Congestive Heart Failure Patients’ Pulse Rate Progression and Time to Death at Debre Tabor Referral Hospital, Ethiopia

Background. Heart failure is a progressive condition marked by worsening symptoms such as shortness of breath, coughing, exhaustion and lethargy, fluid retention with swelling of the legs and abdomen, and a reduced ability to exercise. As a result, this study aims to use a joint model application to determine the joint risk factors of longitudinal change in pulse rate and time to death of congestive heart failure patients and their association admitted to a hospital.Methods. A retrospective study was undertaken on congestive heart failure patients admitted to the Debre Tabor Referral Hospital from January 2016 to December 2019. A statistical joint modeling strategy was employed to match the repeated biomarker pulse rate and a survival outcome at the same time. A total of 271 patients with congestive heart failure were chosen. Data were analyzed with R statistical software via joineRML. Results. According to the findings, the association between longitudinal changes in pulse rate and time to death in heart failure patients is statistically significant. Sex, residence, left ventricular injection fraction, New York Heart Association class, and diabetes mellitus were all found to be significant risk factors for congestive heart failure patients’ short survival time to death. Age, sex, residence, hypertension, left ventricular injection fraction, congestive heart failure, diabetes mellitus, tuberculosis, and etiology were all significant contributors in pulse rate progression. Conclusion. )e computed association parameters revealed subject-specific values. )e subject-specific linear time slope of PR measurement was positively related to the hazard rate of time to death of CHF patients in the study area. To reduce the risk level of CHF, health professionals, governmental organizations, and nongovernmental organizations must promote and allocate a suitable amount of budget for the treatment of CHF patients.


Introduction
Heart failure (HF) is a potentially fatal clinical consequence characterized by structural or functional dysfunction of the pericardium, myocardium, heart valves, and metabolic imbalances in the body [1,2]. Shortness of breath, coughing, exhaustion and lethargy, fluid retention with swelling of the legs and abdomen, and diminished physical exercise ability are all symptoms of heart failure [3]. HF is a leading cause of premature morbidity and mortality, with a lifetime risk of 20-46% [4], and it continues to be a global epidemic affecting millions of people [5,6]. It affects an estimated 33 million people around the world or 26.4% of the adult population, with 65.73% living in industrialized countries and 34.27% in developing nations [7].
According to a study conducted in 2014, the global prevalence of heart failure is estimated to be around 26 million patients [8]. Because this does not account for undetected cases of heart failure, a true estimate of the global burden of heart failure is unknown, although it is considered to be substantial [8]. Mortality rates for heart failure patients remain high, with 17 to 45% of deaths happening within one year of diagnosis and the majority of fatalities occurring within five years [3]. e prevalence of CHF in the adult population in the developed world is approximately 1 to 2%, and it rises to more than 10% in those aged 70 years or older [9].
Heart failure is a well-recognized public health problem in industrialized countries such as the United States and Europe, reflecting a substantial burden of disease, and healthcare systems are the top causes of hospitalization and death in countries [10,11]. Other studies revealed that more than 5.8 million people in the United States had CHF [10,12]. Furthermore, heart failure afflicted over 6 million adults in the United States [13], and according to the 2013 death rate report, more than 2200 individuals died per day owing to cardiovascular illness, with heart failure being the underlying reason for the bulk of those deaths [14]. Heart failure is a particularly difficult ailment in Sub-Saharan Africa, and it occurs at a younger age than in other regions of the world. When access to echocardiography or serological markers is limited, misdiagnosis of HF is more likely [15]. Treatment trends indicate that evidence-based treatments are underutilized, compliance is low, and the hospital case fatality rate among people with HF in Sub-Saharan Africa ranges from 9 to 12.5% [15]. e prevalence of risk factors linked with heart failure is increasing in low-income areas like Sub-Saharan Africa (SSA), and it has emerged as the most prevalent primary diagnosis for patients referred to hospitals in Africa with suspected cardiac disease [16]. According to a recent study, patients with heart failure in Africa were the youngest and most likely to be in New York Health Association functional class IV when compared to those in Asia, the Middle East, and South America [17]. e Sub-Saharan Africa Survey of Heart Failure [18] study identified a growing cause of heart failure from 23 to 43% in persons with heart failure. Diagnosis of heart failure might pose substantial issues in Africa due to a lack of access to proper diagnostics. With the rising trend in HF-related morbidity and death across Africa, especially Ethiopia [16,19], there is a paucity of data on heart failure patients' self-care performance. According to the WHO [20], CHF was responsible for around 9% of all fatalities in Ethiopia in 2012. Depending on the diagnostic criteria employed and the population investigated, the global incidence of HF ranges from 100 to 900 cases per 100,000 person-years [21].
Monitoring the burden of congestive heart failure is required for patients to jointly assess the patient's health and survival time. To investigate the relationship between the two outcomes, the joint model was employed to assess the longitudinal biomarker and survival outcomes concurrently [22][23][24]. When observations over time are correlated, it enhances statistical inference efficiency and decreases bias [25]. Because of the time-to-event outcomes associated with longitudinal trajectories throughout time, separate analyses of longitudinal biomarkers and survival events may result in inefficient or biased conclusions. Joint models of longitudinal biomarkers and survival events incorporate all information at the same time, resulting in reliable and efficient inferences [26]. Joint model interest frequently rests in understanding the relationship between a process's longitudinal history and its effect on the risk of an event [24,[27][28][29][30][31], and it enables more powerful, accurate, efficient, and robust estimations [26,28,32,33]. Monitoring factors and the burden of congestive heart failure is essential to determine the patient's health and survival time.
As a result, the goals of this study are to determine the joint risk factors of longitudinal change in pulse rate and time to death in congestive heart failure patients admitted to Debre Tabor Referral Hospital in Ethiopia, as well as their association, using a joint model application.

