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Abstract: The aim of this study is to implement semi parametric
Bayesian analysis for survival of HIV patients, on data obtained
from Debre Berhan Referral Hospital, Ethiopia of HIV-positive
patients enrolled in ART, the time of an event occurring were
taken. The study subjects were enrolled between the Period
January 2012 to January 2018, and attending treatment until the
first month of2018 and all subjects include in this study were
greater than or equal to 16 years old. A total of 1036 patients, who
fulfill the inclusion criteria were selected for the study. Data were
explored using basic descriptive statistics and the censoring status
of categorical variables was presented. Kaplan-Meier estimation
technique was used to asses survival by each covariates category.
semi parametric Bayesian analysis, Cox proportional hazard
model (cox PH) for the survival data analysis were used along with
their prior selection, model estimation, model diagnosis and
Markov Chain Monte Carlo algorithm was used for data
simulation. The base line CD4 cell count, baseline weight, sex, age,
functional status, marital status, WHO-clinical stage, educational
level, age, religion, residence, opportunistic infection were the
covariates in this study. Semi parametric Bayesian analysis
method with cox proportional hazard was used. During model
diagnosis with MCMC and time to death analysis all variables
were significantly determine survival time of patients except
opportunistic infection and regimen class 4. In this time to event
(time to death) data 113(10.90734%) were practicing the event
with median of age 32.00, mean of age is 34.02, first quartile of age
is 27 and third quartile of age is 40. The variables age, WHO
clinical stages, marital status, functional status, baseline CD4,
regimen class, residence were significantly determines the survival
time of patients. Whereas opportunistic infection have no
significance impact on survival time. The variable residence is also
can affect survival time of patients such as 91.44% chance that the
hazard rate of patients live in urban is greater than that of patients
in rural. Analysis of time to death of HIV/AIDS patient by semi
parametric Bayesian is effective. Markov chain diagnostic show
good convergence and almost perfect mixing. But covariate
opportunistic infection and category 4 in regimen class were not
poor in MCMC convergence.
Keywords: MCMC algorithm, Proportional hazard, Semi
parametric Bayesian, Survival data.
1. Introduction
HIV refers to human immunodeficiency virus; it is a
collection of virus those most likely mutated decades ago from
a virus that infected chimpanzees to a virus that infects humans.
It began to spread beyond the African continent in the late
1970s and is now endemic worldwide. HIV causes disease
because it attacks critical immune defense cells and over time
overwhelms the immune system. When HIV positive people
live without treatment, HIV infection starts to cause symptoms
in an average of eight to ten years with opportunistic infection,
opportunistic infection is caused when people have weak
immune function. The period from infection to the cause of
symptom is known as latent period where as the period started
from symptomatic phase up to death referred to as acquired
immune deficiency syndrome (AIDS) or HIV disease Sandra
Gonzalez Gompf (2018). HIV infection leads to low levels of
CD4+T cells that in turn make the body susceptible to
opportunistic infections. According to the UNAIDS (United
Nation for International Development) report, it was estimated
that 33.2 million people lived with the disease worldwide, and
that AIDS killed an estimated 2.1 million people, including
330,000 children. In 2008, an estimated 33.4 million people
were living with HIV/AIDS worldwide; nearly 70% of these
were found in sub-Saharan Africa Sandra Gonzalez Gompf
(2018).
The introduction of ART in 1996 was a turning point for
thousands of people with sophisticated health car. Roughly 75%
of AIDS patients in need of antiretroviral therapy (ART) in the
world still have no access, and most of them live in Africa
(World Health Organization 2006). This despite the fact that the
three by five initiative of the World Health Organization
(WHO), as well as the resources provided by the Global Fund,
greatly facilitated access to ART in all regions of the world and
boosted ART programs in most of sub-Saharan Africa, where
the number of persons treated was multiplied by more than
eight in just 2 years [World Health Organization (WHO) 2006].
The clinical benefit of ART for AIDS patients, in terms of
mortality reduction and improved quality of life, is well
established but shows regional variations, with higher case
fatality rates in poor countries. There are several predictors of
mortality for patients on ART: viral load, CD4 count, total
Implementation of Semi-Parametric Bayesian
Analysis for Survival of HIV/AIDS Patients in
the Case of Debre Berhan Referral Hospital
A. R. Muralidharan1*, Gethahun Mulugeta2
1,2Assistant Professor, P.G. Department of Biostatistics, College of Natural and Computational Science, Debre
Berhan University, Debre Berhan, Ethiopia *Corresponding author: [email protected]
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lymphocytes, body mass index (BMI), and adherence.
Although these determinants tend to be similar across the
world, there are some striking differences in their relative
frequency, example, the much lower baseline CD4 counts of
patients starting ART in poor countries Isidore Sieleunou. et al.
(2009).
Globally an estimated 34 million people were living with
HIV at the end of 2010. United Nation for International
Development and world health organization estimates since the
availability of effective treatment some 2.9 million lives have
been saved. About 68% of all people living with HIV resided in
sub Saharan Africa, a region with only 12% of the global
population in 2010. Ethiopia is the seriously affected countries
in sub Saharan Africa with more than 1.3 million people living
with HIV and an estimated 277,800 people requiring treatment.
The overall Adult HIV prevalence was 1 .4% and 1.5% in 2005
and 2011. The government of Ethiopia launched its free based
ART initiative in 2003 and free initiative in 2005.peoples ever
started ART were 150,136,208,784 and 268,934 respectively in
2008, 2009 and 2010. Peoples who were on ART on the same
year were 109,930,152,472and 207,733 respectively. (Nurilign
Abebe, 2014) The first HIV infection in Ethiopia was reported
in 1984 from stored sera which later expended as an epidemic
similar to elsewhere in sub-Saharan Africa. The 2005
Demographic and Health Survey estimated national adult HIV
prevalence of Ethiopia to be between 0.9%- 2.1%, with
infection levels highest in the Gambella (6%) and Addis Ababa
(4.7%) regions. Recent expansion of surveillance data and
improved analysis has lowered the 2005 estimate drastically.
Antenatal care surveillance data showed declining HIV
prevalence rate in urban areas being 10.1% and stable trend in
rural (1.8%). The highly vulnerable groups include young
women living in urban areas, commercial sex workers and
members of military and policy. In rural areas no significant
gender difference in risk of infection. (Worku, Pattern and
determinants of survival in, 2009) Statistics show that
approximately 40 million people are currently living with HIV
infection, and an estimated 40 million have died from this
disease since the beginning of the epidemic. HIV has been
particularly devastating in sub-Saharan Africa, which accounts
for almost 70% of new HIV infections globally. However,
infection rates in other countries also remain high. Sandra
Gonzalez Gompf, (2018).
Medical and epidemiological studies are mostly conducted
with an interest in measuring the occurrence of an outcome
event. Studies conducting survival analysis, however, are
focused toward measuring time to event or outcome. Time to
event could vary from time to fatal event that is death, or time
to occurrence of a clinical endpoint such as disease, or
attainment of a biochemical marker. Survival analysis studies
originated with the publication of John Graunt’s Weekly Bills
of Mortality in London. First life table was prepared by Healy.
