Improvement in regularity of meals, body weight changes, and correlation between loss of body weight and regularity of eating meals. (A, B) Times of day of caloric events of 15 representative participants of the EG (A) and the CG (B) during the two-week exploration phase (left) and the six-week intervention phase (right). Each point represents a caloric event. (C, D) Change in MTVS of participants in the CG (gray) and EG (cyan) of breakfast, lunch, and dinner (C) and of all meals combined (D), including snacks, if snacks were taken. 2-way repeated-measures ANOVA with Bonferroni post hoc test comparing CG and EG during the exploration or intervention phase and T0-T1 and T1-T2 within groups, * p ≤ 0.05, ** p ≤ 0.01, **** p ≤ 0.0001. CG: n=33; EG: n=64-67, missing n-values in the EG are due to the different number of meals for each participant. Detailed statistics in Tables S3. (E) Within group differences of body weight during the study. Body weight was collected at different time points, at the beginning of the study (T0), after the exploration phase (T1), after the intervention phase (T2), and after the follow-up phase (T3). During the follow-up phase, 34 EG participants voluntarily continued the intervention (continuing; black line and open circle) while 33 participants no longer followed the intervention (discontinuing; gray, dashed line and open circle). Only three control subjects continued their intervention in the follow-up phase, which is why a division into continuing and discontinuing was omitted in this group. Data are normalized so that all baseline data at T0 equals 0 to represent change. Differences of all CG and EG participants between T0, T1, and T2 were calculated with a 1-way ANOVA, as were differences between T2 and T3 of CG participants (Bonferroni post-hoc test, **** p ≤ 0.0001). Differences between T2 and T3 of continuing and discontinuing EG participants were calculated with a paired t-test °° p ≤ 0.01, °°°° p ≤ 0.0001. Detailed statistics in Table S4. (F) Between group differences of BMI from T0-T3. Mixed-effect model with Bonferroni post-hoc test comparing CG and EG at different phases during the study, **** p ≤ 0.0001. Detailed statistics in Table S5. (G) Significant correlation between body weight/BMI and MTVS. The more participants improved their regularity of meals (decreasing MTVS), the more weight/BMI they lost. Linear regression, CG: n=33; EG: n=67, ** p ≤ 0.01. Detailed statistics in Tab. S6. (H) Significant correlation between change in BMI, baseline BMI, and improvement in MTVS. Individuals with higher BMI benefit more from similar improvements in MTVS (shades of data points) than individuals with lower BMI in EG participants. Multiple regression, n=67, * p ≤ 0.05, ** p ≤ 0.01. Detailed statistics in Tab. S9.

Changes in body weight/BMI are not related to changes in reported caloric intake and composition of macronutrients. Changes in reported daily caloric intake (A), cumulative caloric intake (B) and food composition (E) and their relationship to weight/BMI changes (C, D, and F). Data in (A) are normalized so that all baseline data of the exploration phase equal 1. To represent the x-fold change, data from the intervention phase are divided by data from the exploration phase of the corresponding participant. (A, E) 2-way repeated-measures ANOVA with Bonferroni post hoc test comparing CG and EG during the exploration or intervention phase and T0-T1 and T1-T2 within groups, * p ≤ 0.05. Detailed statistics in Tables S3. (B) Mixed-effects model with Bonferroni post hoc test comparing determined and estimated cumulative energy intake. The estimated energy intake is formed as an assumed continuation of the average daily intake during the exploration phase. The Bonferroni post hoc test showed no significant differences on any study day. (C, D, and F) Linear regression, CG: n=30; EG: n=67 (some participants were excluded subsequently from this analysis because of several erroneous diary entries about unrealistic amounts of food, e.g., 30,000 g chicken for lunch). Detailed statistics in Tab. S6.

