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1. Prepared by A.N.
1
Joint Modeling of Longitudinal Measurements and Survival Time to
Cardiovascular Disease Complication among Hypertensive Patients Treated at
DebreTabour Specialized Hospital, Ethiopia

2. Outline of the presentation
2
 Introduction
 Statement of the research
problem
 Objective of the study
 Materials and methods
 Study Design
 Study Area
 Sampling Procedure
 Study Variable
 Data analysis
 Result
 Discussion
 Conclusion
 Limitation

3. Introduction
3
 Hypertension is one of the silent killers among non-communicable chronic diseases that
is the leading risk factor for cardiovascular disease complications like heart disease (such
as coronary artery disease, congestive heart failure, heart attack), stroke (such as cerebral
infraction, cerebral hemorrhages), kidney disease and impaired vision[1, 2].
 It is also called blood pressure (BP), a situation in which the arteries are elevated,
requiring the heart to work beyond normal to circulate blood through the blood
vessels[3].
 BP is often defined with two measurement quantities (i.e., systolic blood pressure [SBP]
and diastolic blood pressure [DBP].
 Clinically a person is said to be hypertensive if the individual's SBP is greater than 140
mmHg

4. Cont.
4
 and/or DBP is greater than 90 mmHg and those who were already under
medication [4, 5].
 Non-communicable diseases (NCDs) are the major cause of death in the
world and one of the health challenges of the 21st century [6].
 According to WHO report, they were held responsible for 71 %( 41
million) of the 57 million deaths which is occurred globally, the major
NCD responsible for these deaths was cardiovascular disease (17.9 million
deaths accounting for 44% of all NCD deaths)[7].

5. Cont.
5
 A study conducted in, 2017 in 195 countries showed hypertension as a
major public health problem.
 For example, among 1.13 billion deaths globally, 12.8% of these deaths
were attributed to hypertension[8]. Similar study conducted in Africa
revealed 46% of the adult population had hypertension which is the
highest in the world [9].
 According to WHO report, hypertension was responsible for at least
45% of global deaths due to heart death and 51% due to stroke.
 Another study conducted in Australia among 6083 hypertension
patients showed that 373 participants developed heart failure [10].

6. Cont.
6
 Non-communicable diseases like hypertension and vascular disease
are the highest burden of morbidity and mortality in Africa [11].
 In the first half of the 20th century, hypertension was almost non-
existent in Africa, but currently, estimates show that in Africa more
than 40% of adults have hypertension [9].
 It is estimated that the number of hypertensive patients in Sub-
Saharan Africa would rise to 150 million by 2025 because of
demographic and epidemiologic transitions[12, 13].

7. Cont.
7
 Current disease assessments in sub-Saharan Africa suggest that
there is a wide imbalance (0.4-47.5%) in the prevalence of
hypertension, with Ethiopia considered to share a similar high
profile of hypertension in sub-Saharan Africa [14, 15] .
 According to WHO report revealed that 34% of all deaths in
Ethiopia were due to non-communicable diseases (NCDs) among
which 12% contribute to cardiovascular disease.

8. Statement of the research problem
8
 Given the interdependence of these determinants on the onset of
hypertension, jointly evaluating these interrelated factors that may alter
rate of change in cardio metabolic outcomes could be very useful in
developing appropriate public health interventions[17].
 Besides, many researchers have conducted their studies using a cross-
sectional study design, which does not show the progression of the
disease over time or used multiple linear regression or logistic
regression to identify determinants factors without considering the
correlations within the multiple outcomes and subject-specific random
effects.

9. Cont.
9
 Some studies[4, 18] have been conducted related to hypertension and
risk factors that lead to developing cardiovascular disease complication
to determine survival time and longitudinal outcome separately.
 These methods of analysis do not consider the dependencies or
interrelationships between different data types such as longitudinal and
time to event data types.
 As a result, separate analyses may not be appropriate when repeated
measurements and time‐to‐event data are correlated and fail to take into
account all the available information in an integrated manner[19].

10. Cont.
10
 In many clinical studies, longitudinal biomarkers and the event time of interest
are collected simultaneously to explore their association.
 This study applied joint modeling framework since the main significance of this
study was reduced biased associated with measurement error and missing data.
Because survival model with time-dependent covariates may be measured with
an error or maybe missing and to reduce possible biasness associated with
informative dropouts since longitudinal data record with informative dropout
since we need to model time to dropouts (i.e., to detect survival probability of
hypertension patient’s under follow up).

