Communications for Statistical Applications and Methods

  • 제31권1호
  • /
  • Pages.155-178
  • /
  • 2024
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

Regression discontinuity for survival data

  • Youngjoo Cho (Department of Applied Statistics, Konkuk University)
  • Received : 2023.07.04
  • Accepted : 2023.12.08
  • Published : 2024.01.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

Abstract

Regression discontinuity (RD) design is one of the most widely used methods in causal inference for estimation of treatment effect when the treatment is created by a cutpoint from the covariate of interest. There has been little attention to RD design, although it provides a very useful tool for analysis of treatment effect for censored data. In this paper, we define the causal effect for survival function in RD design when the treatment is assigned deterministically by the covariate of interest. We propose estimators of this causal effect for survival data by using transformation, which leads unbiased estimator of the survival function with local linear regression. Simulation studies show the validity of our approach. We also illustrate our proposed method using the prostate, lung, colorectal and ovarian (PLCO) dataset.

Keywords

Acknowledgement

This work was supported by Konkuk University (2021-A019-0164).

References

  1. Andersen PK, Klein JP, and Rosthoj S (2003). Generalised linear models for correlated pseudo-observations, with applications to multi-state models, Biometrika, 90, 15-27. https://doi.org/10.1093/biomet/90.1.15
  2. Andriole GL, Crawford ED, Grubb III RL et al. (2009). Mortality results from a randomized prostate-cancer screening trial, New England Journal of Medicine, 360, 1310-1319. https://doi.org/10.1056/NEJMoa0810696
  3. Bor J, Moscoe E, Mutevedzi P, Newell ML, and Barnighausen T (2014). Regression discontinuity designs in epidemiology: Causal inference without randomized trials, Epidemiology, 25, 729-737. https://doi.org/10.1097/EDE.0000000000000138
  4. Brier GW (1950). Verification of forecasts expressed in terms of probability, Monthly Weather Review, 78, 1-3. https://doi.org/10.1175/1520-0493(1950)078<0001:VOFEIT>2.0.CO;2
  5. Calonico S, Cattaneo MD, and Farrell MH (2020). Optimal bandwidth choice for robust bias-corrected inference in regression discontinuity designs, The Econometrics Journal, 23, 192-210. https://doi.org/10.1093/ectj/utz022
  6. Calonico S, Cattaneo MD, and Titiunik R (2014). Robust nonparametric confidence intervals for regression-discontinuity designs, Econometrica, 82, 2295-2326. https://doi.org/10.3982/ECTA11757
  7. Calonico S, Cattaneo MD, and Titiunik R (2015). rdrobust: An R package for robust nonparametric inference in regression-discontinuity designs, R Journal, 7, 38-51. https://doi.org/10.32614/RJ-2015-004
  8. Calonico S, Cattaneo MD, Farrell MH, and Titiunik R (2019). Regression discontinuity designs using covariates, Review of Economics and Statistics, 101, 442-451. https://doi.org/10.1162/rest_a_00760
  9. Cho Y, Hu C, and Ghosh D (2021). Analysis of regression discontinuity designs using censored data, Journal of Statistical Research, 55, 225-248.
  10. Cho Y, Molinaro AM, Hu C, and Strawderman RL (2020). Regression trees for cumulative incidence functions, Available from: arXiv preprint arXiv:2011.06706
  11. Cho Y, Molinaro AM, Hu C, and Strawderman RL (2022). Regression trees and ensembles for cumulative incidence functions, The International Journal of Biostatistics, 18, 397-419. https://doi.org/10.1515/ijb-2021-0014
  12. Cox DR (1972). Regression models and life-tables, Journal of the Royal Statistical Society: Series B (Methodological), 34, 187-202. https://doi.org/10.1111/j.2517-6161.1972.tb00899.x
  13. Fan J and Gijbels I (1994). Censored regression: Local linear approximations and their applications, Journal of the American Statistical Association, 89, 560-570. https://doi.org/10.1080/01621459.1994.10476781
  14. Fan J and Gijbels I (1996). Local Polynomial Modelling and Its Applications: Monographs on Statistics and Applied Probability 66, CRC Press, London.
  15. Gerds TA and Schumacher M (2006). Consistent estimation of the expected brier score in general survival models with right-censored event times, Biometrical Journal, 48, 1029-1040. https://doi.org/10.1002/bimj.200610301
