Interval estimation and significance testing for cyclic trends in seasonality studies

The statistical analysis for detecting a seasonal trend in epidemiologic studies has traditionally employed Edwards' method (1961, Annals of Human Genetics 25, 83-85) or a modification (Roger, 1977, Biometrika 64, 152-155) which are formulated under a simple harmonic model with two parameters, amplitude and phase angle. In seasonality studies, researchers usually have known seasons at which peak and trough incidences occur. Utilizing this information, we present the most efficient interval estimation of the ratio of maximum and minimum seasonal frequencies and the uniformly most powerful unbiased test for detecting the seasonal variation using the general theory of Bartlett (1953, Biometrika 40, 12-19). The asymptotic power function and the approximate formula for sample size are derived. A simulation study shows that actual values of power of this score test are satisfactorily close to nominal values even for small samples. The proposed simple score test is more powerful and requires substantially smaller samples for a specific power than the standard Edwards or Roger tests. An alternative method based on the logarithm of the maximum likelihood estimator of the ratio is comparable to the simple score method.