## Abstract

A mathematical model is presented for measurements that include substantial fluctuation and error. Under the assumptions that the fluctuation-error variance is the same for all subjects, and that the distributions of fluctuation-error variance within subjects and “true” values of the measurements in the population are normal, Bayes' theorem produces a simple estimate of the “true” value of a measurement, and a standard error, conditional on a single observation. The model is easily extended to several observations. Methods for estimating the parameters of the model from a data set are presented, and applied to diastolic blood pressures of patients in the authors' primary care clinic. The test-retest reliability of a single blood pressure measurement for this population is 0.41. Because continuous measurements are often dichotomized into “normal” and “abnormal” ranges by a threshold criterion, the authors present formulas for the positive predictive value when a decision rule based on a given number of observations is used in a population with respect to a threshold criterion for the “true” values. For example, classifying their patients as hypertensive on the basis of the average of two readings exceeding 90 mm Hg diastolic pressure would have a positive predictive value of 52% for the “gold standard” of average diastolic pressure exceeding 90 mm Hg. Formulas to calculate the frequency with which patients will be classified “abnormal” by one decision rule but will be classified “normal” by later application of another rule are provided and used to “predict” the frequency with which this crossover phenomenon should have occurred in the enrollment phase of the Hypertension Detection and Follow-up Pro grams.^{5,6} The authors' calculation of 36.3% agrees closely with the observed 34.7% crossover rate, enhancing confidence in the validity of their model and generalizability of their parameter estimates.

Original language | English (US) |
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Pages (from-to) | 182-190 |

Number of pages | 9 |

Journal | Medical Decision Making |

Volume | 8 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1988 |

Externally published | Yes |

## Keywords

- Bayes' theorem
- hypertension
- screening tests

## ASJC Scopus subject areas

- Health Policy