Novel statistical approach for assessing the persistence of the circadian rhythms of social activity from telephone call detail records in older adults

Circadian rhythms are endogenous processes characterized by a period close to 24 h depending on individuals. Their ubiquity makes them one of the most perceptible phenomena in an individual’s life, reflecting and affecting biological, physical and social domains. In health care monitoring, analyzing the mechanisms involved in the emergence, maintenance, and characterization of circadian rhythms is increasingly important, with clinical implications for timing treatments appropriately. While chronobiology and actigraphy address biological and physical manifestations, ubiquitous computing—particularly through phone technologies—enables the study of social manifestations of circadian rhythms via passively generated data. Prior work using call detail records (CDRs) has shown that such data permit continuous, objective, and unobtrusive analysis of social rhythms and their persistence over time, indicating personal and robust temporal signatures in communication behaviors. However, these persistence analyses have largely relied on descriptive comparisons and mean estimators without formal statistical validation, leaving the statistical significance of reported persistence unclear. This paper addresses that gap by proposing a novel, statistically grounded procedure tailored to persistence analysis of circadian rhythms in social activity, and demonstrating its use on a 12-month CDR dataset from adults over 65 years to assess persistence in outgoing, incoming, and total call activities.

A growing body of literature uses mobile phone data to model social and behavioral patterns, highlighting the value of CDRs for examining circadian rhythms of social interactions. Saramäki et al. (2014) first analyzed persistence of social signatures over 18 months, showing individual-specific and time-robust communication allocation patterns despite social network turnover. Alessandretti et al. extended this to social and spatial signatures in the Copenhagen Networks Study. Aledavood et al. reported temporal signatures in the distribution of outgoing calls by hour, and other works found similar persistence with text messages and in older populations. Despite these advances, prior methods primarily used simple estimators and heuristic decision rules without formal statistical tests to validate persistence claims. This study reformulates the persistence assessment into a non-parametric statistical framework to provide significance testing, thereby complementing approaches from social physics and computational social science with rigorous statistical validation.

Study population and data collection: The study analyzed 12 months of CDRs from 26 volunteers (20 women, 6 men; median age 84 years; range 71–91). CDRs included date, hour, source ID, recipient ID, direction, and duration of calls. Identities were anonymized. Protocols were approved by the French Data Protection Authority (CNIL; France Telecom 2011 n°44), with written informed consent. This is a secondary analysis of previously published and unpublished datasets. Analytical framework: The procedure formalizes and extends the persistence analysis of daily rhythms to enable statistical validation. Two cases are considered: (1) two successive temporal windows and (2) more than two successive windows. Case N=2 (two successive time periods T1 and T2): Step 1 (Time discretization): Split data into two successive periods T1 and T2; each period is divided into 24 one-hour slots. Step 2 (Daily rhythm computation): For each individual i, compute the daily rhythm for each period as the discrete probability distribution of call fractions across the 24 hours: f_i(t) based on counts n_i(t) in hour t, yielding P_i^{T1} and P_i^{T2}. Step 3 (Intra-individual dissimilarity): Compute D_self(i, T1, T2) = D(P_i^{T1}, P_i^{T2}) as the dissimilarity between i’s two periods; set y_i = D_self. Step 4 (Inter-individual dissimilarity): For each period T_k (k=1,2), compute D_ref(i, j, T_k) = sqrt(D(P_i^k, P_j^k)) for all j ≠ i. Denote x_i^k = (x_{ij}^k)_{j=1..n, j≠i}, each of size n−1. Step 5 (Persistence assessment via sign test of quantiles): Compare intra- vs inter-individual dissimilarities. Define z_i = (1 − 1_{x_{ij}^k > y_i}) over all j ≠ i and k ∈ {1,2}, so z entries are 1 if inter < intra (a “success”), else 0. Let N^i = sum z_{ij}^k be total successes over both periods (2n−2 comparisons). Null hypothesis H0: probability q that inter < intra equals 1/2 (median test); under H0, N^i ~ Binomial(2n−2, q), assuming independence of j’s behaviors across T1 and T2. A significant p-value from the binomial test supports persistence for individual i. Extension to N_T > 2 periods: Apply the N=2 procedure to each pair of successive periods; record for each pair a binary outcome (1 = significant persistence, 0 = not significant). Apply a sign test to the sequence v (length N_T−1); a significant result indicates a trend toward persistent behavior. Implementation details: Significance threshold p < 0.05. Analyses performed in R (v3.1.6). In the empirical application, Jensen–Shannon divergence (JSD) was used as D, and two successive 6-month windows (T1, T2) were considered, separately for outgoing, incoming, and total calls.

- Dataset: 26 older adults (71–91 years; median 84) with 12 months of CDRs analyzed; rhythms computed in two 6‑month windows (T1, T2); JSD used as dissimilarity. - Outgoing calls: Individuals V, W, Y, and Z did not exhibit statistically significant persistence (p > 0.05); all others did (Table 1). - Incoming calls: The only individuals without significant persistence were W and Z (as described in the Results). - Total calls: W and Z were the only individuals without significant persistence. - Overall: Most individuals displayed statistically significant persistence of daily telephone activity rhythms, but persistence was not universal and could depend on call direction (e.g., differences across outgoing vs incoming). - Testing details: For each individual, N_comp = 50 comparisons (2 × (n − 1) with n = 26). Many individuals had extremely small p-values (e.g., 8.88E−16) indicating strong evidence of persistence.

The study addresses the lack of statistical validation in existing persistence analyses of circadian rhythms from phone data by reframing the problem as a simple, non-parametric sign test of quantiles contrasting intra- vs inter-individual dissimilarities. Applying the method to older adults’ CDRs showed that most individuals have significantly persistent daily rhythms of telephone activity, though not universally and with dependence on call direction (outgoing, incoming, total). This provides statistically grounded support for the robustness and distinctiveness of individuals’ social circadian patterns. The approach complements methods in social physics and computational social science that have relied on descriptive estimators and qualitative interpretation by adding formal statistical significance to findings. The inter/intra dissimilarity framework is situated within established statistical traditions (e.g., variance decomposition and clustering concepts), thereby embedding persistence analysis within a coherent scientific methodology. In mHealth, the method can inform on the personal nature of social behavior rhythms relevant to personalized care and the validation of digital phenotypes. It also complements alternative modeling approaches (e.g., trigonometric Poisson models and Fourier analyses) depending on data characteristics and research questions.

This work introduces a novel, statistically validated procedure to assess the persistence of circadian rhythms in social activity from CDRs by comparing intra- and inter-individual dissimilarities via a non-parametric sign test. Applied to a 12‑month dataset of older adults, the method demonstrated that most individuals exhibit significant persistence in daily telephone rhythms, though not universally and with variation by call direction. The approach augments existing CDR-based analyses by providing formal significance testing and can support applications in personalized medicine and health care monitoring. Future research should deploy this persistence analysis longitudinally in clinical populations (e.g., bipolar disorder) to quantify social rhythm regularity amid specific disruptions and to better understand interactions between social, biological, and physical circadian manifestations.

- Population and generalizability: Small sample (n = 26) of older adults (71–91 years) limits generalization to other age groups or settings. - Temporal design: The main analysis considers two 6‑month windows; broader or different windowing could affect persistence detection. - Statistical assumptions: The binomial test assumes independence of other individuals’ behaviors across periods T1 and T2; violations could influence p-values. - Metric choice: Persistence was assessed using Jensen–Shannon divergence; alternative dissimilarity measures could yield different sensitivities. - Modality scope: Only telephone call activity (outgoing, incoming, total) was analyzed; other communication channels or behavioral signals were not included.