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IntroductionLongitudinal individual response profiles could exhibit a mixture of two or more phases of increase or decrease in trend throughout the follow-up period, with one or more unknown transition points (changepoints). The detection and estimation of these changepoints is crucial. Most of the proposed statistical methods for detecting and estimating changepoints in literature rely on distributional assumptions that may not hold. In this case, a good alternative is to use a robust approach; the quantile regression model. There are methods in the literature to deal with quantile regression models with a changepoint. These methods ignore the within-subject dependence of longitudinal data.MethodsWe propose a mixed effects quantile regression model with changepoints to account for dependence structure in the longitudinal data. Fixed effects parameters, in addition to the location of the changepoint, are estimated using the profile estimation method. The stochastic approximation EM algorithm is proposed to estimate the fixed effects parameters exploiting the link between an asymmetric Laplace distribution and the quantile regression. In addition, the location of the changepoint is estimated using the usual optimization methods.Results and discussionA simulation study shows that the proposed estimation and inferential procedures perform reasonably well in finite samples. The practical use of the proposed model is illustrated using COVID-19 data. The data focus on the effect of global economic and health factors on the monthly death rate due to COVID-19 from 1 April 2020 to 30th April 2021. the results show a positive effect on the monthly number of patients with COVID-19 in intensive care units (ICUs) for both 0.5th and 0.8th quantiles of new monthly deaths per million. The stringency index, hospital beds, and diabetes prevalence have no significant effect on both 0.5th and 0.8th quantiles of new monthly deaths per million.