Analysis of Recurrent Events with Associated Informative Censoring: Application to HIV Data

Abstract

In this study, we adapt a Cox-based model for recurrent events; the Prentice, Williams and Peterson Total-Time (PWP-TT) that has largely, been used under the assumption of non-informative censoring and evaluate it under an informative censoring setting. Empirical evaluation was undertaken with the aid of the semi-parametric framework for recurrent events suggested by Huang [1] and implemented in R Studio software. For validation we used data from a typical HIV care setting in Kenya. Of the three models under consideration; the standard Cox Model had gender hazard ratio (HR) of 0.66 (p-value=0.165), Andersen-Gill had HR 0.46 (with borderline p-value=0.054) and extended PWP TT had HR 0.22 (p-value=0.006). The PWP-TT model performed better as compared to other models under informative setting. In terms of risk factors under informative setting, LTFU due to stigma; gender [base=Male] had HR 0.544 (p-value =0.002), age [base is < 37] had HR 0.772 (p-value=0.008), ART regimen [base= First line] had HR 0.518 (p-value= 0.233) and differentiated care model (Base=not on DCM) had HR 0.77(p-value=0.036). In conclusion, in spite of the multiple interventions designed to address incidences of LTFU among HIV patients, within-person cases of LTFU are usually common and recurrent in nature, with the present likelihood of a person getting LTFU influenced by previous occurrences and therefore informative censoring should be checked.

Full text

International Journal of Statistics in Medical Research, 2020, 9, 20-27 20
E-ISSN: 1929-6029/20 © 2020 Lifescience Global
Analysis of Recurrent Events with Associated Informative
Censoring: Application to HIV Data
Jonathan Ejoku1, Collins Odhiambo1,* and Linda Chaba1
1Strathmore Institute of Mathematical Sciences, Strathmore University, Madaraka Estate, Ole Sangale Road,
P.O. Box 59857, 00200, City Square, Nairobi, Kenya
Abstract: In this study, we adapt a Cox-based model for recurrent events; the Prentice, Williams and Peterson Total
-Time (PWP-TT) that has largely, been used under the assumption of non-informative censoring and evaluate it under
an informative censoring setting. Empirical evaluation was undertaken with the aid of the semi-parametric framework for
recurrent events suggested by Huang [1] and implemented in R Studio software. For validation we used data from a
typical HIV care setting in Kenya. Of the three models under consideration; the standard Cox Model had gender hazard
ratio (HR) of 0.66 (p-value=0.165), Andersen-Gill had HR 0.46 (with borderline p-value=0.054) and extended PWP TT
had HR 0.22 (p-value=0.006). The PWP-TT model performed better as compared to other models under informative
setting. In terms of risk factors under informative setting, LTFU due to stigma; gender [base=Male] had HR 0.544
(p-value =0.002), age [base is < 37] had HR 0.772 (p-value=0.008), ART regimen [base= First line] had HR 0.518
(p-value= 0.233) and differentiated care model (Base=not on DCM) had HR 0.77(p-value=0.036). In conclusion, in spite
of the multiple interventions designed to address incidences of LTFU among HIV patients, within-person cases of LTFU
are usually common and recurrent in nature, with the present likelihood of a person getting LTFU influenced by previous
occurrences and therefore informative censoring should be checked.
Keywords: Recurrent events, Loss to follow-up, HIV, Prentice, Williams and Peterson Gap-Time, Informative
censoring.
1. BACKGROUND
Recurrent events occur in a variety of
disciplines/areas of life such as recurrent opportunistic
infections in HIV patients, episodes of asthmatic
attacks. Underlying processes that generate data from
these events are called “recurrent event processes and
the data they provide are called “recurrent event data”
[3]. There is a wide range of research on the analysis of
this data including the analysis of recurrence of
sports injuries, multiple episodes of childhood
diseases [4] and hospitalizations for chronic kidney
kidney disease [5].
