In medicine and public health research, the randomized delayed-intervention controlled trial (RDICT), also known as a wait-listed or stepped wedge design, is commonly used to study overt, slow-acting treatments in comparison to a control condition over time. Ten RDICT designs are specified as generalizations of the motivating example, a longitudinal psychology study of a psychoeducational intervention for children with bipolar disorder. These designs vary according to number of observation occasions, time between observations, and length of delay before the control group receives treatment.
Two estimators of fixed effects in separate linear mixed effects (LME) models, θ1 and θ2, are proposed to measure treatment effect based on data from an RDICT design. The LME models have a piecewise linear mean structure, allowing phases for treatment, placebo, and leveling-off effects. The treatment effect is traditionally conceptualized as the difference in slopes between the immediate treatment (IT) and pre-intervention control groups, which we call θ1.
Alternately, in an RDICT design, the treatment effect can be the change in slope post-intervention in the delayed-treatment (DT) control group, called θ0. The full model, which allows these treatment effects to differ, produces the standard estimator, θ1. A reduced model, nested within the full one, forces the inter and intra treatment effects to be identical and produces the novel estimator, θ2.
A simulation study was conducted to observe the relative efficiency of θ2 to θ1 as it varies over the 10 RDICT designs and 8 scenarios, which differ in size of treatment effect, intraclass correlation, and sample allocation to DT group.
The best-performing and recommended RDICT design, called H2.5 with a DT:IT allocation ratio of 2:1, achieved a relative efficiency of 1.3 when the group-specific treatment effects are identical. The H2.5 design has the longest overall calendar duration of the 10 designs considered and is an extension of the design used in the motivating example study of childhood mood disorders.