# Diagnostic and screening tests

### From Ganfyd

**(Editorial comment.) This page and Interpreting test results are very similar. Neither discusses in detail prior and posterior probabilities as perhaps they should, or explains clearly why e.g. a rare condition needs a much more sensitive screening test. The two pages could be improved, and perhaps merged. **

## Contents |

## Two by two table

By convention, the real status, gold standard or reference test is at the top, while the diagnostic test being assessed is down the side. |

Disease | present | |

Test +ve | Yes | No |

Yes | a | b |

No | c | d |

*a*represents the number of**true positives**- people who have a positive result**and**have disease.*d*represents the number of**true negatives**- people who have a negative result**and**do not have disease.*b*represents**false positives**- people who have a positive result**but do not**have disease.*c*represents the number of**false negatives**- people who have a negative result**but do actually**have disease.

## Sensitivity

- = True positive rate (where positive in disease, and population is all those with positive tests)
- = No of true positives that are detected/¬Total number with disease
- = Chance of +ve test, given +ve disease
- =
*a*/ (*a*+*c*)

Answers the question “how good is this test at picking up people who have the condition”

## Specificity

- = True negative rate (where negative in health, and population is all those with negative tests)
- = No of true negatives that are detected/¬Total number with disease
- = chance of negative test, given no disease
- = No of true ves / No of people without the disease
- =
*d*/ (*b*+*d*)

Answers the question “how good is this test at correctly excluding people without the condition”

## Positive predictive value

- = chances of having the disease, given that the test is +ve (post test probability of a positive test)
- = No with +ve test and disease / all people with +ve test
- =
*a*/ (*a*+*b*)

Answers the question “if a person tests positive, what is the probablility that he or she has the condition?”

For a common condition, the positive predictive value may be high with a relatively insensitive test. For a rare condition, however - where the prior probability of disease is very low, even a highly sensitive test may have a relatively low positive predictive value, and yield many false positive results.

## -ve predictive value

- = chances of not having the disease, given that the test is –ve (post test probability of a positive test)
- = No with ve test and no disease / all people with ve test
- =
*d*/ (*c*+*d*)

Answers the question “if a person tests positive, what is the probablility that he or she has the condition?”

## Accuracy

- = True positives and true negatives of a test as a proportion of all results.

Answers the question “what proportion of all tests have given the correct result?”

## Likelihood ratio of a positive result

Answers the question “How much more likely is a positive test to be found in a person with the condition than in a person without it?” (Likelihood ratios are now considered the most important findings).

If prior probability of disease known for an individual patient, then posterior probability of diseasecan be calculated using a nomogram developed by Sackett and colleagues.

Test may not prove presence or absence of disease, but can give more accurate probability of presence or absence of disease.

## Likelihood ratio of a negative result

- =

Answers the question “How much more likely is a negative test to be found in a person without the condition than in a person with it?” (Likelihood ratios are now considered the most important findings).

## Questions to ask yourself

Greenhalgh suggests asking yourself the following questions when reading a paper about a diagnostic or screening test:^{[1]}
PMID:

- Is this test potentially relevant to my practice?
- Has the test been compared with a true gold standard?
- Did the validation study include and appropriate spectrum of subjects? (Affects PPV, NPV, LRs, if not sensitivity and specificity).
- Has workup bias been avoided? (In some studies only those positive on study test are also given gold standard test.)
- Has expectation bias been avoided? (i.e. was the person interpreting the test blinded – e.g. if looking at ECG, does the person interpreting it know the patient’s history?)
- Was the test shown to be reproducible?
- What are the features of the test as derived from this validation study?
- Were confidence intervals given?
- Has a sensible “normal range” been derived?
- Has this test been placed in the context of other potential tests in the diagnostic sequence?

## Worked example

Result of glucose tolerance (gold standard) test | (gold standard) test | |

Result of urine test for glucose | Diabetes positive (n=27) | Diabetes negative (n=973) |

Glucose present (n=13) | True positive (n=6) | False positive (n=7) |

Glucose absent (n=13) | False negative (n=21) | True negative (n=966) |

Features of worked example

Feature | Formula | Data (from worked example) | Value |

Sensitivity | a/(a+c) | 6/27 | 22.2% |

Specificity | d/(b+d) | 966/973 | 99.3% |

PPV | a/(a+b) | 6/13 | 46.2% |

NPV | d/(c+d) | 966/973 | 97.8% |

Accuracy | (a+d)/(a+b+c+d) | 972/1000 | 97.2% |

Likelihood ratios | |||

Positive test | Sensitivity/(1 – specificity) | 22.2/(1-99.3) = 22.2/0.7 | 32 |

Negative test | (1 – sensitivity)/specificity | (1-22.2)/99.3 = 77.8/99.3 | 0.78 |

If an individual patient has a fairly high chance of having diabetes (clinical history, age, obesity…) – say 40% – then a positive test almost certainly confirms the diagnosis (probability about 97% from the nomogram); whereas a negative makes them only a little less likely about 40% from the nomogram).

## See also

## External links

*Do doctors understand test results?*- a nice explanation in lay terms with good graphics and worked examples - for example, an explanation of how the positive predictive value of mammography screening for breast cancer is only about 10%.^{[2]}- Supercourse lecture on "Epidemiology Applications"
- Supercourse lecture "Screening"
- Supercourse lecture "Diagnosis II"
- Supercourse lecture "Screening and Disease Prevention"

## References

- ↑ How to read a paper. Papers that report diagnostic or screening tests. BMJ. 1997 Aug 30;315(7107):540-3. Erratum in: BMJ 1997 Oct 11;315(7113):942. and BMJ 1998 Jan 17;316(7126):225. Direct link: http://bmj.bmjjournals.com/cgi/content/full/315/7107/540
- ↑ William Kremer.
*Do doctors understand test results?*.**2014**(7 July). BBC World Service Web Site. Last viewed 2014 (7 July).