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"model adjusting for" is correct and usable in written English.
This phrase is typically used in academic writing when referring to a statistical model or other analytical model that has been altered to control the outcome for certain variables. For example, "The study used a multivariate regression model adjusting for education and income levels."
Exact(60)
Adjusted comparisons were performed using a general linear model, adjusting for age, sex, and percent of total body fat.
The primary outcome was compared using a mixed linear model, adjusting for the period effect.
The interaction term was included in a multivariate logistic model adjusting for design variables in the TTM-trial.
With 95% pointwise confidence limits as estimated by a random intercept model adjusting for age (reference, mean age = 53 years).
Relationship between ARF etiology and hospital mortality was assessed using a multivariable regression model adjusting for confounders.
We compared the outcomes of these binary variables of complication and transfusion using a working Poisson regression model adjusting for covariates.
The data was matched for gender and we used a linear regression model, adjusting for age, to compare the normal population data with the trial data.
In a longitudinal model adjusting for sociodemographic covariates only (Model 1), depression was associated with a threefold increased risk of CM onset.
A multivariate model adjusting for age, sex and study centre confirmed these general trends in prevalence (Figure 1).
We modelled the proband (parent, sibling, spouse) survival utilizing a multivariate proportional hazard (Cox) model adjusting for possible confounders of survival.
Furthermore, ANG-1 (but not TNF) was independently associated with CM in a multivariate logistic regression model, adjusting for the potential confounding effects of multiple covariates (Table 5).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com