A key characteristic of recurrent events is that
observations per individual are usually not independent
and in many cases are correlated, with current event
incidences influenced by previous incidences. A
number of approaches that have been proposed to
analyze recurrent events data, including both
parametric and non-parametric methods such as the
use of the Poisson and Negative binomial models [3].
Both of these however accommodate only
time-independent covariates, with the Poisson further
pre-supposing a constant events rate per individual.
While these and a number of other models have
been suggested, the models most predominant in
recurrent event literature for ordered outcomes are the
Anderson and Gill [6], Prentice, Williams, and Peterson
total time (PWP-TT) and gap time (PWP-GT) models
*Address correspondence to this author at the Strathmore Institute of
Mathematical Sciences, Strathmore University, Madaraka Estate, Ole Sangale
Road. P.O. Box 59857, 00200, City Square, Nairobi, Kenya; Mob: +254 703
034 000/200/300 or [+254] [0] 730-734000/200/300; Fax: +254 20 6007498;
E-mail: codhiambo@strathmore.edu
[7], Wei, Lin and Weissfeld (WLW) [8]; and Lee, Wei
and Amato (LWA). These models are essentially
extensions of the extensively used semi-parametric
Cox Proportional Hazards Model, predominantly
applied under the assumption of non-informative
censoring.
To the best of our knowledge, none of these models
have been applied to researches with an underlying
assumption of informative censoring. Subsequently, we
hope this paper will significantly bridge the gap by
evaluating the common recurrent event based models
in situations where informative censoring exists.
Informative censoring in HIV related-studies exist in
situations, where there are informed drop-outs; such as
sicker persons or those in either WHO staging III or IV
being withdrawn from the study or persons getting lost
to the study due to stigma-related factors. Ghosh et al.,
[9] note that informative censoring occurs in situations
where the censoring times “depend on the observed or
non-observed recurrent times”. An illustration of this in
the HIV setting, is the informative drop-outs such as the
withdrawal of sicker patients from a study way before
the study ends. Ghosh et al., [9] specify two possible
sources of informative censoring in practical settings:-
the voluntary withdrawal of subjects for reasons related
to the event process as well death.
The exclusion of censoring assumption from
different studies may generally lead to biased
estimates. Castelli et al. [10] in adapting the Inverse
Probability of Censoring Weighted [IPCW] to study the
survival times of asthma patients while including
informative censoring [patients felt they were okay and

Analysis of Recurrent Events with Associated Informative Censoring International Journal of Statistics in Medical Research, 2020, Vol. 9 21
did not need to consult a doctor] show that information
coming from censoring process improves the survival
estimate. Another approach is that by Ghosh et al., [9]
where they introduce a semi-parametric approach for
recurrent events in the presence of dependent
censoring and apply it ALIVE cohort study. A
comparison with the accelerated failure times model as
proposed by Lin et al. [11], which assumes
non-informative censoring found that their proposed
method yielded “a much larger estimate for the effect of
baseline HIV status on hospitalizations than the
method proposed by Lin”.
There is a body of literature to show that drop-outs
in HIV programs are informative. Berheto et al., [12] in
assessing the predictors of LTFU in Patients Living with
HIV/AIDS after Initiation of Antiretroviral Therapy found
that sicker patients [baseline CD4 < 200 cells/mm3 –
HR 1.7, 95% Cis 1.3-2.2, regimen substitution – HR
5.2; 95% Cis 3.6-7.3] and receiving non-isoniazid (INH)
prophylaxis [HR 3.7; 95% CIs 2.3-6.2] as accelerators
for LTFU. According to Assemie et al., [13], being on
WHO clinical stage IV as well as receiving isoniazid
preventive therapy were significant predictors of LTFU.
On the premise of this, informative censoring is thus
incorporated in this study.
