Professor Rose-Helleknat's PCR Data for Breast Cancer Study

Transcription

1 Professor Rose-Helleknat's PCR Data for Breast Cancer Study Summary statistics for Crossing Point, cp = - log 2 (RNA) Obs Treatment Outcome n Mean Variance St_Deviation St_Error 1 Placebo Cancer Placebo No_Cancer Tamoxifen Cancer Tamoxifen No_Cancer Usual ANOVA Sum of Source DF Squares Mean Square F Value Pr > F Model Error Corrected Total Source DF Type I SS Mean Square F Value Pr > F Treatment Outcome Treatment*Outcome Source DF Type III SS Mean Square F Value Pr > F Treatment Outcome Treatment*Outcome Treatment Outcome cp LSMEAN Placebo Cancer Placebo No_Cancer Tamoxifen Cancer Tamoxifen No_Cancer Standard Parameter Estimate Error t Value Pr > t Taxoxifen - Placebo Cancer - No Cancer Outcome Effect in Placebo Outcome Effect in Taxoxifen Parameter 95% Confidence Limits Taxoxifen - Placebo Cancer - No Cancer Outcome Effect in Placebo Outcome Effect in Taxoxifen

2 Model Comparisons with AICC For maximum likelihood estimation: Add 1 for the mean,, in the model. Constant Variance q=1 Covariance Parameter Estimates Cov Parm Estimate Residual Fit Statistics -2 Log Likelihood 56.2 AIC (smaller is better) 66.2 AICC (smaller is better) 70.5 BIC (smaller is better) 71.2 Variances Differ in Treatments q=2 Cov Parm Group Estimate animal Treatment Placebo animal Treatment Tamoxifen Fit Statistics -2 Log Likelihood 48.8 AIC (smaller is better) 60.8 AICC (smaller is better) 67.2 BIC (smaller is better) 66.7 Variances differ in Outcomes q=2 Fit Statistics -2 Log Likelihood 55.6 AIC (smaller is better) 67.6 AICC (smaller is better) 74.0 BIC (smaller is better) 73.5 Variances Differ in All 4 Groups q=4 Cov Parm Group Estimate animal group Placebo_Cancer animal group Placebo_No_Cancer animal group Tamox_Cancer animal group Tamox_No_Cancer Fit Statistics -2 Log Likelihood 46.7 AIC (smaller is better) 62.7 AICC (smaller is better) 75.8 BIC (smaller is better) 70.6

3 Analysis with Final Model Using REML, restricted maximum likelihood, for more unbiased variance estimates. For example in ANOVA table, MS Error = SS Error/df Error = REML estimate of For maximum likelihood (ML), estimate of SS Error/n, a smaller estimate of For ML: proc mixed method=ml data=here.pcr; For REML: proc mixed data=here.pcr; * REML is the default method; In comparing AICC values, if the model statement changes, the REML AICC values are not comparable. It's safest just to compare AICC values from ML rather than REML, even though REML will work fine most of the time. For testing fixed effects such as treatment effects, it is best to use F-tests, rather than comparing likelihood ratio statistics to a chi-square distribution. o The F-test is the likelihood ratio test with the exactly correct F distribution. o Comparing to the chi-square table essentially sets the error df to infinity, knowing. For single df tests, such as treatments in this example, this would be doing a Z test rather than the correct t-test. proc mixed method=ml data=here.pcr; title 'Variances differ in Treatments'; class animal treatment outcome; model cp = treatment outcome treatment*outcome/ddfm=satterthwaite; repeated animal/group=treatment; estimate 'Taxoxifen - Placebo' treatment -1 1; ods select estimates covparms fitstatistics; Variances Differ in Treatments Cov Parm Group Estimate animal Treatment Placebo animal Treatment Tamoxifen Fit Statistics -2 Res Log Likelihood 48.7 AIC (smaller is better) 52.7 AICC (smaller is better) 53.6 BIC (smaller is better) 54.7 Type 1 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F Treatment Outcome Treatment*Outcome

