Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
158 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Causal Rule Ensemble: Interpretable Discovery and Inference of Heterogeneous Treatment Effects (2009.09036v6)

Published 18 Sep 2020 in stat.ME and stat.ML

Abstract: In health and social sciences, it is critically important to identify subgroups of the study population where there is notable heterogeneity of treatment effects (HTE) with respect to the population average. Decision trees have been proposed and commonly adopted for the data-driven discovery of HTE due to their high level of interpretability. However, single-tree discovery of HTE can be unstable and oversimplified. This paper introduces the Causal Rule Ensemble (CRE), a new method for HTE discovery and estimation using an ensemble-of-trees approach. CRE offers several key features, including 1) an interpretable representation of the HTE; 2) the ability to explore complex heterogeneity patterns; and 3) high stability in subgroups discovery. The discovered subgroups are defined in terms of interpretable decision rules. Estimation of subgroup-specific causal effects is performed via a two-stage approach, for which we provide theoretical guarantees. Through simulations, we show that the CRE method is highly competitive compared to state-of-the-art techniques. Finally, we apply CRE to discover the heterogeneous health effects of exposure to air pollution on mortality for 35.3 million Medicare beneficiaries across the contiguous U.S.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (85)
  1. Efficient estimation of models with conditional moment restrictions containing unknown functions, Econometrica 71(6): 1795–1843.
  2. Recursive partitioning for heterogeneous causal effects, Proceedings of the National Academy of Sciences 113(27): 7353–7360.
  3. Generalized random forests, The Annals of Statistics 47(2): 1148–1178.
  4. Simple models in complex worlds: Occam’s razor and statistical learning theory, Minds and Machines 32(1): 13–42.
  5. Heterogeneous causal effects with imperfect compliance: a bayesian machine learning approach, The Annals of Applied Statistics 16(3): 1986–2009.
  6. Causal tree with instrumental variable: An extension of the causal tree framework to irregular assignment mechanisms, International Journal of Data Science and Analytics 9: 315–337.
  7. Heterogeneous treatment and spillover effects under clustered network interference, arXiv preprint arXiv:2008.00707 .
  8. Examining the effects of air pollution composition on within region differences in pm2. 5 mortality risk estimates, Journal of Exposure Science & Environmental Epidemiology 23(5): 457–465.
  9. Inference in high-dimensional panel models with an application to gun control, Journal of Business & Economic Statistics 34(4): 590–605.
  10. Improving stability in decision tree models, arXiv preprint arXiv:2305.17299 .
  11. Breiman, L. (1996). Heuristics of instability and stabilization in model selection, The annals of statistics 24(6): 2350–2383.
  12. Breiman, L. (2001). Random forests, Machine Learning 45(1): 5–32.
  13. In pursuit of evidence in air pollution epidemiology: the role of causally driven data science, Epidemiology 31(1): 1–6.
  14. Xgboost: A scalable tree boosting system, Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, pp. 785–794.
  15. Double/debiased/neyman machine learning of treatment effects, American Economic Review 107(5): 261–65.
  16. Locally robust semiparametric estimation, arXiv preprint arXiv:1608.00033 .
  17. BART: Bayesian additive regression trees, The Annals of Applied Statistics 4(1): 266–298.
  18. Cox, D. R. (1975). A note on data-splitting for the evaluation of significance levels, Biometrika 62(2): 441–444.
  19. Benchmarking heterogeneous treatment effect models through the lens of interpretability, arXiv preprint arXiv:2206.08363 .
  20. Nonparametric tests for treatment effect heterogeneity, The Review of Economics and Statistics 90(3): 389–405.
  21. Premature mortality related to united states cross-state air pollution, Nature 578(7794): 261–265.
  22. Deng, H. (2019). Interpreting tree ensembles with intrees, International Journal of Data Science and Analytics 7(4): 277–287.
  23. Air pollution and mortality in the Medicare population, New England Journal of Medicine 376(26): 2513–2522.