Influence of other changes in eating times and of personalization of meal schedules on weight loss. (A) 95th percentile of the time period during which food was ingested by 15 example participants during the exploration phase (yellow) and the intervention phase (purple). (B) Change in length of this period and its relation to weight/BMI changes. (C, D) Change in time of first (C) and last (D) caloric intake and their association with weight/BMI changes. (B-D) 2-way repeated-measures ANOVA with Bonferroni post hoc test comparing CG and EG during the exploration or intervention phase and T0-T1 and T1-T2 within groups, *** p ≤ 0.001, **** p ≤ 0.0001. Linear regression. EG: n=67, varying n-numbers result from incomplete entries in the diaries. Detailed statistics in Tables S3 and S6. (E) The relation between mid-Sleep phase and mid-Eat phase (brown) on the weekends of the exploration phase. The goodness of fit of this association improves during through EG intervention and affects both workdays and weekend days (purple). Linear regression, n=65, **** p ≤ 0.0001. Detailed statistics in Table S6. (F) Relation of the mid-Sleep phase (mSP) and mid-Eat phase (mEP) during exploration and intervention phase. The circles represent 24 h, the gray area represents the estimated sleep time, and the black arrow represents the mid-sleep phase, which is normalized for all subjects. The colored triangles represent the mid-Eat phase of each subject in relation to their mid-Sleep phase. The red arrow shows the average mid-Eat phase across all subjects. n=65. Detailed statistics in Table S10. (G) The smaller the residuals, i.e., the vertical distances of observation points from the regression line, became, the more BMI the EG subjects lost. Linear regression, n=65, ** p ≤ 0.01. Detailed statistics in Table S6. (H) Representative example of a meal diary showing a shift from meals on weekends. The purple arrows represent the calculated times, based on the events of the more frequent workdays, for the meal schedule of the intervention phase. (I) Shifts from weekend meals caused by the EG intervention. Paired t-test, n=65, *** p ≤ 0.001, **** p ≤ 0.0001. Data are normalized so that all baseline data at T0-T1 equal 0 to represent the change in hours. Detailed statistics in Table S11. (J) Large phase shifts of breakfast and dinner, equivalent to a correction of the social jetlag of meals on weekends, are related to greater weight loss. Linear regression, breakfast: n=55, lunch: n=64, dinner: n=63, ** p ≤ 0.01. Missing n-numbers are due to incomplete diary entries on weekends during the exploratory phase or because participants usually did not have a particular meal. Detailed statistics in Table S6. (K) Results of a multiple regression to investigate the influence of individual variables while holding the others constant on the BMI of EG participants. The Quantile-Quantile (QQ) plot shows the data are normally distributed (left). The multiple regression plot and R2 value shows that the multiple regression model explains the data well (middle). Additionally, the assignment of each regression beta coefficient to the independent variables is shown along with the p-values showing the influence on BMI. The data used are the same as those used in the individual regressions shown previously. Detailed statistics in Tab. S9. (L) Covariance matrix with normalized covariances for each pair of parameters. Values close to 1 (blue) or -1 (red) indicate high intertwining of the data, values close to 0 (white) indicate independence or orthogonality of the data. The assignment of the coefficients to the independent variables is the same as in (K).

Improvement in overall well-being over the course of the study. (A) Significant improvements are observed in various aspects of physical and mental health (SF-36), sleep quality (PSQI), depressed mood (IDS-SR), and self-efficacy (SWE) in participants of the EG (colored columns), but hardly among CG participants (gray columns). Scales are either upward or downward, depending on whether low or high scores on the questionnaires mean subjectively good or poor well-being. (B) The chronotype of EG and CG participants did not change during the study. 2-way repeated-measures ANOVA with Bonferroni post hoc test comparing CG and EG during the exploration or intervention phase and T0-T1 and T1-T2 within groups, * p ≤ 0.05, ** p ≤ 0.01, *** p ≤ 0.001, **** p ≤ 0.0001. CG: n=33; EG: n=67. Detailed statistics in Tab. S3.

