Modeling the longtiudnal change of viral load of HIV positive patients on antiretroviral therapy

Abstract

HIV/AIDS continues to be a major public health concern and cause of death in the world. Even though WHO recommended viral load testing as the preferred monitoring approach to diagnose and confirm ARV treatment failure, but in most cases, factors influencing the trend of viral load were not well identified. The main objective of this study was to modeling the change of viral load and identifying its associated factors among HIV positive patients. In this retrospective longitudinal data analysis, data was collected from 287 HIV positive patients registered for ART between January 2017 and June 2019 in Zewditu hospital and unstructured covariance structure was parsimonious for the data. Linear mixed model with different random effect were applied to the data. Linear mixed model with random intercept and slope were selected as a best model to fit the data based on different model selection criteria. The findings of the study revealed that there was a decrement over time in the log VL of patients with HIV on ART. Furthermore, time, baseline CD4 count, WHO clinical stage, functional status of the patient, adherence, smoking status, initial ART Regimen and time interaction with adherence and WHO stage were found to be significant predictors of log VL evolution. Linear mixed model with random intercept and slope were selected to fit the data based on different information criteria. There was a significant variation in log VL of patients at baseline and through ART treatment time. Therefore, patients should take ART regimens with good adherence to decrease their viral load over time.

Keywords:

• HIV/AIDS
• viral load
• unstructured covariance structure
• linear mixed model

PUBLIC INTEREST STATEMENT

HIV continues to be a major global public health issue. It is known that how HIV hurts our globe in social as well as in economic aspects. Even though several scientists attempted to discover the medication, but still there is no treatment found that can completely cure the disease. Now, WHO and other huge international health organizations mainly focus on how to prolong the life of those HIV infected peoples and they suggested continuous viral load testing is the leading mechanism to achieve that goal. Although routine viral load testing is the standard of care for people living with HIV on antiretroviral therapy in wealthy countries, the cost of acquiring technology and appropriate laboratory space designated for nucleic acid based tests, the need to train scientists, the lack of access to technical support and infrequent participation in quality assurance programmes limit availability in resource-poor settings.

1. Introduction

Human immunodeficiency virus is a virus spread through certain body fluids that attacks the body’s immune system, specifically the CD4 cells, often called cells. Over time, HIV causes Acquired Immune-Deficiency Syndrome, a condition in which the immune system begins to decline, exposing infected individuals to life-threatening opportunistic infections (Blut, 2016).

The viral load which is the number of HIV viral particles per milliliter of blood, determinations are important prognostic marker of disease progression than CD4 count and, when used appropriately, provide a valuable tool for the management of individual patient (Shoko & Chikobvu, 2019)

Globally, around 74.9 million people have been infected with HIV and 32.0 million people have died of AIDS-related illnesses since its emergence in 1981. By the end of 2018, about 37.9 million people globally were living with HIV of which 36.2 million are adults. Sub-Saharan Africa remains among the hardest hit regions by the pandemic, with nearly one in every 25 adults 4.2% living with HIV, accounting for nearly two-thirds of the global total HIV cases (UNAIDS, 2019).

In Ethiopia, 2018, about 690,000 people were living with HIV and 23,000 people were newly infected with HIV. According to EDHS 2016 report show Gambella region (4.8%) and Addis Ababa (3.4%) to have the highest HIV prevalence rates while Somali (<0.1%), and Southern Nations, Nationalities and peoples (SNNP, 0.4%) regional states have the lowest. The adult HIV prevalence in Ethiopia is 0.9%, with varying burdens by sex, age, and other demographic characteristics, across sub-regions and population groups. The urban HIV prevalence (2.9%) is seven times higher than the prevalence in rural settings (0.4%), women (1.2%) having twice higher HIV prevalence than men (0.6%) (CSA, 2017).

In Ethiopia, there are no studies to the best of our knowledge that documented the area of longitudinal change of viral load among HIV infected patient even in Africa few numbers of studies like (Chendi et al., 2019) with their massive limitations attempted to determine the trend of viral load and its associated factors after patients started ART. Therefore, this study aimed to modeling the change of viral load and identifying its associated factors among HIV-positive patients following ART by applying advanced models that can account for correlation within a patient over time since classical statistical models are not appropriate for longitudinal viral load data.

