Table of Contents
- Statement of the Problem
- Objectives of the Study
- Specific Objectives
- Justification of the Problem
- Limitations of the Study.
- Literature Review
- The Review of Related Literature
The heart is an organ in animals, including human beings that acts as a pumping mechanism for blood around the body, through veins and arteries. The heart and the blood vessels together form the cardiovascular or circulatory system. Cardiovascular diseases refers to the diseases and disorders that affect this system, of which there are several types, such as, for the heart: angina, arrythmia congenital heart disease, coronary artery disease, heart attack, heart failure, dilated and hypertrophic cardiomyopathy, mitral regurgitation, mitral valve prolapse, pulmonary stenosis, atrial fibrillation, rheumatic heart disease, radiation heart disease; and for the vessels: peripheral artery disease, aneurysm, atherosclerosis, renal artery disease, Raynaud’s disease, peripheral venous disease, ischemic stroke, venous blood clots, blood clotting disorders and Buerger’s disease.
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Cardiovascular diseases are the leading cause of death worldwide. The main heart diseases in particular are the stroke and heart attacks. According to WHO, an estimated 17.9 million people died from CVDs in 2016, which was 31% of all global deaths in that same period. Heart attacks and strokes in particular covered 85% of that number. Closer to home, estimates show that CVDs are responsible for 25% of hospital admissions as well as 13% of deaths in Kenya
A multi-state model is a model for a continuous time stochastic process allowing individuals to move among finite number of states. A simplest form is the survival analysis/mortality model with states alive and dead and only one possible transition. Another form of a multi-state model is the illness-death model used in medical used in medical literature to describe the disease progression. In medical applications, the study period might end before the absorbing state(i.e. death in this case) is reached, causing right censored observation times. It can also happen that the process is not observed from origin, causing left censorship of data if events are known to occur before entry but the times of these events are unknown.
The idea for this project came about when while looking for a problem in society, heart disease was a candidate because there was recently a lot of news about the increase in cardiovascular disease around the world and in Kenya, as the Kenya Guidelines on Management of CVDs were released last year by the Ministry of Health. We sought a way to approach this issue which was related to our course, and thus settled on survival analysis which we learnt just this semester, which has implications for the pricing of medical insurance.
Common industry practice on survival analysis of Heart disease is to use multistate models like our own, especially involving the Kaplan Meier estimate as well as the Cox regression model. However, while we are using the simple multistate model, other studies and approaches to the question of survival consider more than two states((i.e. more than one transition) e.g. the health-illness-death model.
The Kaplan Meier estimate is a method based on individual survival times, and assumes that censoring is independent of survival time, and censorship of an observation is unrelated to cause of failure. The states of interest must be both mutually exclusive, i.e. either one or the other but not both, and, collectively exhaustive, such that one of the two must occur at any given time. It involves computing of probabilities of occurrence of an event at a certain point and multiplying these successive probabilities by any earlier computed probabilities to get the final estimate, which is why it is also known as the product limit estimator. It is a non-parametric estimator for the survival function, named after Edward Kaplan and Paul Meier who each submitted similar works, after which they were convinced to combine into one paper.
Statement of the Problem
Insurance companies as well as other social security related companies utilise risk considerations in pricing of their products and/or computation of benefits. Where life and health are involved, this takes into account mortality and survival rates., these firms had long been using rates from standard mortality rates of other countries, for lack of a local set of tables; the A1949-52 and the SA85-90 from the UK and the US respectively were the tables of choice. According to a study done by George Nyakundi, the first steps to solve this problem were taken with the creation of the KE2001-03(Nyakundi, G., 2014), which was followed up by the KE2007-2010 tables. Nonetheless, the mortality data measured is not current enough, and in the case of individual causes of mortality, not specific enough and thus usage, for instance in pricing, does not truly represent the real death rates or risk. Moreover, the mortality due to heart disease has been on the rise, largely due to changes in lifestyle such as diet and fitness. This study seeks to solve this problem, by carrying out a survival analysis, on heart disease patients in particular.
Objectives of the Study
Determine the survival rates of heart disease patients.
- Collecting data on survival of heart patients from health centres.
- Analysis of collected data using Kaplan Meier estimator and Cox regression model.
- Interpretation of the results of analysis.
Justification of the Problem
The study seeks to analyse and determine survival rates for heart patients. This is important because survival rates are useful to the process of underwriting process, as they are used to estimate the risks involved in the policy, and thus crucial in determining prices as well as the benefits to be paid from insurance policies.
