# Bioinformatics 2018 - Distinguishing prognostic and predictive biomarkers: An information theoretic approach 

Information theoretic predictive biomarker ranking 

**Date:** 02/02/2018

**Paper:** Distinguishing prognostic and predictive biomarkers: An information theoretic approach 

**Authors:** Konstantinos Sechidis, Konstantinos Papangelou, Paul D. Metcalfe, David Svensson, James Weatherall and Gavin Brown

**Platform:** R Version 3.3.1

**Required packages:** MASS, infotheo

**Maintainer:** Konstantinos Sechidis konstantinos.sechidis@manchester.ac.uk

**Description:** Deriving rankings that capture the predictive biomarker strength through univariate (INFO) or higher-order (INFO+) methods

**Functions:**

```INFOplus.Output_Categorical.Covariates_Categorical(data,labels,treatment,top_k)$ranking``` 

This function returns the predictive ranking, the input arguments are

**data:** A matrix containing the covariates (biomarkers). The columns capture the different covariates, while the rows the different examples (patients). For this function the covariates are categorical (nominal).

**labels:** A vector that contains the output (target) label for each patient, in this case it takes categorical (nominal) values.

**treatment:** A vector that describes the treatment allocation (i.e. T=0 control group, T=1 experimental treatment).

**top_k:** The number of top-k predictive biomarkers to be returned.

Furthermore we provide functions that can be used for various data types:

```INFOplus.Output_Categorical.Covariates_Continuous```:  The covariates can be either all continuous or mixed (continuous and categorical). To discretise continuous covariates we follow by default Scott's rule.

```INFOplus.Output_Survival.Covariates_Categorical```: For survival (time-to-event) output targets and categorical covariates.

```INFOplus.Output_Survival.Covariates_Categorical```: For survival (time-to-event) output targets and continuous or mixed (continuous and categorical) covariates.

Finally, we provide the same functions for deriving the uni-variate INFO ranking.

Example

We provide a source code (```Functions-GenerateData.R```) to generate the synthetic scenarios presented in the paper. The following example shows how to derive the predictive rankings using our code.

```

## Load libraries

library(MASS) # To generate synthetic data by sampling a Multivariate Normal

library(infotheo) # Information theoretic library  

## Load sources

source("Functions-GenerateData.R") # Function to generate synthetic data

source("InformationTheory-PredictiveRankings.R") # Functions to derive predictive rankings

###################################

##### Generate synthetic data #####

###################################

model <- 3 ;         # Which model to use (1, 2, 3, 4, 5, 6, 7) - details on the paper

theta_pred <- 1      # Strength of predictive part

num_features <- 20   # Number of covariates

sample_size <- 2000  # Number of examples

dataset <- Generate.Data(sample_size,num_features,theta_pred,model)

# The methods will return the top-k biomarkers

top_k <-5

####################################################### 

# Ranking the biomarkers on their predictive strength #

#######################################################

# INFO, which captures first order interactions (returns the top_k = 5 biomarkers)

INFO.Output_Categorical.Covariates_Categorical(dataset$data,dataset$labels,dataset$treatment)$ranking[1:top_k] # this function returns the ranking

# INFO+, which captures second order interactions (returns the top_k = 5 biomarkers)

INFOplus.Output_Categorical.Covariates_Categorical(dataset$data,dataset$labels,dataset$treatment,top_k)$ranking # this function returns the ranking

```