Motivated by Buckley and James' modification of the least squares procedure for censored regression data, we derive a score process that incorporates the time evolution and handles staggered entry data in a natural way. By censored regression data we mean that the responses are subject to a possible right censorship. Such cases often arise from clinical trials and industrial life tests. The score process can be interpreted as a weighted comparison of (transformed) survival times. This is especially suitable for the accelerated failure time regression model. By expressing it in an appropriate form so that the counting process and its associate martingale theory can be applied, we show that the score process is approximated by a mean 0 multidimensional Gaussian process. A consistent estimator of its covariance matrix function is provided. Based on the covariance matrix estimator and the sequential test of Slud and Wei, a repeated significance test is then proposed. Usefulness of the procedure is illustrated with two well-known data sets: the beta-blocker heart attack trial data and the Stanford heart transplant data. Both data sets are also analyzed using the more familiar repeated log-rank test. Comparing results from the log-rank and the proposed tests shows that the two procedures tend to reach similar conclusions. Simulation studies are conducted to investigate the accuracy of the normal approximations when sample sizes are moderate and to compare efficiency with the commonly used log-rank statistic. The results indicate that the proposed test is superior when the underlying error distribution is normal, and the log-rank method is superior when the error distribution is extreme value. We also show how the proposed test can be modified to adjust for ancillary covariates.