Application of quantile mixed-effects model in modeling CD4 count from HIV-infected patients in KwaZulu-Natal South Africa

Abstract

Abstract Background The CD4 cell count signifies the health of an individual’s immune system. The use of data-driven models enables clinicians to accurately interpret potential information, examine the progression of CD4 count, and deal with patient heterogeneity due to patient-specific effects. Quantile-based regression models can be used to illustrate the entire conditional distribution of an outcome and identify various covariates effects at the respective location. Methods This study uses the quantile mixed-effects model that assumes an asymmetric Laplace distribution for the error term. The model also incorporated multiple random effects to consider the correlation among observations. The exact maximum likelihood estimation was implemented using the Stochastic Approximation of the Expectation–Maximization algorithm to estimate the parameters. This study used the Centre of the AIDS Programme of Research in South Africa (CAPRISA) 002 Acute Infection Study data. In this study, the response variable is the longitudinal CD4 count from HIV-infected patients who were initiated on Highly Active Antiretroviral Therapy (HAART), and the explanatory variables are relevant baseline characteristics of the patients. Results The analysis obtained robust parameters estimates at various locations of the conditional distribution. For instance, our result showed that baseline BMI (at $$\tau =$$ τ = 0.05: $${\widehat{\beta }}_{4}=0.056, \mathrm{p-}\mathrm{value}<0.0064; \mathrm{at }\,\tau = 0.5: {\widehat{\beta }}_{4}=0.082, \mathrm{p-}\mathrm{value}<0.0025; \mathrm{at}\,\tau = 0.95: {\widehat{\beta }}_{4}=0.145,\mathrm{p-}\mathrm{value}<0.0000$$ β ^ 4 = 0.056 , p - value < 0.0064 ; at τ = 0.5 : β ^ 4 = 0.082 , p - value < 0.0025 ; at τ = 0.95 : β ^ 4 = 0.145 , p - value < 0.0000 ), baseline viral load (at $$\tau =$$ τ = 0.05: $${\widehat{\beta }}_{5}$$ β ^ 5 $$=-0.564, \mathrm{p-}\mathrm{value}<0.0000; \mathrm{at}\,\tau = 0. 5: {\widehat{\beta }}_{5}=-0.641, \mathrm{p-}\mathrm{value}<0.0000; \mathrm{at }\,\tau = 0.95: {\widehat{\beta }}_{5}=-0.739,\mathrm{p-}\mathrm{value}<0.0000$$ = - 0.564 , p - value < 0.0000 ; at τ = 0.5 : β ^ 5 = - 0.641 , p - value < 0.0000 ; at τ = 0.95 : β ^ 5 = - 0.739 , p - value < 0.0000 ), and post-HAART initiation (at $$\tau =$$ τ = 0.05: $${\widehat{\beta }}_{6}=1.683,\mathrm{p-}\mathrm{value}<0.0000; \mathrm{at}\,\tau = 0.5: {\widehat{\beta }}_{6}=2.560,\mathrm{p-}\mathrm{value}<0.0000; \mathrm{at }\,\tau =0.95: {\widehat{\beta }}_{6}=2.287,\mathrm{p-}\mathrm{value}<0.0000$$ β ^ 6 = 1.683 , p - value < 0.0000 ; at τ = 0.5 : β ^ 6 = 2.560 , p - value < 0.0000 ; at τ = 0.95 : β ^ 6 = 2.287 , p - value < 0.0000 ) were major significant factors of CD4 count across fitted quantiles. Conclusions CD4 cell recovery in response to post-HAART initiation across all fitted quantile levels was observed. Compared to HIV-infected patients with low viral load levels at baseline, HIV-infected patients enrolled in the treatment with a high viral load level at baseline showed a significant negative effect on CD4 cell counts at upper quantiles. HIV-infected patients registered with high BMI at baseline had improved CD4 cell count after treatment, but physicians should not ignore this group of patients clinically. It is also crucial for physicians to closely monitor patients with a low BMI before and after starting HAART.

Keywords

• Quantile regression
• Quantile mixed model
• Stochastic approximation of the expectation maximization
• Asymmetric Laplace distribution
• CD4 count
• CAPRISA