A Restricted Test of Circadian Rhythm

Abstract

In medical applications there is interest in whether deaths or other events occur randomly throughout the day, as opposed to in a definite circadian pattern. At times, knowledge of the circadian phenomenon will suggest that a single cluster of events should occur during a specific period during the day, such as mid-morning. We propose a test that incorporates such knowledge. The test can be viewed as the likelihood ratio test for a restricted alternative for data from the von Mises (i.e., circular normal) distribution. The test's power is compared to a commonly used test of randomness that ignores when a peak is likely to occur. Methods for dealing with interval censored data are discussed, and an example is given. A Bayesian alternative is also explored.

Key Words:

• Bayes factor
• Circle data
• Directional data
• Imputation
• Missing data
• von Mises distribution