Generalizing the information content for stepped wedge designs: A marginal modeling approach

Abstract

Stepped wedge trials are increasingly adopted because practical constraints necessitate staggered roll-out. While a complete design requires clusters to collect data in all periods, resource and patient-centered considerations may call for an incomplete stepped wedge design to minimize data collection burden. To study incomplete designs, we expand the metric of information content to discrete outcomes. We operate under a marginal model with general link and variance functions, and derive information content expressions when data elements (cells, sequences, periods) are omitted. We show that the centrosymmetric patterns of information content can hold for discrete outcomes with the variance-stabilizing link function. We perform numerical studies under the canonical link function, and find that while the patterns of information content for cells are approximately centrosymmetric for all examined underlying secular trends, the patterns of information content for sequences or periods are more sensitive to the secular trend, and may be far from centrosymmetric.

Keywords: centrosymmetry; cluster randomized trials; generalized estimating equations; symmetric block correlation structure; variance-stabilizing link function.

FIGURE 1

Two examples of incomplete stepped wedge CRTs with I = 8 clusters and J = 10 calendar periods. A white cell indicates a cluster-period under usual care and outcome data collection, a colored cell indicates a cluster-period under treatment and outcome data collection, a cell with ‘×’ indicates a cluster-period without any outcome data collection. (a) A schematic of a incomplete stepped wedge design with I = 8 clusters and J = 10 calendar periods and one transition period. (b) A schematic of a incomplete stepped wedge design with I = 8 clusters and J = 10 calendar periods, one before and two after measurements [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 2

Information content of cells under two correlation models and three secular trends with a binary outcome and logistic link. The baseline prevalence is $e^{{\beta }_1}/\left(1+e^{{\beta }_1}\right)=20\%$. [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 3

Information content of sequences under two correlation models and three secular trends with a binary outcome and logistic link. The baseline prevalence is $e^{{\beta }_1}/\left(1+e^{{\beta }_1}\right)=20\%$. [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 4

Information content of periods under two correlation models and three secular trends with a binary outcome and logistic link. The baseline prevalence is $e^{{\beta }_1}/\left(1+e^{{\beta }_1}\right)=20\%$. [Colour figure can be viewed at wileyonlinelibrary.com]