Joint Modelling of the Relationship between CD4 Cell Count and Survival Analysis of HIV Infected Patients Receiving Antiretroviral Therapy, Gweru, Zimbabwe

Background of the Study

The Gweru District ART cohort: The Gweru District ART cohort was run by Medecins Sans Frontieres (MSF) Holland. MSF is an international, independent, medical humanitarian organisation. Its main mandate is to deliver emergency aid to people affected by armed conflicts, epidemics, natural disasters, and exclusion from healthcare. The organisation assists people based on need, irrespective of race, religion, gender, or political affiliation.

MSF was offering humanitarian aid to people infected with HIV in Gweru district starting in year 2006, before it handed over the operations to the Ministry of Health and Child Welfare (MOHCW) in 2011. The organisation operated at Mkoba 1 and Lower Gweru Mission Hospital Opportunistic Infections clinics. Their operations constituted the biggest HIV care service in the Midlands province of Zimbabwe. The clinics were established in 2006 and were involved in among other services HIV/AIDS interventions, nutritional and preventive services, and training of medical personnel.

Patients were enrolled into the cohort through voluntary counselling and testing (VCT) and through prevention of mother to child transmission programme (PMTCT). The organisation had a laboratory for conducting HIV tests through the services of qualified personnel. Patients were voluntarily counselled and tested for HIV. Those who consented were enrolled into the cohort and were offered treatment. An electronic database was designed to capture patient’s information. Demographic information of the patient at enrolment was captured and this includes gender, age, marital status, WHO disease staging, weight, height, CD4 cell counts, haemoglobin, ALAT (Alanine aminotransferase, creatinine, and history of HIV treatment. Baseline measurements for the patients were taken. Immunologic markers (such as CD4 cell counts) were measured after ART initiation at six months intervals. Date of death for the deceased patients was also recorded. Patients were followed up through a comprehensive patient monitoring system, capturing specific patient variables and outcomes overtime. The treatment protocols, drug regimens and programme reporting tools used at the centres were conforming to the national guidelines.

Human Immune Virus (HIV) infection leads to a depletion in CD4 T-helper cells leading to acquired immune deficiency syndrome (AIDS) in a period of 2 to 10 years depending on the patient. This variation in period of death due to AIDS has been mainly linked to differences in viral load [5]. AIDS progression also varies by age and the relative risk of developing AIDS by any given time after sero-conversion was 1.45 for each ten year increase in age [6]. Younger patients had a higher chance, 20 year survival than older patients [7].

There is an association between progression to AIDS and a rapid decline in CD4 cell counts [8]. Antiretroviral therapy (ART) which fights against HIV infection has been in use since 1996. ART suppresses the viral load, consequently allowing the patient’s immune system to recover and protecting him or her from developing AIDS and death. ART is mainly recommended to those patients with very high viral load and those experiencing a rapid drop in CD4 cell count. Treatment can also be initiated irrespective of CD4 cell count but also depending on patient’s clinical condition (World Health Organization (WHO) disease staging) or another HIV related condition like renal failure and pregnant mothers.

Increases in CD4 cell counts, and mortality and loss to follow up depend on time on ART as well as on current CD4 cell count [9]. Low CD4 cell counts are highly related to development of opportunistic infections (SMART study group, 2008) [10]. Initiation of ART at a CD4 cell count more than 350 cells/µl was seen to result in longer quality- adjusted survival compared to starting ART at lower CD4 cell counts [11]. Data from the EUROSIDA study suggested that all patients could eventually experience normalization of their CD4 cell counts, regardless of their starting CD4 cell count [12].

Researchers often opt for cross sectional analyses even if exposed to longitudinal data. Their analyses usually make use of a single wave of data or focus on change in scores between only two waves. Such an analysis discards an enormous amount of data that are useful and central in describing the complex health trajectories over time.

