Analyzing biological rhythms in clinical trials

The human body exhibits a variety of biological rhythms. There are patterns that correspond, among others, to the daily wake / sleep cycle, a yearly seasonal cycle and, in women, the menstrual cycle. Sine/cosine functions are often used to model biological patterns for continuous data, but this model is not appropriate for analysis of biological rhythms in failure time data.

We consider a method appropriate for analysis of biological rhythms in clinical trials. We present a method to provide an estimate and confidence interval of the time when the minimum hazard is achieved. A motivating example from a clinical trial of adjuvant of pre-menopausal breast cancer patients provides an important illustration of the methodology in practice.

Adapting the Cosinor method to the Weibull proportional hazards model is proposed as useful way of modeling the biological rhythm data. It presents a method to estimate the time that achieves the minimum hazard along with its associated confidence interval. The application of this technique to the breast cancer data revealed that the optimal day for pre-resection incisional or excisional biopsy of 28-day cycle (i.e. the day associated with the lowest recurrence rate) is day 8 with 95% CI 5-10. We found that older age, fewer positive nodes, smaller tumor size, and experimental treatment are important prognostic factors of longer relapse-free survival.

The analysis of biological/circadian rhythms is usually handled by Cosinor rhythmometry method. However, in FTD this is simply not possible. In this case, we propose to adapt the Cosinor method to the Weibull proportional hazard model. The advantage of the proposed method is its ability to model survival data. This method is not limited to breast cancer data, and may be applied to any biological rhythms linked to right censored data.