Causal inference for continuous-time processes when covariates are observed only at discrete times

Annals of Statistics

Volumn 39, Issue 1, 2011, Pages 131-173

  Zhang, Mingyuan ^a   Joffe, Marshall M ^b   Small, Dylan S ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Causal inference; Continuous time process; Deterministic model; Diarrhea; G estimation; Longitudinal data; Structural nested model

Indexed keywords

EID: 79551580850     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AOS830     Document Type: Article

References (27)

1. ANDERSEN, P. K., BORGAN, Ø., GILL, R. and KEIDING, N. (1992). Statistical Models Based on Counting Processes. Springer, New York.
2. BRUMBACK, B.A.,HERNÁN, M. A.,HANEUSE, S. J. and ROBINS, J.M. (2004). Sensitivity analyses for unmeasured confounding assuming a marginal structural model for repeated measures. Stat. Med. 23 749-767.
3. COCHRAN, W. G. (1965). The planning of observational studies of human populations (with discussion). J. Roy. Statist. Soc. Ser. A 128 134-155.
4. DEL NINNO, C., DOROSH, P., SMITH, L. and ROY, D. (2001). The 1998 floods in Bangladesh: Disaster impacts, household coping strategies and response. Research Report 122, International Food Policy Research Institute, Washington, DC.
5. DEL NINNO, C. and LUNDBERG,M. (2005). Treading water: The long-term impact of the 1998 flood on nutrition in Bangladesh. Economics and Human Biology 3 67-96.
6. DURRETT, R. (2005). Probability: Theory and Examples, 3rd ed. Brooks/Cole-Thomson Learning, Belmont, CA.
7. GASSER, T., MULLER, H., KOHLER, W., MOLINARI, L. and PRADER, A. (1984). Nonparametric regression analysis of growth curves. Ann. Statist. 12 210-229. MR0733509
8. GUERRANT, R. L., KOSEK, M., LIMA, A.A.M., LORNTZ, B. and GUYATT, H. L. (2002). Updating the Dalys for diarrhoeal disease. Trends in Parasitology 18 191-193.
9. HERNÁN, M. A., BRUMBACK, B. and ROBINS, J. M. (2002). Estimating the causal effect of zidovudine on CD4 count with a marginal structural model for repeated measures. Stat. Med. 21 1689-1709.
10. JOFFE, M. M. and ROBINS, J. M. (2009). Controlling the future: Revised assumptions and methods for causal inference with repeated measures outcomes. Working paper.
11. KASLOW, R. A., OSTROW, D. G., DETELS, R., PHAIR, J. P., POLK, B. F. and RINALDO, C. R., Jr. (1987). The Multicenter AIDS Cohort Study: Rationale, organization, and selected characteristics of the participants. American Journal of Epidemiology 126 310-318.
12. KOSEK, M., BERN, C. andGUERRANT, R. L. (2003). The global burden of diarrhoeal disease as estimated from studies published between 1992 and 2000. Bulletin of the World Health Organization 81 197-204.
13. LOK, J. J. (2008). Statistical modeling of causal effects in continuous time. Ann. Statist. 36 1464-1507. MR2418664
14. MARTORELL, R. and HO, T. J. (1984). Malnutrition, morbidity and mortality. Population and Development Review 10 Supplement: Child Survival: Strategies for Research.
15. MOORE, S. R., LIMA, A. A.M., CONAWAY, M. R., SCHORLING, J. B., SOARES, A.M. and GUERRANT, R. L. (2001). Early childhood diarrhea and helminthiases associate with long-term linear growth faltering. International Journal of Epidemiology 30 1457-1464.
16. ROBINS, J. M. (1986). A new approach to causal inference in mortality studies with sustained exposure periods-Application to control of the healthy worker survivor effect. Math. Model. 7 1393-1512 [errata (1987) 14 917-921].
17. ROBINS, J. M. (1992). Estimation of the time-dependent accelerated failure time model in the presence of confounding factors. Biometrika 79 321-334. MR1185134
18. ROBINS, J. M. (1994). Correcting for non-compliance in randomized trials using structural nested mean models. Comm. Statist. 23 2379-2412. MR1293185
19. ROBINS, J. M. (1997). Causal inference from complex longitudinal data. In Latent Variable Modelling and Applications to Causality (M. Berkane, ed.). Lecture Notes in Statist. 120 69-117. Springer, New York. MR1601279
20. ROBINS, J. M. (1998). Marginal structural models. In 1997 Proceedings of the Section on Bayesian Statistical Science 1-10. Amer. Statist. Assoc., Alexandria, VA.
21. ROBINS, J. M. (2000). Marginal structural models versus structural nested models as tools for causal inference. In Statistical Models in Epidemiology, the Environment and Clinical Trials (M. E. Halloran and D. Berry, eds.). The IMA Volumes in Mathematics and Its Applications 116 95-133. Springer, New York. MR1731682
22. ROBINS, J. M. (2008). Causal models for estimating the effects of weight gain on mortality. International Journal of Obesity 32 S15-S41.
23. ROGERS, L. C. G. and WILLIAMS, D. (1994). Diffusions, Markov Processes, and Martingales 1. Wiley, Chichester. MR1331599
24. ROSENBAUM, P. R. (1984). The consquences of adjustment for a concomitant variable that has been affected by the treatment. J. Roy. Statist. Soc. Ser. A 147 656-666.
25. SINGER, B. (1981). Estimation of nonstationary Markov chains from panel data. Sociological Methodology 12 319-337.
26. TSIATIS, A. (2006). Semiparametric Theory and Missing Data. Springer, New York. MR2233926
27. VAN DER VAART, A. W. (2000). Asymptotic Statistics. Cambridge Univ. Press.