Department of Biomedical Informatics, Vanderbilt University Medical Center, Nashville, Tennessee, United States of America.
Department of Biological Sciences, Vanderbilt University, Nashville, Tennessee, United States of America.
PLoS Comput Biol. 2021 Jan 6;17(1):e1008567. doi: 10.1371/journal.pcbi.1008567. eCollection 2021 Jan.
The chi-square periodogram (CSP), developed over 40 years ago, continues to be one of the most popular methods to estimate the period of circadian (circa 24-h) rhythms. Previous work has indicated the CSP is sometimes less accurate than other methods, but understanding of why and under what conditions remains incomplete. Using simulated rhythmic time-courses, we found that the CSP is prone to underestimating the period in a manner that depends on the true period and the length of the time-course. This underestimation bias is most severe in short time-courses (e.g., 3 days), but is also visible in longer simulated time-courses (e.g., 12 days) and in experimental time-courses of mouse wheel-running and ex vivo bioluminescence. We traced the source of the bias to discontinuities in the periodogram that are related to the number of time-points the CSP uses to calculate the observed variance for a given test period. By revising the calculation to avoid discontinuities, we developed a new version, the greedy CSP, that shows reduced bias and improved accuracy. Nonetheless, even the greedy CSP tended to be less accurate on our simulated time-courses than an alternative method, namely the Lomb-Scargle periodogram. Thus, although our study describes a major improvement to a classic method, it also suggests that users should generally avoid the CSP when estimating the period of biological rhythms.
卡方周期图（CSP）是 40 多年前开发的，它仍然是估计昼夜节律（约 24 小时）节律周期的最流行方法之一。以前的工作表明，CSP 有时不如其他方法准确，但对为什么以及在什么条件下会这样，我们的理解仍不完整。通过模拟有节奏的时间过程，我们发现 CSP 容易低估周期，这种低估的方式取决于真实周期和时间过程的长度。这种低估偏差在短时间过程（例如 3 天）中最为严重，但在较长的模拟时间过程（例如 12 天）和实验中小鼠轮跑和离体生物发光的时间过程中也可见。我们将偏差的来源追溯到与 CSP 用于计算给定测试周期的观察方差的时间点数有关的周期图中的不连续性。通过修改计算以避免不连续性，我们开发了一种新版本，即贪婪 CSP，它显示出降低的偏差和提高的准确性。尽管如此，即使是贪婪的 CSP 在我们的模拟时间过程中也往往不如另一种方法，即 Lomb-Scargle 周期图准确。因此，尽管我们的研究描述了对经典方法的重大改进，但它也表明用户在估计生物节律的周期时通常应避免使用 CSP。
