I am working on a logistic regression approach to predict the clinical status of patients (No disease vs Disease). I already have quite strong evidence indicating that the number of genes hit by a certain kind of variation is significant in predicting disease. Among the genes that I am considering, one of them (gene A) apparently plays a central role: I would like to investigate if the effect caused by the number of genes involved is driven by "gene A + others" combinations or "any multiple genes combination". I developed a model with the 3 independent dummy variables geneA.alone (T if a sample has variation only in gene A), geneA.plus.others (T if a sample has variation in gene A and other gene(s)), and only.others (T if a sample has variation in one or more genes, but not in gene A).
I performed two nested model comparisons using the anova() function in R:
anova(glm(Status~geneA.alone,...),glm(Status~geneA.alone+geneA.plus.others,...), test="Chisq") anova(glm(Status~geneA.alone+geneA.plus.others,...), glm(Status~geneA.alone+geneA.plus.others+only.others,...),test="Chisq")
In both cases I observe an improvement of the model fit, with a significant p-value (in the order of e-5 / e-6). So, my first conclusion was that, when multiple genes are involved, it is not only the combinations "geneA+other(s)" that are important in determining disease, but also those not involving gene A. However, I am really doubting that this is the right way to investigate it:
- Does it make sense to have three mutually exclusive variables as predictors? Can they be considered as independent variables? My feeling is that the significant p-values are a natural consequence of the fact that, by using mutually exclusive predictors, I deliberately subtract part of the information from a variable, and shift it to another...hance the significance.
- Would it be more appropriate to use only the variables number.of.genes (numeric) and geneA.involved (T/F), and compare the model
Status~n.of.genes*geneA.involved? My thought, in this case, is that if the second model results in a significantly better fit, it may be a demonstration that the n.of.genes is important only if geneA is involved...does it make sense?
Any help would be greatly appreciated! Thank you!