Inference for mutually exclusive competing events through a mixture of generalized gamma distributions

Time-to-event data with 2 or more types of endpoints are found in many epidemiologic settings. Instead of treating the times for one of the endpoints as censored observations for the other, we present an alternative approach where we treat competing events as distinct outcomes in a mixture. Our objective was to determine if and how the mixture was modified in response to an intervention.

We used a mixture of generalized gamma distributions to concatenate the overall frequency and distribution of the times of 2 competing events commonly observed in critical care trials, namely (1) unassisted breathing followed by discharge home alive and (2) in-hospital death. We applied our proposed methods to data from 2 randomized clinical trials of critically ill patients.

Mechanical ventilation with lower tidal volumes modified the mixture (P = 0.103) when compared with traditional tidal volumes by lowering the overall frequency of death (P = 0.005), rather than through affecting either the distributions of times to unassisted breathing (P = 0.477) or times to death (P = 0.718). Likewise, use of a conservative versus a liberal fluid management modified the mixture (P < 0.001) by achieving earlier times to unassisted breathing (P < 0.001) and not through affecting the overall frequency of death (P = 0.202) or the distribution of times to death (P = 0.693).

A mixture approach to competing risks provides a means to determine the overall effect of an intervention and insights into how this intervention modifies the components of the mixture.