The attributable fraction is commonly used in epidemiology to quantify the impact of an exposure on a disease. Several estimation methods have been suggested in the literature, including maximum likelihood estimation. In this article we propose an additional estimation method, based on inverse probability weighting. This method is particularly useful when a model for the exposure distibution can be well specified. We carry out a simulation study to examine the performance of the inverse probability weighted estimator, and to compare it to the maximum likelihood estimator.
Get full access to this article
View all access options for this article.
References
1.
Benichou J.Attributable risk. In Armitage P, Colton T, eds. Encyclopedia of biostatistics (2nd edn). John Wiley & Sons, UK; 2005.
2.
Rothman KJ, Greenland S., Lash TLModern epidemiology (3rd edn). Lippincott Williams & Wilkins, Philadelphia ; 2008.
3.
Levin MLThe occurrence of lung cancer in man. Acta Unio Internationalis Contra Cancrum1953; 9: 531-41.
4.
Hernan M., Robins JMEstimating causal effects from epidemiological data. Journal of Epidemiology and Community Health2006; 60: 578-86.
5.
Robins JM, Hernan M., Brumback B.Marginal structural models and causal inference in epidemiology. Epidemiology2000; 11: 550-60.
6.
Rubin DBEstimating causal effects of treatments in randomized and nonrandomized studies . Journal of Educational Psychology1974; 66(5): 688-701.
7.
Pearl J.Causality: models, reasoning and inference. Cambridge University Press, New York; 2000 .
8.
Greenland S. , Drescher K.Maximum likelihood estimation of the attributable fraction from logistic models . Biometrics1993; 49: 865-72.
9.
Lagerros YTPhysical activity from the epidemiological perspective - measurement issues and health effects. PhD thesis, Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden, 2006.
10.
Poirier P., Giles TD, Bray GA, Hong Y., Stern JS, Pi-Sunyer FX, Eckel RHObesity and cardiovascular disease: pathophysiology, evaluation, and effect of weight loss. Circulation2006; 113: 898-918.
11.
WHO.Physical status: the use and interpretation of anthropometry. Report of a WHO Expert Committee. WHO Technical Report Series854. World Health Organization, Geneva; 1995.
12.
Balke A., Pearl J.Bounds on treatment effects from studies with imperfect compliance . Journal of the American Statistical Association1997; 92(439): 1171-76. 13 Cai Z., Kuroki M., Pearl J., Tian J.Bounds on direct effects in the presence of confounded intermediate variables . Biometrics2007; 64(3): 695-701.
13.
Sjölander A.Bounds on natural direct effects in the presence of confounded intermediate variables. Statistics in Medicine2008; 28: 558-71.
14.
Rotnitzky A. , Robins JM, Scharfstein DOSemiparametric regression for repeated outcomes with nonignorable nonresponse. Journal of the American Statistical Association1998; 93(444): 1321-39.
15.
Gilbert PB, Bosch JB, Hudgens MGSensitivity analysis for the assessment of causal vaccine effects on viral load in HIV vaccine trials. Biometrics2003 ; 59: 531-41.
16.
Sjölander A., Humphreys K., Vansteelandt S., Bellocco R., Palmgren J.Sensitivity analysis for principal stratum direct effects, with an application to a study of physical activity and coronary heart disease. Biometrics2009; 65(2): 514-20.
17.
Angrist JD, IMbens GW, Rubin DBIdentification of causal effects using instrumental variables. Journal of the American Statistical Association1996; 91(434): 444-55.
18.
Zhang JL, Rubin DBEstimation of causal effects via principal stratification when some outcomes are ‘truncated by death’. Journal of Educational and Behavioral Statistics2003; 28: 353-68.
19.
Robins JM, Greenland S.Comment on ‘Causal inference without counterfactuals.’ Journal of the American Statistical Association2000; 95: 431-35.
20.
Robins JM, Rotnitzky A., Vansteelandt S.Discussion of ‘Principal stratification designs to estimate input data missing due to death.’Biometrics2007 ; 63: 650-53.