Non-randomized and randomized stepped-wedge designs using an orthogonalized least squares framework

Abstract

Randomized stepped-wedge (R-SW) designs are increasingly used to evaluate interventions targeting continuous longitudinal outcomes measured at T-fixed time points. Typically, all units start out untreated, and randomly chosen units switch to intervention at sequential time points until all receive intervention. As randomization is not always feasible, non-randomized stepped-wedge (NR-SW) designs (units switching to intervention are not randomly chosen) have attracted researchers. We develop an orthogonlized generalized least squares framework for both R-SW and NR-SW designs. The variance of the intervention effect estimate depends on the number of steps (S), length of step sizes (t_s), and number of units (n_s) switched at each step (s=1,…, S). If all other design parameters are equal, this variance is higher for the NR-SW than for the equivalent R-SW design (particularly if the intercepts of non-randomly stepped switching strata are analyzed as fixed effects). We focus on balanced stepped-wedge (BR-SW, BNR-SW) designs (where t_s and n_s remain constant across s) to obtain insights into optimality for variance of the estimated intervention effect. As previously observed for the BR-SW, the optimal choice for number of time points at each step is also $t_s\equiv 1$ for the BNR-SW. In our examples, when compared to BR-SW designs, equivalent BNR-SW designs even with intercepts of non-randomly stepped switching strata analyzed using fixed effects sacrifice little efficiency given an intra-unit repeated measure correlation $\rho \ge 0.50$ . Compared to traditional difference-in-differences designs, optimal BNR-SW designs are more efficient with the ratio of variances of these designs converging to 0.75 when T > 10. We illustrate these findings using longitudinal outcomes in long-term care facilities.