Trend change estimation for interrupted time series with heteroscedastic and autocorrelated errors: application in syphilis occurrences in Brazil

Abstract

The impact evaluation of exogenous policies over time is of great importance in several areas. Unfortunately, an adequate time-series analysis has not always been taken into account in the literature, mainly in health problems. When regression models are used in the known interrupted time-series approach, the required error assumptions are in general neglected. Specifically, usual linear segmented regression (lmseg) models are not adequate when the errors have nonconstant variance and serial correlation. To instigate the correct use of intervention analysis, we present a simple approach extending a linear model with log-linear variance (lmvar) to estimate linear trend changes under heteroscedastic errors (lmsegvar). When the errors are autocorrelated, the Cochrane-Orcutt (CO) modification is implemented to correct the estimated parameters. As an application, we estimate the impact in temporal trend of the Brazilian Rede Mãe Paranaense (RMP) program in gestational syphilis occurrences in the state of Parana, Brazil. The comparison of the proposed linear segmented model (lmsegvar+CO) modeling both the average and variance, with the usual segmented linear model (lmseg), where just the average is modeled, shows the importance of taking heteroscedasticity and autocorrelation into account.