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Background Count time series (e.g., daily deaths) are a very common type of data in environmental health research. The series is generally autocorrelated, while the widely used generalized linear model is based on the assumption of independent outcomes. None of the existing methods for modelling parameter-driven count time series can obtain consistent and reliable standard error of parameter estimates, causing potential inflation of type I error rate. Methods We proposed a new maximum significant ρ correction (MSRC) method that utilizes information of significant autocorrelation coefficient ρ estimate within 5 orders by moment estimation. A Monte Carlo simulation was conducted to evaluate and compare the finite sample performance of the MSRC and classical unbiased correction (UB-corrected) method. We demonstrated a real-data analysis for assessing the effect of drunk driving regulations on the incidence of road traffic injuries (RTIs) using MSRC in Shenzhen, China. Moreover, there is no previous paper assessing the time-varying intervention effect and considering autocorrelation based on daily data of RTIs. Results Both methods had a small bias in the regression coefficients. The autocorrelation coefficient estimated by UB-corrected is slightly underestimated at high autocorrelation (≥ 0.6), leading to the inflation of the type I error rate. The new method well controlled the type I error rate when the sample size reached 340. Moreover, the power of MSRC increased with increasing sample size and effect size and decreasing nuisance parameters, and it approached UB-corrected when ρ was small (≤ 0.4), but became more reliable as autocorrelation increased further. The daily data of RTIs exhibited significant autocorrelation after controlling for potential confounding, and therefore the MSRC was preferable to the UB-corrected. The intervention contributed to a decrease in the incidence of RTIs by 8.34% (95% CI, -5.69–20.51%), 45.07% (95% CI, 25.86–59.30%) and 42.94% (95% CI, 9.56–64.00%) at 1, 3 and 5 years after the implementation of the intervention, respectively. Conclusions The proposed MSRC method provides a reliable and consistent approach for modelling parameter-driven time series with autocorrelated count data. It offers improved estimation compared to existing methods. The strict drunk driving regulations can reduce the risk of RTIs.

During the last few years, there was increasing interest in SPC methods for time-dependent processes of counts. We survey recent developments in this field: feasible models for autocorrelated counts processes are presented, approaches for corresponding control charts are considered, and also the topic of process capability indices is briefly discussed. The article is accompanied by a comprehensive list of relevant references, and it concludes by outlining promising directions for future research.