The Annals of Applied Statistics

Assessing lack of common support in causal inference using Bayesian nonparametrics: Implications for evaluating the effect of breastfeeding on children’s cognitive outcomes

Jennifer Hill and Yu-Sung Su

Full-text: Open access

Abstract

Causal inference in observational studies typically requires making comparisons between groups that are dissimilar. For instance, researchers investigating the role of a prolonged duration of breastfeeding on child outcomes may be forced to make comparisons between women with substantially different characteristics on average. In the extreme there may exist neighborhoods of the covariate space where there are not sufficient numbers of both groups of women (those who breastfed for prolonged periods and those who did not) to make inferences about those women. This is referred to as lack of common support. Problems can arise when we try to estimate causal effects for units that lack common support, thus we may want to avoid inference for such units. If ignorability is satisfied with respect to a set of potential confounders, then identifying whether, or for which units, the common support assumption holds is an empirical question. However, in the high-dimensional covariate space often required to satisfy ignorability such identification may not be trivial. Existing methods used to address this problem often require reliance on parametric assumptions and most, if not all, ignore the information embedded in the response variable. We distinguish between the concepts of “common support” and “common causal support.” We propose a new approach for identifying common causal support that addresses some of the shortcomings of existing methods. We motivate and illustrate the approach using data from the National Longitudinal Survey of Youth to estimate the effect of breastfeeding at least nine months on reading and math achievement scores at age five or six. We also evaluate the comparative performance of this method in hypothetical examples and simulations where the true treatment effect is known.

Article information

Source
Ann. Appl. Stat., Volume 7, Number 3 (2013), 1386-1420.

Dates
First available in Project Euclid: 3 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1380804800

Digital Object Identifier
doi:10.1214/13-AOAS630

Mathematical Reviews number (MathSciNet)
MR3127952

Zentralblatt MATH identifier
1283.62220

Keywords
Common support overlap BART propensity scores breastfeeding

Citation

Hill, Jennifer; Su, Yu-Sung. Assessing lack of common support in causal inference using Bayesian nonparametrics: Implications for evaluating the effect of breastfeeding on children’s cognitive outcomes. Ann. Appl. Stat. 7 (2013), no. 3, 1386--1420. doi:10.1214/13-AOAS630. https://projecteuclid.org/euclid.aoas/1380804800


