Sample size determination for an exponential survival model with an unrestricted covariate

We derive formulae for estimating sample size and power for detecting the effect of an unrestricted covariate on survival time. These are useful in designing survival studies with different patterns of recruitment and follow-up when survival time is exponentially distributed. We use the asymptotic covariance matrix, conditional expectation and Taylor's expansion techniques to develop these formulae. Computer simulations indicate that the asymptotic approximations used in developing the formulae are good over a range of parameter values and different patterns of recruitment and follow-up that are relevant to survival studies.