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Title: Joint modelling of general and mental health using copula models: a simulation-based evaluation for COVID-19 health research.
COVID-19, the disease caused by the SARS-CoV-2 coronavirus, led to a global pandemic that began in December 2019. In the UK, government-mandated lockdowns were imposed to reduce the spread of the disease and understanding the impact of these actions on the general and mental health of the population has become of increasing interest to medical scientists. However, most analyses treat these outcomes separately, especially when they differ in measurement scales. The aim of this study was to model the general health score and mental health score of the population following COVID-19 infection.
We propose and evaluate copula-based modelling frameworks for jointly correlated health outcomes with mixed data types. Using simulation studies, we assess model performance across three scenarios: continuous–continuous, binary–continuous and categorical-continuous. The simulations mimic a pre-existing UK data from the ‘Next Step’ national longitudinal cohort adjusted by results from COVID-19 survey that was conducted during three waves of the pandemic. We analyse how general health score (continuous, binary or categorical) and mental health score (continuous) are influenced by common covariates such as sex, COVID-19, smoking status, alcohol consumption, exercising, long-lasting health conditions and vaccination status. Models are fitted using the GJRM package in R, employing Gaussian, Ali-Mikhail-Haq (AMH) and Plackett copulas with normal, log-normal and probit marginal distributions. To evaluate the model performance for each of the scenarios, measures including bias, coverage probability, mean square error, and standard error have been calculated.
Our results showed that the modelling the outcomes in the different scenarios affected the accuracy of the copula models. Across all scenarios, data from the second and third waves was best represented by the copula models. We found that wave one acts differently to the other waves and across all models the confidence interval coverage was the most erratic element, in some cases providing very poor coverage.
Keywords: joint modelling, copula models, simulation study, Covid-19
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