1 Get the Tomm and CVLT ata ready

Use a cut-off of 14 for the CVLT-II Forced Choice score for determining validity. Those with a score of 15 or 16 on this measure will be in the credible group Those with a score of 14 or lower will be in the non-credible group

We only keep the complete records of data with values in CVLT and Trial 1, Trial 2 and Retention. The dimention of the complete data is 704 rows and 9 columns.

Here is the top 6 records of the current dataset.

##    gender education num.dep time.since.inj num.blast cvlt tomm.T1 tomm.T2
## 1       1        12      NA             NA        NA   16      46      50
## 6       2        12      NA             NA        NA   16      46      50
## 7       1        13       3             NA         2   13      50      50
## 8       1        12       2             NA         2   16      41      50
## 10      1        13       2             NA         2   16      34      50
## 11      1        12       2             NA        NA   16      48      50
##    tomm.Retention
## 1              50
## 6              50
## 7              50
## 8              49
## 10             50
## 11             50

2 CVLT info.

The cutoff value of cvlt is 14.

The total number of positive cases (inflated score, where score < 15) is 73, and thus, the proportion of positive cases in CVLT is 0.1036932. Below is the

3 From CVLT to Tomm

3.1 Preliminary result with uniform cutoff value

If CVLT classification is set as the gorund truth, and 45 is used as the cutoff score for T1, T2, and Retention, the sensitivity and specificity of T1 are 0.836, 0.688 resp., the sensitivity and specificity of T2 are 0.548, 0.926resp, and the sensitivity and specificity of Retension are 0.63, 0.922

3.2 Searching for alternative cutoff values for T1, T2, and Retention

This section is for the search of alternative cutoff values.

3.3 T1

##    cut.off   sen  nspe   spe    BA
## 1       35 0.438 0.057 0.943 0.691
## 2       36 0.534 0.079 0.921 0.728
## 3       37 0.603 0.089 0.911 0.757
## 4       38 0.671 0.108 0.892 0.782
## 5       39 0.726 0.122 0.878 0.802
## 6       40 0.740 0.146 0.854 0.797
## 7       41 0.781 0.170 0.830 0.806
## 8       42 0.808 0.200 0.800 0.804
## 9       43 0.836 0.230 0.770 0.803
## 10      44 0.836 0.271 0.729 0.782
## 11      45 0.836 0.312 0.688 0.762
## 12      46 0.863 0.365 0.635 0.749
## 13      47 0.877 0.428 0.572 0.724
## 14      48 0.877 0.501 0.499 0.688
## 15      49 0.904 0.604 0.396 0.650

The figure above is based on the sensitivity and specificity values, calculated based on different cutoff values for T1. For example, when the cutoff value for T1 is 35, accoring to the table above, the seneitivity value is 0.438 with specificity value of 0.943.

A ROC curve (scatter plot of sensitivity and (1-specificity) )is plotted in the figure above, where the number in the circle represents the cutoff value for T1.

Another pattern can be observed is that as the cutoff value change from low to high, sensitivity is increasing and specificity is decreasing.

BA score calculates a trade off value between sensitivity and specificity. It appears that a cutoff of 41 for T1 giving the highest BA score of 0.806

3.4 T2

##    cut.off   sen  nspe   spe    BA
## 1       35 0.274 0.010 0.990 0.632
## 2       36 0.301 0.016 0.984 0.643
## 3       37 0.315 0.017 0.983 0.649
## 4       38 0.370 0.025 0.975 0.672
## 5       39 0.370 0.027 0.973 0.671
## 6       40 0.397 0.030 0.970 0.684
## 7       41 0.452 0.036 0.964 0.708
## 8       42 0.452 0.038 0.962 0.707
## 9       43 0.466 0.051 0.949 0.708
## 10      44 0.493 0.062 0.938 0.716
## 11      45 0.548 0.074 0.926 0.737
## 12      46 0.644 0.087 0.913 0.778
## 13      47 0.644 0.108 0.892 0.768
## 14      48 0.644 0.128 0.872 0.758
## 15      49 0.671 0.155 0.845 0.758

3.5 T3

##    cut.off   sen  nspe   spe    BA
## 1       35 0.356 0.013 0.987 0.672
## 2       36 0.411 0.021 0.979 0.695
## 3       37 0.411 0.024 0.976 0.694
## 4       38 0.438 0.024 0.976 0.707
## 5       39 0.466 0.029 0.971 0.719
## 6       40 0.507 0.033 0.967 0.737
## 7       41 0.562 0.035 0.965 0.763
## 8       42 0.562 0.046 0.954 0.758
## 9       43 0.575 0.057 0.943 0.759
## 10      44 0.603 0.063 0.937 0.770
## 11      45 0.630 0.078 0.922 0.776
## 12      46 0.685 0.090 0.910 0.797
## 13      47 0.712 0.109 0.891 0.801
## 14      48 0.767 0.135 0.865 0.816
## 15      49 0.767 0.166 0.834 0.800