Journal of the Iranian Statistical Society

Finite Sample Properties of Quantile Interrupted Time Series Analysis: A Simulation Study

Authors

Department of Family and Community Medicine, Faculty of Medicine, University of Toronto, 500 University Avenue, Toronto, Ontario M5G 1V7, Canada

10.52547/jirss.20.1.247

Abstract

Interrupted Time Series (ITS) analysis represents a powerful quasi-experime-ntal design in which a discontinuity is enforced at a specific intervention point in a time series, and separate regression functions are fitted before and after the intervention point. Segmented linear/quantile regression can be used in ITS designs to isolate intervention effects by estimating the sudden/level change (change in intercept) and/or the gradual change (change in slope). To our knowledge, the finite-sample properties of quantile segmented regression for detecting level and gradual change remains unaddressed. In this study, we compared the performance of segmented quantile regression and segmented linear regression using a Monte Carlo simulation study where the error distributions were: IID Gaussian, heteroscedastic IID Gaussian, correlated AR(1), and T (with 1, 2 and 3 degrees of freedom, respectively). We also compared segmented quantile regresison and segmented linear regression when applied to a real dataset, employing an ITS design to estimate intervention effects on daily-mean patient prescription volumes. Both the simulation study and applied example illustrate the usefulness of quantile segmented regression as a complementary statistical methodolo-gy for assessing the impacts of interventions in ITS designs.

Keywords

  1. Astivia, O. L. O., and Zumbo, B. D. (2019), Heteroskedasticity in Multiple Regression Analysis: What it is, How to Detect it and How to Solve it with Applications in R and SPSS. Practical Assessment, Research, and Evaluation, 24(1).
  2. Austin, P. C., and Tu, J. V., and Daly, P. A., and Alter, D. A. (2005), The use of quantile regression in health care research: a case study examining gender differences in the timeliness of thrombolytic therapy. Statistics in medicine, 24(5), 791-816. [DOI:10.1002/sim.1851]
  3. Baltagi, B. H. (2010), Econometrics. Springer.
  4. Burton, A., and Altman, D. G., and Royston, P., and Holder, R. L. (2006), The design of simulation studies in medical statistics. Statistics in medicine, 25(24), 4279-4292. [DOI:10.1002/sim.2673]
  5. Campbell, D. T., and Stanley, J. C. (2015), Experimental and quasi-experimental designs for research. Ravenio Books.
  6. Cook, T. D., and Campbell, D. T., and Day, A. (1979), Quasi-experimentation: Design & analysis issues for field settings. Houghton Mifflin Boston.
  7. Ferron, J., and Rendina-Gobioff, G. (2005), Interrupted time series design. Encyclopedia of Statistics in Behavioral Science.
  8. Geraci, M., and Bottai, M. (2007), Quantile regression for longitudinal data using the asymmetric Laplace distribution. Biostatistics, 8(1), 140-154. [DOI:10.1093/biostatistics/kxj039]
  9. Gillings, D., and Makuc, D., and Siegel, E. (1981), Analysis of interrupted time series mortality trends: an example to evaluate regionalized perinatal care. American journal of public health, 71(1), 38-46. [DOI:10.2105/AJPH.71.1.38]
  10. Honda, T. (2013), Nonparametric quantile regression with heavy-tailed and strongly dependent errors. Annals of the Institute of Statistical Mathematics, 65(1), 23-47. [DOI:10.1007/s10463-012-0359-8]
  11. Kezdi, G. (2003), Robust standard error estimation in fixed-effects panel models. Available at SSRN 596988 .
  12. Kocherginsky, M., and He, X., and Mu, Y. (2005), Practical confidence intervals for regression quantiles. Journal of Computational and Graphical Statistics, 14(1), 41-55. [DOI:10.1198/106186005X27563]
  13. Koenker, R. (2005), Quantile Regression. Cambridge.
  14. Koenker, R., and Bassett Jr, G. (1978), Regression quantiles. Econometrica: journal of the Econometric Society, 33-50. [DOI:10.2307/1913643]
  15. Koenker, R., and Chernozhukov, V., and He, X., and Peng, L. (2017), Handbook of quantile regression . CRC press.
  16. Koenker, R., and Hallock, K. F. (2001), Quantile regression. Journal of economic perspectives, 15(4), 143-156. [DOI:10.1257/jep.15.4.143]
  17. Nolan, J., P and Ojeda-Revah, D. (2013), Linear and nonlinear regression with stable errors. Journal of Econometrics, 172(2), 186-194. [DOI:10.1016/j.jeconom.2012.08.008]
  18. Sherman, M. (1997), Comparing the sample mean and the sample median: An exploration in the exponential power family. The American Statistician, 51(1), 52-54.
  19. Tarr, G. (2012), Small sample performance of quantile regression confidence intervals. Journal of Statistical Computation and Simulation, 82(1), 81-94. [DOI:10.1080/00949655.2010.527844]
  20. Wagner, A. K., and Soumerai, S. B., and Zhang, F., and Ross-Degnan, D. (2002), Segmented regression analysis of interrupted time series studies in medication use research. Journal of clinical pharmacy and therapeutics, 27(4), 299-309. [DOI:10.1046/j.1365-2710.2002.00430.x]
  21. Xiong, W., and Tian, M. (2019), Weighted quantile regression theory and its application. Journal of Data Science, 17(1), 145-160.
  22. Yang, X. R., and Zhang, L. X., (2008), A note on self-weighted quantile estimation for infinite variance quantile autoregression models. statistics & probability letters, 78(16), 2731-2738.
Journal of the Iranian Statistical Society
Volume 20, Issue 1
June 2021
Pages 247-267
  • Receive Date: 23 July 2022
  • Revise Date: 20 May 2024
  • Accept Date: 23 July 2022