SARS-CoV-2 and climate factors: a study between linear regression and quantile regression model using longitudinal count data

Regression is the most popular statistical tool used to assess the relationship between predictors and response variables. SARS-CoV-2 infections counts, however are typically right-skewed, heteroskedastic, and show episodic surges. In longitudinal epidemic data, mean-based linear regression-which focusses on the conditional mean under homoscedasticity and normality assumptions- may provide an incomplete representation of transmission dynamics, particularly when extreme outbreak periods disproportionately influence estimates. Quantile regression offers a flexible alternative by allowing covariate effects to vary across the conditional distribution of the response, thereby capturing heterogeneous effects across different transmission regimes. This feature is especially useful for understanding epidemic extremes. The aim of this study is to determine the predictors of SARS-CoV-2 infected cases, using quantile regression and comparing the models at several quantiles. The data utilized in this study were sourced from the website of the Institute of Epidemiology Disease Control and Research (IEDCR), Dhaka Bangladesh. The daily temperature and humidity with a number of daily infected case are taken as predictors and to describe the spread of SAR-CoV-2, we consider the daily number of SAR-CoV-2 infected cases as a response variable, during the period of March 08, 2020 to May 31, 2023. Classical mean regression and Quantile regression was performed to understand the association among climate variables and the results were compared across quantiles. Under the mean and quantile regression framework we found that high temperature and high humidity have a substantial impact on spread of SARS-CoV-2 (in log scale) at a different levels of quantiles (0 < τ < 1). Temperature’s effect steadily decreases as we move from low to high infection quantiles. Temperature effect flips from positive to slightly negative (-1.8%) at the highest quantile 95th quantile and 10.2% at 25th quantile. Humidity remains positively associated across all quantiles but with decreasing strength. For τ = 0.25,0.50,0.75,0.90 and 0.95, Humidity’s effect drops significantly as move to higher quantile: 8.2%, 3.9%, 1.5%, 2.1%, 2.0%, respectively. We also compared conditional quantile models using HQC, AIC, BIC values and found quantile regression model fit at τ = 0.75 is relatively stable across all the conditional distribution. The findings of this study shows that temperature and humidity have significant impact on SARS-CoV-2 transmission in Bangladesh, with heterogeneous effects across different levels of infection intensity. By modeling multiple points of the conditional distribution, quantile regression provides a more comprehensive understanding of epidemic behavior than mean-based approaches. The regression models also suggest that, even in lower infection scenarios, warmer and more humid conditions are linked to higher infection levels. However, Quantile regression is distribution-agnostic, which is both a strength and a limitation in this work. Nevertheless, as the data are longitudinal in nature and the models do not explicitly incorporate dynamic temporal structures, the results should be interpreted as associative rather than causal. Future research incorporating time-series–based quantile or autoregressive frameworks may further elucidate the role of climate in epidemic progression.