Biomaterial Database

Estimation and asymptotic theory for transition probabilities in Markov renewal multi-state models. 2012

Cristian Spitoni, and Marion Verduijn, and Hein Putter

Department of Medical Statistics and Bioinformatics Leiden University Medical Centre, The Netherlands.

In this paper we discuss estimation of transition probabilities for semi-Markov multi-state models. Non-parametric and semi-parametric estimators of the transition probabilities for a large class of models (forward going models) are proposed. Large sample theory is derived using the functional delta method and the use of resampling is proposed to derive confidence bands for the transition probabilities. The last part of the paper concerns the presentation of the main ideas of the R implementation of the proposed estimators, and data from a renal replacement study are used to illustrate the behavior of the estimators proposed.

UI	MeSH Term	Description	Entries
D008390	Markov Chains	A stochastic process such that the conditional probability distribution for a state at any future instant, given the present state, is unaffected by any additional knowledge of the past history of the system.	Markov Process,Markov Chain,Chain, Markov,Chains, Markov,Markov Processes,Process, Markov,Processes, Markov
D008875	Middle Aged	An adult aged 45 - 64 years.	Middle Age
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000328	Adult	A person having attained full growth or maturity. Adults are of 19 through 44 years of age. For a person between 19 and 24 years of age, YOUNG ADULT is available.	Adults
D015233	Models, Statistical	Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.	Probabilistic Models,Statistical Models,Two-Parameter Models,Model, Statistical,Models, Binomial,Models, Polynomial,Statistical Model,Binomial Model,Binomial Models,Model, Binomial,Model, Polynomial,Model, Probabilistic,Model, Two-Parameter,Models, Probabilistic,Models, Two-Parameter,Polynomial Model,Polynomial Models,Probabilistic Model,Two Parameter Models,Two-Parameter Model
D016019	Survival Analysis	A class of statistical procedures for estimating the survival function (function of time, starting with a population 100% well at a given time and providing the percentage of the population still well at later times). The survival analysis is then used for making inferences about the effects of treatments, prognostic factors, exposures, and other covariates on the function.	Analysis, Survival,Analyses, Survival,Survival Analyses
D056808	Biostatistics	The application of STATISTICS to biological systems and organisms involving the retrieval or collection, analysis, reduction, and interpretation of qualitative and quantitative data.	Biological Statistics,Biological Statistic,Statistic, Biological,Statistics, Biological
D018709	Statistics, Nonparametric	A class of statistical methods applicable to a large set of probability distributions used to test for correlation, location, independence, etc. In most nonparametric statistical tests, the original scores or observations are replaced by another variable containing less information. An important class of nonparametric tests employs the ordinal properties of the data. Another class of tests uses information about whether an observation is above or below some fixed value such as the median, and a third class is based on the frequency of the occurrence of runs in the data. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed, p1284; Corsini, Concise Encyclopedia of Psychology, 1987, p764-5)	Kolmogorov-Smirnov Test,Kruskal-Wallis H Statistic,Mann-Whitney U Test,Rank-Sum Tests,Spearman Rank Correlation Coefficient,Wilcox Test,Wilcoxon Rank Test,Non-Parametric Statistics,Nonparametric Statistics,Statistics, Non-Parametric,Kolmogorov Smirnov Test,Mann Whitney U Test,Non Parametric Statistics,Rank Sum Tests,Rank Test, Wilcoxon,Rank-Sum Test,Statistics, Non Parametric,Test, Kolmogorov-Smirnov,Test, Mann-Whitney U,Test, Rank-Sum,Test, Wilcox,Test, Wilcoxon Rank,Tests, Rank-Sum,U Test, Mann-Whitney