Hundreds of multiple linear regression models

Question

I have high dimensional data (1000 genes for 100 patients). I have few clinical parameters for this data, some demographic data and some different metal levels in blood. In trying to evaluate how each gene responds, I'm trying to fit multiple linear regression using all these clinical, demographic and metal parameters, using gene as my outcome variable. Since I have 1000's of these genes, I am not sure how to go about model selection. Some genes differentiate on race, some on other factors. Some have very low $R^2$ values, I tried to see a few dozens. I am trying to perform univariate analysis to eliminate few genes which are not useful and then take the rest for the multivariate approach.

Answer 1

You could decrease dimensionality of the gene data using an ordination (eg PCA, NMDS). If you can extract a reasonable reduced-dimensionality structure, a few primary-axes loadings can be used for further testing (eg PC loadings in MR, beware of cross-correlations in demographic data).

Or, could use direct ordination approaches such as CCA to relate the primary (gene) and the secondary (clinical parameters) matrices. It all depends on how exactly you formulate your question.

Alternatively, you can do eg Random Forest analyses to choose the best gene predictors for each of the clinical parameters, if that's what you are interested in, or even feed your covariates in with the gene data to select the best model for metal predictors. In any case, this would be way too many repeated univariate analyses.