Abstract

Objectives: The Cox proportional hazard (PH) model is commonly used to evaluate the relative impact of risk factors on the baseline hazard of events in reference population. However Cox PH is limited in its ability to incorporate time dependent variables. While building models with fixed cycle lengths, where variable like medical history changes due to treatment intervention, a risk equation could help us better. Parameter risk equations, like Framingham Heart Study equations, can account for the shape of the baseline event rate which enables the estimation of future risk. The purpose of this study is to develop a set of risk equations that account for clinical evidence and biomarkers for acute heart failure (HF) patients to estimate time to discharge, time to in-hospital mortality, time to readmission and time to post-discharge mortality following an HF hospitalization Methods: We utilized data from the placebo arm population from Pro-B Type natriuretic peptide Outpatient Tailored Chronic heart failure Therapy (PROTECT) study to develop the risk equations. For each outcome, determining the best risk equation involved two steps, (a) selecting the appropriate underlying distribution, and (b) choosing the right set of risk-factors. Various distributions considered including Weibull, exponential, piecewise exponential, logistic, log normal and gamma distribution. The final distribution was chosen based on model fit and its AIC score. A variety of risk factors were considered including patient characteristics, relevant biomarkers and medical history. The best risk factors were chosen based on clinical relevance, systematic literature review, and how they performed on a maximum likelihood ratio test for the chosen distribution. The predicted value for each outcome was compared to observed values from PROTECT for internal validity and Efficacy and Safety of Relaxin for the Treatment of Acute Heart Failure (RELAX-AHF) study for external validity. Results: The gamma, Weibull, piecewise exponential and exponential distributions were selected for the time to discharge, in-hospital mortality, hospital readmission and post-discharge mortality, respectively. The key risk factors included gender, age, SBP, heart rate, ProBNP, GFR, NYHA class, in-hospital diuretic dosage, medication usage and cardiovascular comorbidities. The internal and external validity are confirmed by comparing predicted and observed values from PROTECT and RELAX-AHF study respectively. The predicted and observed LOS is 12.6 and 10.5 days. Although the predicted and observed 30 day post-discharge mortality are 1.20% and 3.30%, the difference between predicted and observed all-cause mortality is 0.1 (11.40% vs 11.3%). Conclusions: Since risk factors (i.e SBP and BNP) that change over time were identified as important risk-factors, parametric risk equations were superior to cox PH model.

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