Confidence Interval for Semiparametric Regression Model Parameters Based on Truncated Spline with Application to COVID-19 Dataset in Indonesia

This study proposed a method for constructing confidence intervals for parameters in a semiparametric regression model using a truncated spline estimator, tailored for multiresponse and multipredictor longitudinal data. The semiparametric model integrated parametric and nonparametric components, facilitating the analysis of complex relationships. Confidence intervals were estimated using a pivotal quantity method.The approach was applied to COVID-19 data from Indonesia, exploring the associations between Time, Temperature, and Sunlight Intensity with the Case Increase Rate (CIR) and Case Fatality Rate (CFR). Data spanning April to November 2020 were sourced from 10 provinces with the highest CIR and CFR, obtained from http://kawalcovid.com/ and https://power.larc.nasa.gov/.The analysis identified an optimal Generalized Cross-Validation (GCV) value of 220, with one knot at 24.35°C for Temperature and two knots at 11.33 and 13 units for Sunlight Intensity. Confidence interval estimation demonstrated that all parametric components associated with Time were statistically significant, reflecting a consistent decline in CIR and CFR over time. For the nonparametric components, four parameters significantly influenced CIR, while three parameters significantly affected CFR, contingent on the knot points.The findings underscored the role of environmental factors in shaping COVID-19 dynamics and provided a robust analytical framework for future pandemic modeling. This study highlighted the utility of semiparametric regression with truncated splines in addressing complex epidemiological data, offering valuable insights for policymakers to design evidence-based mitigation strategies