A Robust Statistical method to Estimate the Intervention Effect with Longitudinal Data
AbstractSegmented regression is a standard statistical procedure used to estimate the effect of a policy intervention on time series outcomes. This statistical method assumes the normality of the outcome variable, a large sample size, no autocorrelation in the observations, and a linear trend over time. Also, segmented regression is very sensitive to outliers. In a small sample study, if the outcome variable does not follow a Gaussian distribution, then using segmented regression to estimate the intervention effect leads to incorrect inferences. To address the small sample problem and non-normality in the outcome variable, including outliers, we describe and develop a robust statistical method to estimate the policy intervention effect in a series of longitudinal data. A simulation study is conducted to demonstrate the effect of outliers and non-normality in the outcomes by calculating the power of the test statistics with the segmented regression and the proposed robust statistical methods. Moreover, since finding the sampling distribution of the proposed robust statistic is analytically difficult, we use a nonparametric bootstrap technique to study the properties of the sampling distribution and make statistical inferences. Simulation studies show that the proposed method has more power than the standard t-test used in segmented regression analysis under the non-normality error distribution. Finally, we use the developed technique to estimate the intervention effect of the Istanbul Declaration on illegal organ activities. The robust method detected more significant effects compared to the standard method and provided shorter confidence intervals.
Wagner, A. K., Soumerai, S. B., Zhang, F., & 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.
Wang, Joanna JJ, W. Scott, G. Raphael, and O. Jake (2013). A comparison of statistical methods in interrupted time series analysis to estimate an intervention effect. In Australasian Road Safety Research, Policing and Education Conference.
Linden, Ariel (2015). Conducting interrupted time-series analysis for single-and multiple-group comparisons. Stata J 15, no. 2 , 480-500.
Box, G. E., & Tiao, G. C. (1975). Intervention analysis with applications to economic and environmental problems. Journal of the American Statistical association, 70(349), 70-79.
Glass, G. V., Willson, V. L., & Gottman, J. M. (Eds.). (2008). Design and analysis of timeseries experiments. IAP.
French, B., & Heagerty, P. J. (2008). Analysis of longitudinal data to evaluate a policy change. Statistics in medicine, 27(24), 5005-5025.
Efron, B. (1982).The Jackknife, the Bootstrap, and Other Resampling Plans. Philadelphia, Society for Industrial and Applied Mathematics.
Efron, B. (1979). Bootstrap methods: Another look at the Jackknife. Annals of Statistics, 7, 1-26
Efron, B. and Tibshirani, R. (1994). An Introduction to the Bootstrap. Chapman and Hall, New York.
Sen, P. K. (1968). Estimates of the regression coefficient based on Kendall's tau. Journal of the American statistical association, 63(324), 1379-1389.
Theil, H. (1992). A rank-invariant method of linear and polynomial regression analysis. In Henri Theil’s contributions to economics and econometrics (pp. 345-381). Springer, Dordrecht.
Simon, J. L., & Bruce, P. (1991). Resampling: A tool for everyday statistical work. Chance, 4(1), 22-32.
Davison, A.C. and Hinkley, D.V. (1997): Bootstrap Methods and Their Applications. Cambridge University press, Cambridge, New York
Newey,W. K., and K. D. West. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55: 703–708.
Prais, S. J., & Winsten, C. B. (1954). Trend estimators and serial correlation (Vol. 383, pp. 1-26). Chicago: Cowles Commission discussion paper.
Ahmadi AR, Lafranca JA, Claessens LA, Imamdi RM, Jzermans JN, Betjes MG, Dor FJ(2015). Shifting paradigms in eligibility criteria for live kidney donation: a systematic review. Kidney Int. Jan; 87(1),31-5.
Organ trafficking and transplant tourism and commercialism: the Declaration of Istanbul. The Lancet 372.9632 (2008): 5-6.
World Bank Open Data. http://data.worldbank.org/.
Islam, M.M., Webb, B., and Kuddus, R. (2019). Assessing the effects of the Istanbul Declaration on Internet reporting of illegal and immoral activities related to human organ acquisition using Interrupted Time Series Analysis (ITSA) and a Meta-Analysis approaches. Submitted to Transplantation Proceedings.
Myles Hollander, Douglas A. Wolfe, Eric Chicken (2013). Nonparametric Statistical Methods. John Wiley & Sons, New York.
Delmonico, F. L. (2009). The implications of Istanbul Declaration on organ trafficking and transplant tourism. Current Opinion in Organ Transplantation, 14(2), 116-119.
Yang, Jing (2012). Interpreting Coefficients in Regression with Log-Transformed Variables. StatNews #83, Cornell University, Ithaca, NY, USA.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).