Background and objective

Cosinor analysis, developed by Franz Hallberg and colleagues in the 1960s, allows for the fitting of a cosine curve to data of a known period. Cosinor analysis is frequently used in the analysis of biological rhythm data. While software exists to perform these analyses, we are not aware of any published SAS procedures or macros which would facilitate them.

Methods

To meet this gap, we herein describe SAS macros which perform cosinor analyses that assume either normally or gamma distributed outcomes and fixed period. The macros can 1) produce datasets with cosinor parameters including acrophase, mesor, amplitude, nadir and test for rhythmicity 2) output datasets with fitted and observed values from the model, and 3) plot the resulting curve and underlying data.

Results

We demonstrate the use of these macros with data from our research on circadian rhythms of heart rate and sleep in critically ill patients.

Conclusions

Cosinor analysis provides a parsimonious and intuitive set of estimates to summarize periodic data. We are hopeful that the publication of our macro will allow a wider spectrum of users to avail themselves of this technique.

中文翻译：

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使用余弦分析对周期性数据进行建模的 SAS 宏

背景和目标

由 Franz Hallberg 及其同事在 1960 年代开发的余弦分析允许将余弦曲线拟合到已知时期的数据。余弦分析经常用于生物节律数据的分析。虽然存在执行这些分析的软件，但我们不知道有任何已发布的 SAS 程序或宏可以促进这些分析。

方法

为了弥补这一差距，我们在此描述了 SAS 宏，它执行假设正态或伽马分布结果和固定周期的余弦分析。宏可以 1) 生成具有余弦参数的数据集，包括 acrophase、mesor、幅度、最低点和节律性测试 2) 输出具有模型的拟合值和观察值的数据集，以及 3) 绘制结果曲线和基础数据。

结果

我们通过我们对重症患者心率和睡眠的昼夜节律的研究数据证明了这些宏的使用。

结论

余弦分析提供了一组简洁且直观的估计来总结周期性数据。我们希望我们的宏的发布将使更广泛的用户能够利用这种技术。