Hello Mr Oviedo-Trespalacios, I read the Aust and New Z J of Public Health journals so fi I come across any articles of interest I will email you. Thanks
Sort of depends on how you've modelled your independent variable. But there are three main presentation techniques that I use.
1. A table, where each row corresponds to one of the models and the columns correspond to model parameters, such as the Odds ratios, 95% CIs, number of cases & controls, name of outcome variable and p value. see table 2 in the linked reference to get a rough idea. In this example, the independent variable is a continuous variable that has been broken up into quintiles (5 dummy variables). If your independent variable has been modelled continuously with a single parameter in the model, then you would have only one column for each ORs (95% CI).
2. A forest plot, where you plot the odds ratios & 95% CIs for each disease. The x axis is the odds ratio & 95% CI. The y axis is just each model/outcome variable. See Figure 2 in the linked reference. Ignore the fact that the figure is modelling a genetic effect. Each row in my figure happens to be a study name. In your example, each row would be one of your models.
3. If your variable is continuous and if you're interested in the shape of the association between the independent variable and the outcome variable, you could do a scatter plot of the odds ratios by different levels of the independent variable. You could superimpose all your models on the same scatter plot. See Figure 1 in the linked reference. Ignore the fact that the Y axis is a hazard ratio. In your case the Y axis would be an odds ratio.
if the response variables are related in some way, for instance if they are different variables corresponding to the same process or representing different quantifications of similar concepts, you should consider the possibility of applying some sort of dimension reduction technique on them, most likely PCA (Principal Component Analysis), and then perform logistic regression addressing the one or two main principal components to your independent variables.