Modeling biological rhythms in failure time data

Order restricted inference in chronobiology

This paper is motivated by applications in oscillatory systems where researchers are typically interested in discovering components of those systems that display rhythmic temporal patterns. The contributions of this paper are twofold. First, a methodology is developed based on a circular signal plus error model that is defined using order restrictions. This mathematical formulation of rhythmicity is simple, easily interpretable and very flexible, with the latter property derived from the nonparametric formulation of the signal. Second, we address various commonly encountered problems in the analysis of oscillatory systems data. Specifically, we propose a methodology for (a) detecting rhythmic signals in an oscillatory system and (b) estimating the unknown sampling time that occurs when tissues are obtained from subjects whose time of death is unknown. The proposed methodology is computationally efficient, outperforms the existing methods, and is broadly applicable to address a wide range of questions related to oscillatory systems.

Spatial and temporal patterns in Cimex lectularius (Hemiptera: Cimicidae) reporting in Philadelphia, PA

We analyzed a comprehensive telephone log of pest infestation reports to assess the spatial and temporal trends in Cimex lectularius L. (bed bug) reporting throughout Philadelphia, PA. Citywide spatial analyses of reports from September 2011 to June 2012 revealed several statistically significant bed bug hotspots. However, these were small and diffuse. Temporal analyses of reports from December 2008 to May 2011 detected prominent seasonality in bed bug reporting, peaking in August and reaching a nadir in February each year. Controlling for seasonal cycling, the number of bed bug reports in Philadelphia increased steadily at a rate of approximately 4.5% per month (or 69.45% per year) from December 2008 to May 2011. While it may be difficult to spatially target citywide bed bug control measures because of the insects' widespread migration, interventions informed by seasonal trends may enhance efforts to curb the recent increases in urban bed bug populations.

Analyzing biological rhythms in clinical trials

BACKGROUND

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.

METHODS

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.

RESULTS

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.

CONCLUSIONS

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.

Cosinor analysis for temperature time series data of long duration

The application of cosinor models to long time series requires special attention. With increasing length of the time series, the presence of noise and drifts in rhythm parameters from cycle to cycle lead to rapid deterioration of cosinor models. The sensitivity of amplitude and model-fit to the data length is demonstrated for body temperature data from ambulatory menstrual cycling and menopausal women and from ambulatory male swine. It follows that amplitude comparisons between studies cannot be made independent of consideration of the data length. Cosinor analysis may be carried out on serial-sections of the series for improved model-fit and for tracking changes in rhythm parameters. Noise and drift reduction can also be achieved by folding the series onto a single cycle, which leads to substantial gains in the model-fit but lowers the amplitude. Central values of model parameters are negligibly changed by consideration of the autoregressive nature of residuals.