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Time-dependent effects on competing-risk endpoints
Deaths from any cause without prior relapse of the original dis- ease are events assigned to the non-relapse mortality endpoint. Its competing event is relapse. Transplant-related mortality rep- resents deaths which were classified by the treating physician as directly related to the transplant. Non-relapse mortality com- prises these events but, in addition, also includes all other deaths not related to transplantation and also not related to relapse or progression of the primary disease (other deaths). The patients’ consent to perform analysis of their clinical data was obtained upon their registration in the EBMT database. The study was approved by the ethical committee of Ulm University, Germany (n. 108/15).
Statistical methods
We used cause-specific Cox proportional hazards models to relate covariates to the competing survival outcomes. Covariates not satisfying the proportional hazard assumption were first iden- tified using the test described by Therneau and Grambsch and subsequently modeled to have piecewise time-constant effects in order to facilitate interpretation.11 Preferential candidate break- points were as previously reported. They were confirmed using smoothed time-dependent regression coefficients resulting from the Therneau and Grambsch test and subsequently maximizing the maximal partial likelihood.12,13 Finally, the piecewise constant Cox model was fitted, thereby obtaining regression estimates before and after the individual cutpoints. Predictors evaluated in the models were age, disease stage, year of transplantation (scaled in the periods 1976-2000, 2001-2005, 2006-2013 in order to get conceivable effect estimates), graft source, conditioning treat- ment, and KPS (<80% poor versus 80-100% good). Missing data for the KPS were treated as ‘good’, choosing a conservative esti- mation in the sense of an underestimated effect of a poor KPS (see Table 1). Analyses were stratified for diagnosis, donor type and transplantation center, summarized in seven categories according to the total number of transplants. To detect only strong time- dependent effects, the significance level for the proportional haz- ard assumption test was set at 0.01. For an effect-estimator a sig- nificance level of 0.05 was used.
Results
The results of the standard Cox model with the propor- tional hazard test amended by the results of the piecewise constant Cox analysis are presented in Tables 3-6 for all
competing-risk endpoints. Furthermore, a comparison of hazard ratios for selected covariables is given in Table 7.
Covariate: age
Higher patients’ age increases risk following hematopoietic stem cell transplantation. This effect is constant over time (HR for transplant-related mortality: 1.015; for death from other causes: 1.009; for relapse: 1.003; and for non-relapse mortality: 1.019; all statistically significant estimates) (Tables 3-6). The estimates describe the increasing risk per life year for each endpoint.
Covariate: disease stage
The Cox model showed a higher risk conferred by relapse for all endpoints. In particular, for patients trans- planted in advanced disease stage, the risk of relapse in the first 8 months after transplantation was 2.92-fold higher than that of patients transplanted in early disease stage. This risk reduced afterwards markedly to a hazard ratio of 1.73. In line with this, patients in intermediate or advanced disease stage had a distinctly higher risk of death from other causes in the first 10 months. This trend remained subsequently, although it was moderated (Tables 3-7).
Covariate: year of transplantation
Another covariate included in the Cox model was the year of transplantation. The effect of this covariate was time-dependent for relapse, non-relapse mortality, trans- plant-related mortality and death from other causes (1976-2000 versus 2006-2013). For all four endpoints, the event-specific cutpoints could be set at 8 months. Recent transplants showed lower risk estimates in comparison to earlier transplants (Tables 3-7).
Covariate: source of stem cells
While for relapse and death from other causes the source of stem cells had no impact (Tables 4 and 5), we observed opposing effects for the different time phases in the analy- sis of non-relapse mortality and transplant-related mortali- ty when considering the piecewise constant Cox model. In the first time period a peripheral blood stem cell graft showed a protective effect for both outcome endpoints, although this effect was subsequently inverted. The chang- ing point of this effect was at 1 year for transplant-related
Figure 1. Schematic display of competing-risk settings. OS: overall survival; DFS: disease-free survival, CR: competing risks; TRM: transplant-related mortality; NRM: non-relapse mortality; sec.: secondary.
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