COMPUTING ESTIMATES IN THE PROPORTIONAL ODDS MODEL

DAVID R. HUNTER^{1} AND KENNETH LANGE^{2}

1Department of Statistics, Penn State University, University Park, PA 16802-2111, U.S.A.,

e-mail: dhunter@stat.psu.edu 2Departments 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.