Bayesian Survival Analysis with PROC LIFEREG (Example 2)

This script illustrates a survival analysis on industrial fan reliability data. It begins by creating the 'Fan' dataset containing operating times and censoring indicators. The LIFEREG procedure is then used to fit a log-normal parametric model with a Bayesian approach (BAYES statement), generating posterior samples in the 'Post' table. A subsequent DATA step uses these samples to estimate the probability distribution of failure at 8000 hours. Finally, PROC MEANS provides descriptive statistics (mean and percentiles) on this estimated probability.

Data Analysis

Type : INTERNAL_CREATION

Data is defined directly in the script via the 'datalines' statement in the DATA Fan step.

1 Code Block

DATA STEP Data

Explanation :
Creates the SAS table 'Fan' by reading internal data (datalines). The 'Lifetime' variable represents the lifespan and 'Censor' indicates whether the observation is censored (1) or not (0).

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1	DATA Fan;
2	INPUT Lifetime Censor @code_sas_json/8_SAS_Intro_ReadFile_MultiCol_@@.json;
3	DATALINES;
4	450 0 460 1 1150 0 1150 0 1560 1
5	1600 0 1660 1 1850 1 1850 1 1850 1
6	1850 1 2030 1 2030 1 2030 1
7	2070 0 2070 0 2080 0 2200 1 3000 1
8	3000 1 3000 1 3000 1 3100 0 3200 1
9	3450 0 3750 1 3750 1 4150 1 4150 1
10	4150 1 4150 1 4300 1 4300 1 4300 1
11	4300 1 4600 0 4850 1 4850 1 4850 1
12	4850 1 5000 1 5000 1 5000 1 6100 1
13	6100 0 6100 1 6100 1 6300 1 6450 1
14	6450 1 6700 1 7450 1 7800 1 7800 1
15	8100 1 8100 1 8200 1 8500 1 8500 1
16	8500 1 8750 1 8750 0 8750 1 9400 1
17	9900 1 10100 1 10100 1 10100 1 11500 1
18	;

2 Code Block

PROC LIFEREG

Explanation :
Performs a regression analysis on survival data with a log-normal distribution. The 'bayes' statement activates Bayesian analysis, sets a random seed for reproducibility (seed=1), and exports posterior distribution samples to the 'Post' table.

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1	ods graphics on;
2	PROC LIFEREG DATA=Fan;
3	model Lifetime*Censor( 1 )= / dist=lognormal;
4	bayes seed=1 outpost=Post;
5	RUN;

3 Code Block

DATA STEP Data

Explanation :
Uses the estimated parameters (Intercept, Scale) stored in the 'Post' table to calculate the 'Frac' variable. This variable represents the estimated probability of failure at 8000 hours for each iteration of the Bayesian simulation.

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1	DATA Prob;
2	SET Post;
3	Frac = ProbNorm(( log(8000) - Intercept ) / Scale );
4	label Frac= 'Fraction Failing in 8000 Hours';
5	RUN;

4 Code Block

PROC MEANS

Explanation :
Calculates descriptive statistics (number of observations, mean, and various percentiles) on the 'Frac' variable from the 'Prob' table to summarize the posterior distribution of the probability of failure.

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1
2	PROC MEANS
3	DATA = Prob(keep=Frac) n mean p10 p25 p50 p75 p90;
4	RUN;
5

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