The author presents a multivariate proportional hazards model for data that are clustered at two hierarchical levels and applies it to the study of the covariates of child mortality in Northeast Brazil. The model provides corrected parameter estimates and standard errors — as well as estimates of intra-group correlation of survival times at both levels — with survey data collected via a hierarchically clustered sampling scheme, such as the data from Northeast Brazil that are analyzed in this paper. The model accounts for the hierarchical clustering in the data by including two random-effects or frailty-effects. The author assumes that the two random-effects are independent and that each follows the gamma distribution. The parameters of the hazard model and the mixing distributions are estimated using the expectation-maximization (EM) algorithm. The author uses the incomplete data log-likelihood function to calculate standard errors. The author's results indicate that family and community clustering effects in Northeast Brazil are fairly small in magnitude but are of importance because they alter parameter estimates and standard errors in a systematic pattern.
Sastry, Narayan, A Multilevel Hazards Model for Hierarchically Clustered Data: Model Estimation and an Application to the Study of Child Survival in Northeast Brazil. Santa Monica, CA: RAND Corporation, 1995. https://www.rand.org/pubs/drafts/DRU1101.html.
Sastry, Narayan, A Multilevel Hazards Model for Hierarchically Clustered Data: Model Estimation and an Application to the Study of Child Survival in Northeast Brazil, RAND Corporation, DRU-1101-RC, 1995. As of January 11, 2023: https://www.rand.org/pubs/drafts/DRU1101.html