Academic journal article Economic Inquiry

I Am Immortal

Academic journal article Economic Inquiry

I Am Immortal

Article excerpt

I. INTRODUCTION

Cardiology is a branch of medicine that studies the functioning of the heart. Since the invention of the electrocardiogram (ECG) by Willem Einthoven in 1903, medical science has made tangible progress in the study of heart diseases, including cardiac events prevention, diagnosis, treatment, and risk assessment.

Today, the cardiology literature can be split into two main branches: (1) diagnosis and treatment of heart diseases and (2) cardiovascular risk assessment. Regarding the first one, the literature offers a vast number of papers that study the electrical activity of the heart and correlated dysfunctions. The field includes medical diagnosis and treatment of congenital heart defects, coronary artery diseases, heart failures, valvular heart diseases and electrophysiology (few examples include Hunt et al. 2005; Hemingway and Marmot 1999). Regarding the second one, mathematical models have been developed to estimate the risk of cardiovascular diseases studying patients' observable characteristics (including life styles) and genetic propensities. These studies (see for instance Wilson et al. 1998; Franklin et al. 2001) are designed to estimate the probability of a future cardiac event (typically in the next 5-10 years) and result in widely used clinical cardiovascular risk assessment tools. (1)

However, despite the importance of the subject and the abundance of the aforementioned contributions, the scientific literature still misses a model to predict a patient's life expectancy using heart activity signals. In other words, the literature misses a model able to estimate the approximate date in the future in which a fatal cardiac event might occur. The cardiovascular risk assessment tools have certainly helped in estimating the probability of a cardiac event but these models are still mute about whether the patient will survive to the event or not. Furthermore, the risk assessment models can estimate a probability of a cardiac event considering only a limited number of periods in the future.

In this paper, I go well beyond the frontier. I employ time series econometrics techniques to suggest a decomposition of the heart electrical activity using an unobserved components state-space model. My approach is innovative because the model allows not only to study electrical activity at different frequencies with a very limited number of assumptions about the underlying data generating process but also to forecast future cardiac behavior (therefore estimating the date of death), overcoming the "sudden death forecast" issue which typically arises when using standard time-series models. (2)

My results are duo-fold. First, I show how the heart electrical activity can be modeled using a simple state-space approach and that the suggested model has superior out-of-sample properties compared to a set of alternatives. Second, I show that when the Kalman filter is run to forecast future cardiac activity using data of my own ECG I obtain a striking result: the n-step ahead forecast remains positive and well bounded even after one googol period, implying that my life expectancy tends to infinite. Therefore, I am immortal.

The rest of the paper is organized as follows: Section II briefly explains the technical background of electrocardiography and ECGs. Section III explains the dataset. Section IV introduces the econometric model. In Section V I discuss my results and Section VI concludes.

II. TECHNICAL BACKGROUND: ELECTROCARDIOGRAPHY AND ECGs

Electrocardiography is the process of recording the electrical activity of the heart over a period of time using electrodes (typically in the number of ten) placed on a patient's body. These electrodes detect the tiny electrical changes on the skin that arise from the heart muscle depolarizing during each heartbeat. The overall magnitude of the heart's electrical potential is measured from 12 different angles (or "leads") and is recorded over a period of time. …

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