Jorjani Biomedicine Journal

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Abstract
Background and objectives: Leukemia is one of the most prevalent cancers worldwide. The relapse of the disease mitigates patient survival time. The convenience of explaining the results obtained from analyzing tree models have encouraged doctors and paramedics to employ them in their research. The current study is an attempt to determine the five-year survival time and factors influencing it in children suffering from acute lymphoblastic leukemia based on tree survival model in the presence of competing risks.
 
Methods: The required data were collected from 255 children younger than 15, who suffered from acute lymphoblastic leukemia and referred to Dr. Sheikh Hospital in Mashhad, Iran during the years 2007-2015. Afterwards, the survival of the patient until the end of March 2015 was scrutinized. In this regard, various variables like sex, age, treatment period, white blood cells count, hemoglobin, platelet count, LDH level, CNS involvement, mediastan mass, rheumatologic symptoms, etc. were also considered.
The relapse of the disease was considered the desired event, whereas the relapse-free death is called competing event. The survival time of the patients from diagnosis date to the date of event (censoring) was calculated on a monthly basis. The fitting of the model is implemented according to maximum within-node homogeneity, which, in turn, is based on the partition function of sum of squares of Event-Specific Martingale Residual changes.
 
Results: The estimated mean survival time during the relapse and relapse-free death periods as well as in the presence of either events was obtained 55.51, 47.53 and 44.20 months, respectively, implying a decrease in the mean survival time in the presence of competing risks. White blood cell count and platelet count were considered the most influential factors contributing to the relapse or survival. Three sub-groups of patients at risk were identified, and those with white blood cells ≥ 50000 were recognized as the ones with the least mean survival time.
 
Conclusion: The factors affecting the survival rate of patients and their spots in the model can be employed in making clinical decisions and proposing therapeutic protocols. Identification of sub-groups with identical mean survival rate is the most salient capabilities of the research model.
 

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Background: In medical research and survival analysis, it is common for an individual or item's failure to be attributable to multiple causes, also known as competing risks. This article focuses on examining the competing risks model as the data increasingly becomes type II censored and randomly removed. The model assumes that the causes of failure are independent and that the lifetimes of individuals are described by the Cox model. At each failure time, the number of items or people removed follows a binomial distribution. The article derives estimators for the indefinite parameters in the model. The study presents a set of detailed data and includes a simulation study that also illustrates the results.
Methods: Different reasons, frequently known as competing risks, are frequently embroiled in an individual's or an item's failure in medical research survival analysis. The competing risks shown under sort II dynamic censoring with random removals are the subject of this research.
We get the maximum likelihood and inexact most extreme probability estimators of the obscure parameters. The asymptotic distribution of the maximum probability estimators is utilized to decide the CIs. Then, Monte Carlo simulations were applied to demonstrate the approach. The analyses were performed utilizing R 4.0.4 software.
Results: For stroke, systolic blood pressure (SBP) and hypertension status are the only significant variables. In contrast, gender, body mass index (BMI), smoking status, the logarithm of urinary albumin and creatinine ratio, and diabetes status are significant variables for coronary heart disease (CHD) and other cardiovascular diseases (CVDs). The results suggest that significant risk factors differ for different types of CVD events.
Conclusion: The outcomes of the simulation study indicate that progressively right-censored type II sampling designs outperformed the usual censored type II sampling designs. Therefore, the estimated parameters on the defined pattern setting are recommended. They can be used in many practical situations when competing risks occur, and progressive censoring could be considered.