Study Area.
is study was carried out at the Debre Tabor Referral Hospital (DTRH), which is located in North-West Ethiopia. is hospital serves as a referral hospital for the people in the surrounding area.

Study Design.
To achieve the study's aims, a retrospective study was done to gather essential information from the medical files of patients with HF.

Data Source.
e population for this trial was made up of DTRH patients with congestive heart failure. Data were acquired from the medical charts of DTRH congestive heart failure patients from January 1, 2016, to December 31, 2019. e timing of the death of congestive heart failure patients was the survival endpoint of interest.

Study Variable.
e longitudinal changes in pulse rate and the survival time of CHF patients after initiating medication were the study's response variables.
Gender, residence, weight, type of CHF in patients, etiology of HF, NYHA classification, LVEF, observation time, presence of diabetes mellitus disease, presence of hypertension disease, presence of pneumonia disease, presence of tuberculosis disease, and presence of chronic kidney disease were all factors considered (see Table 1).

Statistical Analysis.
e joint model of the longitudinal linear mixed-effect model and the event time model was investigated concurrently in this study. A statistical choice was taken at a 5% level of significance, and the analysis was carried out using R version 4.0.0. A linear mixed-effect (LME) model for longitudinal data and a Cox proportional hazard (PH) model for time-to-event data, with an association parameter, shows the effect of true longitudinal measurement on CHF time to death [26].
is is often referred to as the shared parameter α model approach.

Data Exploratory.
e number of patients reduced from 271 at the start to 11 at the end of the 16 consecutive visiting occasions. HF patients had mean and median survival periods of 18.83 and 18 months, respectively. From a total of 271 CHF patients, 56 (20.7%) died, while 216 (79.3%) were censored (Table 1). e average age of CHF patients admitted to the hospital was 50 years, with a standard deviation of 18.53 years, while the patients' minimum and maximum ages were 18 and 86 years, respectively. e mean weight of CHF patients was 58.10 kg, with a standard deviation of 11.24 kg, and the lowest and highest weights were 35.0 and 93.0 kg, respectively. e mean LVEF of CHF patients was 51.29 with a standard deviation of 16.32, while the minimum and maximum LVEF were 13 and 84, respectively (Table 2).