Survival analysis is also known as lifetime data analysis, time
to event analysis, reliability and event history analysis
depending on focus and stream where it is used. However,
survival analysis is plagued by problem of censoring in design
of clinical trials which renders routine methods of
determination of central tendency redundant in computation of
average survival time. The present essay attempts to highlight
different methods of survival analysis used to estimate time to
event in studies based on individual patient level data in the
presence of censoring. (Shankar Prinja, 2010).
The three most commonly used semi parametric Bayesian
survival models, PH, proportional odds (PO), and accelerated
failure time (AFT), is developed and illustrated on several a real
and simulated data sets (Hanson). In this study the focused is
on Semi-parametric Bayesian models along with associated
Bayesian statistical methods. The Semi-parametric nature of the
model allows considerable generality and applicability. But
enough structure for useful interpretation and understanding
particular application in the medical research. Semi-parametric
is a model with two parts, that are parametric (such as
regression coefficients). Particularly in medicine (survival
analysis) and nonparametric parts (such as hazard function).
Semi-parametric models are quite popular, for being a good
compromise between too restrictive parametric and too non-
informative non-parametric models. The popularity of Semi-
parametric approaches for analyzing univariate survival data
begins with the seminal paper of cox (1972) on the proportional
hazard model, Following the path of cox several other survival
analysis following hem (K.Dey 2012). In many practical
situations, a parametric model cannot be expected to describe
in an appropriate manner the chance mechanism generating an
observed dataset, and unrealistic features of some common
models could lead to unsatisfactory inferences. In these cases,
we would like to relax parametric assumptions to allow greater
modeling flexibility and robustness against misspecification of
a parametric statistical model. In the Bayesian context such
flexible inference is typically achieved by models with
infinitely many parameters. These models are usually referred
to as Bayesian Nonparametric (BNP) or Semi parametric (BSP)
models depending on whether all or at least one of the
parameters is infinity dimensional, While BSP and BNP
methods are extremely powerful and have a wide range of
applicability within several prominent domains of statistics. A
direct benefit of MCMC algorithms approach is that the
sampling algorithms can be made dramatically more
efficient(Jara).
2. Objectives
The general objective of this study is to implement the Semi
parametric Bayesian analysis for survival of HIV patients who
follow in the ART.
Specific Objectives
1. To asses time to death of HIV/AIDS patients
2. To apply the semi parametric Bayesian analysis on
survival HIV
3. To identifying factors that affect survival of
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HIV/AIDS patients who were in ART clinic.
3. Data and Methodology
Location of Debre Berhan is a city and woreda in central
Ethiopia. Located in the Semien Shewa Zone of the Amhara
Region, about 120 kilometers north east of Addis Ababa on the
paved highway to Dessie, the town has a latitude and longitude
of 9°41′N 39°32′ECoordinates, 9°41′N 39°32′E and an
elevation of 2,840 meters was an early capital of Ethiopia and
afterwards, with Ankober and Angolalla, was one of the capitals
of the kingdom of Shewa. It is the administrative center of the
Semien Shewa Zone of the Amhara Region. Debre Birhan is
located in Ethiopia (Amhara region) and time zone
Africa/Addis Ababa. Places in the near are Debre Sīna, Abomsa
and Fichē.
The study population was included HIV positive adults
whose age is started from 16 and above initiated ART treatment
in the Debre Berhan Referral Hospital. All patients who have
initiated to ART and their baseline CD4 cell count, baseline
weight who started first line regiment class wasincluded in the
study population, while patient started ART with their age is
less than 16 years old and patient who starts ART before
January 2013 and after January 2018 are not included in the
study population. All patients who fulfill the inclusion criteria
were included in the study. When the data is recording from
medical charts Identification numbers were used to each
individual patients to make it easy to identify individuals
visiting profile by keeping patients medical secrete.
Study Variables
The interest of the study is survival analysis; the data have
the nature of time-to-event, from the time started medication in
the ART clinic to the occurrence of an event (or occurrence of
death).
Response Variable
Time to event of interest is the dependent variable. This data
is with the “Right censored observation”. This was computed
as the time difference between the event occurred and the time
of the ART started (initiated).
Death (Code: Event=1 No Event =0)
Explanatory variables
4. Data analysis
This study aimed at Implementation of the semi-parametric
Bayesian for survival of HIV patients. In order to address the
objectives of the study, 1036 patient population of Debre
Berhan referral hospital patients of HIV in the ART treatment
were taken. In the case of analysis the SAS (Statistical Analysis system) software with PHREG procedure were used. In the
semi parametric Bayesian analysis selected model was cox
(PH) with constant prior known as uniform prior for models
parameter. In this section results obtained from descriptive data
analysis and from Semi parametric Bayesian will be presented.
Baseline Demographic Factors
The baseline covariates of this study were compared by cross
tabulation. It shows the distribution of patients in each category.
And also association of explanatory covariates is checked by
Pearson chi-square test. Table of this result are shown below.
Table 2 Patients with their censoring status 60.4% of censored
patients were females and 6.3 % of females were died and 28.7
% of males were censored, 4.6% of male patients were died.
Regarding functional status 91.0% of working patients were
censored, 85.0% of working patients were died, 8.1% of
ambulatory patients were censored, 9.7% of ambulatory patients were died, 0.9% of bed ridden patient were censored,
5.3% of bed ridden patients were died. the other classification
of the patients were WHO clinical stages there are four clinical
stages these are stage I 47.9% of patients in stage I were
censored, 18.6% of patients in stage I were died, the in
in stage II 20.7% of patients in stage II were censored, 29.2%
Table 1
Explanatory Variables (Code)
Table 1a
Measures Taken (Time, weight and CD4 Count)
Variable Names Time Weight CD4 count
Measures Taken In months Baseline Weight of the patients Baseline CD4 cell count
Table 1b
Age
Age 16-25 26-35 36-45 46-55 56-65 >65
Code 1 2 3 4 5 6
Table 1c
Sex
Sex Marital status Religion Education Residence Functional status Opportunistic illness Code
Female Single Orthodox No education Rural Working Yes 0
Male Married Muslim Primary Secondary and Urban others No 1
--- Other Protestant Tertiary school level ------ 2
Table 1d
WHO Stages and Regimen classes
Code 0 1 2 3 4
WHO Clinical Stages Stage 1 Stage2 Stage3 Stage4 ---
Regimen Classes AZT-3TC-NVP, AZT-3TC-EFV TDF-3TC-EFV TDF-3TC-NVP, ABC-3TC- NV
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of patients in stage II were died in stage III 26.9% of patients in
stage III were censored,46.0% of patients in stage III were died,
in stage IV 4.6% of patients in stage IV were censored, 6.2% of
patients in stage IV were died. In opportunistic infection 4.6%
of patients without opportunistic infection were censored,
100.0% of patients without opportunistic infection were died,
95.4% of the patients with opportunistic infection were
censored and 0.0% of the patients with opportunistic infection
were died. The other category of patients is regimen class 8.4% of censored patients were use AZT-3TCNVP, 0.8% of died
patients were use AZT-3TC-NVP,3.0% of censored patients
were use AZT-3TC-EFV, 0.2% of censored patents were use
AZT-3TC-EFV. 72.2% of censored patients were use TDF-
3TC-EFV. 8.3% of died patients were use TDF-3TC-EFV.
