Evaluation of factors related to longitudinal CD4 count and the risk of death among HIV-infected patients using Bayesian joint models

doi:10.21203/rs.3.rs-4923817/v1

Background

In many epidemiological HIV studies, patients are frequently monitored over time to predict their survival by examining their CD4 levels repeatedly. This study aims to evaluate factors related to longitudinal CD4 count and the risk of death among HIV-infected patients using Bayesian joint models.

Methods

The information of patients who were infected with HIV in Fars Province, from 2011–2016 and followed up until 2022 was used in this study. A joint model of count longitudinal outcome and time to death is used to model information of HIV patients.

Results

The majority of patients were male (64.8%) with a median age of 35 years. During the follow-up, 123 patients (19%) died. The age-standardized mortality and incidence rates from 2011 to 2016 were 0.496 and 2.49 per 100000 person-years respectively. The 1-year and 5-year survival rates are 98% (95%CI: 97%, 99%) and 88% (95%CI: 85%, 91%) respectively. There is a significant association in this model between the CD4 cell count and the risk of death. Age, addiction, and unemployment were all significantly linked to a lower CD4 cell count. Age was positively correlated with the risk of death. Men, unemployed individuals, and those with hepatitis B had a higher risk of death.

Conclusion

In this study, we used the Bayesian joint model to investigate the association between the risk of death and the change in CD4 biomarkers that is repeatedly measured over time to determine the factors associated with the survival of HIV-infected persons. The joint model finds a strong association between the CD4 cell count and the risk of death. The joint model allows for a more comprehensive understanding of the factors influencing the CD4 cell count and survival time, compared to using separate models.

Joint model

CD4 cell count

Longitudinal

Time to death

Association

HIV

Human Immunodeficiency Virus (HIV) remains a significant public health concern globally. According to WHO since the beginning of the epidemic, 85.6 million people have been infected with the Human Immunodeficiency Virus (HIV), and about 40.4 million people have died of HIV. Globally, 39.0 million people were living with HIV at the end of 2022. HIV is also a public health challenge in Iran. According to the latest estimates of the United Nations Program on HIV/AIDS (UNAIDS), a total of 54000 people were living with HIV, and 3200 people died of HIV at the end of 2020 in IRAN[1]. HIV is an infection that attacks the body's immune system, specifically the white blood cells called CD4 cells. HIV destroys these CD4 cells, weakening a person's immunity against opportunistic infections, such as tuberculosis and fungal infections, severe bacterial infections, and some cancers. The CD4 count measures how many CD4 cells are present in a person's blood. A normal CD4 count in a healthy adult ranges from 500 to 1,500 cells per cubic millimeter of blood. HIV is considered to have progressed to AIDS (Acquired Immunodeficiency Syndrome) when the CD4 count drops below 200 cells per cubic millimeter of blood. Monitoring CD4 counts is an important part of managing HIV infection. Low CD4 counts indicate a weakened immune system and an increased risk of opportunistic infections [2].

The number of CD4 cells in a sample of blood can be an important indicator of the strength of the immune system. The trends of CD4 changes are associated with the progress of HIV and the death of HIV-infected persons. Therefore, a decrease in the number of CD4 cells over time suggests the deterioration of the immune system and infection vulnerability [3, 4]. In many medical and epidemiological researches, patients are often followed up over time, and longitudinal measurements are recorded until the time to event of interest. In such studies, the association between the survival of patients and longitudinal markers is commonly of interest. For example, in AIDS clinical trials, CD4 count is the most important clinical measurement that indicates disease progression among HIV/AIDS patients earlier than disease or death. We can use this extra information to improve the accuracy of survival prediction. Analyzing a longitudinal biomarker measuring disease progression, such as CD4 count, and a survival outcome separately can lead to biased estimates of both the biomarker and survival processes, as such an analysis ignores the dependence between the repeated longitudinal measurements and survival. Joint modeling of longitudinal and survival data is preferred to separate analyses both to optimally use the available information and to obtain unbiased estimates of parameters describing both processes[5, 6].

Modeling longitudinal and time-to-event data jointly assumes that the longitudinal outcome offers extra insights into the risk of event occurrence, gaining popularity in the medical field over recent decades. Joint models handle the relationship at the individual level and relate the longitudinal and survival components. This approach allows for the simultaneous analysis of repeated measurements of an outcome and time-to-event data in a single model. One of the key advantages of joint modeling is that it can account for the interdependence between the longitudinal and survival outcomes, allowing for a more efficient and accurate estimation of the effects of covariates on both outcomes. This can lead to more precise estimates of the risk factors associated with disease progression and mortality in HIV patients. In this study, we explored factors associated with survival time in HIV-infected individuals using a Bayesian joint model.

