TP = test positive in diseased subjects

FP = test positive in nondiseased subjects

FN = test negative in diseased subjects

TN = test negative in nondiseased subjects

T+ = abnormal test results

T- = normal test results

D+ = diseased subjects

D- = nondiseased subjects

## STATISTICS

Incidence = number of diseased people per 100,000 population annually

Prevalence = number of existing cases per 100,000 population at a target date

Frequency = number of times an event occurred; often graphically represented in histograms

Mortality = number of deaths per 100,000 population annually

Fatality = number of deaths per number of diseased

**Sensitivity**

= ability to detect disease

= probability of having an abnormal test given disease

= number of correct positive tests / number with disease

= true positive ratio = TP / (TP + FN) = TP / D+

• D+ column in decision matrix

◊ Independent of prevalence

**Specificity**

= ability to identify absence of disease

= probability of having a negative test given no disease

= number of correct negative tests / number without disease

= true negative ratio = TN / (TN + FP) = TN / D-

• D- column in decision matrix

◊ Independent of prevalence

### Accuracy

= number of correct results in all tests

= number of correct tests / total number of tests

= (TP + TN) / (TP + TN + FP + FN) = (TP + TN) / total

◊ Depends much on the proportion of diseased + nondiseased subjects in studied population

◊ Not valuable for comparison of tests

*Example:* same test accuracy of 90% for two tests A and B

**Positive Predictive Value**

= positive test accuracy

= likelihood that a positive test result identifies disease

= number of correct positive tests / number of positive tests

= TP / (TP + FP) = TP / T+

• T+ row in decision matrix

◊ Dependent on prevalence

◊ PPV ↑ with ↑ prevalence for given sensitivity + specificity

◊ PPV ↑ with ↑ specificity for given prevalence

### Negative Predictive Value

= negative test accuracy

= likelihood that a negative test result identifies absence of disease

= number of correct negative tests / number of negative tests

= TN / (TN + FN) = TN / T-

• T- row in decision matrix

◊ Dependent on prevalence

◊ NPV ↑ with ↑ prevalence for given sensitivity + specificity

◊ NPV ↑ with ↑ sensitivity for given prevalence

### False-positive Ratio

= proportion of nondiseased patients with abnormal test result

• D- column in decision matrix

= FP / (FP + TN) = FP / D-

= 1 – specificity = (TN + FP – TN) / (TN + FP)

### False-negative Ratio

= proportion of diseased patients with a normal test result

• D+ column in decision matrix

= FN / (TP + FN) = FN / D+

= 1 – sensitivity = (TP + FN – TP) / (TP + FN)

### Disease Prevalence

= proportion of diseased subjects to total population

= (TP + FN) / (TP + TN + FP + FN) = D+ / total

◊ Sensitivity + specificity are independent of prevalence!

◊ Affects predictive values + accuracy of a test result

*Example:*

*Test A, C, D:* 90% sensitivity + 90% specificity

### Bayes Theorem

= the predictive accuracy of any test outcome that is less than a perfect diagnostic test is influenced by

(a) pretest likelihood of disease

(b) criteria used to define a test result

### Receiver Operating Characteristics (ROC)

= degree of discrimination between diseased + nondiseased patients using varying diagnostic criteria instead of a single value for the TP + TN fraction

= curvilinear graph generated by plotting TP ratio as a function of FP ratio for a number of different diagnostic criteria (ranging from definitely normal to definitely abnormal)

*Y-axis:* true-positive ratio = sensitivity

*X-axis:* false-positive ratio = 1 – specificity; reversing the values on the X-axis results in an identical “sensitivity-specificity curve”

*Use:* variations in diagnostic criteria → reported as a continuum of responses → ranging from definitely abnormal to equivocal to definitely normal ← based on subjectivity + bias of individual radiologists

◊ A minimum of 4–5 data points of diagnostic criteria are needed!

*Difficulty:* subjective evaluation of image features; subjective diagnostic interpretation; data must be ordinal (= discrete rating scale from definitely negative to definitely positive)

*Interpretation:*

◊ ↑ in sensitivity leads to ↓ in specificity!

◊ ↑ in specificity leads to ↓ in sensitivity!

◊ Most sensitive point is the point with the highest TP ratio

→ equivalent to “overreading” by using less stringent diagnostic criteria (all findings read as abnormal)

◊ Most specific point is the point with the lowest FP ratio

→ equivalent to “underreading” by using more strict diagnostic criteria (all findings read as normal)

◊ Does not consider disease prevalence in the population

◊ The ROC curve closest to the Y-axis represents the best diagnostic test