2. Material and methods

2.1. Study design and period

A retrospective follow-up study was conducted in patients who are 15 and above years of age (adult) from January 2017 to June 2019.

2.2. Study population

Study populations were all adult HIV/AIDS patients on ART at Zewditu Hospital from January 2017 to June 2019.

2.3. Sample size and sampling procedure

As with cross-sectional studies, investigators conducting longitudinal studies need to know in advance the number of subjects approximately required to achieve a specified statistical power (Diggle et al., 2002) suggested that the required number of subjects can be computed by:

$N=\frac{4{\left(\frac{Z\alpha }{2}+Z\beta \right)}^2{\sigma }^2\left(1+\left(m-1\right)\rho \right)}{m{d}^2}$

N is the total sample size, d is effect size sample, m is number of times points repeated measurement was taken, $\rho$ is correlation between repeated measurements, and ${\sigma }^2$ is variance of outcome variable.

Assuming significance level of 0.05, power of 0.8, $\rho$ = 0.475 and effect size of 0.5 from study conducted by Brien et al. (1996), we have m = 6, ${\sigma }^2$=4.06, Using $\frac{Z\alpha }{2}$= 1.96, $Z\beta$=0.842 and inserting all quantities in the formula:

$N=\frac{4{\left(1.96+0.842\right)}^{2}4.06\left(1+\left(6-1\right)0.475\right)}{6\ast 0.5\ast 0.5}=287$

Therefore, the final sample size for this study was 287.

Sampling frame was prepared by collecting the identification number of RVI patients from the registration book. After identifying the patients who fulfill inclusion criteria, study subjects were selected by simple random sampling technique.

2.4. Variables in the study

2.4.1. Dependent variable

In this study, viral load in copies/ml is used as a dependent variable.

2.4.2. Independent variable

The independent variables are Age, Sex, Marital status, Adherence, Hemoglobin at Baseline, Functional status of patients, WHO RVI clinical-stage, Educational level, Occupation, Baseline CD4 counts, Alcohol use, Cigarette smoking, Initial ART Regimen, History of TB, Opportunistic infection, and Body mass index.

2.5. Linear mixed-effects model

Linear mixed-effects model is an extension of a linear regression model to model longitudinal data for the continuous response. It contains fixed effects and a random-effects model. In the context of longitudinal data, there are three special cases of LMMs. The first one is the random intercept model, which is the simplest type of linear mixed model, the second one is random slope model and the last one is a random intercept and slope model.

2.6. Estimation of parameters in linear mixed models

The most often used methods of estimation in Gaussian mixed models are maximum likelihood and restricted maximum likelihood. The REML procedure is most popular when it comes to the estimation of variance components in mixed models assuming Gaussian random terms. REML maximizes the joint likelihood of all error contrasts rather than of all contrasts as in ordinary maximum likelihood (Feddag & Mesbah, 2006).

2.7. P-Value

A p-value is a measure of the probability that an observed difference could have occurred just by random chance. P-value can be used as an alternative to or in addition to pre-selected confidence levels for hypothesis testing. It is a common practice among medical researchers to quote whether the test of hypothesis they carried out is significant or non-significant and many researchers get very excited when they discover a “statistically significant” finding without really understanding what it means. Additionally, while medical journals florid of statement such as: “statistical significant”, “unlikely due to chance”, “not significant,” “due to chance”, or notations such as, “P > 0.05”, “P < 0.05”, the decision on whether to decide a test of hypothesis is significant or not based on P value has generated an intense debate among statisticians.

2.8. Result and discussion

The mean baseline age of patients was 36.93 years with a standard deviation of 12.04 years whereas, the mean baseline CD4 count was 296.51 cells/mm³ with a standard deviation of 158.79 cells/mm³. Also patient’s average hemoglobin level at the baseline was 13.67 g/dl with a standard deviation of 6.43 g/dl (Table 1).

