TABLE OF CONTENTS The accelerated failure time model is a general model for survival data, in which covariates measured on an individual are assumed to act multiplicatively on the time-scale, and so can be thought of as influencing the rate at which an individual proceeds along the time axis. Such models can be interpreted in terms of the speed of progression of a disease. Algebraically, such models are of the form:
where ? i = exp( ? ?x) is the acceleration factor for the ith patient compared with the baseline patient group.
The exponential and Weibull have already been introduced as possible survival distributions. Another distribution that is frequently used for survival data is the log-normal with density function:
where ? is the mean and ? 2 is the variance. The log-normal distribution has a relatively heavy right tail, a feature that makes it useful for situations in which events occur later in the follow-up period.
The accelerated failure time model is most easily considered when it is expressed in log-linear form. Letting t i denote the survival time for the ith subject, the model is:
where ? is a scale parameter and ? i assumed to have some suitable distribution. Gaussian errors and no censoring simply correspond to linear regression of log-survival time. More generally the model is used with distributions such as the exponential, Weibull, log-logistic, and gamma. It can be shown that if the errors are...