2. METHOD AND SETTING
Let the rate of occurrence of recurrent events in a
given time interval i.e. (0, ΓO), where ΓO > 0 is set with
the information of possible epochs of recurrences
observable up to ΓO. Suppose ℕ" (t) is the number of
recurrent events that occur on or before t, t > 0. The
functional rate of a recurrent event at !,!!∈![0,!!
!], is
expressed as
!!=lim
∆→!!
Pr[ℕ[t!+!∆]!−!ℕ[t]!>!0]!
∆
.
The rate is considered theoretically different from
the intensity function. We define the functional rate as
the occurrence rate of recurrent events and is not
conditional to the event history. The intensity function
on the other hand is the occurrence rate and is
conditional on the event history.
Let the cumulative rate function be described as
Ʌ!=![!]
!
!
!".
Also, suppose ϒ be the censoring time for
observation of the recurrent event process at
termination. The interest remains the occurrence rate
in the time interval (0, ΓO), and therefore, recurrent
event data beyond!!
!, is not important. We define τ =
min [ϒ, !!
!] as the new censoring time used in the
proposed models.
Consider PWP-TT defined as
!!" !=!!!!exp{!!"!}!with the following features
events are ordered and handled by stratification,
everyone is at risk for the first stratum, but only
those who
had an event in the previous stratum are at
risk for the successive one. The model estimates both
overall and event-specific effects and uses robust
standard errors to account for correlation.
2.1. Review of the Prentice, Williams, and Peterson
[PWP] Model
The PWP model as proposed by Prentice, Williams,
and Peterson [7] is a ‘conditional model’ where the
individuals are at risk for an event if and only if they
were at risk for a previous event. To achieve this, each
event occurrence is put into a different stratum with all
participants at risk in the first stratum. Under this model,
only participants that experienced the previous event
would then be at risk for the next event [14]. When time
since entry is of interest, this model condenses to total
time model (PWP-TT), while when time since last event
is of interest the model becomes a gap time model
Figure 1: Representation of the PWP Models.

22 International Journal of Statistics in Medical Research, 2020, Vol. 9 Ejoku et al.
commonly abbreviated as PWP-GT. See Figure 1. The
key difference between this model and the
Andersen-Gill (AG) is in terms of the effects of the
covariates in different strata. In the AG model, effects
of covariates are constant across all strata, while this
varies in different strata for the PWP [14].
2.2. Mathematical Representation of PWP Model
To include informative censoring, we built on
generic the approach proposed by Huang et al. [1]
where they jointly model the recurrent event process
and failure times. The key to this approach is to model
this relationship via a subject specific latent variable,!!,
that models the association between the intensity of the
recurrent event and the hazard of the failure time. This
approach is able to account for only time- independent
predictors while also allowing for informative censoring.
As relayed by Huang et al., the intensity function is
!!!=!!!!!exp x!.
And Hazard of the failure time, D, is given by:
ℎ!=!!ℎ!!exp !" .
Where:
!! and ℎ! are baseline intensity and hazard functions
respectively.
! and ! are coefficients.
!![!] is the p-dimensional set of time-dependent
covariates
Based on the proposed intensity function by Huang,
the PWP models are modified as below. A
mathematical representation of each of the models is
presented below, as well as the individual model
specification with informative censoring incorporated
(Table 1). Essentially, each model is multiplied by the
unobserved frailty, !!.
Where:-
PWP-GT is the Prentice, Williams, and Peterson
Gap-Time Model,
PWP-TT is the Prentice, Williams, and Peterson
Total-Time Model
And: -
!!! is the at risk indicator for the j-th event and ith
person at time t. This is 1 when at risk for event j, and
zero when not at risk for event j
!! is the baseline intensity function
!![!] is the p-dimensional set of time-dependent
covariates
! is a q x 1 dimensional parameter.
2.3. Evaluation of the PWP-GT model under
informative censoring
2.3.1. Parameter Estimation
The key to this approach is to use a subject specific
latent variable to model the association between the
recurrent event and hazard of the failure times.
