The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Causal inference from nonrandomized data: key concepts and recent trends

비실험 자료로부터의 인과 추론: 핵심 개념과 최근 동향

  • Received : 2018.12.03
  • Accepted : 2019.01.22
  • Published : 2019.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

Causal questions are prevalent in scientific research, for example, how effective a treatment was for preventing an infectious disease, how much a policy increased utility, or which advertisement would give the highest click rate for a given customer. Causal inference theory in statistics interprets those questions as inferring the effect of a given intervention (treatment or policy) in the data generating process. Causal inference has been used in medicine, public health, and economics; in addition, it has received recent attention as a tool for data-driven decision making processes. Many recent datasets are observational, rather than experimental, which makes the causal inference theory more complex. This review introduces key concepts and recent trends of statistical causal inference in observational studies. We first introduce the Neyman-Rubin's potential outcome framework to formularize from causal questions to average treatment effects as well as discuss popular methods to estimate treatment effects such as propensity score approaches and regression approaches. For recent trends, we briefly discuss (1) conditional (heterogeneous) treatment effects and machine learning-based approaches, (2) curse of dimensionality on the estimation of treatment effect and its remedies, and (3) Pearl's structural causal model to deal with more complex causal relationships and its connection to the Neyman-Rubin's potential outcome model.

과학적 연구에서 핵심적인 연구 주제 또는 가설은 대부분 인과적 질문(causal question)을 포함한다. 예를 들어, 전염병 예방을 위한 치료법의 효과 연구, 특정 정책의 시행으로 인한 효용(utility)의 평가에 대한 연구, 특정 사용자를 대상으로 노출된 광고의 종류에 따른 광고의 효과성에 대한 연구는 모두 인과 관계(causal relationship)의 추론이 요구된다. 이러한 인과 관계를 다루는 통계적 인과 추론(statistical causal inference)의 주요 관심사 중 하나는 모집단에 일종의 개입(정책 혹은 처치)을 적용한 후 개입의 효과를 정확하게 추정하는 것이다. 인과 추론은 임상실험과 정책결정에서 주로 이용되었으나, 이른바 빅데이터 시대의 도래로 가용한 관측자료가 폭발적으로 증가하였고 이로 인하여 인과 추론에 대한 잠재적 응용가치와 수요가 지속적으로 증가하고 있다. 하지만 가용한 대부분의 자료는 임의실험 기반의 자료와 달리 개입이 임의로 분배되지 않은 비실험 관측자료이다. 따라서, 본 논문은 비실험 관측자료로부터 개입의 효과를 추정하기 위한 인과 추론의 핵심 개념과 최근의 연구동향을 소개하고자 한다. 이를 위하여 본문에서는 먼저 개입의 효과를 Neyman-Rubin의 잠재 결과(potential outcome) 모형으로 나타내고, 개입의 효과를 추정하는 여러 접근법 중 특히 성향점수(propensity score) 기반 추정법과 회귀모형 기반 추정법을 중점적으로 소개한다. 최근 연구동향으로는 (1) 평균 효과 크기 추정을 넘어선 개인별 효과 크기의 추정, (2) 효과크기 추정에 있어서 자료 규모의 증대로 인한 차원의 저주가 야기하는 난제들과 이에 대한 해결방안들, (3) 복합적 인과관계를 반영하기 위한 Pearl의 구조적 인과 모형(structural causal model) 및 잠재 결과 모형과의 비교의 3가지 주제로 구분하여 소개한다.

Keywords

GCGHDE_2019_v32n2_173_f0001.png 이미지

Figure 4.1. 구조적 인과모형식에 대응되는 방향성 비순환 그래프들. 좌측: (4.2), 우측: (4.3).

