On analyzing circadian rhythms data using nonlinear mixed models with harmonic terms
On analyzing circadian rhythms data using nonlinear mixed models with harmonic terms
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DOI：
10.1111/j.0006-341x.2005.464_1.x
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发表时间：
2005-12-01
期刊：
影响因子：
1.9
通讯作者：
Hunsberger, S
中科院分区：
文献类型：
--
作者：
Albert, PS;Hunsberger, S
Wang，Ke和Brown(2003，Biometrics 59,804-812)开发了一种基于平滑的方法来模拟具有随机效应的昼夜节律。他们的方法是灵活的，因为固定和随机协变量可以影响非参数平滑周期函数的幅度和相移。在激励他们的方法方面，王等人。指出简单的正弦函数过于严格。此外，他们还表示，“虽然加入谐波可以改善拟合，但很难决定在模型中包含多少次谐波，结果也很难解释。”我们不同意这样的观点，即调和模型不能成为建模纵向昼夜节律数据的有用工具。在这篇笔记中，我们展示了带有调和项的非线性混合模型如何允许一个简单而灵活的替代方法来代替Wang等人的S方法。我们展示了如何使用惩罚似然来选择谐波数目来灵活地模拟昼夜节律并估计协变量对节律的影响。我们将调和模型与Wang等人提供的皮质醇昼夜节律数据进行拟合来说明我们的方法。此外，我们通过一个小的模拟研究来评估我们的方法的性质。所提出的参数方法提供了Wang等人的S半参数方法的替代方法，并且具有易于在大多数统计软件包中实现的优点。
Wang, Ke, and Brown (2003, Biometrics 59, 804-812) developed a smoothing-based approach for modeling circadian rhythms with random effects. Their approach is flexible in that fixed and random covariates can affect both the amplitude and phase shift of a nonparametrically smoothed periodic function. In motivating their approach, Wang et al. stated that a simple sinusoidal function is too restrictive. In addition, they stated that "although adding harmonics can improve the fit, it is difficult to decide how many harmonics to include in the model, and the results are difficult to interpret." We disagree with the notion that harmonic models cannot be a useful tool in modeling longitudinal circadian rhythm data. In this note, we show how nonlinear mixed models with harmonic terms allow for a simple and flexible alternative to Wang et al.'s approach. We show how to choose the number of harmonics using penalized likelihood to flexibly model circadian rhythms and to estimate the effect of covariates on the rhythms. We fit harmonic models to the cortisol circadian rhythm data presented by Wang et al. to illustrate our approach. Furthermore, we evaluate the properties of our procedure with a small simulation study. The proposed parametric approach provides an alternative to Wang et al.'s semiparametric approach and has the added advantage of being easy to implement in most statistical software packages.