Longitudinal study of change in CD4+ cell counts on HIV-Positive patients at Dalhatu Araf Specialist Hospital, Lafia

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Introduction
CD4+ T lymphocyte (CD4) cell counts are the primary laboratory markers used to study the progression from HIV to AIDS.However, it is a subject of debate among clinicians on the appropriate CD4 level to initiate HIV treatment.The 2013 WHO guideline recommends that HIV therapy be initiated when CD4+ cell counts is less than 500 / cells L  which is a departure from previous guidelines which gives a threshold of 350 / cells L  .The debate of when to initiate therapy is also fuelled by the lack of evidence from HIV treatment initiation randomized clinical trials due to ethical implications, (WHO, 2013).
HIV infection causes severe depletion of CD4 T cells in the gut-associated lymphoid tissue with subsequent reduced levels of circulating CD4 lymphocytes in the peripheral blood.The CD4 T cells are terribly reduced in acute HIV infections but are seen to rebound over several weeks.If a patient remains untreated, CD4 T cells declines over several years.Studies have shown that prior to seroconversion, CD4 count is measured at around / cells mm at one year of follow- up.Subsequently, the CD4 cell counts declines at a yearly average rate of approximately 3 50 / cells mm .Significant depletion of CD4 T cells can give access to opportunistic infections and mortality in patients not undergoing therapy.
In longitudinal studies, measurements are taken from the same individual repeatedly over time.The primary goal of a longitudinal study is to characterize the change in response over time and to discover the factors that influence the change of the response.In longitudinal studies, responses between subjects may be independent but the repeated measurements within subjects are very likely to be correlated.When modelling longitudinal data, the within-subject correlation must be taken into account.The observed usually contains missing data, dropouts, censoring, outliers and measurement errors and are often unbalanced since the subjects were measured at different times and on different number of times.
Parametric models such linear mixed model are popularly useful in modelling longitudinal especially change in CD4 cell count over time., because the mixed effect models are parsimonious and efficient when the models are specified correctly.

Problem statement
Clinicians have used different markers to evaluate the progress of HIV in patients, among these markers are the viral load and CD4+ cell count.Viral load is quite expensive to use in terms of cost and technology.As such, the CD4+ cell count is commonly used, where a means of predicting future CD4+ count becomes very necessary.Since CD4 is the most important factor in deciding whether to initiate antiretroviral therapy, we hope to use this work to understand the prediction of future CD4+ cell counts for better administration of ART.

Justification
CD4+ count response to antiretroviral therapy (ART) are important measures of the efficacy of ART in individual patients.In Nasarawa State, almost no study is seen on long-term CD4+ response to ART among patients receiving care in resource limited setting.Among those patients who are able to remain on ART, robust immunologic response can be maintained for long periods and the risk of serious morbidity and mortality may eventually diminish.Hence the need for tools to predict CD4 cell counts into future times.

Aim
The aim of this research is the Longitudinal Study of Change in CD4+ Cell Counts on HIV-Positive Patients Initiated on Antiretroviral Therapy.

Objectives
 To identify the trajectory of the mean response over time. To obtain the average difference between groups of individuals. To estimate the relationship between the response and time vary according to groups of individuals.

Literature review
Many studies have been done on the change in CD4+ cell counts of HIV patients on ART.Nearly all studies in the first instance attempted to identify and establish factors in addition to HIV, that contributes to the change in CD4+ cell counts in HIV patients already enrolled in the antiretroviral therapy system.Some of these factors are seen to be demographic, such as, age, sex, area of residence, WHO clinical stage, initial CD4+ Xiuhong et al (2011) both used linear regression models to study some predictors of CD4+ cell counts recovery in HIV-1 positive patientsalready on ART beyond five (5) years of active ART.These studies majorly assumed that the change in CD4+ cell counts is linear, however, Adams & Luguterah (2013) suggested a longitudinal approach where they carried out a longitudinal analysis of change in CD4+ cell counts of HIV-1 patients on antiretroviral therapy (ART) in the Builsa district hospital.Secondary data sets were obtained from HIV/AIDS monitoring program at the Builsa District Hospital, in which patients already enrolled into the ART were being monitored and thus generating repeated measurements of their CD4+ cell counts and other variables.The aim of the study was to investigate plausible determinants that affect change in CD4+ cell counts.Mixed effects modelling approach was deployed to model the CD4+ cell counts of different subjects.Results revealed that the correlation between CD4+ cell counts at different times had a first order autoregressive moving average variance-covariance structure.The CD4+ cell counts of subjects at initiation into ART, the duration of treatment and the drug type used in the treatment were seen to be predictor variables that determine the change in CD4+ cell counts.This study considered the changes in CD4+ cell count over the period of the study and the longitudinal approach was seen to be nonlinear and more advantageous.
Awoke, Principal and Zewotir (2017) looked at adherence and CD4 cell count change measure of the progression of the disease in HIV patients after the commencement of HAART.A retrospective longitudinal cohort study was conducted to examine the joint predictors of CD4 cell count change and adherence to HAART among HIV adult patients enrolled in the first ten months of the year 2009 and followed up till June, 20012.A joint model was deployed to detect determinants of two response variables.It was seen that joint model was more parsimonious than separate models as it reduces type-I error and subject-specific analysis improved its model fit.Also noted in the result is that as adherence increases, CD4 cell count also increased.Meaning that adherence to HAART boosts the immune system of subjects.

