1. BAHIR DAR UNIVERSITY
College of Science
Department of Statistics
Joint Modeling of Multivariate Longitudinal Measures of Hypertension and
Time to Develop Cardiovascular Disease Complication among Hypertensive
Outpatients Treated at DebreTabor General Hospital, Ethiopia.
By: Abebe Nega Zelelew
August, 2020
BahirDar, Ethiopia
2. Outline of presentations
Introduction
Statement of the problem
Objective of the study
Significance of the study
Methodology
Study design and Area
Sample size and sampling procedure
Variables in the study
Joint models of longitudinal and
survival data analysis
Method of parameter estimation
Result and Analysis
Results
Discussion
Conclusion
Recommendation
3. Introduction
a study conducted by Son 2018, Workie 2017 and world health
organization 2019, Hypertension defined as, a chronic elevation of blood
pressure of an individual whose systolic blood pressure (SBP) is greater
than 140 mmHg and/or diastolic blood pressure (DBP) is greater than 90
mmHg and those who were already under medication.
In addition, a patient whose pulse rate (PR) is greater than 80 beat per
minute(bpm) and above also consider hypertensive (Cunha and Marks,
2011).
hypertension is the most frequent cardiovascular disease like coronary
artery disease, congestive heart failure, renal failure, stroke, acute
myocardial infarction, and impaired vision .
4. Conti.
According to World health organization 2017,Cardiovascular disease (CVD)
defined as an abnormal functioning of the heart or blood vessels in the body
(Organization).
According to World Health Organization 2019 statistical report revealed that
17.9 million of death in the world was caused by cardiovascular disease
among these death 7.4 million were due to coronary heart disease and 6.7
million were due to congestive heart failure (Kaptoge et al., 2019).
study conducted by (Twagirumukiza et al., 2011), hypertension has become
major public health problem of human being globally. Among 1.13 billon
death in the world 12.8% of death contributed hypertension.
5. Conti.
Similar study conducted in Africa showed that 47.5% of adult population had
hypertension in sub -Saharan country (Anteneh et al., 2015).
sub-Saharan country had the highest burden of raised blood pressure as
compared with the highest income country(Zhou et al., 2017)
A research conducted in Ethiopia also revealed that 15% of all deaths were due
to non-communicable disease (NCD) among this cardiovascular disease was
contributed 24%, from this hypertension was contributed 12% of the total
cardiovascular disease deaths(Misganaw et al., 2012).
6. Statement of the research problem
Studies conducted by (Urrutia, 2016, Seifu , 2017) revealed that the problem
of chronic diseases is severing issue and cardio vascular disease have
significantly increased and the incidence and prevalence of hypertension is
continue to increase.
studies have been conducted related to hypertension and risk factor that leads
to develop cardiovascular disease complication to determine survival time and
longitudinal outcome separately.
For instance, Workie, 2017 and Fissuh, 2017 conducted a study by using
mixed effect model with unstructured variance covariance matrix in order to
explore the association between SBP and DBP response variables (Workie et
al., 2017, Fissuh, 2017).
7. Conti.
Gesese, 2017 was conducted a study on time to cardiovascular disease
complication of hypertensive outpatients to compare the survival experience of
patients.
These methods of analysis are do not consider association between longitudinal
and time to event data types.
In addition researchers conducted based on cross-sectional study design, identify
determinant factors without considering the correlations within the multiple
outcomes and subject specific random effects.
Therefore to handle this issue, this study focused on identifying factors that affect
the multivariate longitudinal measures and time to develop cardiovascular disease
complication jointly among hypertensive outpatients treated at DebreTabor
General Hospital.
8. Objective of the study
General objective
The general objective of this study was identify factors that affect multivariate
longitudinal change of hypertension and time to develop cardiovascular disease
complication jointly among hypertensive outpatients under follow up at
DebreTabor General Hospital, DebreTabor, Ethiopia
Specific objectives
To determine the factors that affects the time to cardiovascular disease
complication among hypertensive outpatients at the study area.
To identify factors that affect SBP, DBP, PR and time to develop
cardiovascular disease complication jointly at study area.
9. Conti.
To identify the association between SBP, DBP, and PR with time to
cardiovascular disease complication among hypertensive outpatients
jointly in the study area.
To compare separate multivariate linear mixed model and multivariate
linear mixed model with time to event data jointly.