Additionally, no assumptions are made on the
distributions of censoring times and latent variables.
Specifically, we estimate the cumulative hazard and
intensity functions. For estimation, we use the
approach relayed by Huang et al. as it remains
consistent with the PWP model with the at risk indicator
treated as a nuisance parameter.
The estimation by Huang is briefly provided below.
Starting with notation:-
Let N[t] which represents events occurring at or
before some time To, D be failure time, say LTFU due
to stigma for this study, C failure time due to other
reasons than D, x is a vector of 1xp covariates.
Let Y be the point at which the observation of
recurrent events ceases, such that, Y=min[C, D, To].
We introduce a non-negative latent variable z, such
that given X=x, and Z=z, the intensity function is
given by
!!!=!!!!!exp x!,
with E[Z|x] = E[z]
And Hazard function by
ℎ!=!!ℎ!!exp !" .
Implicitly, a large/small z increases or decreases
the intensity and hazard respectively. The rate function
is defined as !!!!!exp![!" ]
Table 1: Mathematical Representation of the Intensity Functions of PWP Models with Informative Censoring
Name of The Model
Recurrent Model Mathematical presentation
Form under Informative/Non-informative censoring
PWP-GT
!!" !!!"[!−!
!!!]!exp![x′!]
!!!!" !!!"[!−!
!−1]!exp![x′!]
PWP-TT
!!" !!!"[!]!exp![x′!]
!!!!" !!!"[!]!exp![x′!]

Analysis of Recurrent Events with Associated Informative Censoring International Journal of Statistics in Medical Research, 2020, Vol. 9 23
Assuming that for individual i, the collection
{[!!,!!,!!!!,…0,!!"! ,!
!} are iid, then the density
function is given by
!!!!!!!exp![!!!]
!!!!Λ!!exp![!!!].
However we assume that the density does not
depend on Zi, Mi nor x, reducing the density to
!!!
Λ!!
.
Since we assume iid, the conditional likelihood is
generated for n subjects, assuming mi events per
individual as
.
!
!!!
.
!
!!!
!![!!"]
Λ!!!
.
Huang notes that the rate estimator for Λ!!! can
be given by [1−!
!] [1]
where d is the number of patients experiencing event at
time t, and R is total persons at risk. To estimate the
hazard !, a class of estimators given below is solved.
!!!!!!!
![!!Λ!!]!!−exp !" =0.
Huang proposes the estimation of ! by replacing
Λ![!]!! by 1.
Asymptotic properties of these estimators are
extensively studied by Huang and bear no repeating in
this article.
2.3.2. Empirical Evaluation of Data
Patient-level data from four facilities in central
Kenya, collected between 2013 and 2018 was used.
The recurrent event of interest were the incidences of
loss to follow-up. Censoring for a drop-out was
considered informative, based on the reason
provided for drop-out, a person cited ‘stigma’ or
adverse drug reaction. Additionally, time independent
covariates were incorporated in the analysis. Data
preparation was prepared to reflect the PWP-GT
outline format as laid out by Therneau [15]. Primarily,
we sought to establish if the incorporation of
informative censoring improves estimation of the
hazard and rate estimates. While this study
acknowledges the possibility of competing risks, they
were not incorporated in this study.
2.3.3. Computing Environment
The models were assessed under the Rstudio
computing environment. To account for informative
censoring, the ‘method’ function within ‘reReg function’
in the reReg was set to "cox.HW". Fitting the models
was achieved by using the cluster and strata functions
in the base survival package required by the reReg
package. The Hmisc package was used to provide
basic descriptive statistics.
3. APPLICATION TO HIV DATA
3.1. Data Description
Determination of the incidence of due to LTFU was
computed using the cumulative baseline hazard
technique with start of ART as time 0 and LTFU at the
time a particular patient failed to return to CCC clinic for
38 weeks since the scheduled appointment date.
