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Segmented regression is a standard statistical procedure used to estimate the effect of a policy intervention on a time series outcome. A limitation to this method are the assumptions which include normality of the outcome variable, a large sample size, no auto-correlation in the time series outcome, and a linear trend over time. In addition segmented regression is very sensitive to outliers. In a small sample study where the outcome variable does not follow the Gaussian distribution, estimating the effect of the intervention using the normal approximation leads to incorrect inference.
In order to address the small sample problem and non-normality in the outcome variable, we describe and develop a robust statistical method to estimate the intervention effect on longitudinal data. A simulation study is conducted to measure the power of the test using both the standard segmented regression technique and the new robust statistical method. We use a nonparametric bootstrap technique to develop the sampling distribution of the robust statistic. Finally we estimate the intervention effect of the Istanbul Declaration on illegal organ activities in Brazil from 2002 - 2015.
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