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.

Global health services are disrupted by the COVID-19 pandemic. We evaluated extent and duration of impacts of the pandemic on health services utilization in different economically developed regions of mainland China. Based on monthly health services utilization data in China, we used Seasonal Autoregressive Integrated Moving Average (S-ARIMA) models to predict outpatient and emergency department visits to hospitals (OEH visits) per capita without pandemic. The impacts were evaluated by three dimensions:1) absolute instant impacts were evaluated by difference between predicted and actual OEH visits per capita in February 2020 and relative instant impacts were the ratio of absolute impacts to baseline OEH visits per capita; 2) absolute and relative accumulative impacts from February 2020 to March 2021; 3) duration of impacts was estimated by time that actual OEH visits per capita returned to its predicted value. From February 2020 to March 2021, the COVID-19 pandemic reduced OEH visits by 0.4676 per capita, equivalent to 659,453,647 visits, corresponding to a decrease of 15.52% relative to the pre-pandemic average annual level in mainland China. The instant impacts in central, northeast, east and west China were 0.1279, 0.1265, 0.1215, and 0.0986 visits per capita, respectively; and corresponding relative impacts were 77.63%, 66.16%, 44.39%, and 50.57%, respectively. The accumulative impacts in northeast, east, west and central China were up to 0.5898, 0.4459, 0.3523, and 0.3324 visits per capita, respectively; and corresponding relative impacts were 23.72%, 12.53%, 13.91%, and 16.48%, respectively. The OEH visits per capita has returned back to predicted values within the first 2, 6, 9, 9 months for east, central, west and northeast China, respectively. Less economically developed areas were affected for a longer time. Safe and equitable access to health services, needs paying great attention especially for undeveloped areas.