Epi
Contingency Table
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Contingency Table
, Contingency Grid, Cross Tabulation, Cross Tab, Statistics Example
See Also
Screening Test
Bayes Theorem
(
Bayesian Statistics
)
Fagan Nomogram
Experimental Error
(
Experimental Bias
)
Lead-Time Bias
Length Bias
Selection Bias
Likelihood Ratio
(
Positive Likelihood Ratio
,
Negative Likelihood Ratio
)
Number Needed to Screen
(
Number Needed to Treat
,
Absolute Risk Reduction
,
Relative Risk Reduction
)
Negative Predictive Value
Positive Predictive Value
Pre-Test Odds
or
Post-Test Odds
Receiver Operating Characteristic
Test Sensitivity
(
False Negative Rate
)
Test Specificity
(
False Positive Rate
)
U.S. Preventive Services Task Force Recommendations
Technique
Setting up grid for test efficacy or risk factor
Examples
Test efficacy: How well does a test detect a certain condition
Risk Factor: How much is a particular risk associated with a given condition
Draw 2x2 grid
Labels
Upper Boxes: Across the top (x-axis) place the Disease State Labels
Left Box: Disease present (e.g.
Breast Cancer
)
Right Box: Disease not present (e.g. Not
Breast Cancer
)
Left Boxes: Across the left (y-axis) place the Test Result Labels
Upper Box: Test Positive, Screened or exposed to contributing factor
Lower Box: Test Negative, Not screened, no exposed
Example
Breast Cancer Screening
with
Mammogram
Given
Risk of
Breast Cancer
based on age
Age 40 years old: 1 in 69
Age 50 years old: 1 in 42
Age 60 years old: 1 in 29
Mammogram
efficacy
Note: We use the upper end of the
Test Sensitivity
and
Specificity
ranges for this example
Test Sensitivity
: 77-95%
Test Specificity
: 94-97%
Create a hypothetical grid for patients age 40 who undergo
Mammogram
s
Gene
rating example data
Of 100,000 patients, 1449 will have
Breast Cancer
(1 in 69)
Of the 1449 with
Breast Cancer
, 1376 will be detected with
Mammogram
(95%
Test Sensitivity
)
Of the 98,551 without
Breast Cancer
, 95,594 will have a normal
Mammogram
(97%
Specificity
)
Label the grid top
Disease Positive (or D+):
Breast Cancer
positive
Disease Negative (or D-):
Breast Cancer
negative
Label the grid left
Test Positive (or T+):
Mammogram
positive
Test Negative (or T-):
Mammogram
negative
Total patients
Fill in total patients first (bottom row)
Breast Cancer
positive (D+): 1449
Every 69 in 100,000 will have
Breast Cancer
for those at age 40
Breast Cancer
negative (D-): 98,551
The remainder of the 100,000 without
Breast Cancer
Complete the left column (D+)
Top left:
Mammogram
Positive (or T+): 1376
True positive patients represent 95% of 1449 (the
Test Sensitivity
)
Bottom left:
Mammogram
Negative (or T-): 73
False Negative
patients represents 1449 - 1376
Complete the right column (D-)
Bottom right:
Mammogram
Negative (or T-): 95,594
True negative patients represents 97% of 98,551 (the
Test Specificity
)
Top right:
Mammogram
Positive (or T+): 2957
False Positive
patients represents 98,551 - 95,594
Summary of grid
D+ T+: 1376 (true positives)
D- T+: 2957 (
False Positive
s)
D+ T- : 73 (
False Negative
s)
D- T- : 95,594 (true negatives)
Calculations
Test Sensitivity
(
Test Recall
)
Sensitivity: True positives / (true positives +
False Negative
s)
Sensitivity: 1376 / (1376 + 73) = 95%
Test Specificity
Specificity
: True negatives / (true negatives +
False Positive
s)
Specificity
: 95,594 / (95,594 + 2957) = 97%
Positive Predictive Value
(PPV,
Test Precision
)
PPV: True positive / (true positives +
False Positive
s)
PPV: 1376 / (1376 + 2957) = 32%
Negative Predictive Value
(NPV)
NPV: True negative / (true negative +
False Negative
s)
NPV: 95,594 / (95,594 + 73) = 99%
False Positive Rate
(type I error or a)
a: (1 -
Test Specificity
)
a: (1 - 0.97) = 3%
False Negative Rate
(type II error or b)
b: (1 -
Test Sensitivity
)
b: (1 - 0.95) = 5%
Likelihood Ratio
positive (LR+)
LR+: Sensitivity / (1-
Specificity
)
LR+: 0.95 / (1 - 0.97) = 32 (high likelihood of disease if >10)
Likelihood Ratio
negative (LR-)
LR-: (1 - Sensitivity) / (
Specificity
)
LR-: (1 - 0.95) / 0.97 = 0.05 (low likelihood of disease if <0.1)
F1 Score
F1 Score is the harmonic mean of
Test Precision
(PPV) and
Test Recall
(
Test Sensitivity
)
F1 is least accurate at 0, and most accurate at 1
F1 = 2 * (Precision * Recall) / (Precision + Recall)
F1 = 2 * (0.32 * 0.95)/(0.32 + 0.95) = 0.47
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