11. Objective of the study
11
 General Objective
 The objective of this study was to identify factors that affect multivariate
longitudinal change of hypertension and survival time to cardiovascular
disease complication jointly among hypertensive patients under follow up at
DebreTabor Specialized Hospital, DebreTabor, Ethiopia.
 Specific objective
 To determine the factor that affect the survival time to CVDCs among HTN
outpatients treated at DTSH.
 To identify factors that affect SBP,DBP, and survival time to CVDCs among
HTN outpatients jointly at DTSH.

12. Cont.
12
 To identify the association between longitudinal measurements and survival
time to event outcome among hypertensive patients jointly treated at DTSH.
 To compare multivariate linear mixed model and multivariate linear mixed
model with time to event outcome jointly.

13. Materials and Methods
13
 Study Design, Study Area and Sampling Procedure
 Hospital based retrospective studies were conducted among
adult hypertensive outpatients attending at hypertension (HTN)
clinic between September 2017 to December 2019 at Debre
Tabor Hospital. Debre Tabor Hospital is the only specialized
hospital in south Gondar zone. It is located 666 km and 107 km
far from Addis Ababa the capital city of Ethiopia and Bahir Dar
the capital city of Amhara regional state respectively.

14. Cont.
14
 In this study, the sample size was calculated using the Schoenfeld
formula to obtain statistically significant results [20],therefore, based on
the study [21] the risk of developing heart attack were 1.39 with 95%
CI compared to without hypertension and power 0.8.
 The study considered hypertensive outpatients whose age greater than
18 years old using patient's identification number. Therefore, among the
HTN outpatients registered from September 2017 to December 2019
at Debre Tabor Hospital, a total of 178 outpatients were obtained using
simple random techniques in which HTN outpatients satisfied the
inclusion criteria.

15. Study variables
15
 Two longitudinal and one survival outcome variables were considered
in this study. These were SBP and DBP in mmHg for the longitudinal
and time to develop cardiovascular disease complication in months
from September 2017 to December 2019.
 The status of time to develop cardiovascular disease complication
among hypertensive outpatients under follow-up at DTSH was coded
as censored (0) and event (1).Predictors included in this study were
socio-demographic characteristics and clinical related characteristics.
Detail description of predictors depicts in Table 1 to 3 below.

16. Data analysis
16
 In this study, both descriptive and inferential statistical analyses were used.
 The data was coded and entered into a statistical package for social science
(SPSS) version 26 and R version 4.0.0 with joineRML package was used for
analysis and statistical decision was made at 5% level of significance
 The study was used three different models namely; the linear mixed-effects
model for bivariate longitudinal measurements of hypertension [4, 5], the cox-
proportional hazard model for time to develop cardiovascular disease
complication [22], and the bivariate joint model for longitudinal and survival
sub-model linked by shared random effects [23].

17. Cont.
17
 MVJM is linked to sub-models for multivariate longitudinal data, and a sub-
model for survival time. In this study we used models for longitudinal data and
survival time are mixed effect model and cox proportional hazard models
respectively.
 Let 𝒀𝒊𝒌(𝒕𝒊𝒋𝒌) denote the 𝒋𝒕𝒉 observed value of the 𝒌𝒕𝒉 longitudinal outcome for
subject 𝒊, measured at time 𝒕𝒊𝒋𝒌, for 𝑖 = 1, …, 𝑁; 𝑘 = 1, …, 𝐾, and 𝑗 = 1, …, 𝑛𝑖𝑘.
 A multivariate linear mixed model (MLMM) is a common approach, where
measurements for different outcomes can be recorded at different times between
patients and outcomes[16], and is given by:
𝒀𝒊𝒌 𝒕𝒊𝒋𝒌 = 𝑿𝒊𝒌
𝑻
𝒕𝒊𝒋𝒌 𝜷𝒌 + 𝒁𝒊𝒌
𝑻
(𝒕𝒊𝒋𝒌)𝒃𝒊𝒌 + 𝜺𝒊𝒌

