Physical Sciences and Mathematics Commons^™

Nonparametric Estimation Of Transition Probabilities In Illness-Death Model Based On Ranked Set Sampling, Ying Ma

USF Tampa Graduate Theses and Dissertations

The ranked set sampling (RSS) design is applied widely in agriculture, environmental science, and medical research where the exact measurements of sampling units is costly, but sampling units can be ranked by a correlated concomitant variable. RSS is usually a cost-efficient alternate to simple random sampling (SRS) for selecting more representative samples. This study presents a novel methodology to investigate the nonparametric estimation of transition probabilities in illness-death model using the RSS design. We study the Aalen–Johansen estimator of transition probabilities in illness-death Markov model based on RSS design under random right censoring time and propose nonparametric estimators of the …

Inference And Estimation In Change Point Models For Censored Data, Kristine Gierz

Mathematics & Statistics Theses & Dissertations

In general, the change point problem considers inference of a change in distribution for a set of time-ordered observations. This has applications in a large variety of fields and can also apply to survival data. With improvements to medical diagnoses and treatments, incidences and mortality rates have changed. However, the most commonly used analysis methods do not account for such distributional changes. In survival analysis, change point problems can concern a shift in a distribution for a set of time-ordered observations, potentially under censoring or truncation.

In this dissertation, we first propose a sequential testing approach for detecting multiple change …

Survival Analysis: A Modified Kaplan-Meir Estimator, Justin A. Bancroft

MSU Graduate Theses

The popular Kaplan-Meir estimator has traditionally been used to great effect as a survival function estimator. However, the Kaplan-Meir estimator is dependent upon a maximum likelihood parameter estimator which may not be the best estimator in all cases. We modify the Kaplan-Meir estimator, based on a Bayes parameter estimation, in hopes of providing a more accurate survival estimator for small sample sizes. Core elements of survival analysis are presented, acting as a foundation from which to construct and compare our modified Kaplan-Meir estimator. It is hypothesized that our modified Kaplan-Meir estimator is generally more accurate than the standard Kaplan-Meir estimator …

An Exploration Of Non-Detects In Environmental Data, Juliana Fajardo

Statistics

No abstract provided.

Fuzzy Product -Limit Estimators: Soft Computing In The Presence Of Very Small And Highly Censored Data Sets, Kian Lawrence Pokorny

Doctoral Dissertations

When very few data are available and a high proportion of the data is censored, accurate estimates of reliability are problematic. Standard statistical methods require a more complete data set, and with any fewer data, expert knowledge or heuristic methods are required. In the current research a computational system is developed that obtains a survival curve, point estimate, and confidence interval about the point estimate.

The system uses numerical methods to define fuzzy membership functions about each data point that quantify uncertainty due to censoring. The “fuzzy” data are then used to estimate a survival curve, and the mean survival …