# Subgroups Analysis when Treatment and Moderators are Time-varying

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## Abstract

Prevention scientists are often interested in understanding characteristics of participants that are predictive of treatment effects because these characteristics can be used to inform the types of individuals who benefit more or less from treatment or prevention programs. Often, effect moderation questions are examined using subgroups analysis or, equivalently, using covariate × treatment interactions in the context of regression analysis. This article focuses on conceptualizing and examining causal effect moderation in longitudinal settings in which both treatment and the putative moderators are time-varying. Studying effect moderation in the time-varying setting helps identify which individuals will benefit more or less from additional treatment services on the basis of both individual characteristics and their evolving outcomes, symptoms, severity, and need. Examining effect moderation in these longitudinal settings, however, is difficult because moderators of future treatment may themselves be affected by prior treatment (for example, future moderators may be mediators of prior treatment). This article introduces moderated intermediate causal effects in the time-varying setting, describes how they are part of Robins’ Structural Nested Mean Model, discusses two problems with using a traditional regression approach to estimate these effects, and describes a new approach (a two-stage regression estimator) to estimate these effects. The methodology is illustrated using longitudinal data to examine the time-varying effects of receiving community-based substance abuse treatment as a function of time-varying severity (or need).

## Keywords

Effect moderation Treatment effect heterogeneity Collider bias Time-varying treatment effects## Notes

### Acknowledgements

Funding for this work was provided by the following grants: R01-DA-015697 (McCaffrey), R01-DA- 017507 (Ramchand), R01-MH-080015 (Murphy), and P50-DA-010075 (Murphy). The authors would like to thank Andrew R. Morral, Beth Ann Griffin, and Scott N. Compton for comments and suggestions, Cha-Chi Fan for guidance with the data, and three anonymous reviewers and the Associate Editor for helpful comments and suggestions.

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