18. Cont.
18
 where 𝑿𝒊𝒌
𝑻
𝒕𝒊𝒋𝒌 and 𝒁𝒊𝒌
𝑻
(𝒕𝒊𝒋𝒌) are row-vectors of covariates for subject 𝒊,
associated with fixed and random effects respectively which can vary by
outcome; 𝜷𝒌 is a vector of fixed effects parameters for the 𝒌𝒕𝒉 outcome ,and
𝒃𝒊𝒌 is a vector of subject-specific random effects for the 𝒌𝒕𝒉,outcome.
 We denote the vector of subject-specific random effects for all 𝑲 outcomes
by 𝒃𝒊𝒌 = (𝒃𝒊𝟏, 𝒃𝒊𝟐, 𝒃𝒊𝟑)𝐓 ∼ 𝐍(𝟎, ∑ ). The 𝜺𝒊𝒌 is the corresponding
measurement error term such that, 𝜺𝒊𝒌 ∼ 𝐌𝐕𝐍(𝟎, 𝚿) . Assume that the
measurement errors of different longitudinal outcomes are independent of each
other, and they are also independent of the random effects 𝒃𝒊𝒌.

19. Cont.
19
 For survival outcome, we consider the Cox proportional hazard
model[17],given as:
𝒉𝒊 𝒕 = 𝒉𝒐(𝒕)𝐞𝐱𝐩(𝜶𝒊
𝑻
𝑿𝒊 𝒕 + 𝜸𝒊(𝒕))
 Where 𝑿𝒊 represents the vector of baseline covariates with
corresponding parameter estimates 𝜶𝒊 ; 𝒉𝒐(𝒕) denotes the
baseline hazard function, and 𝜸𝒊(𝐭) is the latent process that
captures the association structure between the measurement and
event process.

20. Result
20
Descriptive Statistics
 There were 178 patients in the study with antihypertensive drugs
treated. Among those patients considered in the studies,
52(29.2%) were developing cardiovascular disease, whereas 126
(70.8%) were censored.
 The result showed that 32(30.8%) of female patients were
developing cardiovascular disease which is greater than the male
patients 20(27%).

21. Cont.
21
 In addition, the majority of HTN patients 94(52.8%) resided in urban areas.
Among those, 29(31%) were developing cardiovascular disease complications
while 84(47.2%) lived in rural area; among those, 21(25%) were developing
cardiovascular disease complication.
 About 75 (42.2%) had diabetic disease; among those, 31(41.3%) of patients
were developing cardiovascular disease which is greater than patients who
had no diabetes.
 About 50 (28.1%) of hypertensive patients had a history of hypertension from
their family; among those, 29(58%) of patients were developing
cardiovascular disease complication which is greater than patients who had no
history of hypertension from their family.

22. Cont.
22
 Patients with clinical Stage II accounted for 23(40.4%) of
developing cardiovascular disease complication compared to
pre-stage 10(15.9%), and Stage I 19(27.9%) respectively.
 Patients who had a history of cardiac disease from their family
accounted for 28(73.7%) of developing cardiovascular disease
compared to no history of cardiac disease from their family.

23. Cont.
23
Table 1: the distribution of important socio-demographic and clinical characteristics of
hypertensive patients treated at DebreTabor Hospital.

24. Non-parametric analysis for survival data
24
 The estimates of the Kaplan-Meier survival functions of HTN
patients for different categories of the study variables are
displayed using different plots.
 From Figure 1, the plots indicate that patients who had no
diabetes had higher survival times than patients who had a
diabetic disease, and patients who resided in the rural area had
higher survival times than patients who resided in the urban area.

25. 25
Figure 1: Kaplan-Meier survival estimates of different groups of hypertensive patients
at DebreTabor Hospital, Ethiopia.

26. Cont.
26
 The Log-rank test is used to check the significant differences
among categorical variables.
 Table 2 shows the log-rank test of each categorical variable
reveals that family history of hypertension, diabetic disease,
residence, clinical stage of hypertension, family history of
cardiovascular disease was statistically significant at a 5% level
of significant.

27. 27
Table 2: Results of the Log-rank test for the significant categorical variables of HTN
patients treated at DebreTabor Hospital.

28. Cont.
28
Variables
Categorie
s
rho
chi-
square
statistic
p-
value
Age -0.17029 2.0629
1
0.151
Sex (ref= Female) Male -0.03453 0.0673
7
0.795
FHHTN (Ref=No) Yes -0.06311 0.1637
0
0.686
Diabetic disease
(Ref=No)
Yes -0.09774 0.5852
0
0.444
SHTN (ref= Pre
stage)
Stage I
-0.11181
0.6093
1
0.435
Stage II
-0.1548
1.1685 0.280
Table 3: Results of proportionality assumption for the significant categorical variables
of HTN patients treated at DebreTabor Hospital.

