Specification of TOT regression models
REGRESSION, REGRESSIONS
We tested TOT effects using two-stage least squares IV regression. IV regression is a method commonly used to reduce the impact of confounding in association analysis. It can also be applied to account for contamination/nonadherence in randomized trialsIn our analysis, we used IV regression to estimate the effect of 20% CR on change in measures of biological aging. We focused on a CR dose of 20% instead of the 25% dose prescribed in the trial because few individuals achieved 25% CR, especially through the 24-month follow-up. The 20% CR level represented the 75th percentile of the treatment group CR distribution at 12-month follow-up and the 87th percentile of the treatment group CR distribution at 24-month follow-up.The IV approach we used involved two related regressions. The first regression modeled observed treatment dose (%CR relative to baseline) on pretreatment characteristics and the instrument of randomization condition. The second regression modeled the outcomes (changes in measures of biological aging) as functions of the predicted treatment dose estimated by the first regression and pretreatment covariates.We developed our IV regression model by first modeling intervention group participants’ achieved CR treatment dose as a function of pretreatment covariates: chronological age, sex, BMI, study site. We fitted a saturated regression model including interactions among all pretreatment characteristics and additional covariate adjustment for race/ethnicity, which was included only as a main effect. (Race/ethnicity was omitted from the interaction terms because there was insufficient site- and sex-specific variation in race/ethnicity to fit models.) This analysis identified sex, baseline BMI and their interaction as statistically significant predictors of CR dose at the alpha = 0.05 level.Next, we parameterized our IV regression specifying the first stage to include the ‘instruments’ of intervention group and interactions of intervention group with sex, pretreatment BMI and a three-way interaction between intervention condition, sex and pretreatment BMI. The base first-stage regression took the formSupplementary Fig. 