References

  1. Abadie, A. and Imbens, G. W. (2006). Large sample properties of matching estimators for average treatment effects, Econometrica, 74, 235-267. https://doi.org/10.1111/j.1468-0262.2006.00655.x
  2. An, W. and Ding, Y. (2018). The landscape of causal inference: perspective from citation network analysis, The American Statistician, 72, 265-277. https://doi.org/10.1080/00031305.2017.1360794
  3. Bang, H. and Robins, J. M. (2005). Doubly robust estimation in missing data and causal inference models, Biometrics, 61, 962-973. https://doi.org/10.1111/j.1541-0420.2005.00377.x
  4. Belloni, A., Chernozhukov, V., Fernandez-Val, I., and Hansen, C. (2017). Program evaluation and causal inference with high-dimensional data. Econometrica, 85, 233-298. https://doi.org/10.3982/ECTA12723
  5. Benkeser, D. (2018). rtmle: Doubly-Robust Nonparametric Estimation and Inference. R package version 1.0.4. https://CRAN.R-project.org/package=drtmle
  6. Caliendo, M. and Kopeinig, S. (2008). Some practical guidance for the implementation of propensity score matching, Journal of Economic Surveys, 22, 31-72. https://doi.org/10.1111/j.1467-6419.2007.00527.x
  7. Chakraborty, B. and Murphy, S. A. (2014). Dynamic treatment regimes, Annual Review of Statistics and Its Application, 1(1):447-464. https://doi.org/10.1146/annurev-statistics-022513-115553
  8. Chan, D., Ge, R., Gershony, O., Hesterberg, T., and Lambert, D. (2010). Evaluating online ad campaigns in a pipeline. In Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD '10), 7-15.
  9. Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., and Newey, W. (2017). Double/debiased/Neyman machine learning of treatment effects, American Economic Review, 107, 261-265. https://doi.org/10.1257/aer.p20171038
  10. Cornfield, J., Haenszel, W., Hammond, E. C., Lilienfeld, A. M., Shimkin, M. B., and Wynder, E. L. (2009). Smoking and lung cancer: Recent evidence and a discussion of some questions. International Journal of Epidemiology, 38, 1175-1191. https://doi.org/10.1093/ije/dyp289
  11. 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. https://doi.org/10.1093/biomet/asn055
  12. D'Amour, A., Ding, P., Feller, A., Lei, L., and Sekhon, J. (2017). Overlap in observational studies with high-dimensional covariates, arXiv preprint arXiv:1711.02582, 1-31.
  13. Dawid, A. P. (2000). Causal inference without counterfactuals, Journal of the American Statistical Association, 95, 407-424. https://doi.org/10.1080/01621459.2000.10474210
  14. Fan, J., Imai, K., Liu, H., Ning, Y., and Yang, X. (2016). Improving covariate balancing propensity score: a doubly robust and efficient approach (Technical Report), Princeton University, Princeton.
  15. Farrell, M. H. (2015). Robust inference on average treatment effects with possibly more covariates than observations. Journal of Econometrics, 189, 1-23. https://doi.org/10.1016/j.jeconom.2015.06.017
  16. Fong, C., Ratkovic, M., and Imai, K. (2018). CBPS: Covariate Balancing Propensity Score. R package version 0.19. https://CRAN.R-project.org/package=CBPS
  17. Ho, D. E., Imai, K., King, G., and Stuart, E. A. (2011). MatchIt: Nonparametric Preprocessing for Parametric Causal Inference. Journal of Statistical Software, 42, 1-28.
  18. Huh, M. (2014). Applied Data Analytics, Freedom Academy, Seoul.
  19. Imai, K. and Ratkovic, M. (2014). Covariate balancing propensity score, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76, 243-263. https://doi.org/10.1111/rssb.12027
  20. Imbens, G. W. (2004). Nonparametric estimation of average treatment effects under exogeneity: a review, Review of Economics and Statistics, 86, 4-29. https://doi.org/10.1162/003465304323023651
  21. Imbens, G. W. and Rubin, D. B. (2015). Causal Inference for Statistics, Social, and Biomedical Sciences, Cambridge University Press, Cambridge.
  22. Kang, J. D. Y. and Schafer, J. L. (2007). Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science, 22, 523-539. https://doi.org/10.1214/07-STS227
  23. Kim, M. (2018). Causal Inference in Statistics: A Primer, Kyowoo Book, Seoul.
  24. Kunzel, S. R., Sekhon, J. S., Bickel, P. J., and Yu, B. (2017). Meta-learners for estimating heterogeneous treatment effects using machine learning, arXiv preprint arXiv: 1706.03461, 1-39.
  25. Lunceford, J. K. and Davidian, M. (2004). Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study, Statistics in Medicine, 23, 2937-2960. https://doi.org/10.1002/sim.1903