Patients who did not experience the event [LTFU],
were right censored at the last clinic visit. Other
patients exit such as mortality and transfer out were
considered as non-informative censoring as they relate
to LTFU, as mortality and transfer out that were known
to specific clinics and had happened within 38 days of
the last clinical appointment were managed in a
competing risk framework. After determination of LTFU,
several consulted efforts to retrace clients who are lost
are implemented. The efforts include calling back
clients and visiting them at their homes with the aim of
returning them back to clinic. Patients who return back
to care are exposed to recurrent of the event [LTFU].
Among the sample of LTFU clients, we also collected
other parameters include Patient ID: This is the patient
ID which may be repeated due to recurrence of LTFU,
time to LTFU: the event of interest is LTFU in this
setting which is recurrent, status; for episodes of LTFU
vs no episode; a particular individual can experience
several LTFU episodes, event (Informative Censoring);
the patient is no longer observed-Informative
censoring was defined by the patient being stopped
from highly active antiretroviral therapy (HAART) due
to either drug reaction/ stigma, Differentiated HIV care
for patients who are either under differentiated care
model or not, age of the patient, and gender of the
patient ARV regimen line as defined by WHO. All
PLHIV adults on HAART who enrolled at four facilities
in central Kenya in January 2013 to December 2018
were considered for analysis. Those who had at-least
one follow-up visit were eligible to be included. Children
below 15 years and confirmed pregnant mothers were
excluded. We also excluded PLHIV who had unknown
ART start date, unknown outcome, and transferred in
with incomplete base-line information. Data was pulled
from point of care electronic medical database,
consolidated in MS excel, and exported to R Studio for
further analysis. The main event variable in the
analysis was time to LTFU (in months) with other exits

24 International Journal of Statistics in Medical Research, 2020, Vol. 9 Ejoku et al.
treated as a competing event. LTFU was defined as
patients not taking ART refill for a period of 38 days or
missed clinical appointment over the same duration.
4. DISCUSSION
4.1. Recurrent Events Model
In this study, we extended PWP-TT model to cover
informative censoring when making inferences on
recurrent events under HIV retention setting. The
proposed methodology intrinsically extends the existing
method in literature on recurrent events under typical
HIV resource limited setting. A well-defined truncation
time T, with Zi overall i.e. !!!!" !!!"(!−!
!−
1)!exp![!!!!!] has been assumed. Here, we have
concentrated on the LTFU as recurrent events and
fitted real data. It can also be developed further to other
regression/Cox methods. The concept can be
extended to other approaches by modeling !!"[!]!and
!!![!−!
!−1]!with proportional hazards models. The
main purpose of this work was to provide an overview,
applicable statistical techniques when analyzing
recurrent event data under informative censoring in
HIV retention setting. The typical real data used in this
work is from a routine well established HIV care clinic.
The longitudinal approach to analyze recurrent-event
data applied here can also be applicable to other
observational cohort studies. Because the technical
approach employed here are extensions of Cox
proportional hazards regression, explicit issues that
affect model modification can also be handled in the
same manner as the classic applied techniques.
4.2. Results
Majority of the patients were female 37 (64%). The
average age was 36.4 years (SD=6.28). There were
256 incidences of patients lost to follow up, albeit there
were no noted incidences among seven patients. Table
2 shows a breakdown of incidence of LTFU as well as
those resulting from the informative terminal event,
stigmatization. These are disaggregated by gender and
age [binary covariate set at population mean]. Overall,
6 in 10 patients [61%] experienced 1 to 6 LTFU
incidences. The median time to LTFU was 8.6 months
[range: 3.0-82.9 months].
Patients were either censored at the end of the
study or informative drop-out due to stigma or drug
reaction. Sixteen instances of informative censoring
were reported. Comparison of crude proportions of
LTFU incidence due to stigma revealed a higher
incidence among patients above 37 years. However,
there was no significant difference by gender. The
timing of the LTFU incidences and corresponding
informative censoring arising from either stigma or drug
reaction are shown in Figure 2.