2.1. Data collection

In this study, we used the information of patients who were infected with HIV in Fars Province, from June 29, 2011, to March 15, 2016, and they were followed up until May 12, 2022. The information on patients who are infected with HIV is used in this study. The database was not frozen and is still ongoing. The main dataset contained the information of 1028 patients, but the longitudinal CD4 measurements were not recorded for 282 patients. This data included an unbalanced longitudinal dataset. Among the 746 patients in the dataset, those with only one CD4 measurement were excluded. Ultimately, 628 HIV-positive patients with two or more CD4 measurements were included for statistical analysis. There was no significant difference in the demographic information of individuals with and without repeated CD4 measurements. The frequency of CD4 measurements varied between 2 to 20 times over the follow-up period. However, the CD4 cell count of most of the patients (about 51%) was measured at most 11 times. Demographic and clinical characteristics of patients in the study such as gender, marital status, age, and co-infection with hepatitis B virus (HBV) have been recorded. CD4 cell count from baseline to a maximum of 20 times afterward and time-to-death (time from onset to study until death due to HIV/AIDS in years) have been recorded. The study protocol was approved by the ethics committee of Shiraz University of Medical Sciences (IR.SUMS.REC.1402.280).

2.2. Statistical Analysis

Variables were summarized and demonstrated as frequency (%) for categorical variables or median (IQR) for continuous variables. We used a Bayesian joint model to analyze the longitudinal and survival data. The joint model was created from two sub-models; one sub-model relates to a longitudinal process and the other sub-model relates to the survival process. To fit the joint model, we used a generalized linear mixed effects model for the longitudinal sub-model and a Cox regression model for the survival sub-model and linked them by using unobserved random effects through corresponding shared parameters. The outcome variables considered for this study were the longitudinal CD4 count measurement and time to death. Under the Bayesian approach, estimation of the joint model’s parameters proceeds using Markov chain Monte Carlo (MCMC) algorithms.

2.2.1. The longitudinal sub‑model

We have a set of n independent subjects. Assuming independence between subjects, let $\:{\text{Y}}_{\text{i}\text{j}}$ denote the longitudinal response (CD4 cell count) for subject $\:\text{i}=1,\:2,\:\dots\:,\:\text{n}$ at time $\:\text{j}$ for $\:\text{j}=1,\:2,\:\dots\:,\:{\text{n}}_{\text{i}}$. Let $\:{\text{Y}}_{\text{i}}$ denote the $\:{\text{n}}_{\text{i}}$×1 longitudinal response vector for the ith subject, with element $\:{\text{Y}}_{\text{i}\text{j}}$ denoting the value of the longitudinal outcome taken at time point $\:{\text{t}}_{\text{i}\text{j}}$. The distribution of $\:{\text{Y}}_{\text{i}}$ is

$$\:{\text{Y}}_{\text{i}}\sim\;Poisson\left({{\lambda\:}}_{\text{i}}\right)$$

$\:{{\lambda\:}}_{\text{i}}\:$ depends on the covariates via logarithmic link function as:

$$\:{log}\left({{\lambda\:}}_{\text{i}}|{b}_{i}\right)=\:{x}_{i}^{t}\left(t\right)\beta\:\left(t\right)+{z}_{i}^{T}{b}_{i}={\eta\:}_{i}\left(t\right)$$

$\:{\text{x}}_{\text{i}}\left(\text{t}\right)$ and $\:{\text{z}}_{\text{i}}\left(\text{t}\right)$ denote the design vectors for the fixed effects $\:{\beta\:}$ and the random effects $\:{\text{b}}_{\text{i}}$, respectively. The random effects are assumed to follow a multivariate normal distribution with mean zero and variance-covariance matrix D.

