Research Article: AFT survival model to capture the rate of aging and age-specific mortality trajectories among first-allogeneic hematopoietic stem cells transplant patients

Date Published: March 2, 2018

Publisher: Public Library of Science

Author(s): Yuhui Lin, Suresh kumar Subbiah.


Accelerated failure time (AFT) model is commonly applied in engineering studies to address the failure rate of a machine. In humans, survival profile of transplant patients is among the rare scenarios whereby AFT is applicable. To date, it is uncertain whether reliable risk estimates and age-specific mortality trajectories have been published using conventional statistics approach. By investigating mortality trajectory, the rate of aging d(log(μ(x)))/dx of Hematopoietic Stem Cells Transplants (HSCTs) patients who had underwent first-allogeneic transplants can be obtained, and to unveil the possibility of elasticity of human aging rate in HSCTs. A modified parametric frailty survival model was introduced to the survival profiles of 11,160 patients who had underwent first-allogeneic HSCTs in the United States between 1995 and 2006; data was shared by Center for International Bone and Marrow Transplant Research. In comparison to stratification, the modification permits two entities in relation to time to be presented; age and calendar time. To consider its application in empirical studies, the data contains arbitrary right-censoring, a statistical condition which is preferred by choice in many transplant studies. The finalized multivariate AFT model was adjusted for clinical and demographic covariates, and age-specific mortality trajectories were presented by donor source and post-transplant time-lapse intervals. Two unexpected findings are presented: i) an inverse J-shaped hazard in unrelated donor-source t≤100-day; ii) convergence of unrelated-related hazard lines in 100-day365-day) must consider for periodic medical improvements, and transplant year as a standalone time-variable is not sufficient for statistical adjustment in the finalized multivariate model. In relevance to clinical studies, biennial event-history analysis and age-specific mortality trajectories of long-term survivors provide a more relevant intervention audit report for transplant protocols than the popular statistical presentation; i.e. survival probabilities among donor-source.

Partial Text

By 2050, approximately 15% of the world population will be aged 65 and older, and with the increasing proportion of the population living to older ages, clinicians and researchers have already observed and reported an increased incidence of age-related chronic diseases such as cardiovascular-related diseases, age-specific cancer-types and neurodegenerative diseases.[1–4] Organ transplants are in demand to not only offer patients a life-saving opportunity, but to also reduce the overall burden in public health. It is uncertain on whether the organ donor-recipient demands will ever be met, but a rigorous data analysis can offer insights into how this life-saving opportunity may alter the age-specific mortality trajectory driven by donor-source, and if extreme changes in the immunological system have the ability to alter the human rate of aging at each post-transplant time-lapse interval.

Estimation of the rate of aging requires the knowledge of the underlying hazard function, i.e. shape. Parametric models are therefore the only approach to obtain the rate of change of the hazard gradient, also known as the rate of aging or the relative derivative for mortality; d(log(μ(x)))/dx. According to post-transplant time-lapse intervals, proportion of GvHD inflammation risk-types, graft failure rates and mortality risk among patients can potentially vary across observational time. The two entities: calendar time (tx) and age (x, j) are determinants for the changes in the likelihood for mortality with the occurrence of continuous progress made in medicine and transplant protocols, and the rate of aging. Calendar time and age were both adjusted for during univariate and multivariate survival analyses; S1–S4 Tables.

Post-transplant survival probability should be heterogeneous-mixed among transplant patients. The modified likelihood survival model permits the inclusion of demographic and transplant covariates, and matrices; pre-specified post-transplant time-lapse intervals and, related and unrelated donor-source; Equations 1–4. The post-transplant survival duration intervals, t≤100-day; 100-day365-day were pre-specified with an interest for changes in the rate of aging and age-specific mortality trajectories (S1 Fig). Univariate and multivariate models selection processes were achieved using the scores from Aikake Information Criterion (AIC—for parametric shape) and likelihood ratio test for finalized multivariate model; S1–S4 Tables. Based on AIC scores, Weibull model appears to be the best fitted model of HSCTs first allogeneic transplant patients. In HSCTs, the anchoring of new HSCs takes approximately six weeks and during this post-transplant interval, patients are highly susceptible to infectious diseases. In this study, deaths in the first six weeks accounted for 47.0% deaths of t≤100-day survival profiles (S2 Fig).




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