Additionally, cumulative sample mean plots are
provided to provide the cumulative number of LTFU
occurrences during the study period. The number of
incidences is shown to increase consistently across the
monitoring window.
To assess the performance of the proposed
PWP-TT model under joint modelling of both the failure
and event time, we apply it to the patient level data
described in section 3.1. For this analysis, sex [1 for
male, 2 for female], age [1 for ≤ 37, 2 for >37 years],
Regimen [1 for first line, 2 for second line], and
differentiated care [1 for on differentiated care, 0 for not
on differentiated care] were used. The event was LTFU
(1 for LTFU occurrence, 0 for no occurrence), while a
composite censoring variable was defined (1 if due to
stigma, 0 for other exits). Specifically, we investigate
the effect of these covariates on rate of LTFU and risk
of LTFU arising from stigma. Parameter estimates,
standard errors (SE), and corresponding p-values are
shown in Table 3. Standard errors were estimated by
resampling 100 times from patient data. Additionally,
Table 2: A distribution of the Total Number of LTFU Incidences Occurring among 58 Patients
Subgroup
Total
Patients
LTFU due to stigma
Number of LTFU incidences since ART start
0
1
2
3
4
5
6
7
8
9
Male
21
8
2
1
0
5
3
0
7
3
-
0
%
36%
50.0%
10%
5%
0%
24%
14%
0%
33%
14%
0%
Female
37
8
5
1
0
8
5
1
6
10
1
%
64%
50.0%
14%
3%
0%
22%
14%
3%
16%
27%
3%
Age ≤ 37
30
6
3
2
0
6
3
0
5
10
1
%
52%
37.5%
10%
7%
0%
20%
10%
0%
17%
33%
3%
Age > 37
28
10
4
0
0
7
5
1
8
3
0
%
48%
62.5%
14%
0%
0%
25%
18%
4%
29%
11%
0%

Analysis of Recurrent Events with Associated Informative Censoring International Journal of Statistics in Medical Research, 2020, Vol. 9 25
results from the AG and Cox model are also computed
(output not included) and compared.
From Table 3, it can be noted that patients on
differentiated care had lower likelihoods for both LTFU
recurrence (30% lower) as well as for the incidence of
LTFU arising from stigma (80% less likely). These
findings are unsurprising given that one well known
benefit of differentiated care models is to fight stigma.
Gender and age are also significant predictors of LTFU
due to stigma. The instantaneous risk for LTFU from
stigma is lower for females [82% less risk], but higher
for persons over the age of 37 years.
For the Cox model, none of the covariates was
significant for risk of LTFU from stigma. On the other
hand, the AG model also indicated a 73% risk of LTFU
from stigma for persons on a differentiated care
program, as well as a 23% reduced recurrence of
LTFU. The effect and direction of the other covariates
for the AG are also comparable with those for the
PWP-TT. These results suggest Cox regression for
recurrent events may not be suitable in observational
studies.
As an alternative to cox regression models, one
may consider using the Generalized Estimating
Equations (GEE), which may be employed in instances
of longitudinal and correlated data, especially if the
responses are binary. One key advantage of this
approach is its robustness in giving consistent results
even with a mis-specification of the correlation
structure. However one key limitation is that responses
need to be correlated, which is not always the case
with recurrent survival data.
On the other hand, the analysis of recurrent-events
based only on the first event time is not ideal when
examining the effect of risk factors. This is underlined
by Ullah et al., [16] who wrote several of articles on
Figure 2: Recurrent history of LTFU per patient. Red triangles represent informative censoring due to stigma/drug reaction. The
green circles are incidences of LTFU.