(A) Logo of the “Time To Eat” study. The logo represents a clock in which the letters act as hands. (B) Consort diagram through the phases of the trial. A total of 148 initial participants were recruited. Of these, 48 were excluded or withdrew from the study in the course of the trial. Thus, the final study sample consisted of 100 participants of whom 67 were allocated to the EG and 33 to the CG. Until the follow-up appointment, 34 EG participants voluntarily continued the intervention. 30 EG participants discontinued the intervention but were available for further data collection, while three EG participants were no longer available and thus no analyzable data were available from them at T3. Of the 33 CG participants, only three voluntarily continued the sham intervention until T3. (C) Timeline of the study. INTRODUCTORY SESSION: Test participants are screened, recruited by a member of the study staff, and sign the consent form. This is followed by an introductory session where they are informed about the contents of the study and familiarized with the FDDB smartphone application. In addition, questionnaires are filled out and weight and abdominal girth are measured. EXPLORATION PHASE: During the following two weeks, the participants are asked to record each caloric event with the FDDB app. Afterwards, a mealtime schedule is developed for each participant. INTERVENTION PHASE: During the following six weeks, the participants are instructed to take their meals only at times according to the mealtime schedule and to report their weight weekly. In the middle of the intervention phase, a telephone appointment is made to maintain compliance. FINAL QUESTIONNAIRE ASSESSMENT: At the end of the intervention phase, the participants are asked to fill out the same questionnaires as at the introduction session. FOLLOW-UP ASSESSMENT: After another four weeks, the test participants are contacted again to explore whether they have continued the intervention voluntarily and to ask again for their body weight.

(A) BMI differences between study completers and drop-outs. Differences were calculated with a Welch’s test (detailed statistics in Tab. S2). (B) Within group differences of BMI during the study. BMI was collected at different time points, at the beginning of the study (T0), after the exploration phase (T1), after the intervention phase (T2), and after the follow-up phase (T3). During the follow-up phase, 34 EG participants voluntarily continued the intervention (continuing; black line and open circle) while 33 participants dropped out (discontinuing; gray, dashed line and open circle). Only three control subjects continued their intervention in the follow-up phase, which is why a division into continuing and discontinuing was omitted in this group. Data are normalized so that all baseline data at T0 equals 0 to represent change. Differences of all CG and EG participants between T0, T1, and T2 were calculated with a 1-way ANOVA, as were differences between T2 and T3 of CG participants (Bonferroni post-hoc test, **** p ≤ 0.0001). Differences between T2 and T3 of continuing and discontinuing EG participants were calculated with a paired t-test °° p ≤ 0.01, °°°° p ≤ 0.0001 (detailed statistics in Tab. S4). (C) Between group differences of BMI from T0-T3. Mixed-effect model with Bonferroni post-hoc test comparing CG and EG at different phases during the study, **** p ≤ 0.0001 (detailed statistics in Tab. S5). Individual body weight (D) and BMI (E) changes of all 34 continuing and all 33 discontinuing participants of the EG group and of CG participants (F) during the study. Data is normalized so that all baseline data at T0 equals 0 to represent change. (G) Between group differences of body weight and BMI from T0-T3 including the last available values of study drop-outs which were carried forward. Mixed-effect model with Bonferroni post-hoc test comparing CG and EG at different phases during the study, **** p ≤ 0.0001 (detailed statistics in Tab. S5). (H) Significant correlation between body weight/BMI and MTVS of lunch and dinner. The more participants improved their regularity of lunch and dinner (decreasing MTVS), the more weight/BMI they lost. Linear regression, CG: n=33; EG: n=67, ** p ≤ 0.01 (detailed statistics in Tab. S6). (I) Correlation between baseline BMI at T1 and change in BMI in EG participants. Linear regression, n=67 (detailed statistics in Tab. S6). (J) Between group differences after stratification according to different baseline BMIs. 2-way repeated-measure ANOVA with Bonferroni post-hoc test, *** p ≤ 0.001 (detailed statistics in Tab. S8). (K) Raw data of change in caloric intake during intervention. 2-way repeated-measure ANOVA with Bonferroni post-hoc test, CG: n=30; EG: n=67, * p ≤ 0.05, (detailed statistics in Tab. S3). (L) Correlation between reported ingested energy during the exploration phase vs. the intervention phase. Linear regression, CG: n=30; EG: n=67 (some participants were excluded from this analysis because of several erroneous diary entries about unrealistic amounts of food), (detailed statistics in Tab. S6). (M) Determined and estimated cumulative intake of fat, carbohydrates, and proteins during the study. Mixed-effects model with Bonferroni post hoc test comparing determined and estimated cumulative energy intake. The estimated macronutrient intake is formed as an assumed continuation of the average daily intake during the exploration phase. The Bonferroni post hoc test showed no significant differences on any study day. (N) No significant correlation between body weight/BMI and changes of cumulative macronutrient intake. Linear regression, CG: n=30; EG: n=67, (detailed statistics in Tab. S6). (K, L, M, N) Some participants were excluded from this analysis because of several erroneous diary entries about unrealistic amounts of food. (O) The absolute deviation between the times of weekend meals and the times of food intake calculated for the EG intervention did not affect the subjects’ BMI change. Linear regression, n=67 (detailed statistics in Tab. S6).

