Develop a lower-variance estimator combining within-case and cross-case comparisons

Develop a design-based estimator for randomized multiple-baseline experiments that combines each case’s within-case comparison of treated and untreated window sessions with information from cases in the same study that remain in baseline at the same session, and determine whether the resulting estimator has a smaller variance.

Background

The proposed estimators use each case as its own comparison, contrasting treated and untreated observations within that case’s randomized onset window. The authors identify additional information in multiple-baseline studies: at a given session, other cases in the same study may still be in the baseline phase and can provide information about the untreated outcome at that session. The unresolved task is to incorporate both sources of comparison in a design-based estimator and assess whether doing so reduces variance.