SMALL SAMPLE BIOSTATISTICAL INFERENCE

Project Details

Description

The ultimate goal of the proposed research is the application of
saddlepoint methodology to biostatistical problems. The main aim of this
work is to refine and extend the Gibbs-Skovgaard algorithm of Kolassa and
Tanner (1192). This method implements Markov chain Monte Carlo methods
in conditional inference by using the Gibbs sampler to construct a Markov
chain whose equilibrium distribution is the null conditional distribution
of interest. Each step in the Markov chain constructed by the Gibbs
sampler is accomplished by cycling through all of the variables whose
values are to simulated, and for each of these variables sampling a new
value conditional on all other variable held fixed. To date, the
methodology has been applied to two-way and three-way contingency tables,
and to logistic regression, with applications to cancer research. The
double-saddlepoint conditional cumulative distribution, which is often
difficult to sample from. This algorithm will be formulated and applied
in cases including that of general hierarchical models for contingency
tables. Furthermore, a variety of extensions of the double-saddlepoint
approximation of Skovgaard (1987), upon which the Gibbs-Skovgaard
algorithm rests, will be developed. Higher-order terms in this expansion
will be calculated. When applied to exponential families, the double
saddlepoint approximation requires the existence of maximum likelihood
estimators for the regression parameters associated with statistics
conditioned on. An extension of these methods removing this requirement
will be developed. The performance of this expansion will be compared
against the performance of competing approximations, including the
sequential saddlepoint approximation of Fraser, Reid, and Wong (1991).
The accuracy of the distribution approximation achieved by using the
Markov chain resulting from the Gibbs-Skovgaard algorithm will be
assessed. Computer software that can be shared with other sophisticated
users will be developed. A subsidiary aim of this work is to explore the
use of saddlepoint methods in performing approximate maximum likelihood
estimation in generalized linear models with random effects. Saddlepoint
integration methods will be used to evaluate the integral defining the
unconditional likelihood.
StatusFinished
Effective start/end date5/11/941/31/05

Funding

  • National Cancer Institute: $64,481.00
  • National Cancer Institute: $99,468.00
  • National Cancer Institute
  • National Cancer Institute: $64,481.00
  • National Cancer Institute
  • National Cancer Institute
  • National Cancer Institute
  • National Cancer Institute

ASJC

  • Computer Science(all)

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