Statisticians have shown great interest in modelling longitudinal and survival data. The genesis of work on joint modelling of longitudinal and survival data was work by Tsiatis et al. [12], Wulfsohn et al. [13], De Gruttola, et al. [14], Wang, et al. [15], and Henderson, et al. [16]. Tsiatis, et al. [12] developed the methods for developing joint models for longitudinal and survival data, Wulfsohn, et al. [13] developed a joint model for survival and longitudinal data measured with error, De Gruttola, et al. [14] modelled the progression of CD4-lymphocyte count and its relationship to survival time. Furthermore, Wang, et al. [15] modelled longitudinal and event time data with application to acquired immunodeficiency syndrome and Henderson, et al. [16] also modelled longitudinal and event time data.

Limitations of the study: The study mainly concentrated on secondary data analysis. Other variables which may be of interest in explaining changes in cd4 cell count were not captured for example viral load.

Study Variables

The longitudinal outcome variable is the CD4 cell count and the survival time is the survival outcome, with death as the censoring indicator. The variable cd4 count was transformed into the natural logarithm of cdd4 (lncd4). The covariates to be examined are gender, age, profession, marital status, WHO disease stage and nutritional status (defined using body mass index (BMI). BMI is calculated by dividing the patients’ weight in kilograms by the square of the height in metres. Patients were grouped into three nutritional groups using BMI (BMI < 18.5 underweight, 18.5- 24.9 Normal weight and > 25 overweight). A new variable age group was generated with patience below 15 years recoded as 1, 15 to 49 years recoded as 2 and above 49 years recoded as 3.

• Data Management The variable bmi_n for body mass index was generated in Stata13 and patients were regrouped into three nutritional groups using BMI as stated above. A value 3 represent the underweight, 2 the normal weight and 1 the overweight. Dummy variables were also created for bmi_n (bmi_n1, bmi_ n2 and bmi_n3), WHO disease staging (fstwhoc1, fstwhoc2, fstwhoc3, fstwhoc4), profession, marital status and place of residence and for the variable age group (agegrp1, agegrp2, agegrp3). Marital status was further categorized as staying with a partner (marit_stat= 1) or not staying with a partner (marit_stat= 0), with those married classified as staying with a partner and those single, widowed, divorced and separated as not staying with a partner. WHO disease staging was further categorized as patient_condition =1 for the patients in WHO disease stages 3 and 4 and patient_condition = 0 for the patients in WHO disease stages 1 and 2. Employment status was further categorized as employed (employ_stat =1for formal employment, health worker, self-employed) and unemployed (employ_stat=0 for unemployed, student/ child and other). The Xtset command was used to transform the data into longitudinal data. The Stset command was used to transform the data into survival data. A patient who died during the follow up period was recoded 1 and surviving patient was recoded 0. Missing data were assumed to be missing at random.

Data Analysis

The joint model for the longitudinal process and the survival process was developed by considering the situation where the longitudinal model is the primary model and the survival model is the secondary model. Separate longitudinal model is developed using CD4 cell count as the longitudinal outcome and considering gender, age, profession, marital status, WHO stage and nutritional status as the explanatory variables. Separate survival model using time to death as the outcome variable and considering gender, age, profession, marital status, WHO stage and nutritional status as the explanatory variables is also developed [17].

• Longitudinal Model Development Individual CD4 measurements are plotted overtime and fitting a smoothing spline overtime, to identify general trends within subjects and suggest possible transformations to be done on CD4 data depending on the nature of the distribution. Mixed linear regression models are run in Stata 13 software with CD4 cell count as the outcome variable and gender, age, profession, marital status, WHO stage and nutritional status as the explanatory variables. The Lemeshow-Hosmer statistic was used to determine the covariates to be considered in the model. A full linear mixed effects model (with all the main effects and the time by main effects interactions) is fit using statistically significant and subject matter importance covariates by the Maximum Likelihood Estimation (MLE) method. Backward elimination technique is used in model development with the least statistically significant interaction term removed first.

