  Segmented 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.