2.2.2. The survival sub-model

For the survival process, we assume that the risk for an event depends on a function of the subject-specific linear predictor $\:{{\eta\:}}_{\text{i}}\left(\text{t}\right)$. More specifically, we have

$$\:{h}_{i}\left(t\right)={h}_{o}\left(t\right)exp\{{w}_{i}^{T}\left(t\right)\:\gamma\:+f\left\{{\eta\:}_{i}\left(t\right)\right\}\alpha\:\}$$

$\:{\text{h}}_{0}\left(\text{t}\right)\:$ denotes the baseline hazard function, $\:{\text{w}}_{\text{i}}\left(\text{t}\right)$is a vector of exogenous, possibly time-varying, covariates with corresponding regression coefficients $\:{\gamma\:}$. Parameter vector $\:{\alpha\:}$ quantifies the association between features of the marker process up to time t and the hazard of an event at the same time point.

Parameters in the joint model were estimated under the Bayesian framework and implemented using Markov chain Monte Carlo (MCMC) methods. All statistical analyses were performed using R software, version 4.4.1 with JMBayes2 package at a significance level of 0.05.

3.1. Descriptive Result

The median age of patients was 35 years ($\:{Q}_{1}-{Q}_{3}=\:$interquartile range (IQR) =10.25). The higher percentage of patients were male (64.8%) with a median age of 35 years (IQR=11). The median of baseline CD4 cells was 256 (IQR=336 cells/mm3). Follow-up times varied between individuals and in total, 6028 measurement occasions were available with a median number of visits per subject was 6 (IQR= 6). During the follow-up, 123 patients (19%) died. 67.2% of patients have a history of unsafe sexual behavior, 32% of patients have a history of unsafe injection, 61.4% have a history of addiction, 58.3% of them were unemployed and, 5.7% have hepatitis B. 47.4% have been infected with this virus through injection addiction, 39.3% through sexual intercourse and 4.13% through mother-to-child transmission.

The 1-year and 5-year survival rates are 98% (95%CI: 97%, 99%) and 88%(95%CI: 85%, 91%) respectively. More details about the demographic and clinical characteristics of the patients by the years from 2011 to 2016 are shown in Table 1. Figure 1 shows an apparent non-linearity of the subject-specific CD4 count profiles for 63 randomly selected individuals. The Kaplan-Meier survival plot is shown in Figure. 2, females, employed individuals, and those without hepatitis B had a higher survival rate.

The computation of age-standardized incidence and mortality rate (per 100000 population) is shown in Table 2. The incidence rate of HIV (per 100000 people) was reported by age group. The age-standardized mortality and incidence rates during the years 2011 to 2016 were 0.496 and 2.49 per 100000 person-years respectively.

Table 1. Demographic and clinical characteristics of patients in the study

Years

2011

2012

2013

2014

2015

2016

Total

No. of cases

88

118

131

107

145

39

628

No. of Death

(Until 2022)

19

25

24

23

22

10

123(19%)

1-year survival

(95% CI)

98%

(95%, 100%)

100% (100%,100%)

96%

(93%, 100%)

99%

(97%, 100%)

98%

(96%, 100%)

92%

(84%, 100%)

98% (97%,99%)

5-year survival

(95% CI)

89%

(82%, 96%)

92%

(88%, 97%)

88%

(82%, 94%)

84%

(77%, 91%)

89%

(84%, 94%)

79%

(68%, 93%)

88%

(85%,91%)

Gender

Male

Female

62

26

82

36

82

49

67

40

90

55

24

15

407(64%)

221(36%)

Age

1st Qu.

Median

3rd Qu.

27

34

39

30

33

38

29

34

39

31

35

42

30

35

44

35

38

44

29.75

35

40

Marital status

Married

Single

Unknown

41

46

1

52

66

0

61

70

0

49

58

0

71

74

0

20

19

0

294(46.8%)

333(53.0%)

1(0.2%)

Educational level

Diploma &less

Academic

Unknown

83

5

0

125

9

0

122

6

3

102

4

1

134

7

4

34

5

2

579(92.6%)

36(5.73%)

10(1.59%)

History of unsafe sexual behavior

Yes

No

Unknown

58

30

0

50

34

4

50

1

74

30

3

102

42

1

28

11

0

422(67.2%)

197(31.3)

9(1.5%)

History of addiction

Yes

No

Unknown

62

23

3

73

41

4

75

55

0

65

41

1

84

60

1

26

13

0

386(61.4)

233(37.1%)

9(1.5%)

History of unsafe injection

Yes

No

Unknown

58

30

0

40

13

65

40

14

77

35

6

66

38

14

93

10

4

25

201(32.0%)

58(9.2%)

