# Assessing the Total Effect of Time-Varying Predictors in Prevention Research

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Observational data are often used to address prevention questions such as, “If alcohol initiation could be delayed, would that in turn cause a delay in marijuana initiation?” This question is concerned with the total causal effect of the timing of alcohol initiation on the timing of marijuana initiation. Unfortunately, when observational data are used to address a question such as the above, alternative explanations for the observed relationship between the predictor, here timing of alcohol initiation, and the response abound. These alternative explanations are due to the presence of confounders. Adjusting for confounders when using observational data is a particularly challenging problem when the predictor and confounders are time-varying. When time-varying confounders are present, the standard method of adjusting for confounders may fail to reduce bias and indeed can increase bias. In this paper, an intuitive and accessible graphical approach is used to illustrate how the standard method of controlling for confounders may result in biased total causal effect estimates. The graphical approach also provides an intuitive justification for an alternate method proposed by James Robins [Robins, J. M. (1998). *1997 Proceedings of the American Statistical Association, section on Bayesian statistical science* (pp. 1–10). Retrieved from http://www.biostat.harvard.edu/robins/research.html; Robins, J. M., Hernán, M., & Brumback, B. (2000). *Epidemiology, 11*(5), 550–560]. The above two methods are illustrated by addressing the motivating question. Implications for prevention researchers who wish to estimate total causal effects using longitudinal observational data are discussed.

## KEY WORDS:

confounding weighting total effect time-varying graphical approach## Notes

### ACKNOWLEDGMENTS

Preparation of this paper was supported by grant P50-DA-10075 from the National Institute on Drug Abuse to the Methodology Center at the Pennsylvania State University, by grant T32-DA-017629 to the Methodology Center and the Prevention Research Center for the Promotion of Human Development at the Pennsylvania State University, and by the National Institute on Drug Abuse award K02-DA-15674-01.