10. Significance of the study
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 error or may be missing.
and to reduced possible biased associated with informative dropouts because
longitudinal data record with informative dropout since we needs to model time
to dropouts.
identify the association between multivariate longitudinal sub model and
survival sub model, that means to identify the longitudinal biomarkers (SBP,
DBP, and PR) was associated with time to cardiovascular disease complication.
11. Data and Methodology
Study design and Area
Retrospective study design was conducted at DebreTabor General Hospital, DebreTabor,
northwest Ethiopia.
Sample size and sampling procedure
A simple random sampling method was employed for selecting a representative sample of
hypertensive outpatients attending at hypertension clinic under the follow-up September
2017 to December 2019
Sample size determination
In this study, the sample size determination was take on Schoenfeld formula
𝑛 =
(𝑍𝛽 + 𝑍𝛼
2
)
𝑃1∗𝑃0 ∗𝐻𝑅2
2
where n = the total sample size required ,𝑃1 and 𝑃0 were the probability
of occurring event in the two group, HR were the hazard ratio of event occurrence among
hypertensive patients as compared to non hypertensive patients.
Then using the above formula the total sample size was estimated to be 178.
12. Variables in the study
Dependent variables
Three Longitudinal and one survival outcomes were considered in this
study as response variables.
These were SBP and DBP in mmHg and PR in beat per minute for the
longitudinal measurements and time to develop cardiovascular disease
complication in months from September 2017 to December 2019.
Independent variables
The independent variables for this study were socio-demographic variables
and clinical factors presented in the table here
13. Statistical Models of Data Analysis
In this study three types of different statistical models were applied.
survival model to investigate the determinate factors that can affect survival
time to event.
Linear mixed model were used to determine factors that affect the three
longitudinal change of SBP & DBP in mmHg and PR in bpm.
Joint longitudinal and survival analysis were used to evaluate the impact of
longitudinal change of SBP, DBP and PR on survival time to cardiovascular
disease complication among hypertension outpatients.
normal Q-Q plot, P-P plot, box plot, individual profile plot, mean profile plot
and the Kaplan Meier curve were used as data exploration.
14. Linear mixed model
Linear mixed model (LMM) is a parametric linear model for longitudinal or
repeated measures data that quantifies the relationships between a continuous
dependent variable and various predictor variables.
LMM takes in to account both fixed effect and random effect terms.
The random effect contains subject specific random effect and the fixed effect
contains the set of predictors that are fixed across the subjects or the same for
all subjects.
In this study we used multivariate linear mixed model.
16. Survival data analysis
the process of analyzed time data for a certain event of interest to occur.
Analysis the time that an individual has survived over some follow-up
period.
In summarizing survival data there are two functions of central interest.
survivor function S t , it defined to be the probability that the survival time
of a randomly selected subject is survive beyond some specified time t .
S t = P T ≥ t = t
∞
f(u) du = 1 − F t , t ≥ 0
17. Hazard function (h (t))
the risk of event occurrence at time t. It is obtained from an individual
occurred event at time t, given that the individual has survived up to
time t .
Estimation of the survival function
Kaplan-Meier (KM): It describes whether there is difference in time to
event between difference categories of covariates.
Log-rank test: test used to check for significance differences among
categories of covariates.
Cox proportional hazard model
there are no assumptions about the shape of the baseline hazard
function.
test survival times between two or more groups are different after
adjusting other covariates.
18. Joint models of longitudinal and survival data analysis
In clinical studies, the outcomes recorded on each subject include both a repeated
measurements and the time at which an event of particular interest occur.
So JM used to taking account of association between the repeated measurement
and survival time-to-event outcome.
Longitudinal sub model
yik tijk = 𝑋′
ik tijk βk + 𝑍′
ik tijk bik + εik
Survival sub model
the two sub-models are linked through shared parameters.
hi t = ho t exp{ αi
T ∗ ωi + [γ1yi1 t + γ2yi2 t + γ3yi3 t ]}
Where: αi
T
is the design matrix of baseline covariates, yi1(t), yi2(t)& yi3(t) ,
represents the history of the true (unobserved) longitudinal response.
19. Method of parameter Estimation
for this study maximum likelihood estimation methods were used for LMM and
Cox PH model.
a Maximum-likelihood approach using the EM algorithm used parameter
estimation for joint models of multiple longitudinal processes and a time-to-
event outcome.