369(58.7)

Result hbsag test

Positive

Negative

Unknown

7

74

7

6

108

4

8

117

6

5

94

8

131

6

35

2

36(5.7%)

559(89.0%)

33(5.3%)

Job

Employed

Unemployed

Unknown

42

46

0

53

64

1

53

78

0

37

68

2

47

92

6

19

18

2

251(40.0%)

366(58.3)

11(1.7%)

TransmissionWay

Addiction

Sex

MotherToChild

Unknown

55

26

3

4

58

47

7

6

61

57

4

9

49

3

6

58

53

9

25

17

15

0

7

298(47.4%)

247(39.3%)

26(4.13%)

57(9.07)

Table 2 Computation of age-standardized incidence and mortality rate (per 100000 population)

Age group	No. of cases	No. of death	person at risk in 2011–2016 Fars province	Mortality rate Per 100000 population	Incidence rate Per 100000 population	standard population WHO
0–4	15	0	1915000	0	0.783289817	88569
5–9	10	1	1765000	0.056657224	0.566572238	86869
9–14	2	0	1660000	0	0.120481928	85969
15–19	2	0	1797500	0	0.111265647	84670
20–24	44	3	2315000	0.129589633	1.900647948	82171
25–29	110	19	2710000	0.701107011	4.05904059	79272
30–34	158	32	2455000	1.303462322	6.435845214	76073
35–39	136	25	1912500	1.307189542	7.111111111	71474
40–44	74	20	1565000	1.277955272	4.728434505	65876
45–49	42	14	1342500	1.04283054	3.12849162	60378
50–54	13	1	1142500	0.087527352	1.13785558	53681
55–59	14	5	950000	0.526315789	1.473684211	45484
60–64	8	3	697500	0.430107527	1.146953405	37186
total	628	123	22227500	0.553368575	2.825328984	917672

3.2. Joint Model Result

The effects of the various predictors on the hazard of death as well as the trend of CD4 cell count based on the joint model using the MCMC method were given in Table 3. We examined the proportional hazards assumption and excluded the transmission way from the model because this assumption was not met.

We find a strong association between the CD4 cell count and the risk for death, with a unit decrease in the marker corresponding to an exp(−(− 0.6981)) = 2.01-fold increase in the risk for death. Table 3 represents the result of joint models. In addition, the results of the longitudinal model for the CD4 cell count are represented in Table 3 (a). According to the results, having higher ages (P < 0.0001), addiction (P = 0.0424), and those who are unemployed (P < 0.0001) were associated with a decreased count of CD4 cells significantly. Those with academic education (P < 0.0001) had more CD4 cells.

Table 3

The results of the joint modeling of longitudinal measurements (CD4 cell count) and time to event (death) for the HIV/AIDS patients
a) Survival Outcome
Crude						Adjusted
Variable	Mean	StDev	2.5%	97.5%	P	Mean	StDev	2.5%	97.5%	P
Age	0.0326	0.0119	0.0094	0.0552	0.0046	0.0415	0.0097	0.0228	0.0609	0.0000
Gender(Female)	-0.8359	0.3140	-1.4702	-0.2469	0.0016	-0.7470	0.4329	-1.6115	-0.0471	0.0360
Unsafe Injection(No)	-0.2312	0.0094	-0.8815	0.4875	0.4610	-	-	-	-	-
Unsafe Sex(No)	-0.0627	0.2689	-0.5762	0.4613	0.808	-	-	-	-	-
Addiction(Yes)	0.8638	0.3241	0.2641	1.5157	0.0030	0.4826	0.631	-0.2645	1.881	0.2268
Marital(Single)	0.0781	0.2471	-0.3915	0.5525	0.7618	-	-	-	-	-
Education(Academic)	-0.2954	0.7162	-1.8475	0.8897	0.7296	-	-	-	-	-
Job(Unemployed)	0.3295	0.2512	-0.1438	0.8210	0.1974	0.6645	0.2010	0.2592	1.0649	0.0004
Hepatitis B result(negative)	-0.8437	0.3908	-1.5440	-0.0363	0.0404	-0.7985	0.3397	-1.4356	-0.0802	0.0280
Value(CD4)						-0.6981	0.0684	-0.8297	-0.5588	0.0000
b) Longitudinal Outcome
Crude						Adjusted
Variable	Mean	StDev	2.5%	97.5%	P	Mean	StDev	2.5%	97.5%	P
Age	-0.0168	0.0026	-0.0220	-0.0116	0.000	-0.0305	0.0055	-0.0375	-0.0201	0.0000
Gender(Female)	0.3350	0.0662	0.2055	0.4658	0.000	0.4461	0.1428	0.1842	0.6343	0.0000
Unsafe injection(No)	0.0055	0.1194	-0.2298	0.2333	0.9618	-	-	-	-	-
Unsafe Sex(No)	-0.0657	0.0697	-0.2032	0.0682	0.3578	-	-	-	-	-
Addiction(Yes)	-0.3969	0.0658	-0.5275	-0.2701	0.000	-0.0567	0.0370	-0.1032	0.0089	0.0404
Marital(Single)	-0.0776	0.0653	-0.2061	0.0489	0.2426	-	-	-	-	-
Education(Academic)	0.3990	0.1429	0.1231	0.6825	0.0052	0.2613	0.0411	0.1678	0.3275	0.0000
Job(Unemployed)	0.1500	0.0539	0.0198	0.2785	0.0266	-0.6191	0.1658	-0.8370	-0.2991	0.0000
Hepatitis B result(negative)	0.1817	0.1399	-0.0953	0.4529	0.1903	-	-	-	-	-

