which is known as pattern-mixture models (PMMs). Certain PMM-based analyses for continuous outcomes can be formulated in such a way that the estimate of the difference between experimental and control treatments is expressed as a linear combination of Least Squares Means (LSMs) for different effects of a longitudinal model with correlated errors, weighted by the appropriate proportions of study drop-outs and completers. This approach requires special considerations for the estimation of the variance because the proportions of drop-outs and completers used in the linear combination of LSMs are themselves multinomial random variables and their variances need to be incorporated into the overall estimate. This can be done using a delta approximation method for variance estimation. In this paper, we present details of implementing such analyses (including delta variance estimation method ) using exclusively SAS/STAT ® core functionality, such as PROC MIXED, data steps, and PROC FCMP. To illustrate this approach, we are using an example of MNAR assumptions that take into account the reasons for discontinuation from the study.