Interrupted Time Series Methods for Nonrandom Sampling Study Designs With Known Sampling Weights

Including participants from diverse neighborhoods in research may improve generalizability of study results to broader populations. The University of California Irvine Consent-to-Contact (C2C) Registry recently initiated a novel Recruitment Strategy Study (named the C2C-RSS) to assess the effectiveness of interventions (Facebook versus traditionally mailed postcard advertisements) that aimed at recruiting individuals from more disadvantaged neighborhoods, as defined by high Area Deprivation Index (ADI) in Orange County, California. The C2C-RSS utilized a nonrandom sampling design to ensure uniform inclusion across ADI deciles. The primary objective of the C2C-RSS is to estimate a marginal intervention effect across all ADI deciles on recruitment to the C2C Registry. A key secondary objective is to assess effect modification by ADI strata. To adjust for sampling bias in the C2C-RSS design, we extend the Robust-Multiple Interrupted Time Series model to incorporate known sampling weights. We additionally propose two variance estimators. The first quantifies uncertainty of the unknown change point associated with the intervention in all mean function parameters. The second additionally accounts for mis-specification of the mean model. We demonstrate the performance of our methods through empirical simulation studies. Further, we use our proposed methods to assess the design of the C2C-RSS, illustrating comparable power for the primary endpoint and increased power for the secondary endpoint relative to a simple random sampling design.