Quality and Reliability Methods - SAS

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396 Reliability and Survival Analysis II Chapter 20 Nonlinear Parametric Survival Models Lognormal Loss Function Loglogistic Loss Function Weibull Loss Function Example This example uses the VA Lung Cancer.jmp table. Models are fit to the survival time using the Weibull, lognormal, and exponential distributions. Model fits include a simple survival model containing only two regressors, a more complex model with all the regressors and some covariates, and the creation of dummy variables for the covariate Cell Type to be included in the full model. 1. Open the VA Lung Cancer.jmp sample data table. The first model and all the loss functions have already been created as formulas in the data table. The Model column has the following formula: Log(:Time) - (b0 + b1 * Age + b2 * Diag Time) Nonlinear model fitting is often sensitive to the initial values you give to the model parameters. In this example, one way to find reasonable initial values is to first use the Nonlinear platform to fit only the linear model. When the model converges, the solution values for the parameters become the initial parameter values for the nonlinear model. 2. Select Analyze >Modeling > Nonlinear. 3. Select Model and click X, Predictor Formula. 4. Click OK. 5. Click Go. The platform computes the least squares parameter estimates for this model, as shown in Figure 20.21.
Chapter 20 Reliability and Survival Analysis II 397 Nonlinear Parametric Survival Models Figure 20.21 Initial Parameter Values in the Nonlinear Fit Control Panel 6. Click Save Estimates. The parameter estimates in the column formulas are set to those estimated by this initial nonlinear fitting process. The Weibull column has the Weibull formula previously shown. To continue with the fitting process: 7. Select Analyze >Modeling > Nonlinear again. 8. Select Model and click X, Predictor Formula. 9. Select Weibull loss and click Loss. 10. Click OK. The Nonlinear Fit Control Panel on the left in Figure 20.22 appears. There is now the additional parameter called sigma in the loss function. Because it is in the denominator of a fraction, a starting value of 1 is reasonable for sigma. When using any loss function other than the default, the Loss is Neg LogLikelihood box on the Control Panel is checked by default. 11. Click Go. The fitting process converges as shown on the right in Figure 20.22.
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Quality and Reliability Methods - SAS

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