The German National Cohort (NAKO) is a population-based prospective cohort that recruited 205,415 men and women aged 20–75 years across 18 study centers in urban, industrialized, and rural regions of Germany. The study’s design has been described elsewhere [24]. Participants were randomly selected through an age- and sex-stratified sampling process, with 10,000 participants per 10-year age group from 20 to 39 years, and 26,667 per group aged 40–69 years. The baseline response proportion was 17%. Baseline assessments included touchscreen questionnaires, interviews, physical and functional measurements, and biosample collection. In an extended examination module, 70,005 participants wore a triaxial accelerometer over a period of seven days. Ethics approval was obtained from relevant local committees. All participants provided written informed consent.

We excluded participants without valid accelerometry data (<16 h of wear time per day, no valid weekend day and <2 valid weekdays), underweight individuals (BMI < 18.5 kg/m2), and those with missing outcome data, resulting in 61,114 participants for analysis (Supplementary Fig. 1).

We measured physical activity using triaxial ActiGraph models (GT3X + , wGT3X + , and wGT3X-BT; ActiGraph, Pensacola, FL, USA). The device was worn on the right hip during usual activities, starting the day following the visit for seven full days of measurement. To be precise, participants were instructed to wear the device throughout the day and perform their activities as usual. The device should only be removed when in contact with water for more than 30 min. Data processing details are described elsewhere [25]. The mean amplitude deviation (MAD), a measure of physical activity volume, was calculated from the raw data, aggregated to hourly averages, and expressed in milligravity (mg) units. MAD may be superior to other common metrics for hip-worn data as it is less sensitive to calibration errors [26, 27].

We divided physical activity into sex- and age-specific (5-year increments) quartiles of total activity during the day (06:00–23:59) and night (00:00–06:00). Daytime was further divided into morning (06:00–11:59), afternoon (12:00–17:59), and evening (18:00–23:59), consistent with previous methodologies [18, 20].

We examined the association between physical activity timing and the prevalence of obesity (BMI ≥ 30.0 kg/m2) and diabetes (self-report of previous physician’s diagnoses or HbA1c levels ≥6.5%), following World Health Organization guidelines [28]. BMI was calculated as weight divided by height in meters squared. Body height and weight were measured using the seca Stadiometer 274 and the seca Body Composition Analyzer (mBCA) 515, respectively, to the nearest 0.1 cm and 0.1 kg (secaGmbH & Co. KG, Hamburg, Germany), with participants in their underwear, without shoes. HbA1c was analyzed by means of high-performance liquid chromatography, capillary electrophoresis, immunoturbidimetry, or immunoassay on EDTA blood samples from all NAKO study centers using the Tosoh G8 and G11 HPLC Analyzer (Tosoh Bioscience Inc., San Francisco, USA), Hemoglobin Testing Systems (D-100, VariantTM II, VariantTM II Turbo; Bio-Rad Laboratories, Hercules, USA), DxC 800 (Beckman Coulter, Brea, USA), Cobas c502 (Roche Diagnostics, Rotkreuz, Switzerland), Capillarys (Sebia, Lisses, France), and Dimension Vista 1500 (Siemens Healthineers, Erlangen, Germany). We disregarded HbA1c levels above the 99th percentile to exclude extreme outliers.

We examined the relations of physical activity timing to obesity and diabetes, adjusting for sex, age, and study region (south-east, south-west, north-east, north-west, west, central Germany, and the Berlin area), education (still in school; primary school, lower or intermediate secondary school; completed vocational/company training; college entrance qualification/vocational completion; university degree or doctorate), employment (employed; unemployed; outside the labor force), risky alcohol use (no; yes; according to established screening thresholds, i.e., ≥4 points for men and ≥3 points for women in the Alcohol Use Disorders Identification Test-Consumption (AUDIT-C) [29]), smoking (never; former; current), night shift work (never/occasionally; regularly/always), and sleep duration ( ≤ 7 h; 7–9 h, ≥9 h; estimated from self-reported usual wake-up time and bedtime).

Statistical analyses included mean values, standard deviations, and Spearman correlation coefficients for physical activity across different time periods. We employed logistic regression models to estimate odds ratios (ORs) with 95% confidence intervals (CIs) for sex- and age-specific quartiles of physical activity in each time period in relation to obesity and diabetes. Model 1 was adjusted for sex, age, and study region, while model 2 further included education, employment, alcohol use, smoking, night shift work, and sleep duration. Missing covariate data were handled using the missing indicator method, where participants with missing covariates were not excluded but coded as missing to maintain statistical power.

We examined the synergy between daytime and nighttime physical activity by assessing the interaction on multiplicative and additive scales, the latter using the Relative Excess Risk due to Interaction (RERI) and the delta method [30]. To adjust for multiple comparisons, we applied Bonferroni correction (α/6). We estimated p-values using likelihood ratio tests and a 5% statistical significance level. Model fit was evaluated using R2 and the Akaike Information Criterion. Influential observations were analyzed using Cook’s distance, studentized residuals, and hat values [31], while the linearity assumption was checked with restricted cubic splines by testing whether the coefficients of the second and third spline transformations equaled zero [32].

To account for the compositional nature of physical activity during the day, we also examined the impact of substituting physical activity from one time period to another, following the approach of a previous study [33]. Specifically, we quantified the odds of obesity and diabetes when replacing 60 mg of morning activity with equivalent amounts of afternoon or evening activity. Daytime activity periods were standardized by dividing each time period-specific total physical activity by 60, equivalent to approximately one standard deviation of activity per period. Models were mutually adjusted for afternoon and evening activity, along with total daytime activity (sum of morning, afternoon, and evening). The ORs represent the effect of substituting one unit of morning activity with that from another period, rotating the reference period to obtain results for each.

We conducted additional analyses to test the robustness of our findings. First, we modeled time period-specific physical activity as a continuous measure to assess the shapes of the associations with obesity and diabetes. When the linearity assumption was violated, we used restricted cubic splines with knots at the 0.05, 0.35, 0.65, and 0.95 quantiles [32]. Second, we shifted the time periods back and forward by one hour to assess the robustness of the associations. Third, we stratified by employment status to consider the impact of work-related activity. Fourth, we analyzed participants who did not commonly work night shifts to rule out the influence of shift work on nighttime activity. Fifth, we assessed potential sex differences by stratifying the analyses by sex. Sixth, although we viewed BMI as a mediator in the association between physical activity timing and diabetes [34], we conducted an additional analysis including BMI as a covariate to assess its impact. Seventh, we used linear regression to evaluate the relations of physical activity timing to BMI and HbA1c as continuous variables. Eight, we restricted the diabetes analysis to HbA1c measurements from 12 NAKO study centers which were originally re-analyzed centrally to reassure data quality. Finally, we examined the influence of potential non-wear during the night by including the average number of measurement hours in the models as well as the midpoint of self-reported sleep to investigate the potential influence of sleep timing.

All analyses were performed using R version 4.2.3 [35]. Restricted cubic splines were modeled with the rms package [36].