Two Level Proportional Hazards

We extend the proportional hazards model to a two level model with a random intercept term and random coeecients. The parameters in the multilevel model are estimated by a combination of EM and Newton-Raphson algorithms. Even for samples of 50 groups, this method produces estimators of the regression coeecient which are approximately unbiased and normally distributed. Two diierent methods, observed information and proole likelihood information, will be used to estimate the standard errors. This work is motivated by the goal of understanding the fertility patterns of Nepalese women in the Chitwan Valley Family Study (Axinn, Barber and Dirgha 1997). We utilize a two-level hazard model to examine how opportunities for health care and education covary with the timing of permanent contraceptive use.