The risks of death are presented in Table 3 (b). As seen, the variables of age (P < 0.0001) were positively associated with the hazard of death. The risk of death for men was exp(−(− 0.7470)) = 2.11 times more than for women, and among unemployed people it was exp(0.6645) = 1.38 times more than employed people. The risk of death for those with hepatitis B was exp(−(− 0.7985)) = 2.22 times that of those without hepatitis B.

In this study, we used the Bayesian joint model to investigate the association between the risk of death event and the change in CD4 biomarker that is repeatedly measured over time to determine the factors associated with the survival of HIV-infected persons.

The joint model finds a strong association between the CD4 cell count and the risk for death, with a unit decrease in the marker corresponding to a 2.01-fold increase in the risk for death. This finding aligns with the findings of a study carried out in 2019 in North-West Ethiopia, they considered joint latent class modeling to estimate the survival of people living with HIV using CD4 cell counts and time-to-death [7]. They revealed that the risk of death hinged on longitudinal CD4 counts. In another study carried out in 2019 in Iran, the result show that the joint model provided a flexible framework for simultaneous studying of the effects of covariates on the level of CD4 cell count and the risk of progression to TB and AIDS. This model also assessed the effect of CD4 trajectory on the hazards of competing events [8].

According to the result of the joint model, in the survival sub-model: age, gender, job status, and Hepatitis B were statistically significant on the risk of death at a 5% confidence level. These results are in line with a study conducted in 2017 in Fars province in Iran, they used Time-varying Cox regression analyses, the findings of this study implied that some variables could play the role of risk factors in HIV patients, and shorten the patient’s life span e.g. older age, female gender, unemployment, delay in HIV diagnosis, drug injection, and higher Hemoglobin levels [9]. According to our result of the joint model the risk of death was higher in males than females in as much as HIV-infected males were 2.11 times at risk of death than HIV-infected females. This result is consistent with the results of a study conducted in 2019 [10] in which the risk of death in males was 5.145 times the risk of death in females. Similarly, this result is in agreement with those observed in earlier studies [11]. In some studies the causes of shorter survival time in HIV-infected males versus females may be different, for instance, females in earlier stages may be more aware of their infection and take antiretroviral therapy[12, 13].

In the longitudinal sub-model of CD4 cell count, the predictors: age, gender, job status, educational level, and addiction were statistically significant at a 5% confidence level. Gender was a significant covariate on CD4 longitudinal outcome and females had a significantly higher CD4 than males [11, 14]. Education significantly affected the level of CD4 cell count. Hence, more educated patients have a better understanding of adherence to prescribed medication and this further leads to better CD4 cell count as compared to uneducated patients. The result obtained in the current research is consistent with one of the previous investigations [15]. The risk of death for those with Hepatitis B was 2.22 times that of those without hepatitis B. From a clinical point of view, hepatitis B increases the risk of AIDS or death for newly diagnosed patients, even if it is not statistically significant [16, 17]. According to our results, those who are unemployed were associated with a decreased count of CD4 cells significantly. This result is consistent with the results of a study conducted in 2021 in Ethiopia[18]. The risk of death among unemployed people was 1.38 times more than employed people. Increases in unemployment are associated with increased HIV mortality [19]. According to our results, addiction variables were significantly effective in the decreased CD4 counts. The result was also consistent with the previous research [20].

