Biodemography of Human Aging (Gompertz–Makeham Law) Applied to Surgical Mortality Modeling: A Retrospective National Cohort Study

Background: The Gompertz–Makeham law describes a characteristic pattern of mortality in human populations where the death rate is near constant between ages 18 and 30 yr (Makeham law) and rises exponentially thereafter (Gompertz law). This pattern has not been described in surgical populations, but if true, it would have important implications for understanding surgical risk and design and interpretation of surgical risk models. The aim of this study was to determine whether the Gompertz–Makeham law applies to perioperative mortality risk and the conditions under which it may apply. Methods: This study examined the relationship between age and 1-month postoperative all-cause mortality risk in a 10-yr New Zealand administrative dataset comprising 5,615,100 surgical procedures from 2007 to 2016. The dataset includes patient and surgical factors including procedures, American Society of Anesthesiologists (ASA; Schaumburg, Illinois) Physical Status score, diagnoses, and other relevant details. Semilogarithmic graphs of mortality risk and age were plotted. Linear regression models were fitted, with regression line slope and Pearson correlation coefficient calculated. Results: The primary outcome occurred in 114,782 (2.0%) of 5,615,100 included participants. The Gompertz–Makeham law seems to apply to the national surgical population as a whole (slope = 0.0241; R 2 = 0.971). The law applies in all subgroups studied including sex, ASA Physical Status, surgical acuity, surgical severity category, cancer status, and ethnicity (slopes, 0.0066 to 0.0307; R 2 , 0.771 to 0.990). Important interactions were found between age, mortality risk, and three high-risk groups (cancer diagnosis, ASA Physical Status IV to V, and high surgical severity). Conclusions: The Gompertz–Makeham law seems to apply in a national cohort of surgical patients. The inflection point for increased 1-month risk is apparent at age 30 yr. A strict exponential rise in mortality risk occurs thereafter. This finding improves the understanding of surgical risk and suggests a concept-driven approach to improve modeling of age and important interactions in future surgical risk models.