Abstract
Since our retrospective study has formed a mathematical formula, α = f(x1, …, x252), where α is the probability of cardiovascular events in patients with heart failure (HF) and x1 is each clinical parameter, we prospectively tested the predictive capability and feasibility of the mathematical formula of cardiovascular events in HF patients. First of all, to create such a mathematical formula using limited number of the parameters to predict the cardiovascular events in HF patients, we retrospectively determined f(x) that formulates the relationship between the most influential 50 clinical parameters (x) among 252 parameters using 167 patients hospitalized due to acute HF; the nonlinear optimization could provide the formula of α = f(x1, …, x50) which fitted the probability of the actual cardiovascular events per day. Secondly, we prospectively examined the predictability of f(x) in other 213 patients using 50 clinical parameters in 3 hospitals, and we found that the Kaplan–Meier curves using actual and estimated occurrence probabilities of cardiovascular events were closely correlated. We conclude that we created a mathematical formula f(x) that precisely predicted the occurrence probability of future cardiovascular outcomes of HF patients per day. Mathematical modelling may predict the occurrence probability of cardiovascular events in HF patients.
Highlights
Heart failure (HF), one of the leading causes of mortality and morbidity worldwide[1], is the end stage of many cardiovascular diseases
Our hypothesis in the previous study is that we can derive a mathematical formula for the estimation of prognosis, i.e., the equation τ = f(x1, ..., xp), where x1, ..., xp are clinical features and τ represents the day for the cardiovascular event in the patients with heart failure (HF), and we showed the positive evidence to support such a hypothesis in the previous study
Since we found that the mathematical formula applies to predict the occurrence of cardiovascular events in the prospective study, we assumed that each attribute coefficient for this mathematical formula is essential for the clinical practice for HF (Table 2)
Summary
Heart failure (HF), one of the leading causes of mortality and morbidity worldwide[1], is the end stage of many cardiovascular diseases. Even if the multiple factors are identified as necessary for the occurrence of cardiovascular events, the results are qualitative and not quantitative These factors are usually proved retrospectively because researchers usually do not test the reproducibility of the results in the prospective study, which may not lead the definite conclusion for the identified factors. To overcome these limitations, we devised a mathematical formula using all the parameters and factors in the medical records to provide the occurrence probability of cardiovascular events and revealed that more than 250 factors are linked to the occurrence probability of cardiovascular events in patients with HF8. We can obtain the formula to predict the occurrence probability of cardiovascular events using many clinical or social parameters beforehand, leading to the precision medicine of HF10,11
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