# Analysis plan: is there a severity threshold above which bodily load relates differently to depressive symptoms?

## Question

If mild-to-moderate and severe depression are different attractor states rather than points on one continuum, relationships between bodily load and symptom severity should change above a threshold: a steeper slope, with thresholds at similar severity across measures, and a coupling between bodily load and somatic symptoms that strengthens in people functionally impaired by their symptoms. If depression is one continuum, linear relationships should fit as well.

## Data

NHANES 2005-2010 adults (20 years and over) with all nine PHQ-9 items, fetched by digest from the CDC; the loader and measure definitions are those of an earlier registered analysis on the same data (prereg:636c7bedc188ab341b642755cca338661a6363a493d614212d329c2e64d74ef8), copied unchanged as `code/nhanes.py`. That analysis reported linear partial correlations of these measures with somatic and cognitive-affective symptom scores; no breakpoint or severity-band analysis was done. Before registering, we counted adults per PHQ-9 band (0-4: 11,179; 5-9: 2,269; 10-14: 809; 15-19: 345; 20-27: 120) and ran the code with PHQ answers shuffled across participants to check that it executes.

## H1 (primary): breakpoints (`code/breakpoint.py`)

For each load measure (load-bearing limitation, nine-marker allostatic load, BMI): Y = age + age² + male + survey cycle + b1·PHQ + b2·max(0, PHQ − c), with c on the integer grid 8 to 22. Statistic: the largest t of b2 over the grid (one-sided: steeper above c). p-value: wild bootstrap (999 Rademacher replicates of the linear-model residuals, recomputing the statistic). Holm across the three measures. Supported if Holm p < 0.05.

**Negative control:** the same procedure on standing height, which should show no break. If height shows a break at p < 0.05, the method is judged unreliable and H1 results are not interpreted as evidence for a threshold.

**Coincidence (descriptive):** the estimated breakpoints of the three measures are reported; a common threshold is suggested if those with significant breaks lie within three PHQ points of each other.

## H2 (secondary): functional-impairment strata

PHQ item 10 (how difficult symptoms have made work, home or relationships; not part of the total; asked when any symptom is present) defines high (very or extremely difficult) and lower (not at all or somewhat difficult) strata. In each, the partial Spearman correlation of load-bearing limitation with somatic symptoms adjusting for cognitive-affective symptoms, age and sex; one-sided bootstrap test that it is larger in the high stratum (2,000 resamples).

## Limits stated in advance

Cross-sectional; severity is self-reported over two weeks; few adults above 20 points, so breakpoints near the top of the grid are imprecise; nonlinearity can arise from the PHQ's scoring and floor rather than from biology (hence the control); breakpoints in population averages need not reflect transitions within individuals; hysteresis and early warning signals cannot be tested.