1 / 20

Applications - SAS

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,

adlai
Download Presentation

Applications - SAS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 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

  2. 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

  3. Applications – PROC LIFEREG • Log Likelihood • if all the responses are observed , where • If some of the responses are right censored, PubH8420: Parametric Regression Models

  4. 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) For the Exponential Distribution, ALM = PHM For the Weibull Distribution, ALM = PHM when having the same shape parameter (the parameterization for the covariates differs by a multiple of the scale parameter). PubH8420: Parametric Regression Models

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. Applications – PROC LIFEREG Estimated CDF of Residuals Vs. Observed Duration PubH8420: Parametric Regression Models

  11. 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

  12. Applications – PROC LIFEREG • Estimation Comparison PubH8420: Parametric Regression Models

  13. 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

  14. Applications – PROC LIFEREG Median Predicted Values Vs. AGE by the Use of ALG PubH8420: Parametric Regression Models

  15. 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

  16. 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

  17. Applications – PROC LOGISTIC • Dichotomized data Define a new data set, a record for each time point 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

  18. 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

  19. 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

  20. Applications - SAS • Comparison of Parameter Estimates • Hazards Ratio in Log Scale PubH8420: Parametric Regression Models

More Related