Generate odds ratios across deciles / quantiles of an indpendent variable With reference to the following figure from Bellomo et al., 2011:

How exactly are the odds ratios across the deciles 'referenced against the 4th decile' calculated? 
My initial impression is that a logistic model is constructed as such:
binary_outcome ~ 10_deciles_dummy_matrix + covariates + intercept

Where binary_outcome is a Nx1 vector of N samples, 10_deciles_dummy_matrix is a Nx10 matrix, and intercept is a Nx1 vector of 1s, covariates is a NxM matrix of M covariates.
Perhaps plotted in the figure is the coefficient (beta value) for each of the columns in the 10_deciles_dummy_matrix divided by the coefficient of the fourth decile (because they're referenced against the 4th decile).
However, the problem with such a model is that there is perfefct colinearity between 10_deciles_dummy_matrix and intercept. Also how would the standard errors scale given division of coefficient values with the 4th decile?
Since removing the intercept isn't an option, alternatively we can remove a decile (or a column) from 10_deciles_dummy_matrix, but then we are left with a missing decile in our plot (which can't be the fourt decile since we need something to reference against).
Leading to my question, what is the statistical procedure that has been performed to generate the above figure?
 A: PaO2 is a measure of pulmonary function. We are to assume whatever the outcome is here, it's bad, as very low PaO2 has a higher odds of something.
The study team has applied some bad statistical practices here: dividing up a strong predictor into an arbitrary number of percentiles and using odds ratios rather than risk ratios to summarize associations in what we must assume is a prospective study.
When fitting a categorical predictor, one category is chosen as a reference. The odds ratio summarizes association by taking the odds of an outcome for any of the other 9 categories versus a reference. Categorical predictors require a reference for dummy variable encoding by default.
They have chosen PaO2 range 83-93 as the "reference". When you calculate a predictor matrix, you drop indicators of membership to this group. The interpretation of the intercept is the odds of this "bad" outcome given your PaO2 is 83-93 (whatever the units are). Notice on the plot there is no bar for this category.
The odds ratios and their 95% CIs are estimated from logistic regression. "Adjusted" further includes (what we must assume) as possible confounders of association.
