Sample size and power considerations for ordinary least squares interrupted time series analysis: a simulation study

Abstract

Interrupted time series (ITS) analysis is being increasingly used in epidemiology. Despite its growing popularity, there is a scarcity of guidance on power and sample size considerations within the ITS framework. Our aim of this study was to assess the statistical power to detect an intervention effect under various real-life ITS scenarios. ITS datasets were created using Monte Carlo simulations to generate cumulative incidence (outcome) values over time. We generated 1,000 datasets per scenario, varying the number of time points, average sample size per time point, average relative reduction post intervention, location of intervention in the time series, and reduction mediated via a 1) slope change and 2) step change. Performance measures included power and percentage bias. We found that sample size per time point had a large impact on power. Even in scenarios with 12 pre-intervention and 12 post-intervention time points with moderate intervention effect sizes, most analyses were underpowered if the sample size per time point was low. We conclude that various factors need to be collectively considered to ensure adequate power for an ITS study. We demonstrate a means of providing insight into underlying sample size requirements in ordinary least squares (OLS) ITS analysis of cumulative incidence measures, based on prespecified parameters and have developed Stata code to estimate this.

Keywords:

• epidemiology
• interrupted time series
• sample size
• power
• bias

Acknowledgments

This study was partially supported by Oxford NIHR Biomedical Research Unit. Andrew Judge was partially supported by the NIHR Biomedical Research Centre at the University Hospitals Bristol NHS Foundation Trust and the University of Bristol. The views expressed in this publication are those of the authors and not necessarily those of the NHS, the National Institute for Health Research, or the Department of Health.

Author contributions

SH, DP-A, and AJ contributed to study conception and design. SH, MSA, and KB contributed to data simulation. SH, KB, and MSA contributed to data analysis. SH contributed to drafting the manuscript. All authors contributed to revising the manuscript critically for important intellectual content, gave final approval of the version to be published, and agree to be accountable for all aspects of the work.

Disclosure

AJ has received consultancy fees from Freshfields Bruckhaus Deringer and is a member of the Data Safety and Monitoring Board (which involved receipt of fees) from Anthera Pharmaceuticals, Inc., outside the submitted work. DP-A’s research group has received unrestricted research grants from Servier Laboratoires, AMGEN, and UCB Pharma. SH, MSA, and KB report no conflicts of interest in this work.