Table 1. Descriptive Statistics of Continuous Covariates at baseline for HIV/AIDS patients under ART in Zewditu Hospital, Jan 2017 to Jun 2019

	Baseline CD4 count	Body mass index	Baseline Hemoglobin	Baseline age
Mean	296.51	22.02	13.67	36.93
Std. Deviation	158.79	3.9	6.43	12.04

Looking at the sex distribution, more than half 56.4% of them were females. About 9.4% of patients had no formal education, 28.9% had primary education, 40.4% had secondary education and 21.3% had tertiary education level. Considering the marital status of the patients, 30.3% were single, 48.1% were married while a smaller number 2.4% were separated. Also, 33.4% of the patients were alcohol users and 16.4% had smoking status (Table 2).

Table 2. Percentages of the socio-demographic characteristics of HIV/AIDS patients on ART in Zewditu Hospital, Jan 2017 to Jun 2019

Variables	Category	Frequency	Percent (%)
Sex	Male	125	43.6
	Female	162	56.4
occupation	Government employed	45	15.7
	Private	93	32.4
	Merchant	34	11.8
	Driver	19	6.6
	Student	42	14.6
	House wife	54	18.8
Marital status	Single	87	30.3
	Married	138	48.1
	Divorced	27	9.4
	Widowed	28	9.8
	Separated	7	2.4
Educational Status	Primary	83	28.9
	Secondary	116	40.4
	Tertiary	61	21.3
Alcohol	No	191	66.6
	Yes	96	33.4
Smoking Status	No	240	83.6
	Yes	47	16.4

About 53.3% of the patients were at clinical stage 1, 15.7% were at clinical stage 2, 20.6% were at clinical stage 3 and the rest 10.5% were at clinical stage 4 at the time of starting the ART treatment. On the other hand, the predominant ART regimen prescribed for patients at baseline was a combination of (TDF-3TC-EFV). Also, about adherence, 65.9% patients who had good adherence status (Table 3).

Table 3. Percentages of the clinical characteristics of HIV/AIDS patients onART in Zewditu Hospital, Jan 2017 to Jun 2019

Variables	Category	Frequency	Percent (%)
WHO clinical stage	Stage 1	153	53.3
	Stage 2	45	15.7
	Stage 3	59	20.6
	Stage 4	30	10.5
Initial ART regimen	AZT-3TC-NVP	69	24.0
	AZT-3TC-EFV	31	10.8
	TDF-3TC-EFV	142	49.5
	TDF+3TC+NVP	45	15.7
Functional status	Working	234	81.5
	Ambulatory/bedridden	53	18.5
Adherence	Good	189	65.9
	Fair	56	19.5
	Poor	42	14.6
History of opportunistic infection	No	229	79.8
	Yes	58	20.2
History of TB	No	240	83.6
	Yes	47	16.4

3. Final result of linear mixed effects model with AC errors

3.1. Parameter estimates for full linear mixed-effects model

Based on Table 4, the time had a significant effect on the log VL of patients, keeping the effect of other covariates constant over time the average log VL of an individual decreased by a cubic time effect. But specifically, individuals who have fair and poor adherence have additional 0.0106 copies/ml and 0.0185 copies/ml increments respectively, in their log VL for a one-unit increment in the duration of treatment. Conversely, individuals who are at WHO stage 3has a significant decrement in their log VL by 0.0042 copies/ml for a unit increment in time.

