Data

We use the Bioconductor packages GEOquery and Biobase for obtaining the data \((\approx 150\)MB\()\):

#install.packages("BiocManager")
#BiocManager::install(c("GEOquery","Biobase"))
data <- GEOquery::getGEO(GEO="GSE80599")[[1]]
pheno <- Biobase::pData(data)
y <- as.numeric(pheno$`updrs-mds3.12 score:ch1`)
age <- as.numeric(pheno$`age at examination (years):ch1`)
gender <- ifelse(pheno$`gender:ch1`=="Female",1,0)
X <- cbind(age,gender,t(Biobase::exprs(data)))

The vector \(\boldsymbol{y}\) of length \(n\) represents the outcome, and the matrix \(\boldsymbol{X}\) with \(n\) rows and \(p\) columns represents the features. The first two columns include demographic variables (age, gender), and the other columns include the gene expression data.

Filter

We test for marginal association between the ordinal outcome and the features. The smallest adjusted \(p\)-values is insignificant, and the \(p\)-value distribution is not right-skewed. There is probably not much signal in the data.

pvalue <- apply(X,2,function(x) cor.test(x,y)$p.value)
min(p.adjust(pvalue))
hist(pvalue)

We filter the features to artificially increase the signal-to-noise ratio. This filtering leads to bias and overfitting, and must not be done in practical applications!

cor <- abs(cor(y,X,method="spearman"))
X <- X[,cor>0.3] # forbidden!

Model

We use the function cornet for modelling the artifial binary outcome. The argument cutoff splits the samples into two groups, those with an outcome less than or equal to the cutoff, and those with an outcome greater than the cutoff.

model <- cornet(y=y,cutoff=0,X=X)
model

The function coef returns the estimated coefficients. The first column is for the linear model (beta), and the second column is for the logistic model (gamma). The first row includes the estimated intercepts, and the other rows include the estimated slopes.

coef <- coef(model)

The function predict returns fitted values for training data, or predicted values for testing data. The argument newx specifies the feature matrix. The output is a matrix with one column for each model.

predict <- predict(model,newx=X)

The function cv.cornet measures the predictive performance of combined regression by nested cross-validation, in comparison with logistic regression.

cv.cornet(y=y,cutoff=0,X=X)

Here we observe that combined regression outperforms logistic regression (lower logistic deviance). Logistic regression is only slightly better than the intercept-only model.