Variable selection: In this study purpose full variable selection method was used
to fit cox proportional hazard model.
Model selection: choose the better model that provides best fit to the data.
20. Conti.
Model diagnostic: are used to evaluate the model assumptions and adequacy
of the model.in this study we used residual plot and tests.
Missing data treatment: there are several ways of missing data treatment.
In this study we used multiple imputation method, replace each missing item
with two or more acceptable values.
21. Chapter four
Result and Analysis
Descriptive statistics of baseline covariates was illustrated in Table 3.1
The sample was composed of 178 patients with antihypertensive drugs treated
at DTGH, of which 104 (58.4%) were males and 84(47.1%) lived in rural areas.
About 75 (42.2%) had diabetic disease and 50 (28.1%) of hypertensive patients
had history of hypertension from their family.
Among the total of 178 hypertensive patients during the time period 52(29.2%)
were develop cardio vascular disease whereas 126 (70.8%) were censored.
Among 52 cardio vascular disease complication 20(11.3%) were male and
31(17.4%) had diabetic disease and 29(16.3%) had history of hypertension
with their family.
22. Non-parametric analysis for survival data
In order to seen whether there is a difference in time to cardiovascular disease
complication between different categories of the covariates Kaplan- Meier
curves were used.
From the figure 4.1 revealed that the probability of event over a time was
decreased.
Log-rank test is used to check the significance differences among categorical
variable.
From table 4.3 revealed that family history of hypertension, diabetic
disease, residence, clinical stage of hypertension, family history of cardio
vascular disease were statistically significant at 5% level.
23. Cox proportional hazards model
Before fitting the Cox-(PH) model, it is common to check the proportionality
assumption by Scaled Schoenfeld residual tests and plots
From table 4.4 showed that the correlation does not statistically significant
for each of the covariates, and the global test also not statistically significant.
From the graphical inspection(schonfildes residual plot), there is no pattern
with time. Therefore, the assumption of Cox proportional hazard model is
valid.
Variable selection for proportional hazards model
In this study purpose full variable selection method was used to fit cox
proportional hazard model. first fit univariable model for each predictors and
then select variables that were significant at 25% level and taken as candidate
variable for multivariable analysis.
24. Conti..
from Table 4.5 sex, age, diabetes, residence, family history of hypertension,
clinic stage of hypertension, family history of cardio vascular disease, and
adherence status were found to be candidate variables for univariable analysis
at 25% level of significance. except age, sex and adherence status all variable
were candidate variable for multivariable analysis at 5% level of significance.
Data exploration for longitudinal data
To check the normality of the longitudinal measures of SBP, DBP and PR the
normal Q-Q plots, P-P plot and box plot were used.
The plots showed that the normal Q-Q plots, P-P plots and box plot for the
longitudinal measure of SBP, DBP and PR of actual data seems to satisfy the
assumption of normality.
25. Profile analysis
From the figure 4.3 it indicates patients started differently at different
baseline SBP, DBP and PR and patients have different evolutions at different
time point.
From the figure 4.4: Loess smoothing plot with the average trend line of SBP,
DBP, and PR of hypertensive outpatients.
It shows that the black line loess smoothing technique suggests that the mean
structure of the SBP, DBP and PR was nearly linear overtime (i.e., the
relationship between the three biomarkers and visit time seems to be linear)
and the mean SBP, DBP and PR was decreased overtime.
Figure 4.5: shows the profile plot of SBP, DBP, and PR with the average trend
line for age of hypertensive outpatients.
26. Conti.
Plots of SBP, DBP, and PR against age observe that the relationship between
SBP, DBP, PR with age of patients seems to be linear.
The average SBP, DBP and PR was increased when age of patients also
increased.
From figure 4.6: average trend line of SBP, DBP, and PR with cardiovascular
disease complication status.
patients whose blood pressure were higher tends to have high risk of cardio
vascular disease complication.
The mean blood pressure of patients were higher for the event group than
censored group.
From the figure we observed that the three biomarkers and event time had
positively associate.
27. Univariate analysis of linear mixed model
In this model fit separate mixed effects model for each outcome and determine the
components to be included in the model.
Selection of covariance structure in linear mixed model
unstructured variance covariance matrix was used due to the smallest AIC and
BIC for all response variable compared to the remaining covariance structures.
