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Citation: Ahmad T, Munir A, Bhatti SH, Aftab M, Raza MA (2017) Survival analysis of heart failure patients: A case study. PLoS ONE 12(7): e0181001. https://doi.org/10.1371/journal. pone.0181001
Editor: Chiara Lazzeri, Azienda Ospedaliero Universitaria Careggi, ITALY
Received: February 26, 2017 Accepted: June 23, 2017 Published: July 20, 2017
Copyright: © 2017 Ahmad et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability Statement: All relevant data are within the paper and its Supporting Information files.
Funding: The authors received no specific funding for this work.
Competing interests: The authors have declared that no competing interests exist.
RESEARCH ARTICLE
Survival analysis of heart failure patients: A case study
Tanvir Ahmad, Assia Munir, Sajjad Haider Bhatti*, Muhammad Aftab, Muhammad Ali Raza Department of Statistics, Government College University, Faisalabad, Pakistan
* sajjad.haider@gcuf.edu.pk
Abstract
This study was focused on survival analysis of heart failure patients who were admitted to Institute of Cardiology and Allied hospital Faisalabad-Pakistan during April-December (2015). All the patients were aged 40 years or above, having left ventricular systolic dysfunc- tion, belonging to NYHA class III and IV. Cox regression was used to model mortality consid- ering age, ejection fraction, serum creatinine, serum sodium, anemia, platelets, creatinine phosphokinase, blood pressure, gender, diabetes and smoking status as potentially contrib- uting for mortality. Kaplan Meier plot was used to study the general pattern of survival which showed high intensity of mortality in the initial days and then a gradual increase up to the end of study. Martingale residuals were used to assess functional form of variables. Results were validated computing calibration slope and discrimination ability of model via bootstrap- ping. For graphical prediction of survival probability, a nomogram was constructed. Age, renal dysfunction, blood pressure, ejection fraction and anemia were found as significant risk factors for mortality among heart failure patients.
Introduction
Heart failure is the state in which muscles in the heart wall get fade and enlarge, limiting heart pumping of blood. The ventricles of heart can get inflexible and do not fill properly between beats. With the passage of time heart fails in fulfilling the proper demand of blood in body and as a consequence person starts feeling difficulty in breathing.
The main reason behind heart failure include coronary heart disease, diabetes, high blood pressure and other diseases like HIV, alcohol abuse or cocaine, thyroid disorders, excess of vitamin E in body, radiation or chemotherapy, etc. As stated by WHO [1] Cardiovascular Heart Disease (CHD) is now top reason causing 31% of deaths globally. Pakistan is also included in the list of countries where prevalence of CHD is increasing significantly. Accord- ing to report by Al-Shifa hospital [2], 33% of Pakistani population above 45 has hypertension, 25% of patients over 45 years suffer diabetes mellitus, and CHD deaths in Pakistan has reached about 200,000 per year i.e. 410/100,000 of the population). All this results in increased preva- lence of heart failure. Rate of heart failure patients in Pakistan is estimated to be 110 per mil- lion [1]. Rising stress of economic and social issues in the modern era, greasy food with little exercise results towards increased prevalence of heart failure in Pakistan.
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Despite of this alarming situation, Pillai and Ganapathi [3] have reported that there are no reliable estimates of heart failure incidence and prevalence in this region while they are required due to poor and oily diet, lack of exercise and poor health care policies in this region. There are some projections based on prevalence data only from western countries.
In addition to relative scarcity of studies focusing on heart failure in this region, the present study has specific importance in the Pakistani context, as diet patterns in Pakistan are different with other the countries of South Asia like India, Bangladesh, Nepal and Sri Lanka.
The main objective of this study is to estimate death rates due to heart failure and to investi- gate its link with some major risk factors by choosing Faisalabad (third most populous city of Pakistan) as study area.
Methods
Detail of data
Current study is based on 299 patients of heart failure comprising of 105 women and 194 men. All the patients were more than 40 years old, having left ventricular systolic dysfunction and falling in NYHA class III and IV. Follow up time was 4–285 days with an average of 130 days. Disease was diagnosed by cardiac echo report or notes written by physician. Age, serum sodium, serum creatinine, gender, smoking, Blood Pressure (BP), Ejection Fraction (EF), ane- mia, platelets, Creatinine Phosphokinase (CPK) and diabetes were considered as potential var- iables explaining mortality caused by CHD. Age, serum sodium and CPK are continuous variables whereas EF, serum creatinine and platelets were taken as categorical variables. EF was divided into three levels (i.e. EF􏰝30, 3045) and platelets was also divided into three level on the basis of quartiles. Serum creatinine greater than its normal level (1.5) is an indicator of renal dysfunction. Its effect on mortality was studied as creatinine >1.5 vs 􏰝1.5. Anemia in patients was assessed by their haematocrit level. Following McClellan et al. [4] the patients with haematocrit less than 36 (minimum normal level of haematocrit) were taken as anemic. The information related to risk factors were taken from blood reports while smoking status and blood pressure were taken from physician’s notes.
