Academic journal article Iranian Journal of Public Health

Application of the Multiplicative-Additive Model in the Bone Marrow Transplantation Survival Data Including Competing Risks

Academic journal article Iranian Journal of Public Health

Application of the Multiplicative-Additive Model in the Bone Marrow Transplantation Survival Data Including Competing Risks

Article excerpt


Beta thalassemia is the most common monogenic disorder worldwide. Currently, allogeneic hematopoietic stem cell transplantation (HSCT) is the only curative treatment for these patients (1,2).

Mesenchymal stem cells (MSCs) have been used in phase I and II studies on the autologous, allogeneic and haplo-identical or unrelated donor to improve the HSCT outcomes in hematologic malignancies. MSCs are non-hematopoietic cells with the capacity of self-renewal, which can differentiate into various cells lineages of mesenchymal origin (3-5). Generally, the studies have showed the feasibility and safety of MSCs co-infusion without immediate infusional or late MSC-associated toxicities. Safely engineered MSCs may provide targeted and effective cell therapy for graft versus host disease (GVHD).The engraftment capability of MSCs in terms of efficacy remains uncertain. Engraftment is an important milestone in transplant recovery. However, delayed neutrophil engraftment may cause early transplant related mortality primarily from infection(5). In order to evaluate the incidence of neutrophil engraftment in these patients considering the engraftment failures, we planned to use competing risks survival analysis. Recent developments in the field of survival data analysis have led to more powerful and proper data presentation. In the medical research the proportional Cox type models commonly used for regression modeling in the survival data, however it needs to hold the proportionality assumption (68). A very flexible alternative to the proportional hazard model is the additive hazard model proposed by Aalen (9,10). In the Aalen's additive model, the unknown coefficients are allowed to be a function of time and the effect of a covariate may vary over time. It results in plots that are informative regards to the covariates effect on survival, but one limitation of application of Aalen' additive model is that it is not available in commonly used computer packages (11). Another alternative is the additive-multiplicative model is so called Cox-Aalen model (12, 13). Recently the Cox-Aalen model extended for competing risks data (14, 15). In the competing risks data the occurrence of one event precludes the occurrence of another event.

The Cox-Aalen model consists of two components including additive part (like an additive Aalen model) and multiplicative part (like a Cox regression model). This extended model used the Aalen's model instead of simple baseline hazards on the proportional Cox model to handle non-proportional covariates in the model (11, 14, 15).

The aim of the study was to compare the incidence of neutrophil engraftment in patients with beta thalassemia major class III who undergo HSCT alone or in co-transplantation of donor bone marrow-derived MSCs. In these data, we illustrate the application of Cox-Aalen model in the case of proportionality assumption violation.

Materials and Methods

Patients, inclusion and exclusion criteria

In a retrospective study, data on class III thalassemia patients who underwent HSCT along with MSC between 2006 and 2012, in the Hematology-Oncology and Stem Cell Transplantation Research Center, Shariati Hospital, Tehran University of Medical Sciences (TUMS)were collected and compared with a historical control of beta thalassemia patients class III who received HSCT alone between 1993 and 2012. Patients were included in the study if they had an HLA matched identical sibling donors and received busulfan and cyclophosphamide (BUCY) as the conditioning regimen and combination of CsA and methotrexateas GVHD prophylaxis. Written informed consent form was obtained before transplantation.

The outcome of interest was the time to neutrophil engraftment, which is the time interval between the date of transplantation and the date of absolute neutrophil count (ANC) recovery. The ANC recovery defined as the first day of 3 consecutive days with ANC greater than .5×109/L. …

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