Selection of random effects for longitudinal measurements
Based on the information criteria, random slop and random intercept was better
fitting the model.
Variable selection in longitudinal data
by using purposeful variable selection the analysis was started by fit univariate
model with each variable and select the variables that were significant at 25 %
level and taken as candidate variable for multivariable analysis then fit
multivariable model.
28. Multivariate analysis of linear mixed model
MVLMM was used to fit the three response variables, SBP, DBP, and PR
simultaneously.
random intercepts and random slope for each response are correlated rather
than independent.
From the table 4.6 revealed that age, DM, Residence, SHTN, and
observation time were associated with SBP. DM, FHHTN, SHTN, adherence
and observation time were significantly associated with DBP.
The predictor FHHTN, DM and observation time were statistically associated
with PR.
the variance covariance matrixes in MVLMM shows variability was higher in
random intercept than random slop of each markers and there were positive
association evolution between SBP, DBP and PR.
29. Joint model analysis of longitudinal and survival data
In this sub title, identify factors that affect the three biomarkers and time to
cardiovascular disease complication by using joint model of univariate,
bivariate, and multivariate longitudinal with time to event outcome.
And asses the association between the longitudinal sub model and survival
model of hypertensive outpatients.
In univariate join model and bivariate joint model of SBP, DBP and PR with
time to cardio vascular disease complication shows.
the estimated association parameter (𝜸) in the survival sub model under both
univariate joint and bivariate joint analysis was significantly different from
zero, providing that there was an evidence on the association between the
longitudinal sub model and survival sub model.
30. Joint model analysis of SBP, DBP & PR with Time to cardiovascular
diseases complication
In this model the researcher interest was identify the determinate factors that
affect SBP, DBP and PR with time to cardiovascular disease complication
jointly and identify their associations.
Table 4.13 displays that the parameter estimates, the standard errors of
estimates and p-value for the longitudinal and survival sub models.
From the longitudinal sub model, age, diabetes, family history of
hypertension, stage of hypertension, and observation time were significantly
related with SBP.
31. Conti.
diabetes, family history of hypertension, clinical stage of hypertension,
adherence and observation time was significantly related with DBP.
Diabetes, family history of hypertension, and observation time were
significantly related with PR.
And the predictor diabetic disease, family history of cardio vascular disease
and stage of hypertension were significantly related with time to
cardiovascular disease complication in the survival sub model.
The association between the longitudinal measures of SBP, DBP and PR with
time to cardio vascular disease complication in the survival sub model under
multivariate joint analysis were significantly different from zero, provide this
there was strong evidence of association between the two sub models.
32. Model comparison
When as compared based on standard error computed in uiniviratie LMM,
multivariate LMM, and multivariate joint models for significant predictors, the
model with smaller standard error was the better fit for the data.
than when as compared separate multivariate LMM and multivariate joint
model, multivariate joint model had smaller standard error than multivariate
LMM for all significant predictors and multivariate joint model had relatively
smaller residual variability than multivariate LMM.
because the Standard errors were adjusted for the correlation between the
longitudinal and survival sub model.
33. Model diagnostics
The overall goodness of fit test of longitudinal sub model can be assessed using
subject specific and marginal residuals versus the corresponding fitted values.
The subject-specific residuals of SBP, DBP and PR plotted against their
corresponding fitted value shows
All plot shows no any systematic pattern mean that, it shows no more
systematic trend with negative residuals for small fitted values and positive
residuals for high fitted values indicating that the assumptions of
homoscedasticity were satisfied and the model fits the data well .
Normal Q-Q plot of the standardized residuals for SBP, DBP and PR shows fall
close to the straight line, hence the assumption of normality was satisfied.
the Cox-Snell residues versus survival probability with the 95% point wise CI
indicates the survival process fits the data well.
34. Interpretation and discussion of the results
The interpretation and discussion of the parameters of longitudinal sub model
and survival sub model were done based on the result of Joint model of the
three longitudinal biomarkers (SBP, DBP, PR) and time to cardiovascular
disease complication among hypertensive outpatients displayed in table 4.13.
Among covariates, age, diabetes, family history of hypertension, stage of
hypertension, and visiting time were statistically significant effects of SBP
diabetes, stage of hypertension, adherence and visiting time were statistically
significant predictors for DBP.
Diabetes, family history of hypertension and visiting time were the only
significant predictors for PR.
