Least Squares and Robust Rank-Based Double Bootstrap Analyses for Time-Series Intervention Designs

Abstract

Time-series intervention designs that include two or more phases have been widely discussed in the healthcare literature for many years. A convenient model for the analysis of these designs has a linear model part (to measure changes in level and trend) plus a second part that measures the random error structure; the error structure is assumed to follow an autoregressive time-series process. Traditional generalized linear model approaches widely used to estimate this model are less than satisfactory because they tend to provide substantially biased intervention tests and confidence intervals. We describe an updated version of the original double bootstrap approach that was developed by McKnight et al. (2000) to correct for this problem. This updated analysis and a new robust version were recently implemented in an R package (McKean & Zhang, 2018). The robust method is insensitive to outliers and problems associated with common departures from normality in the error distribution. Monte Carlo studies as well as published data are used to demonstrate the properties of both versions. The R code required to perform the analyses is provided and illustrated.