# Plot versus criterion values

Command: | Statistics ROC curves Plot versus criterion values |

## Description

In this graph (part of ROC curve analysis) you can plot the following statistics against the criterion values:

- Sensitivity and specificity, and optionally their 95% Confidence Intervals
- Youden index
The Youden index for a single point on the ROC curve is defined as
$$ sensitivity + specificity - 1 $$
- Positive predictive value
Probability that the disease is present when the test is positive.
$$ PPV = \frac {sensitivity \times prevalence } {sensitivity \times prevalence + (1-specificity)\times (1-prevalence) } $$
- Negative predictive value
Probability that the disease is not present when the test is negative.
$$ NPV = \frac {specificity \times (1-prevalence) }{ (1-sensitivity) \times prevalence + specificity \times (1-prevalence) } $$
- Efficiency
Efficiency is defined as (Greiner et al., 2000):
$$ Efficiency = P \times Se + \left ( 1-P \right ) \times Sp $$with P = Prevalence, Se = Sensitivity, and Sp = Specificity
- Cost
The Cost is the average cost resulting from the use of the diagnostic test at a particular decision level.
It takes into account disease prevalence and cost of true and false positive, and true and false negative decisions.
$$\begin{align} Cost = & \,\quad FNc \times \left(1-Se\right) \times P \\ & + FPc \times \left(1-Sp\right) \times \left(1-P\right) \\ & + TPc \times Se \times P \\ & + TNc \times Sp \times \left(1-P\right) \end{align}$$with P = Prevalence, Se = Sensitivity, Sp = Specificity, FN
_{c}the cost of a false negative decision and FP_{c}the cost of a false positive decision, TP_{c}the cost of a true positive decision, and TN_{c}the cost of a true negative decision. The Misclassification-Cost Term (MCT, Greiner et al., 2000) takes into account disease prevalence and cost of false positive and false negative decisions only:$$ MCT = \frac {FN_c} {FP_c} \times P \times \left ( 1-Se \right ) + \left ( 1-P \right ) \times \left ( 1-Sp \right ) $$Costs can be financial costs or health costs, but all 4 cost factors need to be expressed on a common scale. The minimum value of Cost or MCT may be used as an indicator for an optimal selection criterion.

## Required input

**Variable**: select the variable of interest.**Classification variable**: select a dichotomous variable indicating diagnosis (0=negative, 1=positive). If your data are coded differently, you can use the Define status tool to recode your data.**Filter**: (optionally) a filter in order to include only a selected subgroup of cases (e.g. AGE>21, SEX="Male").**Options**:You can select one of the following 2 plots: sensitivity/specificity or misclassification-cost term- Sensitivity and specificity
95% Confidence Intervals options:
- error bars: show the 95% Confidence Interval of sensitivity and specificity as error bars
- connected lines: show the 95% Confidence Interval of sensitivity and specificity as connected lines (recommended when number of criterion values is high)
- do not show CI: do not show the 95% Confidence Interval of sensitivity and specificity in the graph

- Youden index
- Positive Predictive Value
- Negative Predictive Value
- Efficiency
- Cost
Option Misclassification-Cost Term (MCT) : see above.
You need to enter
- FNc: the cost of a false negative decision
- FPc: the cost of a false positive decision
- TPc: the cost of a true positive decision - not required for the calculation of the Misclassification-Cost Term (MCT).
- TNc: the cost of a true negative decision - not required for the calculation of the Misclassification-Cost Term (MCT).

- For Positive and Negative Predictive Value, Efficiency and Cost, data on disease prevalence are required. The program can create curves for different prevalences in the same graph.
- Select Observed prevalence if the number of cases in the positive and the negative group reflect the real prevalence of the disease in the population (this value will be indicated with an asterisk in the graph's legend),
- Or enter up to 4 different values for prevalence, expressed as percentages (0..100).

- If the data require a logarithmic transformation (e.g. when the data are positively skewed), select the Logarithmic transformation option.

- Sensitivity and specificity
95% Confidence Intervals options:

## Graph

In the graph the selected statistic is plotted against the criterion value.

Sensitivity and specificity, Positive and Negative Predictive values are displayed as percentages.

The maximum values of Youden index and Efficiency, and the minimum values of Cost are reported in the graphs info box. To obtain the info box you right-click in the graph and click **Info** on the context menu.

Plot of sensitivity and specificity versus criterion values:

Plot of cost versus criterion values for different levels of disease prevalence:

## Literature

- Krouwer JS (1987) Cumulative distribution analysis graphs - An alternative to ROC curves. Clinical Chemistry 33:2305-2306.