From an Observed Sample: Estimates of Population Prevalence, Sensitivity, Specificity, Predictive Values, and Likelihood Ratios Given a sample of subjects cross-classified according to whether a certain condition is present or absent, and according to whether a test designed to indicate the presence of that condition proves positive or negative, this page will calculate the estimated population midpoints and 95% confidence intervals for

• prevalence of the condition;_T
  
• test sensitivity (conditional probability that the test will be positive if the condition is present);_T
  
• test specificity (conditional probability that the test will be negative if the condition is absent);_T
  
• predictive values of the test (probabilities for true positive, true negative, false positive, and false negative); and_T
  
• positive and negative likelihood ratios._T
  

To proceed, enter the observed frequencies for each of the four cross- classifications into the designated cells, then click the «Calculate» button. To perform a new analysis with a new set of data, click the «Reset» button.

	Condition		Totals
	Absent	Present
Test Positive
Test Negative
Totals

	Estimated Value	95% Confidence Interval
		Lower Limit	Upper Limit
Prevalence
Sensitivity
Specificity
For any particular test result, the probability that it will be:
Positive
Negative
For any particular positive test result, the probability that it is:
True Positive (Positive Predictive Value)
False Positive
For any particular negative test result, the probability that it is:
True Negative (Negative Predictive Value)
False Negative
likelihood Ratios:    [C] = conventional    [W] = weighted by prevalence      [definitions]
Positive [C]
Negative [C]
Positive [W]
Negative [W]
The entry 'NaN' in any of the above cells means that the calculation cannot be performed because the values entered include one or more instances of zero. Technical note on calculation of confidence intervals.

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©Richard Lowry 2001-
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Technical Note on Calculation of Confidence Intervals

95% confidence intervals for proportions (which include all but the last four of the above) are calculated according to the efficient-score method (corrected for continuity) described by Robert Newcombe, based on the procedure outlined by E. B. Wilson in 1927. As Newcombe notes in his 1998 paper, the familiar Gaussian approximation

p ± 1.96 × √p(1-p)/n

is ill suited to situations where the proportion is quite small, as is often the case with prevalence measures, or quite large, as is optimally the case with measures of sensitivity and specificity.

References:

Newcombe, Robert G. "Two-Sided Confidence Intervals for the Single Proportion: Comparison of Seven Methods," Statistics in Medicine, 17, 857-872 (1998).

Wilson, E. B. "Probable Inference, the Law of Succession, and Statistical Inference," Journal of the American Statistical Association, 22, 209-212 (1927).

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Definitions of likelihood Ratios:
Conventional Positive:

=

conditional probability of positive test result if the condition is present conditional probability of positive test result if the condition is absent

=

sensitivity 1-specificity

Conventional Negative:

=

conditional probability of negative test result if the condition is present conditional probability of negative test result if the condition is absent

=

1-sensitivity specificity

Positive [weighted for prevalence]

=

probability that a positive test result is a true positive probability that a positive test result is a false positive

=

(prevalence)(sensitivity) (1-prevalence)(1-specificity)

Negative [weighted for prevalence]

=

probability of false negative result probability of true negative result

=

(prevalence)(1-sensitivity) (1-prevalence)(specificity)

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