MATH2209 Chap.11 Screening Tests, Risk and Odds
Screening Tests, Risk and Odds
Epidemiological measures depend on the group used as denominator and the direction of study sampling. Screening accuracy conditions on true disease status, while predictive values condition on test results. Cohort studies begin with exposure groups and compare risks; case-control studies begin with outcome groups and compare exposure odds.
This chapter constructs two-by-two tables, calculates sensitivity and specificity, and chooses relative risk or odds ratio from the design.
What this chapter covers
- 01
Screening-test tables
- 02
Sensitivity and specificity
- 03
Predictive values
- 04
Prospective and retrospective cohorts
- 05
Case-control studies
- 06
Relative risk and odds ratios
Worked example · free
Calculate screening sensitivity and specificity
- 1False negatives = 50 - 42 = 8.
- 1True negatives = 150 - 18 = 132.
- 1Sensitivity = 42 / 50 = 84%.
- 1Specificity = 132 / 150 = 88%.
Key terms
- Sensitivity
- The proportion testing positive among people who truly have the condition.
- Specificity
- The proportion testing negative among people who do not have the condition.
- Odds Ratio
- A ratio comparing odds across groups, including exposure odds in case-control studies.
Screening Tests, Risk and Odds FAQ
Why do sensitivity and specificity use different denominators?
Sensitivity evaluates detection within people who have disease, so its denominator is true positives plus false negatives. Specificity evaluates exclusion within people without disease, so its denominator is true negatives plus false positives.
Why can a case-control study not estimate risk directly?
Investigators choose how many cases and controls enter the sample, so the sample disease proportion is fixed by design rather than observed from exposure groups. The design compares prior exposure odds and supports an odds ratio.
What should a relative risk interpretation include?
Name the outcome, exposed group, reference group and follow-up context. A ratio above one indicates higher observed risk in the exposed group, below one indicates lower risk, and one indicates equal risk under the comparison.
How do I choose the right epidemiological denominator?
Write the group named after the condition first. Sensitivity uses everyone with disease, specificity uses everyone without disease and predictive values use people grouped by test result. For study associations, identify how participants entered: exposure-defined cohorts support risk comparisons, while outcome-defined case-control samples support exposure odds and do not directly estimate disease risk.
Label numerator and reference groups before forming a ratio, because reversing them creates the reciprocal and changes the verbal direction. Keep the four cell counts beside any percentages, then discuss temporality, selection, confounding and measurement before suggesting causation. A correct formula cannot repair a denominator that the sampling design does not represent.
Assessment move
Draw every screening or study-design question as a two-by-two table and label disease status, test result, exposure and outcome explicitly. Recalculate all four margins before selecting a formula. For sensitivity, circle everyone with disease and ask what fraction tested positive. For specificity, circle everyone without disease and ask what fraction tested negative.
Reverse the conditioning for predictive values and explain why prevalence in the tested population then matters. Use denominator-first sentences so that similarly named measures do not become interchangeable. Build paired examples with identical sensitivity and specificity but different disease prevalence.
Calculate the positive predictive value and observe how the false-positive path changes the composition of positive results. Connect this chapter back to Bayes without copying sensitivity as the probability of disease after a positive test. For study design, begin with the direction of sampling. Cohort studies start from exposure groups and observe outcomes, which allows risks, risk difference and relative risk.
Case-control studies start from outcome groups and inspect prior exposure, so the investigator-fixed numbers of cases and controls do not estimate disease risk directly; use an odds ratio. Draw arrows for both designs and state which margin was fixed. Practise ratio interpretations around one. Name the numerator group, reference group, outcome and time frame.
If the group order is reversed, take the reciprocal and rewrite the interpretation rather than preserving the old direction. Keep association distinct from causation by reviewing temporality, selection, confounding and measurement. For screening questions, retain the underlying counts beside percentages because two tests with the same accuracy may create different numbers of false positives and false negatives.
Discuss which error matters in the clinical setting without inventing a universal preference. Finish revision with mixed tables where the task is not named. Decide whether the requested denominator indicates sensitivity, specificity, predictive value, risk or odds, then calculate.
Your final sentence should identify the population and comparison, use risk or odds accurately and avoid turning a case-control odds ratio into a direct risk statement.
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