Study Design
The study was a retrospective research that covered the duration 1 st December, 2021 to 31 st December, 2022.Data sets of fifty (50) patients already on ART was collected from Dalhatu Araf Specialist Hospital, Lafia, Nasarawa State.Gender, age at initiation of ART, Baseline weight, CD4+ cell count taken at the initiation of ART and thereafter every six-weekly CD4 cell count up to eight months, world health clinical staging at the initiation of ART and other factors were collected.

Sampling Procedure and Size
The sampling frame of this study was fifty (50) HIV-positive patients above 18 years started on ART between December 1 st , 2021 and December 31 st , 2022.

Selection Criteria
Data sets of fifty (50) patients above 18 years currently on ART who visited the Dalhatu Araf Specialist Hospital Lafia, Nasarawa State between the period December, 2021 to December, 2022 was used.The fifty patients were subjects whose records for six (6) observations were identified.Subject names were not used in this study.

Data Collection Criteria and Variables
The study used secondary data collected by well trained staff of the records unit of the health facility, where further orientation was given on the peculiar nature of the study.The data extraction template was designed and used to collect the data.The count variable of interest was the CD4+ cell count 3 ( / ) cells mm with repeated measurements every six (6) weeks, the gender, WHO clinical staging at initiation of ART, BMI from initiation of ART and age at start of study.Other variables of interests include water source, insect treated net, meals per day, food supplement, coping with medication, self reported adherence, educational level, occupational status, risk factors and drug allergies.

Ethical Consideration
The process of obtaining data sets for this study was based on permission received from prospective health facilities following guidelines stipulated by the Nasarawa State ministry of health.Data protection laws of Nigeria were strictly adhered to in carrying out this research.All facets of any other relevant ethics were adequately addressed.

Validity and Reliability
Content validity was based on the adequacy with which the items in an instrument measure the attributes of the study (Nunnally, 1978).This was ensured through constructive criticism from colleagues and those with extensive experience in research.Also, the reliability of the method was ensured through fitting of models to hypothetical data sets.Furthermore, the reliability and validity of results was obtained through member checks to help indicate whether the findings appeared to match with perceived authenticity.This was done in order to limit the distorting effects of random errors on the findings.

Data analysis and results obtained 4.1. Variable description
This analysis was conducted using data collected from fifty (50) patients at the Dalhatu Araf Specialist Hospital, Lafia, Nasarawa State.The data contains the variables as described below obtained from thirty-five (35) female and fifteen (15) male patients. PATID= Patients ID  CD4COUNT= Measurement of CD4+ Cell Counts of patients, taken every 12 weeks for six times. GENDER= Sex of the participating patient  OBSERVATION = Six observations of 12 weekly observations on patients  AGE= Age of patient as at first introduction to ART and subsequent measurements. WEIGHT=Weight of patients as at first introduction to ART and subsequently.

Descriptive Plots Figure 1 Box-plot of CD4+ Count Cell According to Gender and Observation
The first plot in Fig. 1 above shows that the female patients have a higher median CD4+ cell count than the male patients, although it is observed that they have the highest and lowest CD4+ cell count.This means that the female patients are observed to have a higher range of CD4+ cell count.The second plot in Fig. 1 also tells us same thing as the first except that based on the first observation, it further tells us that the female patients averagely came in with lower CD4+ cell count than the male.The observation (OBS2) shows that there is a rise in the CD4+ cell count after the commencement of ART with a slight drop in OBS3, rise in CD+ cell in OBS4 and OBS5, where we see that in the sixth observation, the CD4+ cell count is higher in male than female.The plots in Fig. 2 and Fig. 3 shows the individual line plot of all participating patients where it was seen that the range of values in the female plot is wider and more variable than that of the male.

Mean Response Over Time
The average responses for both male and female subjects based on age are seen to have a high variability with the least variability observed in the second observation for both male and female.

