Study design, data collection and study period
A retrospective longitudinal study conducted at an institution was used to gather relevant secondary data from the ART follow-up chart. In order to include at least two visit time responses after the beginning of their regiment, HIV/AIDS infected patients who are >15 years old and start ART between September 11, 2013 and September 5, 2016, CD4 cells measurement just before beginning of ART, were considered as predictors. Utilizing a standardized checklist, data were extracted. Using SPSS for data entry, coding, and cleaning, the secondary data were exported and analyzed in R version 3.6.1.
Study area, population and sampling procedures
This information was gathered from HIV/AIDS patients who began taking ART between September 11, 2013, and September 5, 2016, at Mekelle General Hospital in Tigray Region State, Ethiopia. Mekelle, the state capital of the Tigray Region State, is located in northern Ethiopia and approximately 783 kilometers northwest of Addis Abeba. It also has an estimated 4,664,071 inhabitants overall, of which 2,367,032 are women. According to estimates, more over 80% of the population lives in rural areas. Tigray Region State has 14 hospitals and 205 health centers in 2012, according to a data from the regional health agency [7]. Out of 865 HIV/AIDS patients, a random sample of 216 was chosen utilizing systematic random selection methods.
Variables of this study
Response variable
The key longitudinal outcome variable for this study was the change in CD4 cells in HIV-positive individuals after they started receiving ART. Patients’ CD4 cells were often noted in medical records.
Predictor variables
The sociodemographic and clinical ART factors that were recorded from the medical charts for this study are listed below on Table 1.
Statistical data analysis
One of the associated datasets is the examination of longitudinal data from CD4 cells. The measurements of the biomarkers are either constant or changing over time. All patients provided measurements at the same set of times, which were regularly and uniformly spaced, such as every six months in this study. While the times are altering, various treatments have been used for various individuals at various times [17,18,19]. In this study, the covariance structure and size of the residual errors were also examined for model selection, and the most preferred model was a random effect model with the least amount of individual variability.
Additionally, missing values are a frequent and difficult problem in longitudinal data analysis, and the most common imputation technique to manage missing values is multiple imputations.
The benefit of utilizing the linear mixed model (LMM) is that it makes use of all available data, including incomplete cases, and that it produces reliable and effective estimators of precision parameters. As a result, CD4 cell variability within and between patients was examined for each patient with i = 1, 2,… n [17, 20, 21].
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1).
Random intercept model
A model with random intercepts is one in which the intercepts are only allowed to vary and the change in the response variable for each subsequent measurement is anticipated.
$${\text{y}}_{ij}= {\beta }_{0} +{b}_{0i} + {\beta }_{1}{\text{t}}_{ij} + {\in }_{ij};$$
(1)
\({b}_{0i}\)~N (0,\({{\delta }_{0}}^{2}\)) , \({\in }_{ij}\)~N (0,\({\delta }^{2}\)), \({b}_{0i}\) and \({\in }_{ij}\) are independent
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2).
Random slope model
In a model where slopes are allowed to vary, changes on the response variable for each subsequent measurement are anticipated by slope that varies between patients, the model is known as a random slope model.
$${\text{y}}_{ij}= {\beta }_{0} +{\beta }_{1}{t}_{ij} + {b}_{1i}{\text{t}}_{ij} + {\in }_{ij};$$
(2)
Where, \({b}_{1i}\)~N (0,\({{\delta }_{1}}^{2}\)) \({\in }_{ij}\)~N (0,\({\delta }^{2}\)) and \({b}_{1i}\) and \({\in }_{ij}\) are independent.
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3).
Random intercept and slope model
The most realistic kind of model is probably one with both random intercepts and random slopes (RI-RS). Both intercepts and slopes may differ between patient groups in this model [22].
$${\text{y}}_{ij}= {\beta }_{0} + {\beta }_{1}{\text{t}}_{ij} + {b}_{i1}{\text{t}}_{ij}+{b}_{i0}+ {\in }_{ij};$$
(3)
$$\left\{\begin{array}{l}\begin{array}{cc}{\text{b}}_{i}=\left[\begin{array}{c}{b}_{i0}\\ {b}_{i1}\end{array}\right]\sim N\left(0,{\Omega }_{b}\right)& (4\text{a})\end{array}\\ \begin{array}{cc}{\Omega }_{b}=\left[\begin{array}{c}{{\delta }_{{b}_{0}}}^{2} {\delta }_{b1} \\ {\delta }_{b1} {{\delta }_{{b}_{0}}}^{2} \end{array}\right]& (4\text{b})\end{array}\\ \begin{array}{l}\begin{array}{cc}{\in }_{i}\sim N\left(0,{{\delta }_{e}}^{2}\right)& (4\text{c})\end{array}\\ \begin{array}{cc}{\text{b}}_{i}\sim MVN\left(0,{\sum .}_{i}\right)& (4\text{d})\end{array}\\ \begin{array}{l}\begin{array}{ll}\text{V ar}\left({y}_{ij}\right)={{\delta }_{1}}^{2} + 2{\delta }_{01}{\text{t}}_{ij} + {{\delta }_{1}}^{2}{\text{t}}_{ij} +{\delta }^{2}& (4\text{e})\end{array}\\ \begin{array}{ll}Cov\left({y}_{ij},{y}_{ik}\right)={{\delta }_{0}}^{2} + {\delta }_{01}\left({\text{t}}_{ij},{\text{t}}_{ik}\right) + {{\delta }_{1}}^{2}{\text{t}}_{ij}, {\text{t}}_{ik} +{\delta }^{2} & (4\text{f})\end{array}\\ \begin{array}{c}\begin{array}{cc}\text{Cov}\left({y}_{ij},{y}_{lk}\right)= 0& (4\text{g})\end{array}\\ and\; {\text{b}}_{1},\dots ..,{\text{b}}_{n}, and\; {\in }_{1},\dots \dots .{\in }_{n}\; are\; independent\end{array}\end{array}\end{array}\end{array}\right.$$
Choosing the best covariance structure and model selection criteria
The process of choosing a model from a group of candidate models is known as model selection. It is necessary to select a covariance model based on an anticipated mean response model. The researcher fitted models with straightforward structures, and it was preferred to choose models with the fewest AIC/BIC values in order to minimize the number of parameters in the variance-covariance structure. In this study, Independent (IND), Compound Symmetry (CS), Heterogeneous Compound Symmetry (CSH), First-Order Autoregressive (AR (1)), and Unstructured (UN) were the most often used. These models aid in making inferences about the mean parameters more effectively. The models with the minimum AIC/BIC were therefore the best fits [23,24,25].
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