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.序贯多重分配随机试验（Sequential multiple assignment randomized trial）设计通过基于受试者对初始治疗的应答情况，将其再随机分配至后续治疗方案，以此实现个体化治疗。若对受试者的初始治疗应答情况发生错分，将导致不恰当的治疗分配，进而影响最终结局。本研究旨在推导一系列公式，以量化错分效应对具有连续结局的单序贯治疗（single sequential treatment, SST）效应的均值、方差及统计推断的影响。相对偏倚以灵敏度、特异度及真应答者概率作为函数形式进行表征。 研究结果表明，错分会为估计治疗效应引入偏倚。尽管偏倚的大小存在差异，但可得到若干一般性结论：（1）对于固定的灵敏度（或特异度），应答者（或非应答者）均值的相对偏倚会随特异度（或灵敏度）的提升，以单调非线性模式逐渐趋近于0；（2）单序贯治疗方差的相对偏倚与灵敏度或特异度始终呈非单调非线性关系；（3）错分情境下的单序贯治疗方差始终被高估。此外，研究结果还显示，错分会对统计推断产生影响，检验效能可呈现单调或非单调模式，并导致估计值出现低估或高估的情况。