Application and extension of a likelihood-ratio test for seasonality in epidemiological data

ABSTRACT

We present a detailed exposition of the development and application of a likelihood-ratio test for seasonality. It is well known that likelihood-ratio tests have optimal power properties. We assess the test's performance by means of a simulation study. The test's application is illustrated with three examples that have different alternative hypotheses, thus extending the original presentation of the test. These examples are not artificial or contrived, but they come from actual, real applications. As far as we know, these are the only completely worked-out examples of this test's application that are available in the literature. Thus, our exposition can serve as a tutorial on the test's application. Our presentation is detailed so as to facilitate further extension and application of the test to other alternative hypotheses. We supply pertinent R computer code in an appendix. For those who teach maximum-likelihood estimation, our examples provide interesting, real-life cases that may be used in teaching.

Keywords:

• Disease etiology
• likelihood-ratio test
• maximum-likelihood estimation
• Newton-Raphson procedure
• one- and two-parameter likelihoods
• seasonality in medical data

Acknowledgments

The author thanks an associate editor and the referees for comments that helped improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Osvaldo Marrero

Osvaldo Marrero is a mathematician and statistician. He earned a PhD in mathematics at the University of Miami and an MPH in biometry at Yale University, where he was also a Postdoctoral Research Fellow. Subsequently, he completed courses at the University of Minnesota and at the Université de Montréal. He has worked in industry and in academia, including affiliations with mathematical and medical groups at several universities. He has been a researcher in several units of Yale University's medical school and served as an Adjunct Professor of Pediatrics at the University of Pennsylvania. He has publications in economics, epidemiology, mathematics, medicine, and statistics. In particular, he has published extensively on the statistical analysis of seasonal variation in medical research. He has presented his work at professional meetings worldwide and delivered invited lectures at universities in the Americas and in Europe. For many years, he is a Professor in the Department of Mathematics and Statistics, Villanova University, Villanova, PA, USA.