Environmental exposures, including some that vary seasonally, may play a role in the development of many types of childhood diseases such as cancer. Those observed in children are unique in that the relevant period of exposure is inherently limited or perhaps even specific to a very short window during prenatal development or early infancy. As such, researchers have investigated whether specific childhood cancers are associated with season of birth. Typically a basic method for analysis has been used, for example categorization of births into one of four seasons, followed by simple comparisons between categories such as via logistic regression, to obtain odds ratios (ORs), confidence intervals (CIs) and p-values. In this paper we present an alternative method, based upon an iterative trigonometric logistic regression model used to analyze the cyclic nature of birth dates related to disease occurrence. Disease birth-date results are presented using a sinusoidal graph with a peak date of relative risk and a single p-value that tests whether an overall seasonal association is present. An OR and CI comparing children born in the 3-month period around the peak to the symmetrically opposite 3-month period also can be obtained. Advantages of this derivative-free method include ease of use, increased statistical power to detect associations, and the ability to avoid potentially arbitrary, subjective demarcation of seasons.