In this study, a joint model was used to analyze the longitudinal CD4 cell count and the survival time data. The association parameter between the longitudinal and survival components was statistically significant. This significance suggests a strong association between the CD4 cell count and the survival time of HIV patients. Patients with higher CD4 cell counts have better survival prospects compared to those with lower CD4 cell counts.

Previous studies have shown that joint models in contrast to separate models can lead to unbiased and more efficient estimates of parameters[21, 22]. The use of the joint model allows for a more comprehensive understanding of the factors influencing both the CD4 cell count and survival time, compared to using separate models [23, 24]. Based on the significant parameters in the joint model, patients with better socioeconomic status have a lower risk of mortality. Patients with higher socioeconomic status are more likely to have access to appropriate dietary and medication management, which can lower their mortality risk. One of the limitations we faced in this study was the issue of repeated measurements of CD4 cell counts, which required a minimum of two measurements per individual. Due to the lack of repeated measurements for each individual, a large number of individuals had to be excluded from the study, this limitation in the available data led to a reduction in the final sample size that could be included in the analysis using the joint modeling approach. A Bayesian joint modeling approach enables individualized predictions of HIV progression and mortality by monitoring patients' CD4 counts [25]. It is also recommended that further studies that use the joint model for dynamic prediction on this data.

The joint model using the MCMC method revealed a strong association between CD4 cell count and the risk of death in HIV-infected individuals. The joint model offered a flexible framework for simultaneously examining the impacts of various factors on CD4 cell count levels and the risk of death. It also allowed us to evaluate the influence of CD4 trajectory on the risk of death in HIV patients. Decreased CD4 cell count was significantly associated with higher age, addiction, unemployment, and lack of academic education. Age and gender were positively associated with the risk of death, with men being at a higher risk. Hepatitis B was found to increase the risk of death. Unemployment and addiction were also associated with decreased CD4 cell counts. These findings align with previous studies on HIV-infected individuals.

Ethics approval and consent to participate

We used secondary data which did not require us to contact participants, thus we did not need to obtain ethics approval. The data used in this study was anonymized before its use. Permission to use the data was approved by the Ethics Committee of Shiraz University of Medical Sciences (IR.SUMS.REC.1402.280).

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.

Funding

There is no funding to report.

Author Contribution

All the authors made substantial intellectual contributions to the study. S.Kh. supervised the whole research work, S.S.P. wrote, analyzed statistics, and interpreted results, M.N. data collection. All authors participated in editing the article. All authors approved the submission of this article. The authors read and approved the final manuscript.

Acknowledgement

We gratefully acknowledge Shiraz University of Medical Sciences for providing the datasets.

Data Availability

The data that support the findings of this study are available from Shiraz University of Medical Sciences but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. We used secondary data which did not require us to contact participants, thus we did not need to obtain ethics approval. The data used in this study was anonymized before its use. Permission to use the data was approved by the Ethics Committee of Shiraz University of Medical Sciences (IR.SUMS.REC.1402.280).

