Chapter 6 OR analysis text output
6.1 TBA How much finished
90%
6.2 Introduction
This chapter illustrates significance testing using the DBM and OR methods.
6.3 Analyzing the ROC dataset
The only change is to specify method = "OR"
in the significance testing function. The same dataset is used as was used in the previous chapter.
6.4 Explanation of the output
The function returns a list with 5 members.
FOMs
: figures of merit, identical to that in the DBM method.ANOVA
: ANOVA tables.RRRC
: random-reader random-case analyses results.FRRC
: fixed-reader random-case analyses results.RRFC
" random-reader fixed-case analyses results.
Let us consider the ones that are different from the DBM method.
- ANOVA is a list of 4
TRanova
is a [3x3] dataframe: the treatment-reader ANOVA table, see below, where SS is the sum of squares, DF is the denominator degrees of freedom and MS is the mean squares, and T = treatment, R = reader, TR = treatment-reader.
VarCom
is a [6x2] dataframe: the variance components, see below, wherevarR
is the reader variance,varTR
is the treatment-reader variance,Cov1
,Cov2
,Cov3
andVar
are as defined in the OR model. The second column lists the correlations defined in the OR model.IndividualTrt
is a [2x4] dataframe: the individual treatment mean-squares, variances and \(Cov_2\), averaged over all readers, see below, wheremsREachTrt
is the mean square reader,varEachTrt
is the variance andcov2EachTrt
isCov2EachTrt
in each treatment.IndividualRdr
is a [2x4] dataframe: the individual reader variance components averaged over treatments, see below, wheremsTEachRdr
is the mean square treatment,varEachRdr
is the variance andcov1EachRdr
is \(Cov_1\) for each reader.
ret$ANOVA$TRanova
#> SS DF MS
#> T 0.00023565410 1 2.3565410e-04
#> R 0.00205217999 3 6.8406000e-04
#> TR 0.00015060792 3 5.0202641e-05
ret$ANOVA$VarCom
#> Estimates Rhos
#> VarR 2.3319942e-05 NA
#> VarTR -6.8389146e-04 NA
#> Cov1 7.9168215e-04 0.51887172
#> Cov2 4.8363767e-04 0.31697811
#> Cov3 5.1250915e-04 0.33590059
#> Var 1.5257762e-03 NA
ret$ANOVA$IndividualTrt
#> DF msREachTrt varEachTrt cov2EachTrt
#> trtTREAT1 3 0.00049266349 0.0015227779 0.00047229915
#> trtTREAT2 3 0.00024159915 0.0015287746 0.00049497620
ret$ANOVA$IndividualRdr
#> DF msTEachRdr varEachRdr cov1EachRdr
#> rdrREADER_1 1 7.3897606e-06 0.0014771675 0.00056158020
#> rdrREADER_2 1 2.3077021e-04 0.0015186058 0.00071581326
#> rdrREADER_3 1 1.4769293e-04 0.0013773788 0.00076508897
#> rdrREADER_4 1 4.0912170e-07 0.0017299529 0.00112424616
- RRRC, a list of 3 containing results of random-reader random-case analyses
FTtests
: is a [2x4] dataframe: results of the F-tests, see below, whereFStat
is the F-statistic andp
is the p-value. The first row is the treatment effect and the second is the error term.ciDiffTrt
: is a [1x7] dataframe: the confidence intervals between different treatments, see below, whereStdErr
is the standard error of the estimate,t
is the t-statistic andPrGTt
is the p-value.ciAvgRdrEachTrt
: is a [2x5] dataframe: the confidence intervals for the average reader over each treatment, see below, whereCILower
is the lower 95% confidence interval andCIUpper
is the upper 95% confidence interval.
