Circadian clocks regulate biological behaviours, such as sleeping and waking times, that recur naturally on an approximately 24-hour cycle. These clocks tend to be influenced by a variety of external factors, sometimes to the extent that it can have an impact on health. As an example in pharmacology, the effects of chemicals on the circadian rhythm in patients can be key in clarifying the relationship of drug efficacy and toxicity with dosing times. While pre-clinical experiments conducted to elucidate these effects may produce correlated data measured over time, such as gene expression profiles, existing methods for fitting parametric nonlinear regression models are however inadequate and can lead to unreliable, inconsistent parameter estimates and invalid inference. A de-trending method is widely used as a pre-processing step to address the non-stationary problem in the data before fitting models based on the assumption of independence. However, as it is unclear that this approach properly accounts for the correlation structure, alternative methods that specifically model the correlation in the data based on conditional least squares and a two-stage estimation procedure are proposed and evaluated. A simulation study covering a wide range of scenarios and models show that the proposed methods more efficient and robust to model mis-specification than de-trending and, furthermore, they lead to reduced bias in estimation of the circadian period and more reliable confidence intervals
