# NONPARAMETRIC ANALYSIS OF CENSORED DATA

> **NIH NIH R01** · UNIVERSITY OF WISCONSIN-MADISON · 1989 · $71,224

## Abstract

1.  Semiparametric Regression Methodology for Censored Data
This specific aim will be to develop methodology for the regression
analysis of lifetime data under right, left and interval censoring, when
one does not assume any particular parametric family of survival
distributions.  The multiple imputation approach presented in Tanner and
Wong (1987a) will be used to develop one such approach, while techniques
of Boos and Monahan (1983), Tanner and Wong (1984) and Wei and Tanner
(1988) will be used to develop more faithful interpretations of the data
augmentation algorithm (Tanner and Wong, 1987b) in the censored
regression context.

2.  Sampling From the Cox Partial Likelihood
Wei and Tanner (1988) have developed a rejection/acceptance algorithm
for sampling from the posterior (likelihood) in the case of parametric
censored regression models.  This specific aim is to extend this
methodology to allow one to sample from the Cox partial likelihood and
then to apply this methodology to a variety of problems related to the
Cox model.  In this way, the need to rely on asymptotic normal
approximations for inferential purposes can be avoided.  Problems
include:  parameter inference in small/unbalanced samples; inference
relating to the survivor and cumulative hazard functions; missing (at
random) covariates; and goodness-of-fit.

3.  Sampling in the Context of Logistic Regression
This specific aim is to investigate techniques to allow sampling from
the likelihood for the logistic regression model and to then apply this
methodology to a variety of problems related to the logistic regression
model.  In small samples or samples with covariate imbalance, the normal
approximation to the scaled likelihood may not be appropriate.  Problems
to be addressed include:  parameter inference in small/unbalanced
samples; patching missing (at random) covariates; calculating the
distribution of the "dose" corresponding to a given percentile;
sequential design for estimating the percentile of a quantal response;
and goodness-of-fit.

4.  Development of Software to Accompany Methodology
This specific aim is to develop transportable, documented, efficient and
well-written code for the non-parametric estimation of the hazard
function from grouped and censored data (Tanner and Wong, 1987a), as
well as for the sampling from the posterior of Beta and Sigma in the
normal, exponential, gamma and Weibull censored regression models (Wei
and Tanner, 1988).  Additional code will be written to support the
methodology developed under this grant.

## Key facts

- **NIH application ID:** 3173018
- **Project number:** 2R01CA035464-06
- **Recipient organization:** UNIVERSITY OF WISCONSIN-MADISON
- **SAM.gov UEI:** LCLSJAGTNZQ7
- **Principal Investigator:** MARTIN A TANNER
- **Activity code:** R01 (R01, R21, SBIR, etc.)
- **Funding institute:** NIH
- **Fiscal year:** 1989
- **Award amount:** $71,224
- **Award type:** 2
- **Project period:** 1984-08-01 → 1990-07-31

## Primary source

NIH RePORTER: https://reporter.nih.gov/project-details/3173018

## Citation

> US National Institutes of Health, RePORTER application 3173018, NONPARAMETRIC ANALYSIS OF CENSORED DATA (2R01CA035464-06). Retrieved via MORVS 2026-10-25 from https://api.morvs.ai/grant/nih/3173018. Licensed CC0.

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