3.2% of censored patients were use TDF-3TC-NVP. 1.6% of
censored patients were used TDF-3TC-NVP, 5.9% of censored
patients were use ABC-3TC-NVP. The patients were classified
based on their educational status 14.4% of not educated patients
were censored, 15.9% of not educated patients were died. The
second category in educational level is primary educational
level 47.7% of primary educated patients were censored, 48.7% of primary educated patients were died. 30.3% of secondary
educated patients were censored, 26.5% of secondary educated
patients were died, 7.6% of tertiary educated patients were
censored, 8.8% of tertiary educated patients were died. Patients
Censoring status with marital status 30.4% of single patients
were censored, 17.7% of single patients were died. The second
categories of marital status 40.2% of Married patients were
censored, 40.7% of married patients were died. 29.4% of other
category of marital status of patients were censored, 41.6% of
other category of marital status of patients were died. The
patient based on religion as 93.3% of orthodox patients were censored, 94.7% of orthodox patients were died. 2.0%of
Muslim patients were censored, 0.9% of Muslim patients were
died.4.8% of protestant patients were 1.5% of patients live in
rural area were censored, 1.8% of patients live in rural area were
died. 98.5% of patients live in urban area censored and 98.2%
of patients live in urban area were died. In table 4.1 the last
column is Pearson chi-square test and level of significance,
these shows us censoring status of patients association with
other covariate.
From Table 3 in the case of opportunistic infection the
patients were classified as patients with opportunistic infection
and patients without opportunistic infection in the number of
patients without opportunistic infection in their functional
status is working patients without opportunistic infection were
12.8%, working patients with opportunistic infection were 77.5
and 2.1%,of widowed and divorced patients with opportunistic
infection, 7.5%of widowed and divorced patients without
opportunistic infection. 4.1% of censored patients without
opportunistic infection whereas 85.0% of censored patients
with opportunistic infection. 10.9% of died patients without
opportunistic infection, death patients with opportunistic
infection were 0.0%. Patients in educational level 2.4% of not
educated patients were without opportunistic infection 12.2%
of not educated patients with opportunistic infection.7.4%of
primary educated patients were without opportunistic infection,
40.3%.of primary educated patients were with opportunistic
infection, 3.9% of secondary educated patients were without
opportunistic infection, 26.1%vof secondary educated patients
were without opportunistic infection, 1.3%of tertiary educated
patients were with opportunistic infection In marital status 3.6%
of single patients were without opportunistic infection, 25.5%of
single patients were with opportunistic infection, 5.5% of
married patients were without opportunistic infection, 34.7% of
married patients were with opportunistic infection. 5.9% of
widowed and divorced patients were with opportunistic
infection, 24.8% of widowed and divorced patients were with
opportunistic infection. Patient’s category in religion 14.1% of
orthodox patients were without opportunistic infection, 79.3%
of orthodox patients were with opportunistic infection, 0.2% of
Muslim patients were without opportunistic infection, 1.6% of
Muslim patients were with opportunistic infection, 0.7% of
Protestant patients were without opportunistic infection, and
Table 2
Cross table for Censoring status with covariates
Covariate\Category Censoring Status(Count)
Chi-Square (P-Value) Censored
N (%)
Death
N (%) Covariate Category
Functional Status Working 840(81 .1) 96(9.3) 15.428(0.040)
Other 83(8.0) 17(1.6)
Educational Status No education 133(12.8) 18(1.7) 0.872*(0.832)
Primary 440(42.5) 55(5.3)
Secondary 280(27.0) 30(2.9)
Tertiary 70(6.8) 10(1.0)
Marital Status Single 281(27.1) 20(1.9) 10.543(0.005)
Married 371(35.8) 46(4.4)
Others 271(26.2) 47(4.5)
Religion Orthodox 861(83.1) 107(10.3) 0.699*(0.176)
Muslim 18(1.7) 1(0.1)
Protestant 44(4.2) 5(0.5)
Residence Rural 14(1.4) 2(0.2) 0.042*(0.837)
Urban 909(8.7) 111(10.7)
Sex Female 626(60.4) 65(6.3) 4.8090(0.28)
Male 297(28.7) 48(4.6)
*no significance association between censoring status with covariate at 0.05 level
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4.1% of protestant patients were with opportunistic infection.
The residence of patients 0.3% of Patients who live in rural
were without opportunistic infection, 1.3% of patients live in
rural were with opportunistic infection, 14.7% of patients live
in urban were without opportunistic infection, 83.6% of patients
live in urban area were with opportunistic infection. The sex of
patients is the other categorical variable 8.6%of Female patients
were without opportunistic infection, 58.1% of female patients
were with opportunistic infection. 6.4% of male patients were
without opportunistic infection, 26.9% of male patients were
with opportunistic infection. Table 4.2 last column is Pearson
chi-square with level of significance. Tells us association
between covariates with opportunistic infection. From the
covariates in table 4.2 sex, marital status, censoring status and
functional status show association with opportunistic infection
of patients.
Table 4 shows that the patients number in each clinical stage
with respect to the other factor such as sex, age, censoring
status, opportunistic infection, functional status, educational
level, marital status, religion, and residence of patients number
of females patients in stage I were 32.7%, number of females
patients in stage II 14.3%, number of females patients in stage
Table 3
Cross table for Opportunistic infection with Covariates
Covariate\Category Opportunistic infection (Count)
Chi-Square (P-Value) Yes
N(%)
No
N(%) Covariate Category
Functional Status Working 133(12.8) 803(77.5) 4.17(0.041)
Other 22(2.1) 78(7.5)
Censoring Censored 42(4.1) 881(85.0) 715.475(0.00)
Death 113(10.9) 0(0.00)
Educational Status No education 25(2.4) 126(12.2) 1.861*(0.602)
Primary 77(7.4) 418(40.3)
Secondary 40(3.9) 270(26.1)
Tertiary 13(1.3) 67(6.5)
Marital Status Single 37(3.6) 264(25.5) 6.46(0.040)
Married 57(5.5) 360(34.7)
Others 61(5.9) 257(24.8)
Religion Orthodox 146(14.1) 822(79.3) 0.34*(0.844)
Muslim 2(0.2) 17(1.6)
Protestant 7(0.7) 42(4.1)
Residence Rural 3(0.3) 13(1.3) 0.173*(0.677)
Urban 152(14.7) 868(83.8)
Sex Female 89(8.6) 602(58.1) 6.707(0.010)
Male 66(6.4) 279(26.9)
*no significance association between Opportunistic infection status with covariate at 0.05 level
Table 4
Cross table for WHO clinical stages with covariates
