AISM 54, 155-168

© 2002 ISM

## Computing estimates in the proportional odds model

### David R. Hunter^{1} and Kenneth Lange^{2}

^{1}Department of Statistics, Penn State University,
University Park, PA 16802-2111, U.S.A., e-mail: dhunter@stat.psu.edu

^{2}Departments of Biomathematics and Human
Genetics, UCLA School of Medicine, Los Angeles, CA 90024, U.S.A.

(Received September 14, 1999; revised November 1, 2000)

Abstract.
The semiparametric proportional odds model for survival data is useful when
mortality rates of different groups converge over time. However, fitting the model by maximum likelihood proves computationally cumbersome for large datasets because the
number of parameters exceeds the number of uncensored observations. We present here an
alternative to the standard Newton-Raphson method of maximum likelihood
estimation. Our algorithm, an example of a minorization-maximization (MM)
algorithm, is guaranteed to converge to the maximum likelihood estimate whenever it exists.
For large problems, both the algorithm and its quasi-Newton accelerated counterpart outperform Newton-Raphson by more than two orders of magnitude.

Key words and phrases:
Majorization, MM algorithm, proportional odds, Newton-Raphson, quasi-Newton, survival analysis.

**Source**
(TeX , DVI )