Evaluating Misclassification Effects on Single Sequential Treatment in Sequential Multiple Assignment Randomized Trial (SMART) Designs

Sequential multiple assignment randomized trial designs tailor individual treatment by rerandomizing participants to subsequent therapies based on their response to initial treatment. Misclassification of participant responses to initial treatment can lead to inappropriate treatment assignment and thus impact the final outcome. The aim of this study is to derive a series of formulas for quantifying potential misclassification effects on the mean, variance, and statistical inference of a single sequential treatment (SST) effect with continuous outcome. Relative bias is expressed as a function of sensitivity, specificity, and the probability of being true responders. Results show that misclassification can introduce bias to the estimated treatment effect. Though the magnitude of bias varies, there are a few general conclusions: (1) for any fixed sensitivity (or specificity) the relative bias of the mean of responders (or nonresponders) always approaches 0 in a monotonic nonlinear pattern as specificity (or sensitivity) increases; (2) the relative bias of SST variance always has nonmonotone nonlinear relationship with sensitivity or specificity; (3) the SST variance under misclassification is always over-estimated. Furthermore, the results show that misclassification can affect statistical inference, with power exhibiting either monotonic or nonmonotonic patterns and resulting in either under- or over-estimation.