# NONPARAMETRIC ANALYSIS OF CENSORED DATA

> **NIH NIH R01** · UNIVERSITY OF ROCHESTER · 1993 · $89,671

## Abstract

1.  Methods for Bayesian Inference

This Specific Aim will be to continue development and application of Data
Augmentation methodology.  Recently, Ritter and Tanner (1992) have
developed a grid-based approach to extend one such algorithm, the Gibbs
Sampler, to the nonconjugate case.  The overall foal will be to compare the
performance of this Griddy-Gibbs algorithm to competing methods such as the
Metropolis algorithm, as well as to hybrids of the Metropolis algorithm in
the context of biostatistical problems.  The first subaim is to use this
methodology to allow one to sample from the partial likelihood and then to
apply this methodology to a variety of problems related to the Cox model.
The second subaim is the application of Data Augmentation methods to allow
sampling from the likelihood or posterior density for the logistic
regression model (with and without random effects).  Problems for subaims
one and two to be addressed include: parameter inference; patching missing
(at random) covariates; and goodness-of-fit.

2.  Semiparametric Regression Methodology for Censored Data

This Specific Aim will be to continue development and application of
methodology for the regression analysis of censored lifetime data, when one
does not assume any particular parametric family of survival distributions.
The multiple imputation approach presented in Wei and Tanner (1992) will be
extended.  The first subaim is to replace the least-squares estimate of the
regression parameters by more robust estimates.  The second subaim is to
use nonparametric methodology to remove the linear assumption regarding the
systematic component of the model.  The third subaim will be an
investigation f large-sample properties of these various estimators.  The
small sample Frequentist properties of these estimators will be examined
via simulation.

3.  Frequentist Calculations using Markov Chain Methods

Barndorff-Nielsen (1983) has developed an approximation to the density of
the maximum likelihood estimator.  In this Specific Aim, Markov Chain
methods (such as the Gibbs Sampler, the Griddy-Gibbs Sampler and the
Metropolis algorithm) will be applied to this Barndorff-Nielsen formula to
perform Frequentist inference.  Thus, the focus is on the behavior of the
estimator in repeated samples, rather than as in Specific Aim #1 where we
focus on the distribution of the parameter given the data.  These Markov
chain methods will be used to obtain marginals of the density of the MLE,
calculate tail areas (p-values), calculate the distribution of the
likelihood ratio statistic and construct Frequentist confidence intervals.
The methodology will be applied to problems in biostatistics.

4.  Development of Software to Accompany Methodology
The goal is to develop Data Augmentation software, as applied to such
problems as parametric and semiparametric censored regression methodology,
as well as to logistic and Cox regression.

## Key facts

- **NIH application ID:** 3173023
- **Project number:** 5R01CA035464-10
- **Recipient organization:** UNIVERSITY OF ROCHESTER
- **SAM.gov UEI:** F27KDXZMF9Y8
- **Principal Investigator:** MARTIN A TANNER
- **Activity code:** R01 (R01, R21, SBIR, etc.)
- **Funding institute:** NIH
- **Fiscal year:** 1993
- **Award amount:** $89,671
- **Award type:** 5
- **Project period:** 1984-08-01 → 1994-07-31

## Primary source

NIH RePORTER: https://reporter.nih.gov/project-details/3173023

## Citation

> US National Institutes of Health, RePORTER application 3173023, NONPARAMETRIC ANALYSIS OF CENSORED DATA (5R01CA035464-10). Retrieved via MORVS 2026-10-25 from https://api.morvs.ai/grant/nih/3173023. Licensed CC0.

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