Understanding how circadian rhythms manifest in human social life is crucial for chronobiology and personalized medicine. While phone use data has advanced our understanding of the personal and robust nature of circadian rhythms in social activity, the statistical validity of these findings remains unclear. This study addresses this gap by proposing a new statistical approach to measure circadian rhythms of social activity from phone data, specifically designed for persistence analysis. This approach is vital for validating the consistency of previous findings and expanding the use of CDRs in personalized medicine applications, particularly in health care monitoring, where statistical significance is essential for reliable patient care. The ubiquity of circadian rhythms, impacting biological, physical, and social aspects of life, makes their analysis critical. The 2017 Nobel Prize in Medicine highlighted the importance of comprehending these rhythms for improved patient health management by tailoring treatments to optimal times of day. While chronobiology and actigraphy address biological and physical circadian rhythms, the social aspects are less readily observable. This study leverages the pervasive use of mobile phones in daily social life to investigate these social manifestations, offering a continuous, objective, and unobtrusive means of data acquisition.

Existing literature explores the use of phone technologies for social and behavioral modeling, highlighting the value of CDRs for analyzing the circadian rhythms of telephone interactions. CDRs offer a continuous, objective, and unobtrusive way to investigate the properties of social rhythms, including persistence over time. Persistence, in this context, refers to the maintenance of a pattern of activity over time, despite external factors. A seminal 2014 study by Saramäki et al. using an 18-month CDRs dataset demonstrated the existence of social signatures in communication patterns among students, showing persistence even after significant life transitions. Subsequent studies utilizing high-resolution CDRs data confirmed the existence of social and spatial signatures, highlighting the ability of CDRs to reveal persistent patterns in how individuals utilize resources in social and spatial contexts. Studies have also shown the persistence of circadian patterns in call frequency across different types of interactions and populations, including older adults. While these studies demonstrate promising results, the lack of statistical validation limits their conclusions. Current methodologies primarily use mean estimators without statistical significance testing, hindering their applicability in clinical settings where such validation is crucial.

This study introduces a novel statistical approach for measuring the persistence of circadian rhythms of telephone call activity. It formalizes and expands on the method initially proposed by Saramäki et al., incorporating additional steps to ensure statistical validation. The approach involves analyzing both two successive temporal windows and multiple successive windows. **Study Population and Data Collection:** The study used 12 months of CDRs from 26 volunteers (20 women, 6 men; median age: 84 years; range: 71–91 years). Data were anonymized and collected with informed consent, adhering to relevant regulations and approved by the French Data Protection Authority. **Data Analysis:** The statistical procedure uses a method adapted from Saramäki et al., enhanced with statistical validation. The five steps are: 1. **Time Discretization:** CDRs are divided into 24 one-hour time slots for each time period. 2. **Calculation of Daily Rhythm:** The daily rhythm of calls is calculated for each individual and time period using the function *f_i(t)* = Σ²³_t=0 *n_i(t)*, where *n_i(t)* is the number of calls in time slot *t*. 3. **Intra-individual Dissimilarity:** *D*_self measures the dissimilarity between an individual's daily rhythms across successive time periods using the Jensen-Shannon Divergence (D). 4. **Inter-individual Dissimilarity:** *D*_ref measures the dissimilarity between the daily rhythms of two different individuals within the same time period, also using the Jensen-Shannon Divergence (D). 5. **Persistence Assessment:** This step assesses persistence using a sign test of quantiles. First, a comparison is made between each inter-individual dissimilarity (*x_ij^k*) and the intra-individual dissimilarity (*y_i*). This generates a vector *z_i* with values in {0, 1}, representing successes (1) and failures (0). The total number of successes (*Nⁱ*) is calculated. A binomial test is then performed under the null hypothesis (H₀) that the probability of an inter-individual dissimilarity being lower than the intra-individual dissimilarity is 0.5 (median test). A significant p-value supports the persistence of the daily rhythm. For more than two time periods, the analysis is repeated for each pair of successive periods, and a sign test is applied to the resulting sequence of “persistence” (1) and “no persistence” (0) events. A significant result indicates a persistent behavior. A p-value < 0.05 was used as the significance level for all statistical tests. All calculations were performed using R software (version 3.1.6).

The analysis was applied to the 12-month CDRs dataset, considering outgoing, incoming, and total call activities separately, with two six-month time periods (N_T=2). Figure 2, 3, and 4 illustrate the daily rhythms for outgoing, incoming, and total calls respectively for each individual across the two periods. Differences between periods are highlighted by colored areas. The statistical results (Table 1) show the number of inter-individual dissimilarities lower than the intra-dissimilarity (N₊) and the corresponding p-value for each individual. Individuals V, W, Y, and Z did not show significantly persistent circadian rhythms of telephone call activity (p-values > 0.05) for at least one call type. For the others, significant persistence (p-values < 0.05) was observed. The results highlight that while most individuals exhibited significant persistent circadian behavior, this was not consistent across all individuals or call types. The persistence of circadian rhythms may be dependent on the direction of calls (outgoing, incoming, or total).

This study addresses the lack of statistical rigor in existing methods for assessing persistence in circadian rhythms of telephone activity. It demonstrates that existing methods can be formulated as a simple non-parametric statistical problem. The proposed statistical approach, using a sign test of quantiles, ensures the statistical validity of results. The application to a CDRs dataset of older adults shows the ability to assess persistence with statistical significance. The findings reveal that while most individuals exhibit significant persistent circadian behavior, this is not universally true and may depend on call direction. The methodology integrates insights from complex network sciences and computational social sciences, enhancing the understanding of human social behavior. The inter-intra dissimilarity approach, with roots in early 20th-century biometrics, is consistent with modern statistical learning methods. The approach is particularly relevant for mHealth studies because it provides statistically significant insights into the personal nature of social behavior and validates the concept of digital signatures in daily social interactions.

This study proposes a novel, statistically robust method for assessing the persistence of circadian rhythms in telephone call activity. The approach enhances the reliability of existing methods and opens new avenues for using CDRs in personalized medicine. Future work should apply this method to longitudinal studies of individuals with specific illnesses or chronic diseases to investigate the role of social circadian rhythms in health and disease.

The relatively small sample size (26 participants) limits the generalizability of the findings. The study focuses on older adults, and the results may not be directly transferable to other age groups. The study only considers telephone call data and does not incorporate other forms of communication (e.g., text messages). Future studies should address these limitations by increasing sample size, incorporating diverse age groups, and expanding the types of communication data analyzed.