Efficiency of observation schemes for proportional hazard regression models with censoring

Proportional hazard regression models are considered. The scheme of observation in which observed and censored survival times are available for analysis is compared with the simpler binary scheme in which it is only known whether or not individuals survived the censoring times. A bound on the expected information matrix for the second scheme is given in terms of the information matrix for the first scheme. When the censoring variables are of degenerate type giving fixed censoring times, it is shown that the loss of efficiency from using the binary scheme of observation will be unimportant provided that there is at least a moderate degree of censoring. Power comparisons for likelihood ratio tests of hypotheses for the regression coefficients in an exponential regression model with a logarithmic link for the failure rate function are made for the two schemes of observation.