The study was approved by Institutional Review Board of Government College University, Faisalabad-Pakistan and the principles of Helsinki Declaration were followed. Informed con- sent was taken by the patients from whom the information on required characteristics were collected/accessed.
Statistical techniques
Due to the presence of censored data, survival analysis was used to estimate the survival and mortality rates. Kaplan & Meier [5] product limit estimator was used to make comparisons between survival rates at different levels explanatory variables. Cox regression as presented by Collett [6] was used to develop a model that can link the hazard of death for an individual with one or more explanatory variables and test the significance of these variables.
Let hazard of death depends on p explanatory variables X1, X2, 􏰊 􏰊 􏰊 Xp then the hazard func- tion for ith individual can be defined by Cox model as
hiðtÞ 1⁄4 h0ðtÞ eb1X1iþb1X1iþ…þb1X1i
For determining the functional form of any particular independent variable following Fitrianto & Jiin [7] and Gillespie [8], plot of Martingale residuals versus different values (or levels) of a variable were used. The functional form of CPK was not linear therefore it was log transformed.
Survival analysis of heart failure patients
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Survival analysis of heart failure patients
Table 1. Baseline characteristics for dead and censored patients. Continuous Variables
Categorical Variables
Dead (96)
Censored (203)
Variable
Dead (96)
1.83
1.18
Male
62 (64%)
135.39
137.22
Smoking
30 (31%)
670
540
Diabetes
40 (42%)
65.21
58.76
BP
40 (42%)
256381
266657
Anemia
54 (56%)
33.46
40.267
Variable
Creatinine Sodium CPK
Age Platelets EF
https://doi.org/10.1371/journal.pone.0181001.t001
Censored (203)
132 (65%) 66 (32%) 85 (42%) 66 (32%) 83 (40%)
Following Pavlou et al. [9] model validation was assessed by bootstrapping [10–12] with 200 bootstrap replications. Internal validation of model was further checked by calculating cal- ibration slope [13] for the average linear predictor. The calibration slope helped in estimating the ability of model for survival probability prediction. Discriminating ability of model was assessed by ROC curve [14]. A nomogram [15] was also built to predict the survival probabili- ties graphically.
Results
Up to end of follow-up period, 96 (32%) patients died due to CHD. Table 1, presents different baseline characteristics of dead and censored patients at the end of follow up period.
The results of Cox regression model are presented in Table 2. As Cox regression is semi parametric model, hence estimate of intercept (baseline hazard) was not provided by model fit- ting. According to Cox model, age was most significant variable.
Coefficient concerning age indicated that chances of death due to CHD increase with grow- ing age. Hazard of death due to CHD increases by 4% for every additional year of age. EF was another significant factor, hazard rate among patients with EF 􏰝30 was 67% and 59% higher as compared to the patients with 3045 Smoking
Diabetes
Blood pressure Serum creatinine Serum sodium log(CPK)
Anemia Platelets(􏰝Q1) Platelets(􏰞Q3)
https://doi.org/10.1371/journal.pone.0181001.t002
P-value
0.0000 0.4239 0.0000 0.0015 0.4431 0.6553 0.0195 0.0026 0.0052 0.1596 0.0096 0.1042 0.1446
β-coefficient
HR
Z-value
0.0462
1.0473
4.81
-0.1978
0.8205
-0.80
-1.1068
0.3306
-4.36
-0.8894
0.4109
-3.18
0.1928
1.2127
0.77
0.0992
1.1043
0.45
0.5043
1.6558
2.33
0.8051
2.2368
3.01
-0.0658
0.9363
-2.79
0.1444
1.1554
1.41
0.5709
1.7699
2.59
0.4054
1.4999
1.62
0.3926
1.4800
1.46
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July 20, 2017
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Fig 1. (a) Kaplan Meier curves were used to study the survival at different levels of EF and in part (b), survival curves of male and female.
https://doi.org/10.1371/journal.pone.0181001.g001
creatinine. Serum sodium was significant with p-value = 0.0052 and its one unit (meq/L) increase decreases the hazard by 6%. Anemia was significant variable with p-value = 0.0096 and an anemic patient had 76% more chances of death as compared to non-anemic patient. According to results in Table 2, gender, smoking, diabetes, CPK and platelets were found to be non-significant.
Ejection fraction is an important measurement of how well one’s heart is pumping and is used to help classify heart failure and guide treatment. The EF is also found to be significant correlate of deaths among heart failure patients from Cox regression for present sample. Keep- ing its importance in view, EF is further analyzed through baseline characteristics (Table 3) and Kaplan Meier curves (Fig 1(a)) which shows similar pattern as presented in Cox regression results.
In Fig 1(b), Kaplan Meier survival curves were constructed for both genders showed almost identical survival pattern.
Model validation
For model validation, calibration slope and ROC curve are developed from 200 bootstrapped samples. Calibration slope was equal to 0.96, which showed that model was not over fitted and predictions made by this model would neither be overestimated nor under estimated.
Survival analysis of heart failure patients
Table 3. Baseline characteristics with respect to EF levels.
Continuous Variables
Categorical Variables
https://doi.org/10.1371/journal.pone.0181001.t003
Censored (203)
Variable
Dead (96)
EF􏰝30 (51)
30