Parametric Survival Models

Parametric modeling requires choosing one or more distributions. TheWeibull and exponential distributions were discussed in Chapter 18. Other commonly used survival distributions are obtained by transforming T and using a standard distribution. The log transformation is most commonly employed. The log-normal distribution specifies that log(T ) has a normal distribution with mean μ and variance σ. Stated another way, log(T ) ∼ μ + σ , where has a standard normal distribution. Then S(t) = 1 − Φ((log(t) − μ)/σ), where Φ is the standard normal cumulative distribution function. The loglogistic distribution is given by S(t) = [1 + exp(−(log(t) − μ)/σ)]−1. Here log(T ) ∼ μ+σ where follows a logistic distribution [1+exp(−u)]−1. The log