Quality and Reliability Methods - SAS

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386 Reliability and Survival Analysis II Chapter 20 Proportional Hazards Model Figure 20.15 ICDevice Output Example: Right-Censored Data; Tobit Model The Tobit model is normal, truncated at zero. However, you can take the exponential of the response and set up the intervals for a right-censored problem. In Tobit2.jmp, found in the Reliability folder of the sample data, run the attached script to estimate the lognormal. Proportional Hazards Model The proportional hazards model is a special semiparametric regression model proposed by D. R. Cox (1972) to examine the effect of explanatory variables on survival times. The survival time of each member of a population is assumed to follow its own hazard function.
Chapter 20 Reliability and Survival Analysis II 387 Proportional Hazards Model Proportional hazards is nonparametric in the sense that it involves an unspecified arbitrary baseline hazard function. It is parametric because it assumes a parametric form for the covariates. The baseline hazard function is scaled by a function of the model’s (time-independent) covariates to give a general hazard function. Unlike the Kaplan-Meier analysis, proportional hazards computes parameter estimates and standard errors for each covariate. The regression parameters (β) associated with the explanatory variables and their standard errors are estimated using the maximum likelihood method. A conditional risk ratio (or hazard ratio) is also computed from the parameter estimates. The survival estimates in proportional hazards are generated using an empirical method. See Lawless (1982). They represent the empirical cumulative hazard function estimates, H(t), of the survivor function, S(t), and can be written as S 0 =exp(-H(t)), with the hazard function H() t = j:t j < t d -------------------- j e x βˆ l l ∈ R j When there are ties in the response, meaning there is more than one failure at a given time event, the Breslow likelihood is used. Example: One Nominal Effect with Two Levels The following example uses the Rats.jmp sample data. To define a proportional hazard survival model, choose Fit Proportional Hazards from the Reliability and Survival submenu. This launches the Fit Model dialog for survival analysis, with Proportional Hazard showing as the Fitting Personality. Alternatively, you can use the Fit Model command and specify the Proportional Hazard fitting personality (Figure 20.16). The Fit Proportional Hazards window contains the following role buttons: Time to Event contains the time to event or time to censoring. Censor nonzero values in the censor column indicate censored observations. (The coding of censored values is usually equal to 1.) Uncensored values must be coded as 0. Freq is for a column whose values are the frequencies or counts of observations for each row when there are multiple units recorded. By is used to perform a separate analysis for each level of a classification or grouping variable. Using the Rats.jmp sample data, assign days as the Time to Event variable, Censor as Censor and Add Group to the model effects list. The next section describes the proportional hazard analysis results.
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Page 419 and 420: Index 419 Fit SEV 242 Fit Weibull 2
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Quality and Reliability Methods - SAS

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