Application of the Multiplicative-Additive Model in the Bone Mar¬row Transplantation Survival Data Including Competing Risks

Cox proportional hazard model is a popular choice in modeling the survival data, but sometimes proportionality assumption is not satisfied. One of the tools for handling the non-proportional effects is the multiplicative-additive model named “Cox-Aalen model”. Recently these flexible regression models developed for competing risks setting. The aim of this paper is showing the application of the multiplicative-additive model in competing risks setting on real bone marrow transplantation (BMT) data when the proportionality assumption is violated. The data was from a retrospective study on class III thalassemia patients who undergo hematopoietic stem cell transplantation (HSCT) in BMT ward of Shariatei Hospital, Tehran, Iran. The neutrophil engraftment time as the early outcome of HSCT on37 patients who received mesenchymal stem cell infusion (MSC group) compared with 50 patients who did not. We fit the standard proportional models and flexible Cox-Aalen model in the sub distribution hazards. By day 30 after transplantation, the cumulative incidence of neutrophil recovery was 97% (95%CI: 89%-100%) and 76%(95%CI: 64%-88%) in MSC and control group, respectively. Based on the Cox-Aalen model for cumulative incidence function, the MSC infusion had a significant delay effect on neutrophil engraftment (P=.044). In patients who did not neutrophil recovery immediately after HSCT, those who received MSC had faster recovery. Cox-Aalen model provides more accurate statistical description for time-varying covariate effects. There is a positive effect of MSCs on the neutrophil recovery, however further study on the advantages and disadvantages of MSCs are needed.