## REFERENCE

- Agerbo, E. (2005). Effect of psychiatric illness and labour market status on suicide: A healthy worker effect?
*Journal of Epidemiology and Community Health, 59*(7), 598–602.Google Scholar - Allison, P. D. (1995).
*Survival analysis using the SAS system: A practical guide*. Cary, NC: SAS Institute.Google Scholar - Angrist, J. D., Imbens, G. W., & Rubin, D. B. (1996). Identification of causal effects using instrumental variables.
*Journal of the American Statistical Association, 91*, 434, 444–455.Google Scholar - Barber, J. S., Murphy, S. A., & Verbitsky, N. (2004). Adjusting for time-varying confounding in survival analysis.
*Sociological Methodology*,*34*, 163–192.Google Scholar - Berkson, J. (1946). Limitations of the application of fourfold table analysis to hospital data.
*Biometric Bulletin*,*2*, 47–53.Google Scholar - Bohrnstedt, G. W., & Knoke, D. (1982).
*Statistics for social data analysis*. Itasca, IL: P. E. Peacock Publishers.Google Scholar - Bollen, K. A. (1989).
*Structural equations with latent variables*. New York: Wiley.Google Scholar - Bray, B. C., Zimmerman, R. S., Lynam, D., & Murphy, S. (2003).
*Assessing the total effect of time-varying predictors in prevention research*(Technical Report 03-59). University Park, PA: The Methodology Center, Pennsylvania State University.Google Scholar - Clayton, R. R., Cattarello, A., Day, L. E., & Walden, K. P. (1991). Persuasive communications and drug prevention: An evaluation of the D.A.R.E. program. In L. Donohew, H. E. Sypher, & W. J. Bukoski (Eds.),
*Persuasive communication and drug abuse prevention*(pp. 279–294). Hillsdale, NJ: Erlbaum.Google Scholar - Clayton, R. R., Cattarello, A. M., & Johnstone, B. M. (1996). The effectiveness of drug abuse resistance education (project DARE): 5-year follow-up results.
*Preventive Medicine*,*25*, 307–318.Google Scholar - Cochran, W., & Rubin, D. (1973). Controlling bias in observational studies.
*Sankya—The Indian Journal of Statistics, Series A*,*35*(Dec), 417–446.Google Scholar - Heckman, J. J. (1979). Sample selection bias as a specification error.
*Econometrica*,*47*(1), 153–161.Google Scholar - Heckman, J. J., & Hotz, V. J. (1989). Choosing among alternative nonexperimental methods for estimating the impact of social programs—The case of manpower training.
*Journal of the American Statistical Association*,*84*, 408, 862–874.Google Scholar - Hernán, M., Brumback, B., & Robins, J. M. (2000). Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men.
*Epidemiology*,*11*(5), 561–570.Google Scholar - Hernán, M., Brumback, B., & Robins, J. M. (2001). Marginal structural models to estimate the joint causal effect of nonrandomized treatments.
*Journal of the American Statistical Association*,*96*, 454, 440–448.Google Scholar - Imbens, G. (2000). The role of the propensity score in estimating dose–response functions.
*Biometrika*,*87*(3), 706–710.Google Scholar - Joffe, M. M., Ten Have, T. R., Feldman, H. I., & Kimmel, S. E. (2004). Model selection, confounder control, and marginal structural models: Review and new applications.
*American Statistician*,*58*(4), 272–279.Google Scholar - Little, R. J., & Yau, L. H. Y. (1998). Statistical techniques for analyzing data from prevention trials: Treatment of no-shows using Rubin's causal model.
*Psychological Methods*,*3*(2), 147–159.Google Scholar - Oakes, J. M. (2004). The (mis)estimation of neighborhood effects: Causal inference for a practicable social epidemiology.
*Social Science and Medicine*,*58*(10), 1929–1952.Google Scholar - Pearl, J. (1998). Graphs, causality, and structural equation models.
*Sociological Methods and Research*,*27*, 226–284.Google Scholar - Raine, A. (1993).
*The psychopathology of crime: Criminal behavior as a clinical disorder*. San Diego, CA: Academic Press.Google Scholar - Robins, J. M. (1998). Marginal structural models.
*1997 proceedings of the American Statistical Association, section on Bayesian statistical science*(pp. 1–10). Retrieved from http://www.biostat.harvard.edu/~robins/research.html - Robins, J. M. (1999). Association, causation, and marginal structural models.
*Synthese*,*121*(1/2), 151–179.Google Scholar - Robins, J. M., Hernán, M., & Brumback, B. (2000). Marginal structural models and causal inference in epidemiology.
*Epidemiology*,*11*(5), 550–560.Google Scholar - Rosenbaum, P. R., & Rubin, D. B. (1984). Reducing bias in observational studies using subclassification on the propensity score.
*Journal of the American Statistical Association*,*79*, 387, 516–524.Google Scholar - Rosenbaum, P. R., & Rubin, D. B. (1985). Constructing a control-group using multivariate matched sampling methods that incorportate the propensity score.
*American Statistician*,*39*(1), 33–38.Google Scholar - Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002).
*Experimental and quasi-experimental designs for generalized causal inference*. Boston: Houghton-Mifflin.Google Scholar - Singer, J. D., & Willet, J. B. (1993). It's about time: Using discrete-time survival analysis to study duration and the timing of events.
*Journal of Education Statistics*,*18*, 155–195.Google Scholar - Wechsler, D. (1981). The psychometric tradition: Developing the Wechsler Adult Intelligence Scale.
*Contemporary Educational Psychology*,*6*(2), 82–85.Google Scholar - White, H. (1982). Maximum likelihood estimation of misspecified models.
*Econometrica*,*50*(1), 1–25.Google Scholar - Winship, C., & Mare, R. D. (1992). Models for sample selection bias.
*Annual Review of Sociology*,*18*, 327–350.Google Scholar - Winship, C., & Morgan, S. L. (1999). The estimation of causal effects from observational data.
*Annual Review of Sociology*,*25*, 659–707.Google Scholar - Zuckerman, M. (1994).
*Behavioral expressions and biosocial bases of sensation seeking*. Cambridge: Cambridge University Press.Google Scholar