Survival Analysis Regression Models - Exponential Regression

Basically, this model assumes that the survival time distribution is exponential, and contingent on the values of a set of independent variables (zi). The rate parameter of the exponential distribution can then be expressed as:

S(z) = exp(a + b1*z1 + b2*z2 + ... + bm*zm)

S(z) denotes the survival times, a is a constant, and the bi's are the regression parameters.

Goodness-of-fit. The Chi-square goodness-of-fit value is computed as a function of the log-likelihood for the model with all parameter estimates (L1), and the log-likelihood of the model in which all covariates are forced to 0 (zero; L0). If this Chi-square value is significant, we reject the null hypothesis and assume that the independent variables are significantly related to survival times.

Standard exponential order statistic. One way to check the exponentiality assumption of this model is to plot the residual survival times against the standard exponential order statistic Theta. If the exponentiality assumption is met, then all points in this plot will be arranged roughly in a straight line.