4 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F Treatment Outcome Treatment*Outcome Standard Label Estimate Error DF t Value Pr > t Alpha Taxoxifen - Placebo Cancer - No Cancer Outcome Effect in Placebo Outcome Effect in Taxoxifen Label Lower Upper Taxoxifen - Placebo Cancer - No Cancer Outcome Effect in Placebo Outcome Effect in Taxoxifen In comparison, we have few df if we use 4 different variances and do all t-tests as in Chapter 6 Variances Differ in All 4 Groups Standard Label Estimate Error DF t Value Pr > t Alpha Taxoxifen - Placebo Cancer - No Cancer Outcome Effect in Placebo Outcome Effect in Taxoxifen

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6 Crossing point = CP = -log 2 (RNA) scale

7 ods html gpath="c:\documents and Settings\rregal\My Documents\My Dropbox\5411_2012\Lectures\Graphics" file="c:\documents and Settings\rregal\My Documents\My Dropbox\5411_2012\Lectures\Graphics\pcr.html"; ods graphics on; proc sgplot data=here.pcr; title 'RNA Scale';

8 scatter y=rna x=group; proc glm plots=diagnostics data=here.pcr; title 'Usual ANOVA'; id gene; class treatment outcome; model rna = treatment outcome treatment*outcome/clparm ss1 ss3; proc sort data=here.pcr; by group; proc means noprint n mean stddev var stderr data=here.pcr; var cp; id treatment outcome; by group; output out=outmean n=n mean=mean var=variance stddev=st_deviation stderr=st_error; proc print data=outmean; var treatment outcome n mean variance St_Deviation st_error; ods graphics on; proc sgplot data=here.pcr; title 'RNA Scale'; scatter y=cp x=group; proc glm plots=diagnostics data=here.pcr; title 'Usual ANOVA'; id gene; class treatment outcome; model cp = treatment outcome treatment*outcome/clparm ss1 ss3; lsmeans treatment*outcome; estimate 'Taxoxifen - Placebo' treatment -1 1; estimate 'Cancer - No Cancer' outcome 1-1; estimate 'Outcome Effect in Placebo' outcome 1-1 treatment*outcome ; estimate 'Outcome Effect in Taxoxifen' outcome 1-1 treatment*outcome ; output out=outresid r=residual p=predicted;

9 proc sgplot data=outresid; scatter y=residual x=treatment/group=outcome; proc sgplot data=outresid; scatter y=residual x=outcome/group=treatment; proc mixed method=ml data=here.pcr; title 'Constant Variance'; class treatment outcome; model cp = treatment outcome treatment*outcome; ods select estimates covparms fitstatistics; proc mixed method=ml data=here.pcr; title 'Variances differ in Treatments'; class animal treatment outcome; model cp = treatment outcome treatment*outcome/ddfm=satterthwaite; repeated animal/group=treatment; ods select estimates covparms fitstatistics; proc mixed method=ml data=here.pcr; title 'Variances differ in Outcomes'; class animal treatment outcome; model cp = treatment outcome treatment*outcome/ddfm=satterthwaite; repeated animal/group=outcome; ods select estimates covparms fitstatistics; proc mixed method=ml data=here.pcr; title 'Variances differ in all 4 groups'; class animal treatment outcome group; model cp = treatment outcome treatment*outcome/ddfm=satterthwaite; repeated animal/group=group; ods select estimates covparms fitstatistics; proc mixed data=here.pcr; title 'Final Model: Variances differ in Treatments'; class animal treatment outcome; model cp = treatment outcome treatment*outcome /htype=1,3 ddfm=satterthwaite;

10 repeated animal/group=treatment; estimate 'Taxoxifen - Placebo' treatment -1 1 /cl; estimate 'Cancer - No Cancer' outcome 1-1 /cl; estimate 'Outcome Effect in Placebo' outcome 1-1 treatment*outcome /cl; estimate 'Outcome Effect in Taxoxifen' outcome 1-1 treatment*outcome /cl;