Additive and Multiplicative Hazards Regression Models In Competing Risks Analysis: Application To The Canadian Heart Health Survey

Abstract

Background: In survival analysis, an event whose occurrence influences the occurrence of another event is termed a competing risk event. The Cox hazards model is applicable in standard survival analysis with a single event. To correctly assess covariate effects in competing risks analysis, the Fine & Gray (F-G) subdistribution hazards and the Cox cause-specific hazards models are appropriate. Equally, additive hazards models can be used to examine the covariate effects in a competing risks framework. Objectives: (i) To examine the additive and multiplicative hazards models in the competing risks setting by applying the said models to the Canadian Heart Health Survey data; (ii) To determine the risk factors for cardiovascular disease using the competing risks approach; (iii) To compare the risk factors identified by the additive and multiplicative hazards models in the context of competing risks. Methods: The observational Canadian Heart Health Survey database collected between 1986 and 1995 is the baseline data used in this study. Two competing outcomes, cardiovascular disease (CVD) and non-CVD-related deaths, are analyzed with the Cox cause-specific and the F-G multiplicative hazards models. Similarly, the additive hazards models of Aalen and that of Lin & Ying (L-Y) are modeled for the outcomes using the competing risks approach. Results: There were 13,996 eligible subjects in my data, and 7,071 (50.5%) of them were women. After a median follow-up time of 15 years (interquartile range = 5.52 years), a total of 1,536 deaths were observed, and 549 (35.7%) of these were CVD related deaths. Factors like male gender, old age, and alcohol abstinence significantly increased the risk of CVD mortality in the additive and multiplicative hazards models. Former alcohol users compared to current alcohol users have a 53% (P-value= 0.002) and a 55% (P-value= 0.001) increased risk of CVD mortality in the Cox cause-specific and the F-G models, respectively. In the L-Y additive model, former alcohol users compared to current users increased CVD mortality by adding 16 new cases per 10,000 person-years (P-value = 0.008). Conclusion: The results from my study suggest that covariate effects in the Cox cause-specific and the F-G subdistribution hazards models may be identical in terms of magnitude and direction. The numerical results from the multiplicative and the additive hazards models give different interpretation of the covariate effects, and using both the additive and multiplicative models together would boost understanding of the data.