Gompertz Distribution for Survival of Inpatients with Cluster Comorbidities

Abstract

Cluster comorbidity explains statistically significant associations between diseases without etiological explanation. Our prior study shown that multimorbidity can be separated into three clinically consistent clusters, namely gastrointestinal low back pain and anxiety disorders (GLAD), cardio-metabolic and pain disorders (CMPD), and cardio-pulmonary disorders (CPD). The aim of this study is to assess the extent at which each cluster influences the survival of elderly patients. The study utilized follow-up clinical data of 154 inpatients in the age group 50+ from a health facility in Ghana. The dataset was computationally formatted as right censored from which the Gompertz survival model was fitted. Overall, 61 mortalities were observed, of which 52.5%, 32.7% and 14.8%were patients with diseases classified under CMPD, CPD and GLAD respectively. We demonstrated that the pattern of survivorship of these patients is Gompertz distributed. As per our model, we found that the risk for mortality associated with the comorbidity clusters increases exponentially over the length of hospital stay. The patients with diseases classified under CPD and CMPD have increased risk for mortality with hazard ratio (HR) of 3.85 and 3.76 respectively, compared to GLAD with HR of 1.0.