Optimized ITS/CITS models for intervention evaluation considering the nonlinear impact of covariates

There is a lack of approaches to evaluate the effectiveness of interventions when there are nonlinear impacts of covariates to the outcome series. Based on the classic framework of ITS/CITS segmented regression, while considering autocorrelation of time series, we adopted a nonlinear dynamic modeling strategy (Hammerstein) to measure the nonlinear effects of covariates, and proposed four optimized models: ITS-A, CITS-A, ITS-HA, and CITS-HA. To compare the accuracy and precision in estimating the long-term impact of an intervention between the optimized and classic segmented models, we constructed a sequence generator to simulate the outcome series with actual characteristics. The relative error with respect to the true value was the accuracy indicator, and the width of the 95% CI and the truth value coverage rate of the corresponding 95% CI are the precision indicator for model assessments. The relative error of impact evaluation in the four optimized models was 4.49 percentage points lower than that in the classic models, specifically ITS-A (14.34%) and ITS-HA (21.47%) relative to ITS (26.66%), CITS-A (16.57%), and CITS-HA (17.94%) relative to CITS (21.59%). The width of the 95% CI of point estimate of long-term impacts in the optimized models was 0.1261, which was expanded by 58.71% compared with 0.0875 for the classic model. However, the optimized models covered the true value in all test scenarios, whereas the coverage rates of the classic ITS and CITS models were 73.33% and 83.33%, respectively. The optimized models are useful tools as they can assess the long-term impact of interventions with additional considerations for the nonlinear effects of covariates and allow for modeling of time-series autocorrelation and lag of intervention effects.