ret$RRRC$FTests
#> DF MS FStat p
#> Treatment 1 2.3565410e-04 4.6940577 0.11883786
#> Error 3 5.0202641e-05 NA NA
ret$RRRC$ciDiffTrt
#> Estimate StdErr DF t PrGTt
#> trtTREAT1-trtTREAT2 0.010854817 0.0050101218 3 2.1665774 0.11883786
#> CILower CIUpper
#> trtTREAT1-trtTREAT2 -0.0050896269 0.026799261
ret$RRRC$ciAvgRdrEachTrt
#> Estimate StdErr DF CILower CIUpper Cov2
#> trtTREAT1 0.84774989 0.024402152 70.121788 0.79908282 0.89641696 0.00047229915
#> trtTREAT2 0.83689507 0.023566416 253.644028 0.79048429 0.88330585 0.00049497620
- FRRC, a list of 5 containing results of fixed-reader random-case analyses
FTtests
: is a [2x4] dataframe: results of the chisquare-tests, see below. Here is a difference from DBM: in the OR method for FRRC the denominator degrees of freedom of the F-statistic is infinite, and the test becomes equivalent to a chisquare test with the degrees of freedom equal to \(I-1\), where \(I\) is the number of treatments.ciDiffTrt
: is a [1x6] dataframe: the confidence intervals between different treatments, see below. An additional column listsciAvgRdrEachTrt
: is a [2x5] dataframe: the confidence intervals for the average reader over each treatmentciDiffTrtEachRdr
: is a [4x6] dataframe: the confidence intervals for each different-treatment pairing for each reader.IndividualRdrVarCov1
: is a [4x2] dataframe: \(Var\) and \(Cov_1\) for individual readers.
ret$FRRC$FTests
#> MS Chisq DF p
#> Treatment 0.0002356541 0.32101347 1 0.57099922
#> Error 0.0007340941 NA NA NA
ret$FRRC$ciDiffTrt
#> Estimate StdErr z PrGTz CILower
#> trtTREAT1-trtTREAT2 0.010854817 0.019158472 0.56658051 0.57099922 -0.026695098
#> CIUpper
#> trtTREAT1-trtTREAT2 0.048404732
ret$FRRC$ciAvgRdrEachTrt
#> Estimate StdErr DF CILower CIUpper
#> trtTREAT1 0.84774989 0.027109386 99 0.79461647 0.90088331
#> trtTREAT2 0.83689507 0.027448603 99 0.78309680 0.89069334
ret$FRRC$ciDiffTrtEachRdr
#> Estimate StdErr z
#> rdrREADER_1::trtTREAT1-trtTREAT2 0.00384441429 0.042792227 0.089839080
#> rdrREADER_2::trtTREAT1-trtTREAT2 0.02148349163 0.040069753 0.536152334
#> rdrREADER_3::trtTREAT1-trtTREAT2 0.01718679331 0.034993994 0.491135520
#> rdrREADER_4::trtTREAT1-trtTREAT2 0.00090456807 0.034805365 0.025989329
#> PrGTz CILower CIUpper
#> rdrREADER_1::trtTREAT1-trtTREAT2 0.92841509 -0.080026809 0.087715638
#> rdrREADER_2::trtTREAT1-trtTREAT2 0.59185327 -0.057051781 0.100018765
#> rdrREADER_3::trtTREAT1-trtTREAT2 0.62333060 -0.051400174 0.085773761
#> rdrREADER_4::trtTREAT1-trtTREAT2 0.97926585 -0.067312693 0.069121830
ret$FRRC$IndividualRdrVarCov1
#> varEachRdr cov1EachRdr
#> rdrREADER_1 0.0014771675 0.00056158020
#> rdrREADER_2 0.0015186058 0.00071581326
#> rdrREADER_3 0.0013773788 0.00076508897
#> rdrREADER_4 0.0017299529 0.00112424616
- RRFC, a list of 3 containing results of random-reader fixed-case analyses
FTtests
: is a [2x4] dataframe: results of the F-tests, see below.ciDiffTrt
: is a [1x7] dataframe: the confidence intervals between different treatments, see below.ciAvgRdrEachTrt
: is a [2x5] dataframe: the confidence intervals for the average reader over each over each treatment.
ret$RRFC$FTests
#> DF MS F p
#> T 1 2.3565410e-04 4.6940577 0.11883786
#> TR 3 5.0202641e-05 NA NA
ret$RRFC$ciDiffTrt
#> Estimate StdErr DF t PrGTt
#> trtTREAT1-trtTREAT2 0.010854817 0.0050101218 3 2.1665774 0.11883786
#> CILower CIUpper
#> trtTREAT1-trtTREAT2 -0.0050896269 0.026799261
ret$RRFC$ciAvgRdrEachTrt
#> Estimate StdErr DF CILower CIUpper
#> TrtTREAT1 0.84774989 0.011098012 3 0.81243106 0.88306871
#> TrtTREAT2 0.83689507 0.007771730 3 0.81216196 0.86162818