29. 29
Similarly, the Sheonofield residual plot shows that there is no systematic departure
in the plots or there is no pattern with time in the covariates sex, clinical stage of
hypertension, family history of hypertension, and family history of cardiovascular
disease since the proportionality assumption is satisfied.

30. Cont.
30
Predictors Categori
es
Estimate
s
Std
error
HR 95% CI (L-
U)
P-
value
Age 0.00465 0.3200 1.0046 0.985 -
1.024
0.0371
1
Sex (ref=female Male .1665 0.3404 1.1812 0.606 -
2.302
0.6246
3
Residence
(ref=Urban
Rural -0.7718 0.3200 0.4621 0.246 -
0.865
0.0158
Diabetes(ref =
No)
Yes 1.394 0.1419 4.033 2.212 -
9.466
0.0002
FHTN(ref = No) Yes 1.2932 0.4641 3.644 1.467 -
9.0521
0.0053
4
SHTN(ref = pre-
stage)
Stage I 1.5449 0.1425 0.6659 1.286 -
2.242
0.0173
4
Stage II -0.4064 0.1708 1.2089 0.5049 –
1.573
0.1831
FHCVD(ref = No) Yes 1.8791 0.1443 6.5480 2.823 - 0.0001
Table 4: Multivariable Cox proportional hazards regression analysis of time to CVDCs of
hypertensive patients treated at DebreTabor Hospital.

31. Longitudinal data analysis
31
 The individual profile plot was obtained in order to gain some
insights of the data over time.
 The individual profile plot showed that there is change over time
in individual HTN outpatients' SBP and DBP measurements.
 In addition, the loess smoothing technique suggests that the mean
structure of SBP and DBP was nearly linear over time and the
average SBP and DBP was linearly decreases over time (Figure 3).

32. 32
Figure 3: Individual profile and loess smoothing plots for SBP and DBP of HTN
outpatients over visiting time at Debre Tabor Hospital, Ethiopia.

33. 33
Figure 4: average trend line of SBP, and DBP over a time with cardiovascular disease
complication

34. Cont.
34
 The blue and red curves represent the mean blood pressure profile for
cardiovascular disease complication (event) and (censored) groups
respectively.
 We observed from Figure 4 shows that patients whose systolic blood
pressure and diastolic blood pressure were higher and fasting blood
progression tend to have a high risk of cardiovascular disease
complications and also mean systolic blood pressure and diastolic
blood pressure were higher overtime for the event group than censored
group, indicating a potential association between the risk of CVD
complication and longitudinal SB, and DBP measurements.

35. Analysis of bivariate longitudinal mixed effect model
35
 Before fitting the joint model, the bivariate longitudinal mixed effects
model was fitted with different covariance structure and bivariate
longitudinal mixed effects model with UN shows that significantly best
with smaller AIC and BIC, which indicates that model with random
intercept and random slope was a better fit for bivariate longitudinal
outcomes
 Thus, the bivariate longitudinal mixed-effects model used to fit for SBP
and DBP.

36. 36

37. 37

38. Joint analysis of SBP & DBP with time to cardiovascular diseases
complication
38
 In this subsection, the longitudinal SBP, DBP, and time to
cardiovascular disease complication were fitted together.
 The association between the repeated measures of SBP, and DBP
with survival time to cardiovascular disease complication among
hypertensive outpatients using a linear mixed-effects sub-model
and a cox proportional hazards survival sub-model jointly were
addressed.

39. Cont.
39
 The estimated association parameter ( 𝜸 ) was significantly
different from zero (p-value < 0.05), indicating that there is a
positive association between SBP, DBP and survival time to
cardiovascular disease complication.
 The result indicates the slope of SBP, and DBP measurement were
positively associated with cardiovascular disease complication. A
unit increase of SBP and DBP measurements increases the risk of
cardiovascular disease complication

40. 40

41. 41

42. Comparison of separate and joint models
42
 When evaluating the overall performance of the separate and joint models in
terms of model parsimony and goodness of fit, the joint model was preferred
as it has a smaller AIC than the separate model.
 Moreover, the statistical significance of the association parameters is
evidence that the joint model is better than the separate models. As Table 4
revealed, the estimate of the association parameters in the survival sub-model
analysis under the joint model were significantly different from zero, this
indicates that the two outcomes were correlated. Therefore, the joint model
was found preferable to fit the data better over the separate.

