# Inverted-U association between daily steps and WHO-5 in university students: non-linear modeling and robustness checks

## TL;DR

More daily steps improve well-being in university students up to about 8,000–12,000 steps, after which benefits level off.

## Contribution

This study identifies a non-linear, inverted-U relationship between daily steps and well-being in university students.

## Key findings

- Subjective well-being increased steeply up to ~8,650 steps/day and then plateaued.
- The plateau occurred near ~19,300 steps/day, with no significant benefit beyond 4,000 steps.
- Results were consistent across models, showing diminishing returns beyond ~8,000–12,000 steps.

## Abstract

Physical activity is linked to mental health, yet the dose–response shape remains debated.

In a cross-sectional sample of Chinese university students, 820 participants (mean age 21.5 years; 51.8% women) wore wrist accelerometers for 7 days. Subjective well-being (SWB) was measured with the WHO-5 (0–100). Restricted cubic spline models adjusted for age, sex, sleep quality, perceived stress, and socioeconomic status. Sensitivity analyses included quadratic and segmented models, trimming/winsorization, and E-value assessment. Peaks/plateaus were estimated via the delta method and bootstrap-BCa confidence intervals.

The steps–SWB association was non-linear (overall p<0.05). SWB rose steeply up to ~8,650 steps/day and then leveled off, with a statistical plateau near ~19,300 steps/day (bootstrap-BCa 95% CI: 7,997–17,896; delta-method 95% CI: 9,394–14,462). No contrast versus 4,000 steps/day exceeded the prespecified minimal clinically important difference (MCID=10 points). Findings were consistent across specifications; right-tail precision was limited due to few very high step counts.

Among university students, higher daily steps are associated with better SWB up to ~8,000–12,000 steps/day, beyond which benefits plateau with diminishing returns rather than harm. Results support range-based, progressive step guidance for student mental health. Please replace the current abstract with the structured IMRaD version provided above.