Semi-Competing Risks Data Analysis

Hospital readmission is a key marker of quality of healthcare; it has been used to investigate variation in quality among patients in a broad range of clinical contexts and has become an important policy measure. Notwithstanding its widespread use, however, readmission remains controversial as a measure of quality. Among the concerns raised, whether and how patient deaths are handled in the analyses and reported represents an important challenge. Joynt and Jha, for example, note that “Factoring a hospital’s mortality rate into its readmission-penalty calculation could ensure that the best institutions ... are not inappropriately penalized.” In the literature, analyses of readmission have generally been conducted with the use of logistic regression models for the binary outcome of readmission within 30 days. Such models are also used by Centers for Medicare and Medicaid Services in their calculation of risk-adjusted readmission rates. Practically, if a patient dies within the 30-day interval before experiencing a readmission event, they are counted as not having experienced the event throughout the interval. That is, person-time after death contributes to the analysis of readmission, even though a patient, by definition, cannot experience a readmission during this time. Arguably, a more appropriate approach would be to explicitly treat death as a competing force that is considered simultaneously with readmission. To this end, researchers could, in principle, use competing risks analysis. One key feature of these methods is that they are specifically designed for settings where patients can experience one of the several so called terminal events, terminal in the sense that if a patient experiences an event of any given type, they cannot subsequently experience an event of any other type. Readmission, in contrast, is nonterminal, in the sense that the occurrence of a readmission event does not preclude the patient from death. Consequently, although a typical data set will contain some information on dependence between readmission and death, competing risks analyses do not make use of it. As an alternative, this article considers embedding the analysis of readmission within the semi-competing risks framework. As we elaborate on, a key benefit of this framework is the explicit use of information on the timing of readmission events post death which provides a means to acknowledge and characterize dependence between the 2 events. In addition to describing semi-competing risks data and analysis, we describe a range of well-known methods that analysts may consider, including the use of a composite end point. As we emphasize throughout, key differences across the various methods we present lie in the interpretation of the model components as well as the extent to which information on the dependence between the 2 events is exploited. Although the ideas and methods are useful in a broad range of settings, we illustrate them using data on N=49 763 Medicare beneficiaries hospitalized between 2011 and 2013 with a principle discharge diagnosis of heart failure. Abstract—Hospital readmission is a key marker of quality of health care. Notwithstanding its widespread use, however, it remains controversial in part because statistical methods used to analyze readmission, primarily logistic regression and related models, may not appropriately account for patients who die before experiencing a readmission event within the time frame of interest. Toward resolving this, we describe and illustrate the semi-competing risks framework, which refers to the general setting where scientific interest lies with some nonterminal event (eg, readmission), the occurrence of which is subject to a terminal event (eg, death). Although several statistical analysis methods have been proposed for semi-competing risks data, we describe in detail the use of illness–death models primarily because of their relation to well-known methods for survival analysis and the availability of software. We also describe and consider in detail several existing approaches that could, in principle, be used to analyze semi-competing risks data, including composite end point and competing risks analyses. Throughout we illustrate the ideas and methods using data on N=49 763 Medicare beneficiaries hospitalized between 2011 and 2013 with a principle discharge diagnosis of heart failure. (Circ Cardiovasc Qual Outcomes. 2016;9:322-331. DOI: 10.1161/CIRCOUTCOMES.115.001841.)