Table 4. Parameter estimates for full linear mixed-effects model

Fixed effects	Estimate	95 % CI		p-value
		Lower	Upper
Intercept	4.1476	3.9682	4.3269	0.0000
Time	−0.1773	−0.1943	−0.1604	0.0000
Time^2	0.0078	0.0065	0.0092	0.0000
Time^3	−0.0001	−0.0002	−0.00009	0.0000
baseline_CD4	−0.0011	−0.0013	−0.0008	0.0000
WHO Clinical Stage
Stage 1	Ref.
Stage 2	0.0148	−0.1672	0.1968	0.8734
Stage 3	0.1908	0.0191	0.3625	0.0295
Stage 4	0.3434	0.0953	0.5915	0.0067
Adherence
Good	Ref.
Fair	0.3736	0.2047	0.5425	0.0000
Poor	0.6595	0.4431	0.8759	0.0000
Functional Status
Working	Ref.
Ambulatory/bedridden	0.2299	0.1089	0.3509	0.0002
Smoking Status
No	Ref.
Yes	0.1679	0.0491	0.2868	0.0058
ART Regimen
AZT-3TC-NVP	Ref.
AZT-3TC-EFV	−0.1728	−0.3357	0.0099	0.0949
TDF-3TC-EFV	−0.1855	−0.3128	−0.0582	0.0043
TDF+3TC+NVP	−0.1298	−0.2821	−0.0226	0.0376
Adherence × Time
Good × Time	Ref.
Fair × Time	0.0106	0.0016	0.0196	0.0206
Poor × Time	0.0185	0.0067	0.0302	0.0021
WHO Clinical Stage × Time
Stage 1 × Time	Ref.
Stage 2 × Time	−0.0016	−0.0124	0.0093	0.7791
Stage 3 × Time	−0.0042	−0.0138	−0.0015	0.0391
Stage 4 × Time	−0.0021	−0.0152	0.0111	0.7572

Ref. =reference category

Regarding an individual’s functional status, patients who are either ambulatory or bedridden in their functional status have an average 0.2299 copies/ml exceedance in their log VL, as compared with those who have working functional status. Also, patients who have smoking habits have average 0.1679 copies/ml exceedance in their log VL, as compared with those who have no smoking habit with keeping the effect of other covariates constant.

The importance of treatment was strongly revealed from this study. Keeping the effect of other covariates constant, taking a combination of (TDF-3TC-EFV) drug lowers patients log VL by 0.1855 copies/ml on average as compared to those who take a combination of (AZT-3TC-NVP) drug. Furthermore, patients who take a combination of (TDF+3TC+NVP) drug also have a lower log VL as compared to those who take a combination of (AZT-3TC-NVP) drugs (Table 4).

3.2. Estimates of random components

The residual standard deviation is =0.4115 and for the random effects, ${\sigma }_{b0i}$ = 0.4864 and ${\sigma }_{b1i}$=0.0163. The total variability between individuals is estimated as ${\sigma }_{b0i}$+ ${\sigma }_{b1i}$= 0.5027 whereas the total variability within an individual is 0.4115. However, the total variation in log VL is estimated to be 0.5027 + 0.4115 = 0.9142. The proportion of total variability that is attributed to within-person variation is given by 0.4115/0.9142 is 45.01% while the proportion of total variability attributed to between individual variations in their general level of log VL is 0.5027/0.9142 is 54.99%. Therefore, more than half of the variation is explained by random effects. Finally, the correlation between the intercept and linear trend is negative; it equals −0.925, which is very strong in size (Table 5).

Table 5. Estimates of random components

Random components	Estimate
${\sigma }_{boi}$	0.4864
${\sigma }_{b1i}$	0.0163
${\rho }_{boi\hspace{0.17em}b1i}$	−0.925
${\sigma }_{\epsilon }$	0.4115
Intra class Correlation (ICC)	0.5499

4. Discussion

uration of treatment has a positive effect on HIV positive patients. For a one-unit increase in treatment duration, the log VL of patients decreased; this finding is in line with studies in Cameroon (Chendi et al., 2019). This means patients with a longer time on treatment have a lower viral load than those of patients with a short duration on the treatment.

When compared with patients at a fair and poor adherence status, those at good adherence have a decreased log VL. This is because the low level of antiretroviral in the body owing to the non-adherence is not sufficient to suppress viral replication, hence leads to the detection of higher viral load in the blood. This indicates that adherence plays an important role in maintaining successful decrement in the viral load of patients. This finding is in agreement with the studies of Bayu et al. (2017) and Hailu et al. (2018).

This study was concordant with a study done by Teshome and Yalew, they showed that starting ART at later stages of WHO (third and fourth) had a risk of poor outcomes as compared as initiation of ART at early stages (Teshome & Yalew, 2015).

