Fig. 1

All panels involve data from our weight-loss-maintenance trial [2, 10], with the exception of c, which comes from Hall et al. [17]. a, b Correlation between TEE at baseline and outcome was stronger using the post-weight-loss versus pre-weight-loss timepoint (Meng’s Z-test, p = 0.003), demonstrating why choice of the post-weight-loss timepoint would be preferable. c “Unaccounted energy” in a metabolic ward study of “ultra-processed” foods [17] calculated from online data (deltabc.sas7bdat), with each participant studied on two diets for 2-week periods with DLW measurement of TEE and DXA measurement of body composition. “Unaccounted energy” (kcal/day) was calculated as energy intake (variable names: ProcAveEI, UnprocAveEI) – TEE (DLWEEProcessed, DLWEEUnproc) – change in stored energy per day (BCEBProcessed, BCEBUnproc). Only 15 of 37 observations were within ±250 kcal/day. d Analysis modeled after b in Hall et al. [9] of “unaccounted energy,” with sequential elimination of 40 (vs 81) individuals with low TEE relative to energy intake (vs low energy intake relative to TEE) in our intention-to-treat group. The observed diet effect inflates (vs deflates), demonstrating the bias introduced by postrandomization exclusion involving variables linked to the primary outcome. Because assumptions of linear regression were not satisfied (a problem that also applies to the corresponding figure in Hall et al. [9]), we used LOESS to visualize the relationship between threshold and ΔTEE. e Diet effect by tertiles of energy intake to TEE ratio in the Per Protocol group. Individual data indicated by circles. Mean (horizontal line) and 95% CIs (vertical bars) derived from a model adjusted for post-weight-loss TEE and other covariates (cohort, sex, age, percent weight loss, post-weight-loss weight). The difference in diet effect across the tertiles diminishes with adjustment, demonstrating the confounding present in raw data segregated by energy intake to TEE ratio. (This adjustment for baseline covariates would not remedy bias arising from postrandomization biological or measurement variation.)