Baseline characteristics of final 100 participants.

Statistical data on the difference between completers and study drop-outs. The data in the table refers to the data shown in Fig. S2A.

Statistical data from all Two-way-RM ANOVAs analyzing time, group, as well as interaction effects between time x group. In data for Figure 1, missing p-values in the and EG are due to the different number of meals for each participant. In the data for Figure 2, some participants were excluded from this analysis because of several probably erroneous diary entries about unrealistic amounts of food. In data for Figure 3, varying n-numbers result from incomplete entries in the diaries. In data for Figure 4, missing data are due to incomplete questionnaires.

Statistical data from the development of normalized body weight and BMI of participants during the exploration and the intervention phase, and of follow-up data of continuing and discontinuing participants. At T3, three participants could no longer be reached, which is why the n-number deviates here. The data in the table refers to the data shown in Figures 1E and S2A.

Statistical data from the development of normalized body weight and BMI of participants at the different phases of the study. At T3 only continuing participants were included, which is why the n-number deviates here from the other time points. The data in the table refers to the data shown in Figures 1F, S2C, and S2G.

Statistical data from all simple regression. The data in the table refers to the data shown in Figs. 3A, B, and C. In data for Figures 2B, D, and S2H, Some participants were excluded from this analysis because of several probably erroneous diary entries about unrealistic amounts of food. In data for Figures 3B-D, varying n-numbers result from incomplete entries in the diaries. In date for Figures 3E, G, J, and S2I, missing n-numbers are due to incomplete diary entries on weekends during the exploratory phase or because participants usually did not have a particular meal.

Association of weekly MTVS with weekly weight loss. The table shows the weekly weight change of all participants during the exploration and the intervention phase while adhering to certain MTVSs in each week. 1-way ANOVA with Bonferroni post-hoc test comparing the mean of each row with the mean of the first row, * p ≤ 0.05.

Statistical data from BMI changes depending of the baseline BMI of each participant. The data in the table refers to the data shown in Figure S2J.

Statistical data from multiple regression analysis testing the effects of different variables while keeping the others constant. The data in the table refers to the data shown in Figures 1H and 3K.

Statistical data from Rayleigh’s uniformity test analyzing phase distribution from the relation between midSleep Phase and midEat Phase. Missing n-numbers are due to incomplete diary entries on weekends during the exploratory phase. The data in the table refers to the data shown in Fig. 3F.

Statistical data on shifts in weekend eating times caused by the change to calculated eating times in the intervention phase. Missing n-numbers are due to incomplete diary entries on weekends during the exploratory phase or because participants usually did not have a particular meal. The data in the table refers to the data shown in Fig. 3I.

Questionnaires collected at T0 and T2 to assess general well-being of participants.