approach uses linear regression for both location and scale parameters. A linear regression can be used, since the typical distributions
used for survival (Weibull, lognormal, exponential, Fréchet, loglo-gistic, and Gompertz) can be made linear through transformation.
A Goodness-of-Fit using a Chi-square statistic can be calculated
by comparing the likelihood of a distribution with a null model,
which allows for a different hazard rate for each interval. This is
shown in Figure 2 using the JMP Parametric Survival Fit platform
for a lognormal fit where the Chi-square value is statistically significant with a probability less than 0.05. A plot of the 0.1, 0.5, and
0.9 quantiles as a function of the regressor is displayed.
A nonparametric approach, typified by the Kaplan-Meier
method, calculates a survival function from continuous survival
times, where each time interval contains one case. The estimate
of this function is a product-time estimator. An advantage to this
method is that it is not dependent on the grouping of the data into
different intervals. A comparison of survival times for two or more
groups can be done using a test, such as the log-rank, Wilcoxon,
Gehan’s generalized Wilcoxon, Peto and Peto’s generalized Wil-
coxon, Cox’s F and Cox-Mantel test. Although there are no hard
and fast rules on which test to use in a given situation, where there
are no censored observations, the samples are from a Weibull or
exponential distribution, and sample size is less than 50 per group,
the Cox’s F test is more powerful than Gehan’s generalized Wil-
coxon test. Regardless of censoring, where the samples are from a
Weibull or exponential distribution, the log-rank and Cox-Mantel
are more powerful than Gehan’s generalized Wilcoxon test. There
are multiple sample tests of the log-rank, Gehan’s generalized
Wilcoxon, and Peto and Peto’s generalized Wilcoxon test. Using
Mantel’s procedure, a score is assigned to each survival time and a
Chi-square value is calculated based on the sums for each group.
An example of survival between males and females is shown in
Figure 3 using the JMP Survival platform where both the log-rank
and Wilcoxon test are statistically significant with a probability
less than 0.05.