Variance estimation for stratified propensity score estimators

Statistics in Medicine

Volumn 31, Issue 15, 2012, Pages 1617-1632

  Williamson, E J ^a,b   Morley, R ^c   Lucas, A ^d   Carpenter, J R ^e  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b MONASH UNIVERSITY   (Australia)

^c MURDOCH CHILDREN'S RESEARCH INSTITUTE   (Australia)

^d UNIVERSITY COLLEGE LONDON   (United Kingdom)

^e LONDON SCHOOL OF HYGIENE AND TROPICAL MEDICINE   (United Kingdom)

Author keywords

Confounding; Inverse probability weighting; Observational study

Indexed keywords

ARTICLE; BOOTSTRAPPING; BREAST FEEDING; CLINICAL PRACTICE; CONFIDENCE INTERVAL; CONFOUNDING VARIABLE; COVARIANCE; DECISION MAKING; HUMAN; INTELLIGENCE QUOTIENT; INVERSE PROBABILITY WEIGHTED ESTIMATOR; LINEAR REGRESSION ANALYSIS; MARGINAL VARIANCE; MATERNAL ATTITUDE; MONTE CARLO METHOD; NERVOUS SYSTEM DEVELOPMENT; PREDICTION; PROPENSITY SCORE; STATISTICAL ANALYSIS; STRATIFIED PROPENSITY SCORE; STRATIFIED SAMPLE; VARIANCE;

CAUSALITY; CHILD; CONFIDENCE INTERVALS; CONFOUNDING FACTORS (EPIDEMIOLOGY); FEMALE; FOLLOW-UP STUDIES; GREAT BRITAIN; HUMANS; INFANT FORMULA; INFANT, LOW BIRTH WEIGHT; INFANT, NEWBORN; INFANT, PREMATURE; INTELLIGENCE TESTS; MALE; MILK, HUMAN; MONTE CARLO METHOD; OBSERVATION; OUTCOME ASSESSMENT (HEALTH CARE); PROPENSITY SCORE;

EID: 84862682313     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.4504     Document Type: Article

References (29)

1. Stürmer T, Joshi M, Glynn RJ, Avorn J, Rothman KJ, Schneeweiss S. A review of the application of propensity score methods yielded increasing use, advantages in specific settings, but not substantially different estimates compared with conventional multivariable methods. Journal of Clinical Epidemiology 2006; 59:437-447. DOI: 10.1016/j.jclinepi.2005.07.004.
2. Williamson E, Morley R, Lucas A, Carpenter J. Propensity scores: From naïve enthusiasm to intuitive understanding. Statistical Methods in Medical Research 2011. DOI: 10.1177/0962280210394483.
3. Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika 1983; 70:41-55.
4. Lunceford JK, Davidian M. Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study. Statistics in Medicine 2004; 23:2937-2960. DOI: 10.1002/sim.1903.
5. Rodgers B. Feeding in infancy and later ability and attainment: a longitudinal study. Developmental Medicine and Child Neurology 1978; 20:421-426.
6. Lucas A, Gore SM, Cole TJ, Bamford MF, Dossetor JFB, Barr I, Dicarlo L, Cork S, Lucas PJ.Multicenter trial on feeding low-birthweight infants - effects of diet on early growth. Archives of Disease in Childhood 1984; 59:722-730.
7. Lucas A, Morley R, Cole TJ, Lucas PJ, Gore SM, Crowle P, Pearse R, Boon AJ, Powell R. Early diet in preterm babies and developmental status at 18 months. Lancet 1990; 335:1477-1481. DOI: 10.1016/0140-6736(90)93026-L.
8. Weschler Intelligence Scale for Children, Anglicized Revised Edition, 1974. Sidcup, Kent: The Psychological Corporation Ltd.
9. Lucas A, Morley R, Cole TJ, Lister G, Leeson-Payne C. Breast-milk and subsequent intelligence quotient in children born preterm. Lancet 1992; 339:261-264. DOI: 10.1016/0140-6736(92)91329-7.
10. Westreich D, Cole SR. Invited commentary: positivity in practice. American Journal of Epidemiology 2010; 171:674-677. DOI: 10.1093/aje/kwp436.
11. Cole SR, Frangakis CE. The consistency statement in causal inference: a definition or an assumption? Epidemiology 2009; 20:3-5. DOI: 10.1097/EDE.0b013e31818ef366.
12. Dawid AP. Conditional independence in statisticaltheory. Journal of the Royal Statistical Society B-Methodological 1979; 41:1-31.
13. Rosenbaum PR, Rubin DB. Reducing bias in observational studies using subclassification on the propensity score. Journal of the American Statistical Association 1984; 79:516-524.
14. Stefanski LA, Boos DD. The calculus of M-estimation. The American Statistician 2002; 56:29-38.
15. Robins JM, Hernán MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiology 2000; 11:550-560.
16. Rubin DB, Thomas N. Matching using estimated propensity scores: relating theory to practice. Biometrics 1996; 52:249-264.
17. Rubin DB. On principles for modeling propensity scores in medical research. Pharmacoepidemiology and Drug Safety 2004; 13:855-857. DOI: 10.1002/pds.968.
18. Brookhart MA, Schneeweiss S, Rothman KJ, Glynn RJ, Avorn J, Stürmer T. Variable selection for propensity score models. American Journal of Epidemiology 2006; 163:1149-1156. DOI: 10.1093/aje/kwj149.
19. Westreich D, Cole SR, Funk MJ, Brookhart MA, Stürmer T. The role of the c-statistic in variable selection for propensity score models. Pharmacoepidemiology and Drug Safety 2011; 20:317-320. DOI: 10.1002/pds.2074.
20. Imbens GW. Nonparametric estimation of average treatment effects under exogeneity: a review. Review of Economics and Statistics 2004; 86:4-29.
21. Hullsiek KH, Louis TA. Propensity score modeling strategies for the causal analysis of observational data. Biostatistics 2002; 2:179-193.
22. Austin PC, Mamdani MM. A comparison of propensity score methods: a case-study estimating the effectiveness of post-AMI statin use. Statistics in Medicine 2006; 25:2084-2106. DOI: 10.1002/sim.2328.
23. Carpenter J, Bithell J. Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians. Statistics in Medicine 2000; 19:1141-1164.
24. Weng HY, Hsueh YH, Messam LL, Hertz-Picciotto I. Methods of covariate selection: directed acyclic graphs and the change-in-estimate procedure. American Journal of Epidemiology 2009; 169:1182-1190. DOI: 10.1093/aje/kwp035.
25. Kang JDY, Schafer JL. Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 2007; 22:523-539. DOI: 10.1214/07-STS227.
26. Bang H, Robins JM. Doubly robust estimation in missing data and causal inference models. Biometrics 2005; 61:962-973. DOI: 10.1111/j.1541-0420.2005.00377.x.
27. Giurcanu M, Trinidade A. Establishing consistency of M-estimators under concavity with an application to some financial risk measures. Journal of Probability and Statistical Science 2007; 5:123-136.
28. Beals RJ. Analysis: An Introduction. Cambridge University Press: Cambridge, 2004.
29. van der Vaart A. Asymptotic Statistics. Cambridge University Press: Cambridge, 1998.