There was a significant decrease in the viral load in combination of (TDF-3TC-EFV) and (TDF+3TC+NVP) drugs. This result is in consistent with the study done by Abu-Raddad and Awadand Edwards et al. (2015).

We found an association between cigarette smoking and viral load. Smokers had exceedance in their log VL by 0.1679 copies/ml than non-smokers. This association is supported by evidence from a study conducted in Cameroon (Ande et al., 2015) and in Vietnam (Pollack et al., 2017).

This study also revealed that the baseline functional status of an HIV/AIDS patient is an important predictor of viral load evolution. Being either ambulatory or bedridden increases log VL by 0.2299 when compared with those who are working. This might be due to the fact that those worker patients may have better income that in turn creates an opportunity to get better care and support. This finding is in disagreement with the studies of Sultan et al. (2019).

5. Conclusion

In this study, we have found an overtime decrement in the log VL of patients with HIV on ART. There was a significant variation in log VL of patients at baseline and through ART treatment time. The effects of several factors on the evolution of log VL were identified. Among these times, baseline CD4 count, WHO clinical stage, functional status of the patient, adherence, smoking status, initial ART Regimen, and Time interaction with adherence and WHO stage were found to be significant predictors of log VL evolution. Specifically, patients with a higher duration on treatment, who have high baseline CD4 count, with earlier WHO clinical stage (stage 1 and stage 2), with working status, with good adherence, had no smoking status, used a combination of (TDF-3TC-EFV) and (TDF+3TC+NVP) drugs were significantly reduce in their log VL.

6. Limitations

In this study we used the latest data from medical charts of HIV positive patients initiated to ART. So, there are some limitations. One of the limitations of this study was not included some variables like psychosocial factors (major depression, disclosure, and perceived stress) and other variables (currently lives with other people, and income status). These variables are not included in the patient’s medical charts. The second limitation this study is age restricted. This study was study was conducted in patients who are 15 and above years of age (adult).

Authors’ contributions

Dawit Getachew conceptualized the proposal identified and reviewed all papers, and analysis, and interpretation of data. Dr. Aragaw Eshtie and and Dessie Melese participated in the conception of the study, provided methodological guidance, supervised the analysis, and prepared the manuscript. All authors reviewed the manuscript critically for content and approved the final version to be submitted.

Availability of data and materials

Authors have Considered HIV/AIDS datasets from Zewditu Hospital patient history card and now, attached as supplementary materials of the submission system.

Ethical consideration

Ethical clearance and Letter of cooperation for selected Hospital was obtained from the Institutional Review Board of the University of Gondar. Waiver letters was obtained from the medical director of Zewditu Hospital in order to access the medical records of patients. Confidentiality during all phases of research activities was kept and data was held on a secured password-protected system.

List of abbreviations

AIDS: Acquired Immune Deficiency Syndrome, ART: Anti-Retroviral Therapy, ARV: Anti-Retro Viral, HIV: Human Immunodeficiency Virus, RVI: Retroviral Infection, REML: Restricted Maximum Likelihood, VL: Viral Load

Acknowledgements

The authors are highly thankful to University of Gondar Postgraduate Program Directorate for subsidizing finance throughout the entire study and also we would like to thank Zewditu hospital administrations, data collectors and supervisors for their support during data collection period.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study was financially supported by the Department of Statistics, University of Gondr, Ethiopia. It is a limited standard budget for postgraduate students; basically for data collection and duplication.

Notes on contributors

Dessie Melese Chekole

Mr. Dessie Melese is a Lecturer at University of Gondar, College of Natural and Computational Sciences, Department of statistics Gondar, Ethiopia. He graduated from University of Gondar in statistics (BSc in Statistics and MSc in biostatistics). From August/2011 to June/2016, he served as Junior Statistician at Central Statistics Agency, Gondar Branch, Ethiopia. Currently, he works as a lecturer at University of Gondar, Department of Statistics. His responsibilities are teaching different courses of statistics; consulting and advising students on academic issue and on their senior research project, working on research and community service in both team and individual level and he strongly participating in different national and international conferences and giving/participating different advanced statistical software trainings. He has conducted more than nine research works, including the current on these areas.