Covariate\Category WHO clinical stages (Count)
Chi-Square (P-Value)
Sta
ge I
Sta
ge I
I
Sta
ge I
II
Sta
ge I
V
Covariate Category
Functional Status Working 445(43.0) 204(19.7) 255(24.6) 32(3.1) 62.849(0.00)
Other 18(1.7) 20(1.9) 45(4.3) 17(1.6)
Opportunistic Infection No 40(3.9) 43(4.2) 64(6.2) 8(0.8) 27.893(0.00)
Yes 423(40.8) 181(17.5) 236(22.8) 41(4.0)
Censoring Censored 442(42.7) 191(18.4) 248(23.9) 42(4.1) 36.03(0.00)
Death 21(2.0) 33(3.2) 52(5.0) 7(0.7)
Educational Status No education 57(5.5) 34(3.3) 48(4.6) 12(1.2) 10.103*(0.342)
Primary 221(21.3) 110(10.6) 143(13.8) 21(2.0)
Secondary 145(14.0) 69(6.7) 83(8.0) 13(1.3)
Tertiary 40(3.9) 11(1.1) 26(2.5) 3(0.3)
Marital Status Single 138(13.3) 62(6.0) 83(8.0) 18(1.7) 4.144*(0.657)
Married 179(17.3) 89(8.6) 132(12.7) 17(1.6)
Others 146(14.1) 73(7.0) 85(8.2) 14(1.4)
Religion Orthodox 434(41.9) 212(20.5) 278(26.8) 44(4.2) 3.945*(0.341)
Muslim 9(0.9) 4(0.4) 4(0.4) 2(0.2)
Protestant 20(1.9) 8(0.8) 18(1.7) 3(0.3)
Residence Rural 5(0.5) 6(0.6) 5(0.5) 0(0.0) 3.350*(0.341)
Urban 458(44.2) 218(21.0) 295(28.5) 49(4.7)
Sex Female 339(32.7) 148(14.3) 176(17.0) 28(2.7) 19.627(0.00)
Male 124(12.0) 76(7.3) 124(12.0) 21(2.0)
*no significance association between WHO clinical stages status with covariate at 0.05 level
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III 17%, number of females patients in stage IV 2.0%. In the
other hand number of male patients in stage I were 12.0%,
number of males patients in stage II were 7.3%, number of male
patients in stage III were 12.0%, number of males patients in
stage IV were 2.0%. Functional status of patients 43% of
working patients were in stage I, 19.7% of working patients
were in stage II, 24.6% of working patient working patients in
stage III, 3.1% of working patients were in stage IV. In category
other 1.7% of patients in other functional status were in stage I,
1.9% of patients in other functional status were in stage II,
4.3%of patients in other functional status were in stage III, 4.3%
of patients in other functional status were in stage IV. The
patients with or without opportunistic infection in each clinical
stages were stage I 3.9% of patients were without opportunistic
infection, in stage II 4.2%, in stage III 6.2, in stage IV 0.8%,
patients were without opportunistic infection. The other one
patients with opportunistic infection were in stage I 40.8%,
stage II 17.5%, in stage III 22.8%, in stage IV 4.0% of patients
were with opportunistic infection. When we see observation
based on educational level there were four level of education
these were not educated patients in this class 5.5% of patients
were in stage I, 3.3% not educated patients were in stage II,4.6
of non-educated patients were in stage III,1.2% of non-educated
patients were in stage IV. The other one patients primary school
level of education 21.3% were in stage I,10.6% of patients were
in stage II, 13.8*% of the patients were in stage III, 2.0% of the
primary school educational level patients were in stage IV.
Secondary school educated patients were 14.0% of the patients
in secondary school level of education were in stage I, 6.7% of
secondary school educational level patients were in stage II, 8
% of the secondary school level patients were in stage III, 1.3%
of secondary school level education patients were in stage IV.
In the marital status of patients 1 .3% of the single patients were
in stage I, 6.0% of the single patients were in stage II, 8.0% of
the single patients were in stage III, 1.7% of the single patients
were in stage IV. 17.3% of married patients were in stage
I,8.6% of married patients were in stage II, 12.7% of married
patients were in stage III, 1.6% of married patients were in stage
IV. 14.1% of patients in other group were in stage I, 7.0% of
others were in stage II, 8.2% of others were in stage III, 1.4%
of other was in stage IV. The religion of patient 41.9% of
orthodox patients were in stage I, 20.5% of orthodox patients
were in stage II, 26.8% of orthodox patients were in stage III,
4.2%of orthodox patients were in stage IV. 0.9% of Muslim
patients were in stage I, 0.4% of Muslim patients were in stage
II, 0.4% of Muslim Patients were in stage III, 0.2% of Muslim
patients were in stage IV. protestant patients in stage I were
1.9%, 0.8% of the protestant patients were in stage II, 1.7% of
protestant patients were in stage III, 0.3% of protestant patients
were in stage IV. In the residence of patients 0.5% of patients
live in rural area was in stage I, 0.6% of patients live in rural
area were in stage II, 0.5% of patients were in stage III, 0.0% of
patients live in rural area were in stage IV. 44.2% of patients
live in urban area was in stage I, 21.0% of patients in urban area
were in stage II, 28.5% of patients live in urban area were in
stage III, 4.7% of patients live in urban area were in stage IV.
The chi-square test of WHO clinical stage with other co-vitiates
shows there is significant association between WHO clinical
stage and functional status, censoring status, marital status and
residence of patients.
Table 5 shows that number of patient population in each
regimen class with respect to other covariates and their
category. There were five types of baseline regimens class for
adult patients were used in the hospital. That is AZT-3TC-NVP
in this 5.5% of the patients use this drug were females, 3.7% of
males patients were users of AZT-3TC-NVP, the drug AZT-
3TC-EFV was the second it was used by 2.0% females and
1.2% male patients. The next one is TDF-3TC-EFV it was used
by 53.4% female, 27.1% male patients; the fourth one is TDF-
3TC-NVP it was used by 5.5% females and 1.4% males. The
last regimen is ABC-CTC-NVP the users of this drug were
0.2% of females and 0.1% of males. On the bases of functional
status 8.4% of the working patients were used AZT-3TC-NVP,
3.0% of the working patients were used AZT-3TC-EFV, 72.6%
of working patients were users of TDF-3TC-EFV,6.2% of the
working patients were users of TDF-3TC-NVP. 0.2% of the
working patients were users of ABC-3TC-NVP, 0.7% of
patients who were not able to work were users of TDF-3TC-
NVP, 0.1% of patients in the others were users of ABC-3TC-
NVP. 8.4% of patients in stage I were use AZT-3TC-NVP,
0.7% of patients in stage I were user of AZT-3TC-EFV.37.2%
of patients in clinical stage I were use TDF-3TC-EFV, 2.4% of
patients in stage I were users of AZT-3TC-NVP,0.1% of
patients in stage I were users of ABC-3TC-NVP, 2.7% of
Patients in stage II were users of AZT-3TC-NVP, 1.0% of
patients in stage II were users of AZT-3TC-EFV, 15.5% of
patients in stage II were users of TDF-3TC-EFV, 2.3% of
patients in stage II were users of the TDF-3TC-NVP.0.1% of
patients in stage I were users of ABC-3TC-NVP, 1.8% of
patients in stage III were users of AZT-3TC-NVP,1.5% of