35. Conti.
diabetes, family history of cardio vascular disease and stage of hypertension
were significant predictors of cardiovascular disease complication.
For one year increment of age, the average SBP of the patients was
significantly increased by 0.1372 mmHg (s.e=0.0690), keeping all variables are
constant.
This result was consistent with the study conducted in Indian and Ethiopia
((Wang et al., 2006), Negash et al., 2016) respectively.
The average SBP of patients who had diabetes disease was significantly
increased by 7.197 mmHg (s.e = 2.2942) as compared to the patients who had
no diabetes disease keeping all other variables are constant. This finding was
consistent with the study done in Indian (Bhansali et al., 2015).
36. Conti.
Patients whose baseline systolic blood pressure increase by one mmHg, the
average SBP of the patients was significantly increased by 0.2130 mmHg (s.e =
0.0610), this indicated higher value of systolic blood pressure at baseline was
contributed to increase the SBP progression.
The average DBP of 3.4413 with standard error 1.4724, which indicates that, the
average DBP of hypertensive outpatients who had diabetic disease was
3.4413mmHg times higher than patients who had no diabetic disease. This
result was supported by previous studies done in Ethiopia by Asresahegn
(Asresahegn et al., 2017).
The parameter estimate 0.0382bpm corresponding to the standard error 0.0125
for PR, indicates that the average PR of patients who had diabetes was
0.0382bpm times the average PR of patients who had no diabetes disease,
keeping all other variable constant.
37. Conti.
the risk of cardiovascular disease complication among diabetic hypertension
outpatients were 4.984 (p-value < 0.0001) times higher than the risk of
developing cardiovascular disease complication among non-diabetic
hypertension patients, keeping all other variables constant. This finding was
in lined with the previous study (He et al., 2001 ,and (Urrutia et al., 2016).
Other variable being constant, the risk of cardiovascular disease
complication for patients who had history of cardiovascular disease with
their family were (HR=7.76, p-value = 0.0094) times higher than the risk of
developing cardiovascular disease complication for patients who had no
history of cardiac disease with their family. This finding was consistent with
the studies done in Filipinos a country of Southeast Asia and Ethiopia
(Urrutia et al., 2016), Gesese, 2017).
38. Conti.
The association of the SBP on survival time to complication, DBP on
survival time to complication and PR on survival time to complication of
hypertensive outpatients were statistically significant when the three
biomarkers of longitudinal repeated measurements and time to complication
was fitted simultaneously.
This result was supported with previous study conducted in India and
Ethiopia by Rodriguez and Tefera (Rodriguez et al., 2014 , Tefera et al.,
2017).
This finding indicates that there was a positive association between SBP and
time to cardiovascular disease complication.
This suggested that a higher value of SBP were associated with higher risk
of cardiovascular disease complication.
39. Conclusion
As compared to separate multivariate longitudinal data, joint multivariate
longitudinal with time to event was significantly accounting the correlations
among the longitudinal measures and investigating their associations with the
risk of cardiovascular disease complication.
The multivariate joint model was performed better than the separate
multivariate longitudinal measures in terms of model parsimony and goodness
of fit.
the predictor age, diabetes, family history of hypertension, stage of
hypertension, and follow up time were statistically significant predictors of
SBP.
diabetes, clinical stage of hypertension, adherence and follow up time were
statistically significant predictors of DBP.
40. Conti.
Diabetes, history of hypertension, and follow up time were statistically
significant predictors of pulse rate.
Diabetes, history of cardiovascular disease with their family, and clinical
stage of hypertension was significant predictors of time to cardiovascular
disease complication in multivariate joint model.
The multivariate joint model revealed that both systolic blood pressure,
diastolic blood pressure and pulse rate were statistically significant and
positively associated with cardiovascular disease complication.
This indicates higher value of SBP ,DBP &PR was significantly associated
with higher risk of survival time to cardiovascular disease complication.
41. Conti.
Based on the findings of the study the researcher recommended that:
Health professionals give special attention for hypertensive outpatients
specially those who had diabetes hypertensive, higher baseline SBP & DBP
and clinically stage I and stage II hypertensive outpatients.
I recommended for hypertensive outpatients, the results suggest strongly that
to minimize the risk of cardiac complication, it is necessary to treat blood
pressure effectively and continuous and taking timely medical care better.
