2x2 Contingency tables for medical screening
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2x2 Contigency tables for medical screening test given sensitivity, specificity, prevalence, and population
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January 2011
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Major edit: July 2014
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Major edit and uploaded to Google Docs: March 2016
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Click on the sheet below labeled "Reference" for definitions, formulas, explanations, etc.
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base rate0.01prevalence of the disease/condtion in the population
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sensitivity0.95probability of test coming out positive given patient has the disease/condition
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specificity0.82probability of test coming out negative given patient does not have the disease/conditionpopulation10,000
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2X2 CONTINGENCY TABLE SHOWING RATES / PROBABILITIES
2X2 CONTINGENCY TABLE SHOWING FREQUENCIES
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Person has conditionTotalsConditional ProbabilitiesPerson has conditionTotalsConditional Probabilities
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yesnoTest results correctTest results incorrectYesNoTest results correctTest results incorrect
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Test positive0.00950.17820.18775.06%positive predictive value94.94%false discovery rateTest positive951,7821,8775.06%positive predictive value94.94%false discovery rate
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Test negative0.00050.81180.812399.94%negative predictive value0.06%false omission rateTest negative58,1188,12399.94%negative predictive value0.06%false omission rate
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Totals0.010.991Totals1009,90010,000
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sensitivity or true positive ratefalse positive rate or alpha or type 1 errorsensitivity or true positive ratefalse positive rate or alpha or type 1 error
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95.00%18.00%95.00%18.00%
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false negative rate or beta or type 2 errorspecificity or true negative ratefalse negative rate or beta or type 2 errorspecificity or true negative rate
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5.00%82.00%5.00%82.00%
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Conditional ProbabilitiesConditional Probabilities
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Person has conditionTotalsConditional ProbabilitiesPerson has conditionTotalsConditional Probabilities
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YesNoTest results correctTest results incorrectYesNoTest results correctTest results incorrect
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Test positiveABA + BA / (A+B)P(has condition | positive)B / (A+B)P(no condition | positive)Test positivetrue positive (TP)false positive (FP)total positive resultsA / (A+B)P(has condition | positive)B / (A+B)P(no condition | positive)
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Test negativeCDC + DD / (C+D)P(no condition | negative)C / (C+D)P(has condition | negative)Test negativefalse negative (FN)true negative (TN)total negative resultsD / (C+D)P(no condition | negative)C / (C+D)P(has condition | negative)
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TotalsA+CB+DA+B+C+D = 1Totalspeople with conditionpeople without conditionpopulation
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P(positive | has condition)P(positive | no condition)P(positive | has condition)P(positive | no condition)
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A / (A+C)B / (B+D)TP / (TP + FN)FP / (FP + TN)
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P(negative | has condition)P(negative | no condition)P(negative | has condition)P(negative | no condition)
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C / (A+C)D / (B+D)FN / (TP + FN)TN / (FP + TN)
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Conditional ProbabilitiesConditional Probabilities
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Click on the sheet below labeled "Reference" for definitions, formulas, explanations, etc.
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Steps in (manually) filling the contigency tables given sensitivity, specificity and base rate (prevalence):
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1. Fill in cell A+C with the base rate
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2. A = base rate * sensitivity
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3. C = base rate - A
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4. B+D = 1 - base rate
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5. D = (B+D) * specificity
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6. B = (B+D) - D
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7. With cells A, B, C, D filled, the other totals and various conditional probabilities can now be easily computed for
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8. To obtain the frequency table, multiply each cell (except conditional probability cells) by the population.
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Table
Reference
Sheet2