patients were in stage III were users of AZT-3TC-EFV,23.5%
of patients in stage III were users of TDF- 3TC-EFV,2.0% of
patients in stage III were users TDF-3TC-NVP, 0.1% of
patients in stage Iv were users of ABC-3TC-NVP. In stage IV
0.3% of patients were users of AZT-3TC-EFV,4.3% of patients
in stage IV were users of TDF-3TC-EFV, 0.1% of patients in
stage IV were users ofTDF-3TC-NVP. 1.4% of Patients without
opportunistic infection were users of AZT-3TC-NVP, 0.2% of
patients without opportunistic infection were users of AZT-
3TC-EFV, 11.6% of patients without opportunistic infection
were users of TDF-3TC-EFV, 1.8% of patients without
opportunistic infection were users of TDF-3TC-NVP. 7.8% of
Patients with opportunistic infection were users of AZT-3TC-
NVP, 3.0% of patients with opportunistic infection were users
of AZT-3TC-EFV,68.9% of patients with opportunistic
infection were users of TDF-3TC-EFV, 5.3% of patients with
opportunistic infection were users of opportunistic infection
were users of TDF-3TC-NVP,0.3% of patients with
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opportunistic infection were users of ABC-3TC-NVP.8.4% of
censored patients were users of AZT-3TC NVP,3.0% of
censored patients were users of AZT-3TC-EFV, 72.2% of
censored patients were users of TDF-3TC-EFV,5.2% of
censored patients were users of TDF-3TC-NVP,0.3% of the
censored patients were users of ABC-3TC-NVP. 0.8% of the
died patients were users of AZT- 3TC-NVP, 0.2% of died
patients were users of AZT-3TC-EFV, 8.3% of died patients
were users of TDF-3TC-EFV, 1.6% of died patients were users
ofTDF-3TC-NVP. In the case of educational level of patients
0.9% of not educated patients were users of AZT-3TC-NVP,
0.4% of patients who were not educated were users of AZT-
3TC-EFV, 12.6% of not educated patients were users of TDF-
3TC-EFV, 0.7% of not educated patients were users of TDF-
3TC-NVP. 4.4% of primary educated patients were users of
AZT-3TC-NVP, 1.6% of primary educated patients were users
of AZT-3TC-EFV, 38.0% of the primary educational level
patients were users of TDF-3TC-EFV, 3.5% of the patient in
the primary school level of education were users of TDF-3TC-
NVP, 0.2% of the primary educated patients were users of
ABC-3TC-NVP. In the secondary school level of education of
patients 3.1 % of the patients were users of AZT-3TCNVP,
0.8% of the patients in the secondary level of education were
users of AZT-3TC-NVP, 23.6% of the patients were users of
TDF-3TC-EFV, 2.5%of patients in secondary level of
education were users of TDF-3TC-NVP. In the tertiary level of
education 0.8% were users of AZT-3TC-NVP, 0.4% of the
patients in the tertiary level of education were users of AZT-
3TCEFV, 6.3% of the patients in the tertiary level of education
were users of TDF-3TC-EFV, 0.2% of patients in tertiary level
of education were users of TDF-3TC-NVP,0.1% of the patients
in the tertiary level of education were users of ABC-3TC-NVP.
Patients in the marital status distributed as 2.6% os single
patients were users of AZT-3TCNVP,1.1% of single patients
were users of AZT-3TC-EFV,23.1% of single patients were
users of TDF-3TC-EFV,2.1% of single patients were users of
TDF-3TC-NVP,0.2% o single patients were users of ABC-
3TC-NVP.3.4% of married patients were users of AZT-3TC-
NVP,1.3% of married patients were users of AZT-3TC-
EFV,32.8% of patients were users of TDF-3TCEFV,2.7% of
patients were users of TDF-3TC-NVP ,0.1 % of married
patients were users of ABC-3TC-NVP. 3.2% of other patients
were users of AZT-3TC-NVP, 0.9% of patients in the other
were users of AZT-3TC-EFV, 24.6% of the patient in the other
were users of TDF-3TCEFV, 2.0% of the other patients were
users of TDF-3TC-NVP.
The patients number in each religion with respect to the
regimen expressed as 8.3% of the Orthodox patients were users
of AZT-3TC-NVP, 3.0% of Orthodox patients were users of
AZT- 3TC-EFV, 75. 2% of Orthodox patients were users of
TDF-3TC-EFV, 6.2% of Orthodox patients were users of TDF-
3TC-NVP, and 0.3% of Orthodox patients were users of ABC-
3TCNVP.0.2% of Muslim patients were users of AZT-3TC-
NVP, 1.4% of Muslim patients were users of TDF-3TC-EFV.
0.7% of protestant patients were users of AZT-3TC-NVP, 0.2%
of protestant patients were users of AZT-3TC-EFV, 0.5% % of
Table 5
Cross table for regimen class with covariates
Covariate\Category Regimen Class
Chi-Square (P-Value)
AZ
T-3
TC
-NV
P
AZ
T-3
TC
-EF
V
TD
F-3
TC
-EF
V
TD
F-3
TC
-NV
P
AB
C-3
TC
-NV
P
Covariate Category
Functional Status Working 87(8.4) 31(3.0) 752(72.6) 64(6.2) 2(0.2) 2.617*(0.624)
Other 8(0.8) 2(0.2) 82(7.9) 7(0.7) 1(0.1)
WHO
Stage 1 45(4.3) 7(0.7) 385(37.2) 25(2.4) 1(0.1)
28.788(0.004) Stage 2 28(2.7) 10(1.0) 161(15.5) 24(2.3) 1(0.1)
Stage 3 19(1.8) 16(1.5) 243(23.5) 21(2.0) 1(0.1)
Stage 4 3(0.3) 0(0.0) 45(4.3) 1(0.1) 0(0.0)
Opportunistic Infection No 14(1.4) 2(0.2) 120(11.6) 19(1.8) 0(0.0) 12.462(0.014)
Yes 81(7.8) 31(3.0) 714(68.9) (5.3) 3(0.3)
Censoring Censored 87(8.4) 31(3.0) 748(72.2) 54(5.2) 3(0.3) 14.491(0.006)
Death 8(0.8) 2(0.2) 86(8.3) 17(1.6) 0(0.0)
Educational Status No education 9(0.9) 4(0.4) 131(12.6) 7(0.7) 0(0.0) 13.137*(0.359)
Primary 46(4.4) 17(1.6) 394(38.0) 36(3.5) 2(0.2)
Secondary 32(3.1) 8(0.8) 244(23.6) 26(2.5) 0(0.0)
Tertiary 8(0.8) 4(0.4) 65(6.3) 2(0.2) 1(0.1)
Marital Status Single 27(2.6) 11(1.1) 239(23.1) 22(2.1) 2(0.2) 3.786*(0.876)
Married 35(3.4) 13(1.3) 340(32.8) 28(2.7) 1(0.1)
Others 33(3.2) 9(0.9) 255(24.6) 21(2.0) 0(0.0)
Religion Orthodox 86(8.3) 31(3.0) 784(75.7) 64(6.2) 3(0.3) 5.322*(0.723)
Muslim 2(0.2) 0(0.0) 14(1.4) 3(0.3) 0(0.0)
Protestant 7(0.7) 2(0.2) 36(3.5) 4(0.4) 0(0.0)
Residence Rural 3(0.3) 1(0.1) 9(0.9) 3(0.3) 0(0.0) 6.696*(0.153)
Urban 92(8.9) 32(3.1) 825(79.5) 68(6.6) 3(0.3)
Sex Female 57(5.5) 21(2.0) 533(53.4) 57(5.5) 3(0.3) 9.512(0.050)
Male 38(3.7) 12(1.2) 281(27.1) 14(1.4) 0(0.0)
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protestant patients were users of TDF-3TC-NVP,0.4%% of
protestant patients were users of TDF-3TC-NVP. The residence
of patients with two categories is 0.3%of the patients in rural
area were users of AZT-3TC-NVP,0.1% of the patients in rural
area were users of AZT-3TC-EFV,0.9% of patients in rural area
were users of TDF-3TC-EFV,0.3% of patients in rural area
were users of TDF- 3TC-NVP.8.9% of the patients in urban
area were users of AZT-3TC-NVP,3.1% of patients were live
in urban users ofAZT-3TC-EFV, 79.6% of the patients in urban
area were users of TDF-3TC-EFV,6.6% of the patients live in
urban were users of TDF-3TC-NVP,0.3% of the patients live in
urban were users of ABC-3TC-NVP. Table 4.4 shows the chi-
square test and level of significance. The association between
regimen class and functional status, censoring status, marital
status and sew shows significant association.
