Handling Time-Varying Treatments

I’ve heard about new methodologies being developed that allow scientists to address novel scientific questions concerning the effects of time-varying treatments or predictors using observational longitudinal data. What are some examples of these scientific questions, and where can I read up on these newer methodologies? —Signed, Time for a Change


Dear TFAC,

Scientists often have longitudinal data that includes time varying covariates, time-varying treatments (or time varying predictors of interest), and longitudinal outcomes. In these settings, scientists may examine a varied number of scientific questions having to do with the impact of additional treatment, the effect of treatment sequences,timing, or treatment duration. One example involves understanding the effect of a putative moderator when both the moderator and primary treatment variable are time-varying. For instance, the following set of questions examine whether baseline and intermediate severity is a time-varying moderator (Almirall, Ten Have et al. 2009; Almirall, McCaffrey et al. under review) of the effect of community-based substance abuse treatment:

(a) “What is the effect of receiving an initial 3 months of community-based substance abuse treatment on substance use frequency among adolescents with less versus more severity at intake (baseline)?” and

(b) “What is the effect of receiving an additional 3 months of treatment some time later, as a function of improvements in severity since intake?”

In the time-varying setting, standard regression approaches that naively adjust for time-varying covariates may not be appropriate, and, in fact, may cause additional bias (Almirall, Ten Have et al. 2009; Almirall, McCaffrey et al. under review; Barber, Murphy et al. 2004; Bray, Almirall et al. 2006; Robins, Hernan et al. 2000). In the example given above, for instance, adjusting for time-varying severity is problematic because intermediate severity may have been affected by treatment during the first 3 months (this may happen, for example, if intermediate severity is a mediator of the effect of earlier treatment on future substance use frequency). Two problems with the traditional regression approach—both of which stem from adjusting for time-varying covariates possibly affected by earlier treatment—are described conceptually in Almirall, McCaffrey, et al (under review) in the context of a substance abuse example. Their article also offers a new 2-stage regression-with-residuals approach to examining the effect of time-varying treatments or predictors; the new approach involves a relatively simple adaptation of the traditional regression approach.


Almirall, D., McCaffrey, D. F., Ramchand, R., & Murphy,S. A. (under review). Subgroups analysis when treatment and moderators are time-varying.

Almirall, D.,Ten Have,T. R., & Murphy, S. A. (in press). Structural nested mean models for assessing time-varying effect moderation. Biometrics.

Barber, J. S., Murphy, S. A., & Verbitsky, N. (2004). Adjusting for time-varying confounding in survival analysis. Sociological Methodology, 34, 163-192.

Bray, B. C., Almirall, D., Zimmerman, R. S., Lynam, D., & Murphy, S. A. (2006). Assessing the total effect of time-varying predictors in prevention research. Prevention Science 7, 1-17.

Robins, J. M., Hernan, M. A., & Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology 11, 550-560.