What is Abnormal?    Page 2


Plot of FEV1 data showing definition of a residual    Having obtained the z-score or SR value for a subject's lung function index we can determine how their result relates to population norms. The figure on the right shows a Gaussian distribution for the z-scores of FEV1 found in a normal healthy population. A z-score of -1.645 defines the lower 90% confidence limit for such a distribution and the pale grey area covers all the values below this level and represents 5% of the total area under the curve and so 5% of a 'normal healthy population' will have a lung function result below this level. This level of z-score of -1.645 is an estimate of the lower 5th centile for the 'normal healthy population'.

   Lung function tests are usually undertaken on patients who have some symptoms or signs suggesting to a clinician that there may be an abnormality in lung function. Thus the a priori probability of there being an abnormal result is raised and the lower 90% confidence limit is used as the lower limit of normal (LLN). Such a LLN means a reduced specificity but a greater sensitivity in identifying abnormal results which is acceptable because of the raised a priori probability of there being an abnormal result.

   However, if lung function tests are being undertaken on subjects where there is no a priori expectation that they will have an abnormal result a LLN of z-score = -1.645 is inappropriate since the false positive rate for stating a result is abnormal will be unacceptably high at 5%. In these circumstances the LLN should be a z-score = -1.96 which is the lower 95% confidence limit and an estimate of the 2.5th centile (false positive rate 2.5%).

   For the example patient from the previous page with a FEV1 z-score of -3.3 this is clearly below -1.645 and so the result is unusual suggesting their FEV1 may be abnormal.