Descriptive statistics for continuous variables
The data set in this study contains survival time of patients in
ART clinic from start up to occurrence of an event with the
minimum 1 month to the maximum 61 months. The first
quartiles of survival time are 7, third quartile of survival time is
40, the median of survival time is 20, the mean of the survival
time is 23. The weight of patients has minimum of 13 maximum
of 89. The first quartile of weight is 46, third quartile of weight
is 49, mean and median of weight is 52. The age of patients
have minimum 16 year, maximum 71 years. Median of age is
32.00, mean of age is 34.02, first quartile of age is 27, third
quartile of age is 40.
Table 6
Descriptive statistics for continuous variables
In Table 6, the mean of age is 34.02027 with its standard error
0 .3178348the minimum value of age is 16 the maximum values
of age is71. The mean of the time is 23.74807 with standard
error, the minimum value of time is 1 month, and the maximum
time in month is 61 months. When we see survival time of
patients, among total of 1036 study subjects 7.43243% of the
patients were died during the first 12 months, 3.7645% of
deaths occurred within the first three months after initiation of
ART. Another 2.027% of the patients were died in the
following three months of follow up; that is a total of 5.792%
of the patients deaths were occurred within six months. In the
last six months, 1.641% of the patients were died.
Descriptive statistics by using Kaplan-Meier plot
Figure 1 shows the trend among sex for female, the observed
and predicted are go in same direction from 0 to 55. Then there
was a little devotion but in the case of male there is fluctuation
in their line. On the other hand, survival of patient is affected
by sex.
Fig. 1. The Kaplan Meier survival estimates by sex
Fig. 2. Kaplan-Meier plot for Survival by Regimen class
Figure 2 shows that survival is affected by regimen class.
Patients who use AZT-3TC-NVP have less survival time than
that of patients use AZT-3TC-NVP.
Fig. 3. Kaplan-Meier plot for opportunistic infection
In figure 3, survival time is affected by opportunistic
infection. Survival of patient with opportunistic infection has
less survival time than that of patients without opportunistic
infection.
Fig. 4. Histogram for age group
In the figure 4, the category shows the age of patients in
group two contain highest number of patients from the other
group which is 26-35 age group.it followed by age group three
then group one, in this graph age group six contains smallest
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number of observation. ART treatment and the curve show an
asymmetric distribution of age.
5. Results
In this study the main objective is to implementing the Semi-
parametric Bayesian analysis. Thus this study includes the data
set contains, 1036 patient under the ART treatment. To
implement the method of simulation of the data Markov chain
(MC) were used. In the simulation process the diagnostic plot
were produced, then the mixing and convergence of Markov
chain were examined by visual assessments of the plots. The
three types of plots are Trace plot, autocorrelation plot and
density plot; these are placed for each of the parameters
included in the model. It is imperative that these (and other
diagnostics) be examined before any conclusions are drawn
from the simulated posterior sample). The results shown on the
next page are almost perfect for most of the parameters. The
trace plot shows excellent mixing, the autocorrelation decreases
to near zero, and the density is bell-shaped or has the shape of
normally distributed data. The trace plots are centered near their
respective posterior mean and traverse the posterior space with
small fluctuations. These results exhibit convergence of the
Markov chain to its stationary distribution. The explanation of
convergence and mixing of Markov chain is presented for each
parameter as follows.
Diagnosis plot for Bayesian analysis
In the Bayesian analysis the parameters were examined by
using Graphical methods. The figure for some of the parameters
were depicts time difference diagram to examine convergence,
Autocorrelation and the density of the parameters. In assessing
the properties of convergence for the posterior distribution there
is a carful assessment method, it is known as Markov chain
mixing and convergence.
Fig. 5. Sex and Opportunistic Infection
As an explanation is made on the methodology the MCMC
process is used to converge the given data. Figure 5 shows that
the model is converge well in sex of males. The trace plot shows
excellent mixing, the autocorrelation decreases to near zero,
and the probability density is bell shaped, it attains almost the
perfect shape of Markov chain. The trace plots are centered near
their respective posterior mean (around negative 0.2) and
traverse the posterior space with small fluctuations. Whereas
the three of the plot are show in the case of opportunistic
infection was poorly mix and these plot are fail to fulfill Markov
chain plots shape.
Fig. 6. Regimen class for AZT-3TC-EFV and TDF-3TC-EFV
Figure 6 displays the trace plot, the autocorrelation function
plot and posterior density plot generated by Markov Chain. In
both regimen class the trace plot show excellent mixing, the
autocorrelation decreases to near zero, and the density has the
shape for Markov chain diagnostic plot. The trace plots are
centered near their respective posterior mean and traverse the
posterior space with small fluctuations.
Fig. 7. Regimen class
Figure 7 shows good mixing in TDF-3TC-NVP that is second
figure, but poor mixing and convergence in the ABC-3TC-NVP
that is first figure. In the other word the effectiveness of regimen
is different from one another. That mean the survival time is
affected by regimen class of patients.
Fig. 8. WHO Clinical stages
Figure 8 shows that the three WHO clinical stages diagnostic
plots. The trace plot shows excellent mixing, the
autocorrelation decreases to near zero, and the density plot
shows excellent shaped of Markov chain. The trace plots are
centered near their respective posterior mean and traverse the
posterior space with small fluctuations.
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Fig. 9. Baseline Weight and CD4 count
Figure 9, three types of plot are displays these plots are good
convergence and good mixing of Markov chain. These are
examining the trace plot show well mixing, density plot shows
good convergence, the autocorrelation function plot show low
correlation. Figure 4. 8. For almost perfect convergence with
excellent Markov chain mixing. In the figure 8 for Baseline
CD4 and Baseline weight are shows the three diagnostic plots
for both of the parameters are perfect mixing of Markov chain.
Trace plots of samples versus the simulation index can be useful
in assessing convergence and also shows that the chain is
mixing well. It may be noted that if the chain does not converge
to its stationary distribution, then there will be long burn-in
period. One can observe from a trace plot that there On the basis
of figure 4, 6, 7, 8 and 9 we conclude that,
Markov chain (MC) has reached convergence.
MC has reached stationary as the distribution of points is
not changing as the chain progress.
The burn-in is a size of 2000. This means that the initial
2000 observations has been discarded.
Trace plot is perfect and the center of the chain is around
0.4 with small fluctuations which indicates that the MC
has reached the right distribution.
The chain is mixing well as it is exploring the distribution
by traversing to areas where its density is very low.
