Electronic Journal of Statistics

Identifying and estimating net effects of treatments in sequential causal inference

Xiaoqin Wang and Li Yin

Full-text: Open access

Abstract

Suppose that a sequence of treatments are assigned to influence an outcome of interest that occurs after the last treatment. Between treatments, there are time-dependent covariates that may be post-treatment variables of the earlier treatments and confounders of the subsequent treatments. In this article, we study identification and estimation of the net effect of each treatment in the treatment sequence. We construct a point parametrization for the joint distribution of treatments, time-dependent covariates and the outcome, in which the point parameters of interest are the point effects of treatments considered as single-point treatments. We identify net effects of treatments by their expressions in terms of point effects of treatments and express patterns of net effects of treatments by constraints on point effects of treatments. We estimate net effects of treatments through their point effects under the constraint by maximum likelihood and reduce the number of point parameters in the estimation by the treatment assignment condition. As a result, we obtain an unbiased consistent maximum-likelihood estimate for the net effect of treatment even in a long treatment sequence. We also show by simulation that the interval estimation of the net effect of treatment achieves the nominal coverage probability.

Article information

Source
Electron. J. Statist., Volume 9, Number 1 (2015), 1608-1643.

Dates
Received: August 2014
First available in Project Euclid: 6 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1438883470

Digital Object Identifier
doi:10.1214/15-EJS1046

Mathematical Reviews number (MathSciNet)
MR3379004

Zentralblatt MATH identifier
1327.62350

Subjects
Primary: 62H12: Estimation
Secondary: 62H15: Hypothesis testing 62F03: Hypothesis testing 62F30: Inference under constraints

Keywords
Net effect of treatment pattern of net effects of treatments point effect of treatment constraint on point effects of treatments treatment assignment condition sequential causal inference

Citation

Wang, Xiaoqin; Yin, Li. Identifying and estimating net effects of treatments in sequential causal inference. Electron. J. Statist. 9 (2015), no. 1, 1608--1643. doi:10.1214/15-EJS1046. https://projecteuclid.org/euclid.ejs/1438883470


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References

  • [1] Frangakis, C. E. & Rubin, D. B. (2002). Principal Stratification in Causal Inference., Biometrics, 58, 21–29.
  • [2] Lok, J. J. & DeGruttola, V. (2012). Impact of Time to Start Treatment Following Infection with Application to Initiating HAART in HIV-Positive Patients., Biometrics, 68, 745–754.
  • [3] Kaslow, R. A., Ostrow, D. G., Detels, R., Phair, J. P., Polk, B. F. & Rinaldo, C. R. (1987). The multicenter AIDS cohort study: rationale, organization and selected characteristic of the participants., American Journal of Epidemiology, 126, 310–318.
  • [4] Henderson, R., Ansell, P. & Alshibani, D. (2010). Regret-Regression for Optimal Dynamic Treatment Regimes., Biometrics, 66, 1192–1201.
  • [5] Murphy, S. A., van der Laan, J., Robins, J. M. & CPPRG (2001). Marginal Mean Model for Dynamic Regimes., Journal of American Statistical Association, 96, 1410–1423.
  • [6] Murphy, S. A. (2003). Optimal dynamic treatment regions., Journal of the Royal Statistical Society: Series B, 62, 331–354.
  • [7] Robins, J. M. (1986). A new approach to causal inference in mortality studies with sustained exposure periods – application to control of the healthy worker survival effect., Mathematical Modeling, 7, 1393–1512.
  • [8] Robins, J. M. (1989). The control of confounding by intermediate variables., Statistics in Medicine, 8, 679–701.
  • [9] Robins, J. M. (1992). Estimation of the time-dependent accelerated failure time model in the presence of confounding factors., Biometrika, 79, 321–334.
  • [10] Robins, J. M. (1997). Causal inference from complex longitudinal data. In, Latent variable modeling and applications to causality, Lecture notes in Statistics (120), (Ed. Berkane, M.), pp. 69–117. New York: Springer-Verlag.
  • [11] Robins, J. M. & Ritov, Y. (1997). Towards a curse of dimensionality asymptotic theory for semi-parametric models., Statistics in Medicine, 16, 285–319.
  • [12] Robins, J. M. (1999). Association, causation, and marginal structural models., Synthese, 121, 151–179.
  • [13] Robins, J. M., Rotnitzky, A. & Scharfstein, D. (1999). Sensitivity Analysis for Selection Bias and Unmeasured Confounding in Missing Data and Causal Inference Models. In, Statistical Models in Epidemiology: The Environment and Clinical Trials, (Eds. Halloran, M. E. & Berry, D.), IMA Volume 116, pp. 1–92. NY: Springer-Verlag.
  • [14] Robins, J. M. (2004). Optimal structural nested models for optimal sequential decisions. In, Lecture notes in Statistics (179), (Ed. Berkane, M.), pp. 189–326. New York: Springer-Verlag.
  • [15] Robins, J. M. (2009). Longitudinal Data Analysis. In, Handbooks of Modern Statistical Methods, (Ed. Fitzmaurice, G.), pp. 553–599. Chapman & Hall / CRC.
  • [16] Rosenbaum, P. R. (1984). The consequence of adjustment for a concomitant variable that has been affected by the treatment., Journal of the Royal Statistical Society: Series A, 147, 656–666.
  • [17] Rosenbaum, P. R. & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects., Biometrika, 70, 41–55.
  • [18] Rosenbaum, P. R. (1995)., Observational studies. New York, NY: Springer.
  • [19] Rubin, D. B. (2005). Causal inference using potential outcomes: design, modeling, decisions., Journal of the American Statistical Association, 100, 322–331.
  • [20] Wang, X. & Yin, L. (2015). Supplement to “Identifying and Estimating Net Effects of Treatments in Sequential Causal Inference” DOI:, 10.1214/15-EJS1046SUPP.
  • [21] Zeger, S. L. & Diggle, P. J. (1994). Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters., Biometrics, 50, 689–699.

Supplemental materials

  • SAS codes and SAS data sets. The supplementary material contains (1) SAS codes and SAS data sets for the simulation study in Section 6.2 and (2) SAS code and SAS data set for the illustrative study in Section 6.3. (Zip file).