Export citation

References

  • Anderson, J. W., Johnstone, B. M. and Remley, D. T. (1999). Breast-feeding and cognitive development: A meta-analysis. Am. J. Clin. Nutr. 70 525–535.
  • Breiman, L. (2001). Random forests. Machine Learning 45 5–32.
  • Breiman, L., Freidman, J. H., Olshen, R. A. and Stone, C. J. (1984). Classification and Regression Trees. Wadsworth, Belmont, CA.
  • Brookhart, M. A., Schneeweiss, S., Rothman, K. J., Glynn, R. J., Avorn, J. and Stürmer, T. (2006). Variable selection for propensity score models. Am. J. Epidemiol. 163 1149–1156.
  • Chase-Lansdale, P., Mott, F. L., Brooks-Gunn, J. and Philips, D. A. (1991). Children of the National Longitudinal Survey of Youth: A unique research opportunity. Developmental Psychology 27 918–931.
  • Chipman, H., George, E. and McCulloch, R. (2007). Bayesian ensemble learning. In Advances in Neural Information Processing Systems 19 (B. Schölkopf, J. Platt and T. Hoffman, eds.). MIT Press, Cambridge, MA.
  • Chipman, H. A., George, E. I. and McCulloch, R. E. (2010). BART: Bayesian additive regression trees. Ann. Appl. Stat. 4 266–298.
  • Chipman, H. and McCulloch, R. (2009). BayesTree: Bayesian methods for tree based models. R package version 0.3-1.
  • Crump, R. K., Hotz, V. J., Imbens, G. W. and Mitnik, O. A. (2009). Dealing with limited overlap in estimation of average treatment effects. Biometrika 96 187–199.
  • Dehejia, R. H. and Wahba, S. (1999). Causal effects in nonexperimental studies: Reevaluating the evaluation of training programs. J. Amer. Statist. Assoc. 94 1053–1062.
  • Der, G., Batty, G. D. and Deary, I. J. (2006). Effect of breast feeding on intelligence in children: Prospective study, sibling pairs analysis, and meta-analysis. British Medical Journal 333 945–950.
  • Drane, D. L. and Logemann, J. A. (2000). A critical evaluation of the evidence on the association between type of infant feeding and cognitive development. Paediatr. Perinat. Epidemiol. 14 349–356.
  • Frolich, M. (2004). Finite-sample properties of propensity-score matching and weighting estimators. The Review of Economics and Statistics 86 77–90.
  • Green, D. P. and Kern, H. L. (2012). Modeling heterogeneous treatment effects in survey experiments with Bayesian additive regression trees. Public Opinion Quarterly 76 491–511.
  • Hansen, B. B. (2008). The prognostic analogue of the propensity score. Biometrika 95 481–488.
  • Hastie, T. (2009). gam: Generalized additive models. R package version 1.01.
  • Heckman, J. J., Ichimura, H. and Todd, P. (1997). Matching as an econometric evaluation estimator: Evidence from a job training programme. Rev. Econom. Stud. 64 605–654.
  • Hill, J. L. (2011). Bayesian nonparametric modeling for causal inference. J. Comput. Graph. Statist. 20 217–240.
  • Hill, J. L., Weiss, C. and Zhai, F. (2013). Challenges with propensity score strategies in a high-dimensional setting and a potential alternative. Multivariate Behavioral Research 46 477–513.
  • Ho, D. E., Imai, K., King, G. and Stuart, E. A. (2013). MatchIt: Nonparametric preprocessing for parametric causal inference. Journal of Statistical Software 42 1–28.
  • Imbens, G. (2004). Nonparametric estimation of average treatment effects under exogeneity: A review. The Review of Economics and Statistics 86 4–29.
  • Jain, A., Concato, J. and Leventhal, J. M. (2002). How good is the evidence linking breastfeeding and intelligence? Pediatrics 109 1044–1053.
  • Kelcey, B. (2011). Covariate selection in propensity scores using outcome proxies. Multivariate Behavioral Research 46 453–476.
  • Kern, H. L., Stuart, E. A., Hill, J. L. and Green, D. P. (2013). Assessing methods for generalizing experimental impact estimates to target samples. Technical report, Univ. South Carolina, Columbia, SC.
  • Kramer, M. S., Aboud, F., Mironova, E., Vanilovich, I., Platt, R. W., Matush, L., Igumnov, S., Fombonne, E., Bogdanovich, N., Ducruet, T., Collet, J.-P., Chalmers, B., Hodnett, E., Davidovsky, S., Skugarevsky, O., Trofimovich, O., Kozlova, L. and Shapiro, S. (2008). Breastfeeding and child cognitive development: New evidence from a large randomized trial. Archives of General Psychiatry 65 578–584.
  • Kurth, T., Walker, A. M., Glynn, R. J., Chan, K. A., Gaziano, J. M., Berger, K. and Robins, J. M. (2006). Results of multivariable logistic regression, propensity matching, propensity adjustment, and propensity-based weighting under conditions of non-uniform effect. American Journal of Epidemiology 163 262–270.
  • Lawlor, D. A., Najman, J. M., Batty, D., O’Callaghan, M. J., Williams, G. M. and Bor, W. (2006). Early life predictors of childhood intelligence: Findings from the Mater-University study of pregnancy and its outcomes. Paediatric and Perinatal Epidemiology 20 148–162.
  • Leuven, E. and Sianesi, B. (2011). PSMATCH2: Stata module to perform full Mahalanobis and propensity score matching, common support graphing, and covariate imbalance testing. Boston College Dept. Economics, Boston, MA.
  • Lundqvist-Persson, C., Lau, G., Nordin, P. et al. (2010). Early behaviour and development in breastfed premature infants are influenced by omega-6 and omega 3-fatty acids. Early Human Development 86 407–412.
  • McCaffrey, D. F., Ridgeway, G. and Morral, A. R. (2004). Propensity score estimation with boosted regression for evaluating causal effects in observational studies. Psychol. Methods 9 403–425.
  • Morgan, S. L. and Harding, D. J. (2006). Matching estimators of causal effects: Prospects and pitfalls in theory and practice. Sociol. Methods Res. 35 3–60.
  • Mortensen, E. L., Michaelsen, K. F., Sanders, S. A. and Reinisch, J. M. (2002). The association between duration of breastfeeding and adult intelligence. Journal of the American Medical Association 287 2365–2371.
  • R Core Team (2012). R: A Language and Environment for Statistical Computing. Vienna, Austria. ISBN 3-900051-07-0.
  • Ridgeway, G. (2007). gbm: Generalized boosted regression models. R package version 1.6-3.
  • Ridgeway, G., McCaffrey, D., Morral, A., Griffin, B. A. and Burgette, L. (2012). twang: Toolkit for weighting and analysis of nonequivalent groups. R package version 1.2-5. Available at http://CRAN.R-project.org/package=twang.
  • Rosenbaum, P. R. (1984). The consequences of adjustment for a concomitant variable that has been affected by the treatment. J. Roy. Statist. Soc. Ser. A 147 656–666.
  • Rosenbaum, P. R. and Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika 70 41–55.
  • Rubin, D. B. (2002). Using propensity scores to help design observational studies: Application to the tobacco litigation. Health Services & Outcomes Research Methodology 2 169–188.
  • Woo, M.-J., Reiter, J. P. and Karr, A. F. (2008). Estimation of propensity scores using generalized additive models. Stat. Med. 27 3805–3816.