HIV data and statistics. https://www.who.int/teams/global-hiv-hepatitis-and-stis-programmes/hiv/strategic-information/hiv-data-and-statistics
HIV. https://www.who.int/health-topics/hiv-aids#tab=tab_1
Hogg RS, et al. Rates of disease progression by baseline CD4 cell count and viral load after initiating triple-drug therapy. JAMA. 2001;286(20):2568–77.
May MT, et al. Mortality According to CD4 Count at Start of Combination Antiretroviral Therapy Among HIV-infected Patients Followed for up to 15 Years After Start of Treatment: Collaborative Cohort Study. Clin Infect Dis. 2016;62(12):1571–7.
Asar Ö, et al. Joint modelling of repeated measurement and time-to-event data: an introductory tutorial. Int J Epidemiol. 2015;44(1):334–44.
Rizopoulos D, Ghosh P. A Bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time-to‐event. Stat Med. 2011;30(12):1366–80.
Tiruneh F, Chewaka L, Abdissa D. Statistical joint modeling for predicting the association of CD4 measurement and time to death of people living with HIV who enrolled in art, southwest Ethiopia. HIV/AIDS-Research and Palliative Care, 2021: pp. 73–79.
Alafchi B et al. Modeling the trajectory of CD4 cell count and its effect on the risk of AIDS progression and TB infection among HIV-infected patients using a joint model of competing risks and longitudinal ordinal data. Epidemiology, Biostatistics, and Public Health, 2019. 16(4).
Rezaianzadeh A, et al. Determinant factors of survival time in a cohort study on HIV patient using by time-varying cox model: Fars province, south of Iran. Epidemiol Health Syst J. 2017;4(2):145–55.
Shabani N et al. Evaluation of Factors Related to Survival Time in HIV-Infected Persons in Mashhad, Iran, Between 1994–2014: A Bayesian Joint Model. Int J Infect, 2019. 6(3).
Roustaei N, et al. A Comparative Study of Different Joint Modeling Approaches for HIV/AIDS Patients in Southern Iran. Iran J Public Health. 2020;49(9):1776.
Mageda K, Leyna GH, Mmbaga EJ. High Initial HIV/AIDS-Related Mortality and‐Its Predictors among Patients on Antiretroviral Therapy in the Kagera Region of Tanzania: A Five‐Year Retrospective Cohort Study. Volume 2012. AIDS research and treatment; 2012. p. 843598. 1.
Setegn T, et al. Predictors of mortality among adult antiretroviral therapy users in southeastern Ethiopia: retrospective cohort study. AIDS Res Treat. 2015;2015(1):148769.
Liu Y, Liu L, Zhou J. Joint latent class model of survival and longitudinal data: An application to CPCRA study. Comput Stat Data Anal. 2015;91:40–50.
Bayabil S, Seyoum A. Joint modeling in detecting predictors of CD4 cell count and status of tuberculosis among people living with HIV/AIDS under HAART at Felege Hiwot teaching and specialized Hospital, North-West Ethiopia. HIV/AIDS-Research and Palliative Care, 2021: pp. 527–537.
Chun HM, et al. Hepatitis B virus coinfection negatively impacts HIV outcomes in HIV seroconverters. J Infect Dis. 2012;205(2):185–93.
Peters PJ, Marston BJ. Preventing deaths in persons with HIV/hepatitis B virus coinfection: a call to accelerate prevention and treatment efforts. Oxford University Press; 2012. pp. 166–8.
Gebre KK. Joint Modeling in Determinants of Status of Tuberculosis and CD4 Cell Count among Antiretroviral Therapy Attendant of HIV Infected Adults Follow Up in Gondar Teaching Referral Hospital, Gonder, Ethiopia. 2021.
Maulsby CH, et al. A Scoping Review of Employment and HIV. AIDS Behav. 2020;24(10):2942–55.
Khorashadizadeh F, et al. Predicting the survival of AIDS patients using two frameworks of statistical joint modeling and comparing their predictive accuracy. Iran J Public Health. 2020;49(5):949.
Ibrahim JG, Chu H, Chen LM. Basic concepts and methods for joint models of longitudinal and survival data. J Clin Oncol. 2010;28(16):2796–801.
Wang P, Shen W, Boye ME. Joint modeling of longitudinal outcomes and survival using latent growth modeling approach in a mesothelioma trial. Health Serv Outcomes Res Method. 2012;12:182–99.
Erango MA. Comparison analysis of separate and joint models in case of time-to-death event of HIV/AIDS patients under ART follow-up. Open Access Medical Statistics; 2018. pp. 25–33.
Guo X, Carlin BP. Separate and joint modeling of longitudinal and event time data using standard computer packages. Am Stat. 2004;58(1):16–24.
Muhammed FK, et al. Dynamic predictions from longitudinal CD4 count measures and time to death of HIV/AIDS patients using a Bayesian joint model. Sci Afr. 2023;19:e01519.

No competing interests reported.

Evaluation of factors related to longitudinal CD4 count and the risk of death among HIV-infected patients using Bayesian joint models

Status:

Version 1

Abstract

Background

Methods

Results

Conclusion

Figures

1. Introduction

2. METHODS

2.1. Data collection

2.2. Statistical Analysis

2.2.1. The longitudinal sub‑model

2.2.2. The survival sub-model

3. Result

3.1. Descriptive Result

3.2. Joint Model Result

4. Discussion

5. Conclusion

Declarations

Competing interests

Funding

Author Contribution

Acknowledgement

Data Availability

References

Additional Declarations

Status:

Version 1