  26. Nie, X. and Wager, S. (2017). Quasi-oracle estimation of heterogeneous treatment effects. arXiv preprint arXiv: 1712.04912, 1-43.
  27. Ning, Y. and Liu, H. (2017). A general theory of hypothesis tests and confidence regions for sparse high dimensional models, The Annals of Statistics, 45, 158-195. https://doi.org/10.1214/16-AOS1448
  28. Ning, Y., Peng, S., and Imai, K. (2017). High dimensional propensity score estimation via covariate balancing (Technical Report), Cornell University, 1-47.
  29. Pearl, J. (2009a). Causal inference in statistics: an overview, Statistics Surveys, 3, 96-146. https://doi.org/10.1214/09-SS057
  30. Pearl, J. (2009b). Causality, Cambridge University Press, Cambridge.
  31. Pearl, J., Glymour, M., and Jewell, N. P. (2016). Causal Inference in Statistics: A Primer, Wiley.
  32. Ponomareva, M. and Powell, J. (2010). Irregular identification, support conditions, and inverse weight estimation, Econometrica, 78, 2021-2042. https://doi.org/10.3982/ECTA7372
  33. Qian, M. and Murphy, S. A. (2011). Performance guarantees for individualized treatment rules, The Annals of Statistics, 39, 1180-1210. https://doi.org/10.1214/10-AOS864
  34. Robins, J. M., Rotnitzky, A., and Zhao, L. P. (1994). Estimation of regression coefficients when some regressors are not always observed, Journal of the American Statistical Association, 89, 846-866. https://doi.org/10.1080/01621459.1994.10476818
  35. Robinson, P. M. (1988). Root-n-consistent semiparametric regression, Econometrica, 56, 931. https://doi.org/10.2307/1912705
  36. Rosenbaum, P. (2017). Observation and Experiment: An Introduction to Causal Inference. Harvard University Press.
  37. Rosenbaum, P. R. and Rubin, D. B. (1984). Reducing bias in observational studies using subclassification on the propensity score, Journal of the American Statistical Association, 79, 516-524. https://doi.org/10.1080/01621459.1984.10478078
  38. Rosenbaum, P. R. and Rubin, D. B. (1985). Constructing a control group using multivariate matched sampling methods that incorporate the propensity score. The American Statistician, 39, 33-38. https://doi.org/10.2307/2683903
  39. Rubin, D. B. (2005). Causal inference using potential outcomes, Journal of the American Statistical Association, 100, 322-331. https://doi.org/10.1198/016214504000001880
  40. Stuart, E. A. (2010). Matching methods for causal inference: a review and a look forward, Statistical Science, 25, 1-21. https://doi.org/10.1214/09-STS313
  41. Van De Geer, S., Buhlmann, P., Ritov, Y., and Dezeure, R. (2014). On asymptotically optimal confidence regions and tests for high-dimensional models. The Annals of Statistics, 42, 1166-1202. https://doi.org/10.1214/14-AOS1221
  42. van der Laan, M. J. and Rose, S. (2011). Targeted Learning, Springer Series in Statistics, Springer New York.
  43. van der Laan, M. J. and Rose, S. (2018). Targeted Learning in Data Science, Springer Series in Statistics, Springer International Publishing, Cham.
  44. Varian, H. R. (2016). Causal inference in economics and marketing. In Proceedings of the National Academy of Sciences, 113, 7310-7315. https://doi.org/10.1073/pnas.1510479113
  45. Wager, S. and Athey, S. (2018). Estimation and inference of heterogeneous treatment effects using random forests, Journal of the American Statistical Association, 113, 1228-1242. https://doi.org/10.1080/01621459.2017.1319839
  46. Yang, S. and Ding, P. (2018). Asymptotic inference of causal effects with observational studies trimmed by the estimated propensity scores. Biometrika, (March), 1-7.
  47. Zhang, B., Tsiatis, A. A., Davidian, M., Zhang, M., and Laber, E. (2012). Estimating optimal treatment regimes from a classification perspective, Stat, 1, 103-114. https://doi.org/10.1002/sta.411
  48. Zhao, Q. (2019). Covariate balancing propensity score by tailored loss functions. The Annals of Statistics, 47(2):965-993. https://doi.org/10.1214/18-AOS1698
  49. Zhao, Q. and Percival, D. (2017). Entropy balancing is doubly robust. Journal of Causal Inference, 5(1):1-21.
  50. Zhao, Q., Small, D. S., and Ertefaie, A. (2017). Selective inference for effect modification via the lasso. arXiv preprint arXiv: 1705.08020, 1-21.
  51. Zhao, Y., Zeng, D., Rush, A. J., and Kosorok, M. R. (2012). Estimating individualized treatment rules using outcome weighted learning, Journal of the American Statistical Association, 107, 1106-1118. https://doi.org/10.1080/01621459.2012.695674