Direct likelihood with influence and residual diagnostics

These SAS macros focus on the direct likelihood analysis approach under MAR assumption with influence and residual diagnostics. In many clinical studies such as in the highly controlled scenario of longitudinal confirmatory trials, it is plausible to start with MAR assumption and missing data may be mostly MAR. Such approach with restrictive models are often a reasonable choice for the primary analysis since they are simple models with few independent variables and often include only the design factors of the experiment.

The primary analysis macro (DL_Primary1) uses SAS PROC MIXED with REPEATED statement as the standard MMRM analysis. Within subject covariance structure can be specified in the REPEATED statement. Visitwise treatment main effects as well treatment difference would be provided through LSMEANS statement. A separate macro (DL_Cov1) can repeat the primary analysis using a list of different user-specified within subject covariance structures and also provide AIC and likelihood as model selection reference.

The general idea of quantifying the influence of one or more observations relies on computing parameter estimates based on all data points, removing the cases in question from the data, refitting the model, and comparing between full-data and reduced-data estimation. Another 3 macros here would implement this idea.

Macro DL_residual1 conducts influence diagnostics for observations with aberrant residuals. The primary direct likelihood analysis model is used to obtain studentized residuals for each observation and users can specify the influential cut off value to determine aberrant observations whose residuals are beyond the cut off values. The PORC MIXED reruns the direct likelihood analysis with aberrant data deleted in placebo arm only, study drug arm only, and all arms so that influence from these aberrant observations on primary analysis can be evaluated accordingly.

The last two macros DL_Influence_Patient1 and DL_Influence_Site1 conduct influence diagnostics for clusters of observations, where the cluster is defined by patients or by investigative site. The influential patients or influential investigative sites will be identified using Cook’s D provided by PROC MIXED as well as cut off values specified by users. Results from the primary analysis (includes all patients/sites) and from datasets with influential patients/sites removed are printed for comparison and evaluation of influence.

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