Data Exploration.
e longitudinal PR measure appears to satisfy the assumption of normality, and the box plot for the longitudinal PR shows that the PR's normality assumptions were approximately normally distributed, as indicated by the relative position of the median within the box that contained half of the data that satisfied the assumption of normality (Figures 1 and 2). e profile plot of HF patients shows the diversity in PR over time within and across patients. Because the measurements were not evenly distributed amongst the subjects, the data were not balanced. e profile plot also shows that the horizontal loss smoothing approach indicates that the mean structure of PR is roughly linear over time (Figures 3  and 4).

Model Comparison.
e AIC and BIC values in the firstorder autoregressive (AR (1)) covariance structure are lower than those in the other covariance structures in PR. is implies that the AR (1) covariance structure is the best fit for our data when compared to the other covariance structures for the longitudinal change in PR of CHF data (Table 3).
Based on its lower AIC (15528.45) and BIC values, the linear mixed-effect model with longitudinal changes in PR considered the model with random intercept and linear temporal slope to be the most parsimonious model for the linear mixed-effect model (15623.31) ( Table 4).

Joint Modeling Approach.
In the univariable analysis of pulse rate (PR), the main effects of sex, age, residence, observation period, LVEF, NYHA class of patients, type of CHF, DM, TB, etiology, and hypertension were significant at a level of significance of 0.25. Gender, residence, NYHA class, baseline weight, CHF type, LVEF, presence of HTN, CKD, TB, and DM were found as significant predictors by the log-rank and univariable Cox models at 25% for creating a multivariable Cox model. e statistical joint model analysis of pulse rate and survival time to death was performed using R software and the joineRML package, and the results are provided in Table 5.
e length of follow-up time for CHF patients had a statistically significant effect on the change in PR over time. When all other model parameters were kept constant, the average longitudinal change in PR in CHF patients was 0.677 bpm (p value � 0.002). A statistically significant longitudinal change in PR was connected with the age of CHF patients. e age of CHF patients was statistically significant in a     When all other parameters were maintained constant, patients with congestive heart failure who had DM illness showed increase in their average longitudinal change in PR by 5.314 bpm (p value � 0.008) compared to patients who did not have DM illness. When all other parameters were maintained constant, patients with congestive heart failure who had TB disease showed increase in their average longitudinal change in PR by 7.017 bpm (p-value � 0.005) compared to patients who did not have TB disease. When all other parameters were maintained constant, patients with congestive heart failure who had HTN disease showed increase in their average longitudinal change in PR by 1.517 bpm (p value � 0.039) compared to patients who did not have HTN illness. When all other parameters were kept constant, HHD as the etiology of CHF patients lowered the average longitudinal change in PR by 6.399 bpm (p value � 0.008) compared to VHD as the etiology of CHF patients. e variation of the random intercepts in PR for the random portion of the linear mixed-effect model was 202.93, with a random slope of 5.795. is indicates that there is a greater baseline difference in PR at the start of their treatment. With the random intercept covariance, the random slope of the biomarker PR was -26.89 and the variance of the joint model was 9.914 (Table 5).
In the combined model, the estimated value of the association parameter alpha was 0.018 (HR � 1.018, p � 0.045), indicating that the average longitudinal change in PR had a positive relationship with the time to death of CHF patients across time.
Being male was statistically related to an increased risk of death in CHF patients (HR � 4.027, p value � 0.0277), implying that male patients had 4.027 times higher risk of death than female patients when all other factors in the model were kept constant. Being an urban patient was statistically related to an increased risk of mortality in CHF patients (HR � 1.094, p value � 0.020), which means that urban

