What is the model for the PROC LIFEREG with a Weibull distribution option?

[TomHsiung]

There are many ways to model a Weibull distribution (reference: https://www.mdpi.com/2227-7390/12/1/56).

Some textbooks use a parametric proportional hazard model to construct the likelihood function. Others include the accelerated failure time (AFT) model, and so on. My question is what is the model used for the PROC LIFEREG procedure? Thanks.

Code below.

proc lifereg data = d202_raw order = formatted;
format x1 x2 x3 x4 x5 grpfmt.;
class x2 x3 x4;
model time*censor(0) = x1 x2 x3 x4 x5 / distribution = weibull;
run;

[sbxkoenk · Accepted solution]

The LIFEREG procedure fits a parametric model to failure time data.

Your statements perform a typical accelerated failure time (AFT) model analysis.

As you point out ... two of the more popular types of models for survival data (failure time data) are the accelerated failure time model (Kalbfleisch and Prentice 1980) and the Cox proportional hazards model (Cox 1972). Each has its own assumptions about the underlying distribution of the survival times. Two closely related functions often used to describe the distribution of survival times are the survivor function and the hazard function.

• The accelerated failure time model assumes a parametric form for the effects of the explanatory variables and usually assumes a parametric form for the underlying survivor function.
• The Cox proportional hazards model also assumes a parametric form for the effects of the explanatory variables, but it allows an unspecified form for the underlying survivor function. 

Cox regression (Cox proportional hazards model) is a semi-parametric model and can be fit with PROC PHREG or with the PHSELECT Viya (CAS) procedure. PHSELECT allows for LASSO variable selection.

If you are dealing with machinery and quality assurance / quality control (f.e. in manufacturing) ... then you are probably more interested in PROC RELIABILITY (SAS/QC).

Koen

[TomHsiung]

Got it. Thank you for your help. Koen.