  16. Graf E, Schmoor C, Sauerbrei W, and Schumacher M (1999). Assessment and comparison of prognostic classification schemes for survival data, Statistics in Medicine, 18, 2529-2545. https://doi.org/10.1002/(SICI)1097-0258(19990915/30)18:17/18<2529::AID-SIM274>3.0.CO;2-5
  17. Hahn J, Todd P, and Van der Klaauw W (1999). Evaluating the effect of an antidiscrimination law using a regression-discontinuity design (Technical report), National Bureau of Economic Research, Retrieved Jan. 17, 2024, Available from: https://www.nber.org/system/files/working papers/w7131/w7131.pdf
  18. Hahn J, Todd P, and Van der Klaauw W (2001). Identification and estimation of treatment effects with a regression-discontinuity design, Econometrica, 69, 201-209. https://doi.org/10.1111/1468-0262.00183
  19. Imbens G and Kalyanaraman K (2012). Optimal bandwidth choice for the regression discontinuity estimator, The Review of Economic Studies, 79, 933-959. https://doi.org/10.1093/restud/rdr043
  20. Zajonc T (2012). Essays on Causal Inference for Public Policy (Doctoral dissertation), Harvard University, Cambridge, MA.
  21. Imbens G and Lemieux T (2008). Regression discontinuity designs: A guide to practice, Journal of Econometrics, 142, 615-635. https://doi.org/10.1016/j.jeconom.2007.05.001
  22. Lee DS (2008). Randomized experiments from non-random selection in us house elections, Journal of Econometrics, 142, 675-697. https://doi.org/10.1016/j.jeconom.2007.05.004
  23. Lin DY and Ying Z (1994). Semiparametric analysis of the additive risk model, Biometrika, 81, 61-71. https://doi.org/10.1093/biomet/81.1.61
  24. Lostritto K, Strawderman RL, and Molinaro AM (2012). A partitioning deletion/substitution/addition algorithm for creating survival risk groups, Biometrics, 68, 1146-1156. https://doi.org/10.1111/j.1541-0420.2012.01756.x
  25. Ludwig J and Miller DL (2007). Does head start improve children's life chances? evidence from a regression discontinuity design, Quarterly Jounral of Economics, 122, 159-208. https://doi.org/10.1162/qjec.122.1.159
  26. Moscoe E, Bor J, and Barnighausen T (2015). Regression discontinuity designs are underutilized in medicine, epidemiology, and public health: A review of current and best practice, Journal of Clinical Epidemiology, 68, 132-143. https://doi.org/10.1016/j.jclinepi.2014.06.021
  27. Prorok PC, Andriole GL, Bresalier RS et al. (2000). Design of the prostate, lung, colorectal and ovarian (PLCO) cancer screening trial, Controlled Clinical Trials, 21, 273S-309S. https://doi.org/10.1016/S0197-2456(00)00098-2
  28. Robins JM, Rotnitzky A, and Zhao LP (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
  29. Rubin DB (1974). Estimating causal effects of treatments in randomized and nonrandomized studies, Journal of Educational Psychology, 66, 688-701. https://doi.org/10.1037/h0037350
  30. Rubin D and van der Laan MJ (2007). A doubly robust censoring unbiased transformation, The International Journal of Biostatistics, 3, 1-19. https://doi.org/10.2202/1557-4679.1052
  31. Shoag J, Halpern J, Eisner B, Lee R, Mittal S, Barbieri CE, and Shoag D (2015). Efficacy of prostate-specific antigen screening: Use of regression discontinuity in the plco cancer screening trial, JAMA Oncology, 1, 984-986. https://doi.org/10.1001/jamaoncol.2015.2993
  32. Silverman BW (1986). Density Estimation for Statistics and Data Analysis, volume 26. CRC press, London.
  33. Steingrimsson JA, Diao L, and Strawderman RL (2019). Censoring unbiased regression trees and ensembles, Journal of the American Statistical Association, 114, 370-383. https://doi.org/10.1080/01621459.2017.1407775
  34. Strawderman RL (2000). Estimating the mean of an increasing stochastic process at a censored stopping time, Journal of the American Statistical Association, 95, 1192-1208. https://doi.org/10.1080/01621459.2000.10474320
  35. Thistlethwaite DL and Campbell DT (1960). Regression-discontinuity analysis: An alternative to the ex post facto experiment, Journal of Educational Psychology, 51, 309-317. https://doi.org/10.1037/h0044319
  36. Tsiatis A (2007). Semiparametric Theory and Missing Data, Springer Science & Business Media, New York.