Epidemiological Decoupling of COVID-19 in Pernambuco, Brazil (2020–2023): A Subnational Time-Series Risk Analysis Using Generalized Models

Background/Objectives: COVID-19 placed substantial pressure on health systems and showed marked spatial and temporal heterogeneity in Brazil. We analyzed monthly and annual patterns of incidence, mortality, and period-specific case fatality in Pernambuco from 2020 to 2023. Methods: This ecological time-series study used 48 monthly surveillance observations. Monthly case and death counts were modeled with calendar year as a categorical predictor. Negative binomial generalized linear models with log offsets were selected as the primary models because Poisson models showed marked overdispersion; heteroscedasticity—and autocorrelation-consistent (HAC) standard errors were used to reduce sensitivity to serial dependence. A log-linear model estimated Monthly Percent Change (MPC) using a four-month moving-block bootstrap. A quasi-Poisson generalized additive model (GAM) with k = 10 was examined as an exploratory description of non-linearity. Results: Annual incidence increased from 2310.85 per 100,000 in 2020 to 4905.65 per 100,000 in 2022 and decreased to 908.18 per 100,000 in 2023. Mortality peaked in 2021 and period-specific CFR declined markedly thereafter. In the primary negative binomial models with HAC inference, incidence was lower in 2023 than in 2020 (RR = 0.39; 95% CI: 0.17–0.89; p = 0.0247). Mortality in 2021 did not differ from 2020 (RR = 1.11; 95% CI: 0.43–2.89; p = 0.8270), whereas mortality was lower in 2022 (RR = 0.22; 95% CI: 0.09–0.52; p = 0.0006) and 2023 (RR = 0.06; 95% CI: 0.03–0.14; p < 0.0001). The global MPC was +2.52% (moving-block bootstrap 95% CI: −5.42% to 11.00%; p = 0.5152), providing no evidence of a consistent global log-linear trend. The exploratory GAM suggested a non-linear trajectory, but its basis-dimension check indicated that k = 10 was insufficient (k-index = 0.469; p < 0.001); therefore, no inferential conclusion was based on the GAM. Conclusions: Pernambuco surveillance data show an epidemiological divergence between reported incidence and severe outcomes, particularly from 2022 onward. Because vaccination, hybrid immunity, circulating variants, testing practices, and clinical management were not directly modeled, these findings support epidemiological decoupling but do not by themselves establish its biological mechanisms.