Discussion
e average longitudinal change in PR demonstrated a negative relationship with the length of follow-up for CHF patients. is conclusion is also consistent with the earlier finding obtained by [34]. e average longitudinal change in PR had a statistically significant detrimental influence on the age of CHF patients. is study's findings contrast those of a previous study conducted in [34]. Age shows a substantial positive correlation with the prevalence of HF [35]. According to another study [36], younger people may have less HF understanding and become at risk. e left ventricular ejection fraction had a negative significant influence on the average longitudinal change in PR and was linked to a higher risk of death in CHF patients.
is finding was consistent with previous research [34]. However, a study conducted in [36] found no indication of a link between LVEF and quality of life in HF patients. Another study [37] revealed that LVEF illness did not affect HF mortality.
e rise in the New York Heart Association class of CHF patients had a positive significant influence on the average PR evaluation of CHF patients admitted to the hospital and was related to an increased risk of death in CHF patients.
is outcome was consistent with the findings of [34]; other studies [36] found that greater NYHA class worsened the quality of life of HF patients. Another study [38] showed that NYHA has no significant effect on the mortality of HF.
Being male had a substantial favorable effect on the average longitudinal change of PR and was a risk factor for death in CHF patients. is finding is consistent with the prior finding in [36], which found that males had a positive correlation with lower quality of life. However this result contradicts a previous study [34] and other research [35] that found a favorable correlation between females and the prevalence of HF. Another study conducted in [39] discovered that gender has no significant effect on HF mortality.
When compared to rural settings, patients who lived in an urban area had a negative significant influence on the average longitudinal change in PR and risk factors for death.
is study supported [36], which found that the quality of life in rural heart failure patients was lower than in urban patients due to poorer perceived control and symptoms of the disease. Patients with congestive heart failure who had DM disease had a beneficial influence on the average longitudinal change of PR and were at a higher risk of death.
is result supports prior research [40] that has shown that the presence of DM has a positive and significant effect on the quality of HF. However, other studies [38] found that DM has no significant effect on HF.
Patients with congestive heart failure who had HTN disease showed a positive significant influence on the average longitudinal change in PR.
is result supports prior research [35,39,41,42] that found HTN to be highly linked with heart failure and to have a favorable significant influence on heart failure. Having an etiology of HHD was connected with a lower PR of congestive heart failure. is is inconsistent with a prior study [41] that found no significant relationship between HF and any of the etiologies of HF (ischemic heart disease, dilated cardiomyopathy, hypertensive heart disease, valvular heart disease, and other etiologies) except cor pulmonale.

Conclusion
e linear mixed-effect model with the subject value of PR measurement (in bpm) was a good fit for the longitudinal change PR evaluation in this investigation. At a 5% level of significance, the cofactors including baseline age, gender, residency, CHF type, NYHA class, DM, HTN, and TB illness, LVEF, etiology, and observation period were statistically significant factors that affect the mean longitudinal change of PR measures of the patients. e Cox PH model showed a good fit for the time to death of patients. e fitted Cox model results revealed that sex, residency, LVEF, NYHA class, and DM disease were the factors that influenced the hazard rate of time to death of CHF patients in the study area at a 5% level of significance. However, the independent variables such as weight, TB, CKD, and CHF type have no association with the hazard rate of time to death of CHF patients.
For the joint modeling of the data, the joint model with random intercepts and time of slope from the longitudinal model and the survival model was appropriate. e computed association parameters revealed subject-specific values, and the subject-specific linear time slope of PR measurement was found to be positively related to the hazard rate of time to death of CHF patients in the study area. To reduce the risk level of CHF, health professionals, governmental organizations, and nongovernmental organizations must promote and allocate a suitable amount of budget for the treatment of CHF patients.

AIC:
Akaike information criterion AR: Autoregressive order BIC: Bayesian information criteria CHF: Congestive heart failure CKD: Chronic kidney disease CS: Compound Data Availability e data, which are now in the hands of the original author, will be made available to public upon request.

Ethical Approval
Ethical approval was acquired from the ethical review board of Bahir Dar University's College of Sciences, and authorization for data collection was acquired from the Debre Tabor Referral Hospital Patient's Ethical Committee.

Consent
Each patient additionally provided informed consent before data collection.

Conflicts of Interest
e authors declare no conflicts of interest.

Authors' Contributions
AT was involved in the study design, performed the data extraction, analyzed the data, and produced the manuscript; DB was involved in the study design, counseled at each stage, and read the paper. AT, DB, and SG contributed to the manuscript's development.
e final paper was critically evaluated and approved by all authors.