Rationale, aims and objectives: This paper discusses the use of bivariate survival curve estimators jointly with a competing risk Cox model to analyse mortality in dilated cardiomyopathy due to heart failure (HF) or sudden death (SD), without assuming independence between outcomes. The goal of the manuscript is to suggest a possible protocol for the analysis of competing risk events, mimicking the common approaches used in the univariate case.
Methods: The non-parametric bivariate survival estimators are used to estimate a multivariate proportional hazard model for dealing with SD or HF in a long-term prospective cohort of 235 patients, recruited from 1978 to 1992. Patients have been stratified, among others, by age, severity and treatment. The latter has been considered under two specific protocols of analysis: intention to treat and actual treatment.
Results: The bivariate survival curves show different survival probabilities for HF and SD. For HF the force of mortality acts early and then slows down as follow-up increases, while for SD the mortality is lower initially and increases later in time. Under competing risk analysis, evidence of treatment effect is shown only in the actual treatment protocol, in contrast with the results provided by standard Cox regression.
Conclusions: One of the advantages of non-parametric bivariate survival estimation in the presence of competing risks is that parameters may be interpreted in much the same way as those estimated by the standard Cox regression. Moreover, ignoring the competing risk structure may provide a misleading interpretation of the results.