Joint Modelling of CD4 Count and Time ToWound Healing in HIV-Positive Men Following Circumcision

Abstract

Background: Modelling longitudinal information and event time outcomes simultaneously helps in describing the progression of the disease over time. Past studies have mostly applied standard Cox proportional hazards model to establish the association between baseline CD4 count and time to wound healing following circumcision. However, Cox proportional hazards model does not take into account the special features of biomarkers besides not utilizing the entire longitudinal history of measurements. Consequently, results reported from Cox proportional hazards model could be biased or ine_cient. To optimally investigate the association between CD4 count and time to wound healing, we used a joint modelling framework. In this framework, we utilized patients’entire longitudinal history of CD4 count, while also properly accounting for measurement error caused by biological variation and missing measurements. Methods: In the _rst step, we _tted a linear mixed e_ects model to describe the evolution of square root CD4 count over time for each patient while adjusting for the priori selected baseline covarites. In the second step, we used the estimated evolution (square root CD4 count) in the Cox proportional hazards model to determine its relationship with time to wound healing. Some CD4 count values were missing for some patients at followup visits. This is a missing data problem synonymous with longitudinal studies and we assumed that the mechanism of missingness was missing at random (MAR), and thus, the results reported from the joint models, are still valid under MAR. Results: 115 out 119 patients completed their follow-up visits and their wounds were certi_ed fully healed. Median time to wound healing was 49 days (IQR:49-63 ). There was no association between the current true value of square root CD4 count and wound healing time (p-value=0.536). However, for patients with the same current true value of square root CD4 count at a given time point t, the log hazard ratio for a unit increase in the rate of change in square root CD4 count trajectory was 1.514 (95% CI: 1.121; 1.908). Conclusion: Circumcising HIV-positive patients with any level of square root CD4 count is not harmful to their post-circumcision wound healing. However, patients with the same current true level of square root CD4 count could exhibit di_erent slopes of the square root CD4 count trajectory at the same time point t, leading to di_erent progression of wound healing between them.