Table 2: Estimates for Risk Factors with Standard Errors, and p-Values
Risk factor
Estimate
SE
z value
p-value
LTFU Recurrence
Gender [base=Male]
0.043
0.131
0.323
0.746
Age [base is < 37]
-0.014
0.087
-0.166
0.868
Regimen [base= First line]
0.067
0.162
0.412
0.681
Differentiated care [Base=not on Differentiated care]
-0.356
0.164
-2.166
0.03
*
LTFU due to stigma
Gender [base=Male]
-1.694
0.544
-3.113
0.002
**
Age [base is < 37]
2.034
0.772
2.634
0.008
**
Regimen [base= First line]
0.618
0.518
1.192
0.233
Differentiated care [Base=not on Differentiated care]
-1.615
0.77
-2.097
0.036
*
Codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1.

26 International Journal of Statistics in Medical Research, 2020, Vol. 9 Ejoku et al.
recurrent injuries with a use of statistical methods,
which only account for the first event thus excluding
key information from subsequent injuries. Odhiambo et
al., [17] applies a Block-Borges-Savits (BBS) minimal
repair model to HIV retention data to recurrent event
data, with subsequent use of smooth tests to assess fit.
Several approaches have been proposed in
literature to account for censoring that rises in survival
analysis setting.
The major assumption in AG model is that the
inter-event time increments are conditionally
uncorrelated with given covariates. It also assumes the
same baseline hazard for all persons, which may not
be the case for LTFU in an HIV setting, given that
intensive adherence counseling may alter the
subsequent likelihood of an individual getting LTFU. On
the other hand, it is best suited to cases of independent
increments across observation units, and is also the
easiest extension to the Cox model to replicate. On the
other hand, either of the PWP models (GT or TT)
adjusts for varying baseline hazards across
observation units which may be efficient in the case of
LTFU, where due to adherence counseling, the
baseline hazard may change.
Generally, the choice of recurrent event data
analysis technique is determined by several factors, i.e.
events; relationship between events; varying effects
across recurrences; the medical/biological process;
and independence/dependence structure. Usually the
stratified models, as PWP [total or gap times] or
multi-state models, are useful whenever there are
relatively few recurrent-events per individual and the
risk of recurrences.
A recurrent events model will ideally help to provide
insights into the program/disease structure and
process. Hence, it is critical to consider the censoring
mechanism and perform analysis that enhances
comprehension of the risk factors.
LTFU
In a typical HIV care clinic, the risk posed by
instances of LTFU is undesired and has the potential of
undoing antiretroviral treatment benefits. Specifically,
patients’ retention in HIV care is critical to ensuring
better health outcomes especially in reduced viral load
suppression, mitigating mortality and averting possible
drug resistance caused by non-adherence.
In spite of the multiple interventions in place to
address incidences of LTFU among HIV patients like
enhanced adherence counselling, within-person cases
of LTFU are usually common and recurrent in nature,
with the present likelihood of a person getting lost to
follow-up influenced by previous occurrences.
ABBREVIATION
AD = Anderson and Gill
AIDS = Acquired Immunodeficiency Syndrome
ART = Antiretroviral Therapy
BBS = Block-Borges-Savits
GEE = Generalized Estimating Equations
HAART = Highly Active Antiretroviral Therapy
CCC = Comprehensive Care Center
DCM = Differentiated Care Model
HIV = Human Immunodeficiency Virus
HR = Hazard Ratio
LTFU = Lost to follow-up
LWA = Lee, Wei and Amato
PWP-GT = Prentice, Williams, and Peterson gap time
PLHIV = Persons Living with HIV
PWP-TT = Prentice, Williams, and Peterson total
time
SD = Standard Deviation
SE = Standard Error
WLW = Wei, Lin and Weissfeld and
INH = Isonicotinylhydrazide
WHO = World Health Organization
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Received on 26-02-2020 Accepted on 19-03-2020 Published on 29-03-2020
https://doi.org/10.6000/1929-6029.2020.09.03
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