There has been an increase in mortality due to cardiovascular diseases around the world, especially in Sub Saharan Africa, and by extension, Kenya. This gives increased significance to both prevention as well as diagnosis and treatment of these disease in order to save more lives, as both cardiovascular disease and death are largely preventable, the diseases even described as reversible.
Moreover, cardiovascular diseases tend to be either one or even both of costly all at one and over the long term, in addition to affecting one’s ability to earn at that particular time. As such, insurance is crucial to being able to access the necessary medical care. Thus, analysis and modelling the mortality of heart disease patients goes a long way in the fight against cardiovascular diseases.
Limitations of the Study.
First, carrying out the study would require funds. Thus, the scope and effectiveness of the study has to be achieved within the constraints of the available budget. Secondly, diagnoses of the illness might be discouraged, due to issues like stigma and negligence. Thus, the studied population might not be accurately representative of the general population.
There has been a good amount of work done on this area o f study, more so recent works
Two of the most commonly used in studies where the response variable is the time from a well-defined moment to the occurrence of some event of interest are the Kaplan and Meier Estimate, and the Cox proportional hazards model.
First, the Kaplan Meier is a nonparametric statistic used to estimate the survival function as a product of the current survival rate at a given time by the preceding survival rates. It was invented by Edward Kaplan and Pal Meier, at first independently but eventually they collaborated on the same.
the other hand, the Cox Proportional-hazard models essentially a regression model commonly used statistically in medical research to investigate the association between survival times and one or more predictor variables
The Review of Related Literature
A research study by George Nyakundi focuses on the development of mortality tables in Kenya, proposing a new Model life table that is constructed after adjustment of the KE2001-03(Nyakundi G., 2014). The adjustment is carried out using the Brass Logit model with current census data being the determinant of the parameters of the model. Additionally, the study seeks to determine how the KE2001-03 life table compares to the A 1949-52 and the SA85-90. This was carried out by a simple comparison of the mortality rates at each age for three mortality tables. The results showed that the KE2001-03 life table had the highest overall mortality rates of the three, followed by the SA85-90 then the A1949-52 table. The study also notes that there is a need to be periodically adjusting the mortality tables used by insurance companies in Kenya in order to ensure that the mortality assumptions used in conducting actuarial valuations match the actual mortality experience of the population in Kenya.
Tanvir Ahmad and others undertook a study that focused on heart failure patients who were Admitted to the Institute of Cardiology and Allied Hospital in Faisalabad Pakistan between April and December 2015, the patients above 40 years old suffering from left ventricular systolic dysfunction, and of NYHA class III and IV, which are advanced stages of the disease(Ahmad T et al, 2017). The authors highlight the alarming situation with regard to CHD in Pakistan, with the rate of heart failure patients being estimated to be 110 per million, despite which there are no reliable estimates of heart failure incidence and prevalence in the region. The study considered age, serum sodium, serum creatinine, gender, smoking, blood pressure, ejection fraction, anaemia, platelets, creatinine phosphokinase and diabetes as potential variables explaining mortality by CHD.
Survival analysis was used to estimate the survival and mortality rates. Kaplan Meier product limit estimator was used to make comparisons between survival rates at different levels of the explanatory variables, Cox regression used to develop a model to link the hazard of death of an individual with one or more explanatory variables and test the significance of these variables. The functional form of the particular independent variable; were determined using plot of Martingale residuals versus different values of a variable. Model validation was assessed by bootstrapping, and further internal validation by calculating calibration slope for the average linear predictor. The survival probabilities were predicted graphically using a nomogram. The authors conclude that growing age, renal dysfunction, high blood pressure, higher levels of anaemia and lower values of ejection fraction are key factors contributing to increased risk of mortality among heart failure patients.
A population-based investigation from Italy on multistate modelling of heart failure care path was undertaken by Francesca Gasperoni and others (Gasperoni F. et al, 2017). The authors propose the application of two different multistate models to investigate the impact of different risk factors on patients on multiple hospital readmissions, integrated home care (IHC) activations or intermediate care unit (ICU) readmissions and death. The first model considers only hospitalisations as possible events and aims at determining the determinants of repeated hospitalisations, the second model considers both hospitalisations and ICU/IHC events and aims at evaluating which risk profiles are associated are transitions in intermediate care with respect to repeated hospitalisations or death. Both are characterised by transition covariates, adjusting for risk factors.
The authors noted that advanced age and higher morbidity load increased the rate of dying and of being rehospitalised (model 1), decreased the rate of being discharged from hospital (models 1 and 2) and increased the rate of inactivation of IHC (models 1 and 2).