Result from posterior sample: As a consideration of semi
parametric model in Bayesian analysis, by using the variable
time-to-event the analysis were carried out. In this analysis
from the model information table the dependent variable is
time, the censoring status (cen), among the coded variables the
code 0 is for the censored and the code 1 is for the event of not-
censored category. The model is cox (PH) along with method
of tie handling is Breslow. From the Burn-in phase 2000 with
the MC sample size 10,000 were carried out. The observed
sample was 1036 and the event were 113(11%) whereas
censored observation 923(89.09%) were found. From this
censored data or category were more than 89% and the rest were
the event category.
Table 7 reports the statistics, posterior mean, credible
intervals, and high probability density (HPD) intervals for each
of the parameters based on the posterior sample of 10000.
Because the priors used are non-informative, the mean,
standard deviation and credible interval are fairly close to the
corresponding maximum likelihood estimates (estimate,
standard error, 95% CI).
Table 7
Posterior summary and posterior interval and maximum likelihood
estimates
Table 7, shows the mean and standard deviation of the
posterior samples are comparable to the MLE and its standard
error, respectively, this is happen because of the use of the
uniform prior. By referencing male, there is a 23.49% chance
that the hazard rate of male is less than that of the hazard rate
of fe male. The result is consistent with the fact that the average
survival time of female is less than that of males. The posterior
mean of age is 0.00667 it indicates there is a 0.667% chance
that the hazard rate of patients is increased by 0.667% as age is
increased by 1. By referencing workers, the posterior mean of
other functional status is 0.6042. There is a 60.42% chance that
the hazard rate of other functional status patients is greater than
that of working patients. The average survival time of working
patients is greater than that of other functional status patients.
The mean of baseline CD4 cell count is 0.00041it shows that
there is 0.41% chance that the baseline CD4 cell count can
decrease the hazard rate of the patients in 0.41% when Base line
CD4 is increased by 1, in other word the base line CD4 cell
increased by 1, the hazard rate of patients increases by 0.41%
rate. The base line weight mean is 0.0126. There is
a1.26%chance that the patients hazard rate decrease as Base
line weight increased by 1. By referencing rural, the mean of
the urban patients is 9144, there is a 91.44% chance that the
hazard rate of patients live in Urban is greater than that of
patients live in rural. By referencing stage I, WHO clinical stage
show that the hazard rate of patients has difference from each
other. the WHO stage 2, there is a 49.99%chance that the hazard
rate of Stage1 is less than that of stage I, The result is consistent
with the fact that the average survival time of patients in
stage1is greater than that of the survival time of patients in
stages 2. There is a 78.67% chance that the hazard rate of WHO
clinical stage stage3 is greater than that of stage 1. The average
survival time of patients in stage3 is less than that of stages1.
The result is consistent with the fact that the average survival
time of patients in stage 4 is less than that of stage1. By
referencing no education, there is a 33.00% chance that the
hazard rate of primary school educated patients less hazard rate
than that of not educated patients. The result is consistent with
the fact that the average survival time of primary educated
patients is greater than that of not educated patients. There is a
53.56% chance that the hazard rate of secondary educated
patients is greater than that of not educated patients. The result
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is consistent with the fact that the average survival time of
secondary educated patients is less than that of not educated
patients. There is an 86.67% chance that the hazard rate of
tertiary educated patients greater than that of not educated
patients. By referencing regimen AZT-3TC-NVP, there is a
92.29% chance that the hazard rate of patients who use TDF-
3TC-EFV is greater than that of patients who were use AZT-
3TC-NVP. The result is consistent with the fact that the average
survival time of patients who were use AZT-3TC-NVP is
greater than that of patients who were use TDF-3TC-
EFV.There is a 98.98% chance that the hazard rate of patients
who were use TDF-3TC-NVP is greater than that of patients
who were use AZT-3TCNVP.
The result is consistent with the fact that the average survival
time of TDF-3TC-NVP users is less than that of AZT-3TC-
NVP users.by referencing single, there is a 50.37% chance that
the hazard rate of married patients is greater than that of single
patients. The result is consistent with the fact that the average
survival time of married patients is less than that of single
patients. There is a 46.88% chance that the hazard rate of
widowed and divorced patients less than that of single patients.
The result is consistent with the fact that the average survival
time of divorced and widowed patients is greater than that of
single patients. By referencing ortho9dox, the values -10.85%
and -84.32% are indicates that the religion of the patients has
no significance impact on the hazard rate of patients, that is the
survival time of the patients does not affected by the religion of
the patients. In the table 4.6 we can see that the likelihood
estimate and its standard error and posterior mean and its
standard deviation of the parameters, in both values for
likelihood estimate and values for posterior mean are lie in
between confidence limit and the higher probability density
intervals. In those maximum likelihood estimates all estimated
values are found in between the confidence limit. The sign of
parameter estimate of these parameters differ from each other.
And also the length of their confidence limit is different from
each other.in the other hand posterior mean and likelihood
estimate are approximately equal
Uniform Prior for model parameters is a default prior
in phreg SAS procedure for Semi parametric Bayesian
analysis, it is constant for all parameters
The fit Statistics gives the information about fitted
model in terms of DIC (Deviance Information
Criterion) and pD (effective number of parameters).
Table 8
Posterior Summary
Table 8 shows that effective sample size the effective sample
size is the test used to compare the covariates with their sample.
The sample of this covariate is show approximately equal to the
sample of the variables given by simulation it is known as good
sample, if it is larger or smaller than that of given sample it is
poor sample. The efficiency of the variables is small it is less
than 1 so the sampling method for each variable is good.
6. Discussion, Conclusion and Recommendation
Discussion: In this study semi-parametric Bayesian analysis
for time-to-event data from ART follow up was presented. The
method of semi-parametric Bayesian analysis for survival of
HIV, cox proportional hazard, prior elicitation and Markov
chain sampling were considered. As Bayesian analysis is based
on prior distribution, prior selection is the first step. In our
findings also the first step was to decide which kinds of prior is
important to perform the analysis with the aim of the study. The
Bayesian analysis method used proper prior if there exist
previous study similar to current study by their variable and the
model which is need to apply in the study. Then posterior
distribution form the first study is used as prior distribution.
Therefore, since there is no previous study to get prior
information for our study, the prior distribution was selected by
default. In other word improper prior or flat prior was used. The
second step of this study is Checking or diagnostics of Markov
chain convergence and mixing. To perform this process SAS
phreg procedure was used. From the variable which were not
significantly converge and mix Markov chain was opportunistic
infection, where as other variables such as sex, age, functional
status, WHO clinical stages, regimen class, educational level,
marital status, religion, residence, baseline weight and baseline
CD4 were satisfy the Markov chain mixing and convergence
criteria. The first objective of this study is implementation of
semi parametric Bayesian for survival of HIV patients. In this
analysis after diagnosis of Markov chain convergence and
posterior sample was produced. The posterior mean and
standard deviation were comparable with likelihood estimation
and standard error respectively. As an example residence is not
affect survival time of patients in the posterior mean whereas it
has impact on survival time of patients in maximum likelihood
estimation. The data which is taken from ART was analyzed by
using different plots and descriptive statistical analysis methods
such as cross tabulation for categorical covariates and mean,
minimum, maximum and standard error for continues co-
variable were carried out. In the other hand Kaplan-Meier plots
for survival of patients with each covariates by using stata
version 12.0(for Kaplan-Meier plot), SPSS version 20 (for
descriptive statistics) and SAS version 9.4 (for inferential
statistical analysis). The Kaplan-Meier plot suggests that
survival time of patients affected by age, sex, WHO clinical
stages, regimen class, opportunistic infection, marital status and
residence. From the semi parametric Bayesian model sex of
patient, age of patients, baseline CD4 cell count, Baseline body
weight, regimen class, WHO clinical stages, residence religion,
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marital status and educational level are significant predictor of
the survival time of the patients or time to death of patient.
