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Core Concepts
Published in Prabhanjan Narayanachar Tattar, H. J. Vaman, Survival Analysis, 2022
Prabhanjan Narayanachar Tattar, H. J. Vaman
Now, let nj and dj respectively denote the number of individuals alive just before time and the number of events (deaths) at time . The well-known Nelson-Aalen estimator of the cumulative hazard function is
The Semiparametric and Nonparametric Cure Models
Published in Yingwei Peng, Binbing Yu, Cure Models, 2021
Given estimated , the survival function of ϵ can also be estimated non-parametrically using the Nelson-Aalen estimator:
Survival Analysis
Published in Atanu Bhattacharjee, Bayesian Approaches in Oncology Using R and OpenBUGS, 2020
Nelson-Aalen estimator is a nonparametric estimator. It is used to estimate the cumulative hazard rate function from censored survival data. Here, no distributional assumptions are required. It is more appropriate for data exploration through graphically. It is also known as: (1) Altshuler estimator, (2) Empirical cumulative hazard estimator, (3) Aalen-Nelson estimator. The Nelson-Aalen estimator for the cumulaive hazard rate function takes the form
Incidence and characteristics of engraftment syndrome after autologous hematopoietic cell transplantation in light chain amyloidosis
Published in Amyloid, 2019
Talha Badar, Muhammad Ali Khan, Aniko Szabo, William Drobyski, Saurabh Chhabra, Binod Dhakal, Timothy S. Fenske, Mehdi Hamadani, Parameswaran Hari, James H. Jerkins, Nirav N. Shah, Bronwen E. Shaw, Anita D'Souza
To identify trends in ES overtime, patients were divided into two time cohorts based on the year of auto-HCT: Era 1 from 1999 to 2008 and Era 2 from 2009 to 2017. Descriptive statistics were used to describe the patient population by occurrence of ES. Univariate comparisons were performed using t-test, Wilcoxon’s rank-sum test or chi-square test as indicated depending on the variable type. Patients who did not engraft were not included in the analysis of the predictors or effects of ES as they were not at risk for developing ES (N = 2). The cumulative incidence of neutrophil and platelet engraftment was estimated using the Nelson–Aalen estimator with death without engraftment as a competing risk, and compared between the groups via Gray's test. The effect of ES on overall survival was analysed from the time of neutrophil engraftment. Overall survival was administratively censored at 180 days to focus on short-term survival effects. Survival curves were estimated using the Kaplan–Meier methods, and compared via the logrank test.
Comparative efficacy of first-line ceritinib and crizotinib in advanced or metastatic anaplastic lymphoma kinase-positive non-small cell lung cancer: an adjusted indirect comparison with external controls
Published in Current Medical Research and Opinion, 2019
Junlong Li, Stefanie Knoll, Iryna Bocharova, Wenxi Tang, James Signorovitch
After matching, efficacy outcomes were compared between balanced patient populations using statistical tests that incorporated the propensity score weights. For PFS and OS, weighted Kaplan-Meier (KM) curves were estimated for both treatments and were compared using a weighted log-rank test. The weighted 95% confidence interval (CI) for median PFS was calculated on the log scale using the Nelson-Aalen estimator. In addition, hazard ratios (HRs) between ceritinib and crizotinib were estimated from a weighted Cox proportional hazards model; the proportional hazards assumption was tested to ensure validity of the Cox models. The PFS and OS rates at month 12 were also compared between treatments using means and standard errors drawn from the extracted PFS curve for crizotinib and the weighted PFS curve for ceritinib.
A Bayesian finite mixture change-point model for assessing the risk of novice teenage drivers
Published in Journal of Applied Statistics, 2018
Qing Li, Feng Guo, Inyoung Kim, Sheila G. Klauer, Bruce G. Simons-Morton
Most of the research on recurrent-event change-point models assume piecewise-constant intensity, rate or hazard functions, which is highly robust [37]. Lawless and Zhan [37] analyzed recurrent-event data using piecewise-constant rate functions by mixed-Poisson-Process method and robust estimation, where the exact occurrence time of events were not observed. Based on the assumption that the event counts were NHPP with piecewise-constant intensity functions, West and Odgen [72] and Aschar et al. [3] estimated the change-points for one individual with multiple events; Frobish and Ebrahimi [14] developed a maximum likelihood estimator (MLE) and a Nelson–Aalen estimator for the change-point; Li et al. [40] developed two recurrent-event change-point models to detect the time of change in driving risks by maximizing the likelihood. The models in Frobish and Ebrahimi [14] and Li et al. [40] assumed identical change-points among subjects.