43. Discussion
43
 This study assessed predictors that are associated with hypertension measurements (SPB;
DBP) and survival time to cardiovascular disease complications among HTN outpatients
at Debre Tabor Hospital in Ethiopia.
 Our study identified factors associated with longitudinal sub-model and survival sub-
model. The longitudinal sub-model showed that age was an important socio-demographic
predictor of SBP, suggesting that the average SBP increases with an increase in age.
 A study conducted in Jimma University Specialized Hospital, and Felege Hiwot Referral
Hospital, Ethiopia using a linear mixed model revealed similar findings where one year
increment of age was associated with increment of SBP in mmHg[4, 24]. The noted
findings shows an age-dependent risk of SBP over time, inferring that an older person has
a higher systolic pressure than a younger person with no minimal risk because arterial
stiffness due to ageing [25, 26].

44. Cont.
44
 The present study stated that average SBP and average DBP were higher for
patients who had diabetes compared to patients who had no diabetic disease.
Consistent with previous studies the average SBP and DBP of patients
who had diabetes disease was significantly increased compared to patients
who had no diabetes disease. Which state that co-existence of diabetes
mellitus and hypertension is also associated with accelerate blood pressure
rising.
 Our studies consistent with previous studies the average SBP and DBP
were higher for patients who had a history of HTN with their families
compared to patients who had no history of HTN with their families.
[4, 27, 28]
[29-31],

45. Cont.
45
 The possible reason could be increased renal proximal sodium
reabsorption.
 The average SBP and DBP with time to cardiovascular disease
complication of hypertensive patients were significantly associated with
the diabetic disease.
 A study conducted in United States revealed similar finding where an
association between increased SBP and DBP, the development of
cardiovascular events which is more pronounced in hypertensive
patients with diabetes than without diabetic disease[32].

46. Cont.
46
 Consistent with previous studies the survival sub-models in the
current study revealed a higher risk of cardiovascular complications with
diabetes than patients who had no diabetic disease or the hazard of
patients with diabetes higher than patients without diabetes.
 It was argued that the risk of cardiovascular complications in patients for
those who had developed diabetic disease has a higher probability risk of
cardiac complication than those who had not to develop the diabetic
disease.
 The risk of patients with a history of cardiovascular disease with their
family was higher than patients who had no history of cardiovascular
disease with their family.
[33, 34],

47. Limitations
47
 This study was conducted only based on secondary data from
one hospital. In addition, the authors did not see the interaction
effect of the predictors and hence results may vary while
considering more hospitals all over Ethiopia and including
interaction effects. Therefore, researchers should consider
hospitals all over Ethiopia and including interaction effects of
predictors in the model.

48. Conclusion
48
 The estimate of the association of SBP and DBP are positively
significant with time to developing cardiovascular disease complication
of HTN patients. And hence in this study the bivariate mixed-effects
and a cox proportional hazards survival sub-model jointly were
preferred based on the minimum AIC value criterion.
 The joint bivariate mixed effects model analysis shows that HTN
patient with family history of HTN and clinical stage II of HTN were
developed cardiovascular disease complication and have high average
SBP and DBP compared to their counter groups.

49. Cont.
49
 Similarly, HTN patients with diabetes were have high SBP and DBP
compared to their counter groups and in general SBP and DBP became
stable over the follow up time of treatment.
 In light of the results of this study, the researchers suggested that health
professionals and concerned bodies should focus on patients with diabetes,
family history of HTN, clinical stage II of HTN, family history of
cardiovascular disease, aged and poor adhere patients to control HTN and
cardiovascular disease complication.
 Further, authors recommended that paying attention to treatment time to
stable progression of DBP and SBP of patients.

50. References
50
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1990 and 2010: a systematic analysis for the Global Burden of Disease Study 2010. The
lancet, 2012. 380(9859): p. 2095-2128.
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renal disease: overview of evidence from observational epidemiologic studies and randomized
controlled trials. American heart journal, 1999. 138(3): p. S211-S219.
 Chobanian, A.V., et al., Seventh report of the joint national committee on prevention,
detection, evaluation, and treatment of high blood pressure. hypertension, 2003. 42(6): p.
1206-1252.
 Workie, D.L., D.T. Zike, and H.M. Fenta, Bivariate longitudinal data analysis: a case of
hypertensive patients at Felege Hiwot Referral Hospital, Bahir Dar, Ethiopia. BMC
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 Unger, T., et al., 2020 International Society of Hypertension global hypertension practice
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