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Applications - SAS. Parametric Regression in SAS PROC LIFEREG PROC GENMOD PROC LOGISTIC. Reference: SAS ver. 8.0 SAS/STAT User’s Guide, SAS Institute, Inc., Cary, NC. Applications – PROC LIFEREG. Mathematical Model where y is a vector of response values,

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Applications - SAS
• Parametric Regression in SAS
• PROC LIFEREG
• PROC GENMOD
• PROC LOGISTIC
• Reference: SAS ver. 8.0 SAS/STAT User’s Guide,SAS Institute, Inc., Cary, NC

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG
• Mathematical Model

where y is a vector of response values,

(often the log of the failure times)

X is a matrix of covariates variables

(usually including an intercept term),

β is a vector of unknown regression parameters

σ is an unknown scale parameter, and

ε is a vector of errors

(assumed to come from any known distribution)

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG
• Log Likelihood
• if all the responses are observed

, where

• If some of the responses are right censored,

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG
• Model & Estimation
• Accelerated Failure Time (Life) Model
• The effect of independent variables on an event time distribution is multiplicative on the event time
• The effect of the covariates : change the scale of a baseline distribution of failure times, not the location
• Estimation : MLE using a Newton-Raphson algorithm
• Standard Errors of the parameter estimates : the inverse of the observed information matrix
• Test : Normal based Test (e.g. chi-sq test, LRT)

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG
• Kidney Transplant Data

PROC FORMAT;

VALUE female 0='Male' 1='Female';

VALUE algfmt 0='Non-ALG' 1='ALG';

RUN

DATA kidney;

INFILE "surd01.dat";

INPUT id 1-4 age 5-6 sex 7 Alg 22

duration 25-27 status 28;

lntime = log(duration);

FORMAT sex female. Alg algfmt.;

RUN;

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG
• Exponential Regression

TITLE1 "Kidney Transplants Data";

PROC LIFEREG DATA=kidney;

CLASS ALG;

MODEL DURATION*STATUS(0)= ALG/

DIST=EXPONENTIAL;

OUTPUT OUT=out CDF=prob;

TITLE2 "Simple Exponential Regression”;

RUN;

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG

Output

Kidney Transplants Data 1

Simple Exponential Regression

The LIFEREG Procedure

Model Information

Data Set WORK.KIDNEY

Dependent Variable Log(duration)

Censoring Variable status

Censoring Value(s) 0

Number of Observations 469

Noncensored Values 192

Right Censored Values 277

Left Censored Values 0

Interval Censored Values 0

Name of Distribution Exponential

Log Likelihood-645.2158149

Algorithm converged.

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG

Output Continued

Type III Analysis of Effects

Wald

Effect DF Chi-Square Pr > ChiSq

ALG 1 6.7769 0.0092

Analysis of Parameter Estimates

Standard 95% Confidence Chi-

Parameter DF Estimate Error Limits Square

Intercept 1 4.2155 0.1400 3.9410 4.4899 906.28

Alg ALG 1 0.4254 0.1634 0.1051 0.7456 6.78

Alg Non-ALG 0 0.0000 0.0000 0.0000 0.0000 .

Scale 0 1.0000 0.0000 1.0000 1.0000

Weibull Shape 0 1.0000 0.0000 1.0000 1.0000

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG
• Interpretation (Risk = λ exp(xβ) )
• λ = Exp(-β0) = exp(-4.215) = 0.015
• β1 = coefficient for ALG = 0.425
• RR(ALG=1:ALG=0) = exp(β1) = 0.654
• the risk of ALG group = λ exp(β1) = 0.015*0.654 = 0.0096
• the risk of Non-ALG group = λexp(0) = 0.015
• Testing & Conclusion
• Using ALG decreased the risk 34.6%
• Significant effect

( )

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG

Estimated CDF of Residuals Vs. Observed Duration

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG
• Multiple Regression

PROC LIFEREG DATA=kidney;

CLASS ALG;

MODEL DURATION*STATUS(0)= AGE ALG/

DIST=EXPONENTIAL;

OUTPUT OUT=out QUANTILES=.5

STD=STD

P=MED_DURATION;

RUN;

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG
• Estimation Comparison

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG
• Predicted Values and Confidence Intervals

DATA out1;

SET out;

ltime=log(med_duration);

stde=std/med_duration;

upper=exp(ltime+1.64*stde);

lower=exp(ltime-1.64*stde);

RUN;

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG

Median Predicted Values Vs. AGE by the Use of ALG

PubH8420: Parametric Regression Models

Applications – PROC LIFEREG
• Other supported distributions
• Generalized Gamma
• Loglogistic
• Lognormal
• Weibull
• Some relations among the distributions:
• The Weibull with Scale=1 : exponential distribution
• The gamma with Shape=1 : Weibull distribution.
• The gamma with Shape=0 : lognormal distribution.

PubH8420: Parametric Regression Models

Applications – PROC GENMOD
• Piecewise exponential distribution

(Poisson Regression)

TITLE1 "Kidney Transplants Data";

PROC GENMOD DATA=kidney;

CLASS ALG;

MODEL STATUS = AGE ALG/

DIST=POISSON

LINK=log OFFSET=lntimetype3;

TITLE2 "Multiple Piecewise Exponential Regression";

RUN;

PubH8420: Parametric Regression Models

Applications – PROC LOGISTIC
• Dichotomized data

DATA kidney1;

SET kidney;

DO month=1 TO duration;

IF month=duration AND status=1

THEN fail=1;

ELSE fail=0;

OUTPUT;

END;

RUN;

PubH8420: Parametric Regression Models

Applications – PROC LOGISTIC
• LOGISTIC REGRESSION with LOGIT LINK

PROC LOGISTIC DATA=kidney1;

CLASS month fail/

PARAM=reference REF=first;

MODEL fail=age ALG;

RUN;

PubH8420: Parametric Regression Models

Applications – PROC LOGISTIC
• LOGISTIC REGRESSION

with CLOGLOG LINK

PROC LOGISTIC DATA=kidney1 ;

CLASS month fail/

PARAM=reference REF=first;

MODEL fail=age ALG/

LINK=CLOGLOG;

RUN;

PubH8420: Parametric Regression Models

Applications - SAS
• Comparison of Parameter Estimates
• Hazards Ratio in Log Scale

PubH8420: Parametric Regression Models