  24. Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition, Statistical Science 34(1): 43–68.
  25. Stable discovery of interpretable subgroups via calibration in causal studies, International Statistical Review 88: 135–178.
  26. Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans, Vol. 38, Philadelphia, PA: Society for Industrial and Applied Mathematics.
  27. Orthogonal statistical learning, arXiv preprint arXiv:1901.09036 .
  28. Subgroup identification from randomized clinical trial data, Statistics in Medicine 30(24): 2867–2880.
  29. Predictive learning via rule ensembles, The Annals of Applied Statistics 2(3): 916–954.
  30. Atlantic causal inference conference (acic) data analysis challenge 2017, arXiv preprint arXiv:1905.09515 .
  31. Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects, Bayesian Analysis .
  32. Incremental value modeling, Journal of Interactive Marketing 16(3): 35–46.
  33. The elements of statistical learning: data mining, inference, and prediction, Vol. 2, Springer.
  34. Statistical learning with sparsity: the lasso and generalizations, CRC press.
  35. Hill, J. L. (2011). Bayesian nonparametric modeling for causal inference, Journal of Computational and Graphical Statistics 20(1): 217–240.
  36. Holland, P. W. (1986). Statistics and causal inference, Journal of the American Statistical Association 81(396): 945–960.
  37. A generalization of sampling without replacement from a finite universe, Journal of the American statistical Association 47(260): 663–685.
  38. Estimating treatment effect heterogeneity in randomized program evaluation, The Annals of Applied Statistics 7(1): 443–470.
  39. Jacob, D. (2019). Group average treatment effects for observational studies, arXiv preprint arXiv:1911.02688 .
  40. Kennedy, E. H. (2020). Optimal doubly robust estimation of heterogeneous causal effects, arXiv preprint arXiv:2004.14497 . https://arxiv.org/abs/2004.14497
  41. Non-parametric methods for doubly robust estimation of continuous treatment effects, Journal of the Royal Statistical Society: Series B (Statistical Methodology) 79: 1229–1245.
  42. Examples are not enough, learn to criticize! criticism for interpretability, Advances in Neural Information Processing Systems, pp. 2280–2288.
  43. Long-and short-term exposure to pm2. 5 and mortality: using novel exposure models, Epidemiology (Cambridge, Mass.) 24(4): 555.
  44. Applied predictive modeling, Vol. 26, Springer.
  45. Metalearners for estimating heterogeneous treatment effects using machine learning, Proceedings of the National Academy of Sciences 116(10): 4156–4165.
  46. Interpretable decision sets: A joint framework for description and prediction, Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1675–1684.
  47. Discovering heterogeneous exposure effects using randomization inference in air pollution studies, Journal of the American Statistical Association pp. 1–33.
  48. Lee, M.-j. (2009). Non-parametric tests for distributional treatment effect for randomly censored responses, Journal of the Royal Statistical Society: Series B (Statistical Methodology) 71(1): 243–264.
  49. Estimating regression models in which the dependent variable is based on estimates, Political Analysis 13(4): 345–364.
  50. Recent trends in premature mortality and health disparities attributable to ambient PM2.5 exposure in China: 2005–2017, Environmental Pollution 279: 116882.
  51. Subgroup identification for precision medicine: A comparative review of 13 methods, Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 9(5): e1326.
  52. Using heteroscedasticity consistent standard errors in the linear regression model, The American Statistician 54(3): 217–224.
  53. Does selective survival before study enrolment attenuate estimated effects of education on rate of cognitive decline in older adults? A simulation approach for quantifying survival bias in life course epidemiology, International Journal of Epidemiology 47(5): 1507–1517.
  54. Stability selection, Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72(4): 417–473.
  55. Miller, T. (2019). Explanation in artificial intelligence: Insights from the social sciences, Artificial Intelligence 267: 1–38.