When we see all this covariate in Kaplan-Meier plot all
covariates have significant impact on survival time. But in semi
parametric Bayesian analysis, opportunistic infection is not
affect survival time of patients, in our point of view the number
of patients with opportunistic infection covers large (93.3%) but
there is no uncensored, whereas patients number without
opportunistic infection was with smaller (%) with all event. In
this variable the result from KM and semi parametric Bayesian
is contradict in opportunistic infection. Semi parametric
Bayesian for cox model used partial likelihood estimate and
generates a chain of posterior distribution samples by the Gibbs
Sampler. Summary statistics, convergence diagnostics, and
diagnostic plots are provided for each parameter. In the proc.
phreg procedure for Bayesian analysis. Since we were not
specifying prior for our model parameters the default prior for
Bayesian is uniform prior. The uniform prior is a flat prior on
the real line with a distribution that reflects ignorance of the
location of the parameter, placing equal probability on all
possible values the regression coefficient can take. When we
use the uniform prior, the expect Bayesian estimate to resemble
the classical results of maximizing the partial likelihood as the
likelihood. This study found that patient survival under ART
was significantly associated with WHO clinical stage, baseline
CD4 cell count, base line body weight, regimen class, sex, and
opportunistic infection was not associated with survival time.
The finding of this study was similar to other study Isidore
Sieleunou et al. (2009). In the other hand association of
explanatory variable with explanatory variables were done by
using Pearson chi-square this shows that association between
regimen classes and WHO clinical stage, opportunistic
infection, censoring status, educational level and residence was
significant. But Regimen class has no association with sex,
marital status and functional status of patients. Censoring status
of Patient is associated with sex, marital status, and functional
status. Opportunistic infection is associated with functional
status, sex, censoring status and marital status. WHO clinical
stage is associated with functional status, opportunistic
infection, censoring status, educational level, residence and sex.
The time is affected by CD4 cell count of the patients. Age of
patients is also affect survival time, as the age increase by one
unite survive time is decreased by 0.667 percent. CD4 cell
count is associated with survival time; if CD4 cell count is large
the hazard rate is low. In this study baseline CD4 cell has a
0.041percent of the hazard rate decrease if CD4 cell is increase
.it is supported by Ketema Kebebe and Eshetu Wencheko
(2011). Patients with smaller weight have higher hazard rate.
Conclusions: This study was about HIV/AIDS patient‟s
survival with semi parametric Bayesian analysis. The method
of data analysis by using Bayesian semi-parametric was
effective for our study data. This analysis method has its own
potential advantage that is we can jointly model the baseline
hazard and the regression coefficients, and then accurately
compute posterior model probabilities and their standard errors
using MCMC simulation techniques. Bayesian inference is
done after the posterior distribution samples have achieved to
the convergence of Markov chain. Factors that affect survival
time of patients in the ART treatment in this study were sex,
age functional status, WHO clinical status, regimen class,
residence, baseline CD4 cell count, and baseline body weight.
The diagnostic plots for Markov chain were trace,
autocorrelation and probability density plots, these three plots
were show the good mixing and convergence of MC. The non-
informative improper prior in all of the highest posterior density
(HPD) intervals for the regression coefficients of the covariates
contain 0. This indicates a moderate association between time
to death and covariates for these data, as was expected. The
posterior distribution of the parameters appears quite symmetric
at the mode. The partial likelihood of the COX model in
PHREG procedure generates a chain of posterior distribution
samples by Gibbs sampler and it is first fits the Cox model by
maximizing the partial likelihood along with 95% confidence
intervals for regression parameters. The Fit Statistics give the
information about fitted model in terms of DIC (Deviance
Information Criterion) and pD (effective number of
parameters). Generally, the hazard rate of patients were affected
by residence, sex, age, functional status, WHO clinical stages,
regimen class, baseline CD4, base line body weight and for
each categories in categorical variable. As an example,
regarding covariate residence living in an urban country is
associated with poor survival time after starting ART treatment.
That is the result indicates that after referencing individual
covariates, the hazard rate of HIV patients lives in urban
country 91.44 percent times larger than that of individual live
in rural country. Likewise regarding the sex of patients there is
a 22.96 chance that the hazard rate of the male is smaller than
that of females. The result is consistent with the fact that the
survival time of male’s patients is greater than that of female
patients. In the other hand covariate religion has no significant
impact on survival of patients.
Recommendation: From this study we can recommend the
following points 1. The survival or time to event analysis for
rare event or the data with large number of censored observation
is analyzed by using Bayesian semi parametric model. 2.In this
study male have less hazard rate than female, it may because
due to lack of giving awareness since by nature female are
easily exposed to HIV/AIDS than male. 3. Female income or
type of job for living leads them to loss their care to live with
HIV. So they need special awareness to manage themselves. 4.
In the other hand this study shows patients live in urban area
have less survival time than who living in rural area, hence it is
suggested that the care to taken based on area of living 5.
Regarding regimen class of patients who takes AZT-3TC-NVP
have high survival time than patients who take other regimens.
In this case at the beginning of ART treatment patients need
special attention taken until they adapt with the regimen and
how to survive with the disease. 6. Finally, this study needs to
International Journal of Research in Engineering, Science and Management
Volume-3, Issue-5, May-2020
www.ijresm.com | ISSN (Online): 2581-5792
100
suggest that Debre Berhan Referral Hospital to maintain a
record for baseline clinical and demographic status of patients,
for a research in future.
References
[1] Alemu A. W, Sebastian M. S. (2010), Determinants of survival in adult
HIV patients on antiretroviral therapy in Oromiyaa, Ethiopia. Global
Health Action. 3: 5398
[2] Alejandro Jara, Applied Bayesian Non- and Semi-Parametric Inference
using DP package
[3] Amanuel Alemu Abajobir, et al. (2014) Survival Status of HIV positive
Adults on Antiretroviral treatment in Debre Markos Referral Hospital,
Nothwest Ethiopia: Retrospective Cohort study.
[4] Andinet Worku, (2009), “Pattern and determinants of survival in adult
HIV patients on antiretroviral therapy, Ethiopia,
[5] Bachani D, Garg R, Rewari B. B et al. (2010), “Two-year treatment
outcomes of patients enrolled in India‟s national first-line antiretroviral
therapy programme. Natl Med J India. 23:7–12
[6] Carlin, B. P. and Chib, S. (1995) Bayesian model choice via Markov chain
Monte Carlo methods‟, Journal of the Royal Statistical Society, Series B:
Methodological 57, 473–484.
[7] Ketema Kebebew and Eshetu Wencheko, (2011), Survival analysis of
HIV-infected patients under antiretroviral treatment at the Armed Forces
General Teaching Hospital, Addis Ababa, Ethiopia.
[8] Shankar Prinja, Nidhi Gupta and Ramesh Verma, (2010) Censoring in
Clinical Trials: Review of Survival Analysis Techniques, Indian J
Community Med; 35(2): 217–221.
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