proc mcmc - sas · pdf fileproc mcmc masud rana,1 rhonda bryce,1 j. a. dosman,2 and punam...

PROC MCMC

Masud Rana,1 Rhonda Bryce,1 J. A. Dosman,2 and Punam Pahwa1,3

1Clinical Research Support Unit, College of Medicine2Department of Medicine

3Department of Community Health & EpidemiologyUniversity of Saskatchewan

Saskatoon, Saskatchewan, S7N 5E5, Canada

Saskatoon SAS User Group (SUCCESS)

May 14, 2013

Masud Rana (CRSU) PROC MCMC May 14, 2013 1 / 26

Outline

1 Bayesian Inference

2 Data

3 Example


Bayesian Inference

Bayesian Inference


Bayesian Inference

Bayesian Inference (Cont.)


Data

Data

F Forced Expiratory Volume in one second (FEV1) is the volume of airthat can forcibly be blown out in one second, after full inspiration.

F FEV1 is a frequently used index for assessing lung function.

F FEV1 is assumed to be correlated with sex, age, height, weight andsmoking habits.

F In 1978 Labour Canada started the Grain Dust Medical SurveillanceProgram to assess the prevalence of respiratory system among grainworkers and ended in 1993 over five different cycles across Canada.

F Data on 5702 personnel were collected in Cycle 1 of the survey.


Example

Model 1

CURRFEV 1i = β0 + β1 ∗ CURREXPi + β2 ∗ Smokeri + β3 ∗ BASEHTi+

β4 ∗ CURRWTi + β5 ∗ CURRAGEi + εi (1)

where εi ∼ N(0, σ2), i = 1, 2, ......, n.

Prior Distribution

βj ∼ N(0,VAR = 10000), j = 0, 1, ..., 5

σ2 ∼ IGAMMA(SHAPE = 0.01,SCALE = 0.01) (2)

Likelihood Function

CURRFEV 1i ∼ N(β0 + β1 ∗ CURREXPi + β2 ∗ Smokeri + β3 ∗ BASEHTi+

β4 ∗ CURRWTi + β5 ∗ CURRAGEi , σ2) (3)


Example

SAS Code for Model 1


Example

Diagnostic Plots for β0


Example



Example

Diagnostic Plots for σ2


Example

Random Effects Model

♣ Correlation coefficient between Age and Experience is 0.77.

♣ Regression coefficients are assumed to vary across different regions.

♣ Regions are:

♦ Atlantic: East of Quebec♦ St. Lawrence: Quebec only♦ Great Lakes: Ontario (East of Thunder Bay)♦ Central: Ontario (Thunder Bay and westward), Manitoba and

Saskatchewan♦ Mountain: Alberta, British Columbia, Yukon and North West

Territories

Model 2

CURRFEV 1ij = α0i + α1i ∗ CURRAGEij + α2i ∗ CURREXPij + εij (4)

where εij ∼ N(0, σ2), i = 1, 2, ......, 5, j = 1, 2, .., ni .


Example

Prior Distribution

θi =

α0i

α1i

α2i

∼ MVN

θc =

α0c

α1c

α2c

,Σc

θc ∼ MVN

µ0 =

000

,Σ0 =

1000 0 00 1000 00 0 1000

Σc ∼ IWISHART

3,

1 0 00 1 00 0 1

σ2 ∼ GAMMA (SHAPE = 3,SCALE = 2)

(5)

Likelihood Function

CURRFEV 1ij ∼ N(α0i + α1i ∗ CURRAGEij + α2i ∗ CURREXPij , σ2) (6)


Example

SAS Code for Model 2


Example

Diagnostic Plots for Region=Atlantic


Example

Diagnostic Plots for Region=St. Lawrence


Example

Diagnostic Plots for Region=Great Lakes


Example

Diagnostic Plots for Region=Central


Example

Diagnostic Plots for Region=Mountain


Example

Diagnostic Plots for σ2


Example

References

Thomas NicholsBayesian Inference.http : //www .fil .ion.ucl .ac .uk/spm/course/slides10−vancouver/08 Bayes.pdf .

Fang ChenThe RANDOM Statement and More: Moving On with PROC MCMCin Proceedings of the SAS Global Forum 2011 Conference.Cary, NC: SAS Institute Inc.

SAS Institute Inc. 2011SAS/STAT 9.3 Users Guide.Cary, NC: SAS Institute Inc.


Example


proc mcmc - sas · pdf fileproc mcmc masud rana,1 rhonda bryce,1 j. a. dosman,2 and punam...

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