  56. Moran, P. A. (1950). A test for the serial independence of residuals, Biometrika 37(1/2): 178–181.
  57. Interpretable subgroup discovery in treatment effect estimation with application to opioid prescribing guidelines, Proceedings of the ACM Conference on Health, Inference, and Learning, pp. 19–29.
  58. Tree ensembles with rule structured horseshoe regularization, The Annals of Applied Statistics 12(4): 2379–2408.
  59. Evaluation of the health impacts of the 1990 clean air act amendments using causal inference and machine learning, Journal of the American Statistical Association pp. 1–12.
  60. Quasi-oracle estimation of heterogeneous treatment effects, Biometrika 108: 299–319. https://arxiv.org/abs/1712.04912v4
  61. Mortality risk and fine particulate air pollution in a large, representative cohort of us adults, Environmental Health Perspectives 127(7): 077007.
  62. Performance guarantees for individualized treatment rules, Annals of Statistics 39(2): 1180.
  63. Toward a curse of dimensionality appropriate (coda) asymptotic theory for semi-parametric models, Statistics in medicine 16(3): 285–319.
  64. Estimation of regression coefficients when some regressors are not always observed, Journal of the American statistical Association 89(427): 846–866.
  65. Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies., Journal of Educational Psychology 66(5): 688–701.
  66. Rubin, D. B. (1986). Comment: Which ifs have causal answers, Journal of the American Statistical Association 81(396): 961–962.
  67. A national difference in differences analysis of the effect of pm2. 5 on annual death rates, Environmental Research 194: 110649.
  68. Debiased machine learning of conditional average treatment effects and other causal functions, The Econometrics Journal 24(2): 264–289.
  69. Evaluation of selective survival and sex/gender differences in dementia incidence using a simulation model, JAMA Network Open 4(3): e211001–e211001.
  70. Nonparametric machine learning for precision medicine with longitudinal clinical trials and bayesian additive regression trees with mixed models, Statistics in Medicine 40(11): 2665–2691.
  71. Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions, Journal of the Royal Statistical Society: Series B (Methodological) 36(2): 111–133.
  72. Identifying latent structures in panel data, Econometrica 84(6): 2215–2264.
  73. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society: Series B (Statistical Methodology) 58(1): 267–288.
  74. U.S. Environmental Protection Agency (2023a). Reconsideration of the national ambient air quality standards for particulate matter, Technical Report: EPA-452/P-22-001 .
  75. U.S. Environmental Protection Agency (2023b). Regulatory impact analysis for the proposed reconsideration of the national ambient air quality standards for particulate matter, Technical Report: EPA-452/P-22-001 .
  76. Estimation and inference of heterogeneous treatment effects using random forests, Journal of the American Statistical Association 113(523): 1228–1242.
  77. Rule ensemble method with adaptive group lasso for heterogeneous treatment effect estimation, Statistics in Medicine .
  78. Causal rule sets for identifying subgroups with enhanced treatment effects, INFORMS Journal on Computing .
  79. Comparing methods for estimation of heterogeneous treatment effects using observational data from health care databases, Statistics in Medicine 37(23): 3309–3324.
  80. White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity, Econometrica 48(4): 817–838.
  81. Evaluating the impact of long-term exposure to fine particulate matter on mortality among the elderly, Science Advances 6(29): eaba5692.
  82. Causal interaction trees: Finding subgroups with heterogeneous treatment effects in observational data, Biometrics . http://dx.doi.org/10.1111/biom.13432
  83. Yu, B. (2013). Stability, Bernoulli 19(4): 1484–1500.
  84. Fine particulate air pollution and its components in association with cause-specific emergency admissions, Environmental Health 8(1): 1–12.
  85. Confounder-dependent bayesian mixture model: Characterizing heterogeneity of causal effects in air pollution epidemiology, arXiv preprint arXiv:2302.11656 .
Citations (14)

Summary

We haven't generated a summary for this paper yet.

Github Logo Streamline Icon: https://streamlinehq.com