Linear Mixed Models
In order to test for a subset of fixed effects, a linear mixed-effects models was fitted using the lmer function in the lme4 package in R. The first section of the model states the fixed effects part of the model, while the second that is put in parenthesis indicate the random effect components.
The estimated marginal mean of the CD4 Cell count is 681.17 cells/mm3.The estimated variance of the random-effect that reflects the between-subject variability is 70977 while the estimated variance of the error term which reflects the within-subject variability is calculated to be 94154.Hence, the correlation between any two repeated measures (ICC) is equal to 70977/(70977+94154)=0.43.
We now go ahead to test the components using an ANOVA like table obtained from the ranova function and lmer test in R.
The small p-value shows that there is evidence of between-individual heterogeneity which also shows that choosing a mixed-effects model instead of an only fixed effects model is in order.

Mean Response with Time
Here, the indicator variables are now used to contrast the mean responses at different occasions.We have measurements of the response at different time intervals OBS1(baseline CD4 Cell Count), OBS2, OBS3, OBS4, OBS5 and OBS6.
X X X X and X are indicator variables for the other five CD4 cell count observations after the baseline observations respectively.As such, the second measurement (OBS2) is the referent.
The model summary above shows that the mean CD4+ cell count at the baseline (OBS1) is 534.14cell/mm 3 but at the initiation of ART, it was observed that the difference between the mean responses of OBS1 and OBS2 is Our results from the Wald-test reveal that the pattern of the mean response over time is not flat.The estimated trajectory from the fitted model by using the predict function in R is shown below.

Figure 5 Fitted model plot
The trajectory of the fitted model shown in blue line where the points are the predicted mean response.It is seen to be slowly increasing.

Group Effect
The next objective is to test if the mean response varies in the two groups of individual that is gender (male =1 and female=2).
X X X X and X are indicator variables for the other five CD4 cell count observations after the baseline observations respectively while 6 ij X is the indicator variable for gender.The mean response for male and female is given as , that is adjusted for time.
The difference between the mean CD4 cell count of male versus female is -113.62CD4 cell count (i.e. 95% CI= -290.64 to 63.39) lower than female, adjusting with time.

Interaction between observations and groups
Here, we try to find out if the change of the mean response over time varies according to the group of individuals.A mixed interaction model was fitted and results below were obtained.
The mean response among female patients for the first observation 546cell/mm 3 .At the second observation, the mean response is noticed to be 79.4cell/mm 3 higher than the first observation but is seen to be insignificant.The mean response at the third observation is 173.5 cell/mm 3 and was observed to increase significantly up till the sixth observation at 246.1 cell/mm 3 .The mean response among male patients was observed to be insignificant.We get to see that the mean response among male and female depends on the time of observation but the change in the mean response over time does not depend on the gender of the patient.

Testing the interaction between gender and observations
The Wald test does not show any significant evidence of interaction between the observations and gender (p=0.2925) which suggests that the mean response based on gender may be parallel.

Figure 6 Fitted group model plot
The above plot confirms the Wald's test which suggested earlier that the mean response based on gender may be parallel.

Conclusion
A longitudinal study of the change in CD4+ cell count of fifty HIV-patients initiated on Antiretroviraltherapy at the Dalhatu Araf Specialist Hospital, Lafia, Nasarawa State was attempted in this study.The study deployed linear mixed effects models to check if the mean response CD4+ cell count varies with time.The study also attempted to test if the mean response varies in the two groups.An attempt to estimate the relationship between the response and observations according to gender.
The study revealed that the trajectory of the mean response over time has a very high variability where we see that there is a general rise in the CD4+ cell counts at the initiation of ART.It was further seen that the CD4+ cell counts in male patients is observed to be higher with higher median value after the sixth observation.
A linear mixed effect model was used and tested where it was noted that there is evidence of between-individual heterogeneity which further shows that the decision to choose a mixed effects model instead of an only fixed effects model was in order.The model summary showed that the mean CD4+ cell counts at the baseline (OBS1) was averagely good, but at the initiation of ART, there was a significant increase in the mean response where it was further revealed that the pattern of the mean response over time is not flat.
In modelling the group effects, we see the difference between the mean CD4+ cell count of male versus female is -113.62CD4 cell count (i.e. 95% CI= -290.64 to 63.39) lower than female, adjusting with time.
Finally, the Wald test does not show any significant evidence of interaction between the observations and gender (p=0.2925) which suggests that the mean response based on gender may be parallel.
cells mm ; it declines to an average of about 3 780 / cells mm at six months post seroconversion and to 3 670

Figure 2Individual Figure 3
Figure 2Individual line plot of Patients based on Observation

Figure 4
Figure 4 Plot of each patient data over time

..
The difference between the mean responses of OBS3 and OBS1 is The difference between the mean responses and subsequent observations are as follows To test whether the mean response will be constant over time, we test the null hypothesis that all the regression coefficients used to model time are simultaneously equal to zero  