• Survival Model Development 1. Univariate Kaplan –Meier curves are plotted in Stata 12 on gender, profession, marital status, WHO stage, ART regimen and nutritional status to gain insights on the shape of the survival functions for each group and to check if the groups are proportional (that is if the survival functions are approximately parallel). Univariate Cox proportional hazard regression is done also in Stata 11 on age and weight. 2. A multivariate model that contains all the covariates that are deemed relevant from Univariate analysis is first considered. The statistical significance of each covariate is judged on the corresponding size of the p-value. Covariates with p-value greater than 0.05 will not be included in the model, except for those covariates of known subject matter importance. 3. Interaction terms are generated and added to the multivariate model built above. Interaction terms are tested based on their p-values. Covariates with p-values above 0.05 are disregarded and those with a p-value less than 0.05 are included in the model. The model with interaction terms will be compared to the one without interaction terms. The likelihood ratio test will be used to test the difference between the two models. Proportional hazard test is done in Stata using the stphtest command and we fail to reject proportionality for p-values greater than 0.05.

• Joint Model (longitudinal-survival model) The modified two step method was used to jointly model the longitudinal process (CD4 cell count) and the survival process (survival time). The longitudinal model developed above is taken as the secondary model and the survival model is taken as the primary model. The steps are are shown in Figure 1.

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Demographics

11 930 HIV infected patients were enrolled into the Gweru district ART cohort between January 2006 and December 2010. The following table gives the demographic characteristics of the Gweru district ART cohort (Tables 1-5).

The mean age of the patients was 33.5 years with a standard deviation of 13.8 years. Majority of the patients were in the 15 to 49 years age category and were married. There were more female patients in the cohort.

Mixed Linear Regression Model

The expected CD4 cell count for a HIV infected patient on ART averages 508 across all patients, but shows little variation, with a standard deviation equal to 2. The gain in CD4 cell count is estimated to be 2 units in female patients compared to male patients and differ by a single unit in the nutritional groups. CD4 cell count gain also decreases by a single unit as we move across the age groups in comparison to the below 15 years age group. Overweight and normal weight patients have a gain of a single unit CD4 cell count compared to the underweight patients.

Survival Analysis

From the above results the Kaplan Meier curves for employment status, marital status and nutritional status are not parallel while those for gender, patient condition, place of residence and age group are parallel. The assumption of

Joint longitudinal Survival Model

proportional hazards is violated in many covariates; hence the proportional hazards model may not be applicable.

Survival of ART patients vary by gender; with the hazard of death for female patients being 41% less than that for male patients. Patients above 49 years of age have a hazard of death 7.97 times compared to patients below 15 years. The 15 to 49 years age group has a hazard of death 4.62 times compared to patients below 15 years. This shows that there is an increase in the hazard of death as we move from one age group to another. This is because young patients respond better to treatment than the old because of the differences in their physiology. Patients who were enrolled at WHO disease stages 3 and 4 have a hazard of death 1.89 times compared to patients enrolled at stages 1 and 2.

A statistically significant direct effect of gender on survival was observed -0.003 (95% CI: -001, -0.002). Also, a highly negative significant association was observed -9.48 (95% CI: -11.7, -7.23), indicating that female patients with high levels of lncd4 had reduced hazard of death compared to male patients. Place of residents of the ART patient had a significant direct effect on survival -0.66 (95% CI: -0.01, 0.003). There is also a highly negative significant association -10.0 (95% CI: -12.4, -7.67), indicating that patients in urban areas and with high lncd4 cell counts had a reduced hazard of death compared to patients in rural areas. Age had a direct effect on survival as the hazard of death increases as we move from one age group to another. A highly negative significant association was observed -9.4 (95% CI: -11.6, -7.17) indicating that the hazard of death for patients with high lncd4 decreases as we who move down the age groups.