Interval estimation and significance testing for cyclic trends in seasonality studies

Area of Science:

• Epidemiology
• Biostatistics
• Statistical Modeling

Background:

• Traditional methods for detecting seasonal trends in epidemiology, such as Edwards' and Roger's tests, rely on a simple harmonic model with two parameters.
• These methods have limitations in efficiency and sample size requirements for seasonality studies where peak and trough incidences are often known.

Purpose of the Study:

• To develop a more efficient statistical method for detecting seasonal variation in epidemiologic studies.
• To present an interval estimation for the ratio of maximum and minimum seasonal frequencies and a uniformly most powerful unbiased test.
• To improve upon the power and sample size efficiency compared to existing methods like Edwards' and Roger's tests.

Main Methods:

• Utilized the general theory of Bartlett (1953) to derive the most efficient interval estimation and a uniformly most powerful unbiased test.
• Developed a simple score test incorporating known peak and trough incidence seasons.
• Derived the asymptotic power function and approximate sample size formula for the proposed test.
• Conducted a simulation study to evaluate the test's performance, especially for small sample sizes.

Main Results:

• The proposed simple score test demonstrates higher statistical power for detecting seasonal variation compared to Edwards' and Roger's tests.
• The new method requires substantially smaller sample sizes to achieve a specific statistical power.
• Simulation results show the actual power of the score test is close to nominal values, even with small sample sizes.
• An alternative method using the logarithm of the maximum likelihood estimator of the ratio is comparable in performance to the score method.

Conclusions:

• The developed simple score test offers a more powerful and sample-efficient approach for analyzing seasonal trends in epidemiologic data.
• This method provides a valuable alternative for researchers studying seasonality, particularly when peak and trough periods are known.
• The findings suggest improved statistical rigor and reduced resource requirements for future seasonality studies in epidemiology.