Combination {IntegratedMRF}

Weights for combination of predictions from different data subtypes using Least Square Regression based on various error estimation techniques

Description

Calculates combination weights for different subtypes of dataset combinations to generate integrated Random Forest (RF) or Multivariate Random Forest (MRF) model based on different error estimation models such as Bootstrap, 0.632+ Bootstrap, N-fold cross validation or Leave one out.

Usage

Combination(finalX, finalY_train, Cell, finalY_train_cell, n_tree, m_feature,
  min_leaf, Confidence_Level)

Arguments

finalX

List of Matrices where each matrix represent a specific data subtype (such as genomic characterizations for drug sensitivity prediction). Each subtype can have different types of features. For example, if there are three subtypes containing 100, 200 and 250 features respectively, finalX will be a list containing 3 matrices of sizes M x 100, M x 200 and M x 250 where M is the number of Samples.

finalY_train

A M x T matrix of output features for training samples, where M is number of samples and T is the number of output features. The dataset is assumed to contain no missing values. If there are missing values, an imputation method should be applied before using the function. A function 'Imputation' is included within the package.

Cell

It contains a list of samples (the samples can be represented either numerically by indices or by names) for each data subtype. For the example of 3 data subtypes, it will be a list containing 3 arrays where each array contains the sample information for each data subtype.

finalY_train_cell

Sample names of output features for training samples

n_tree

Number of trees in the forest, which must be positive integer

m_feature

Number of randomly selected features considered for a split in each regression tree node, Valid Input is a positive integer, which is less than N (which is equal to number of input features for the smallest genomic characterization)

min_leaf

Minimum number of samples in the leaf node, which must be positive integer and less than or equal to M (number of training samples)

Confidence_Level

Confidence level for calculation of confidence interval (User Defined), which must be between 0 and 100

Details

The function takes all the subtypes of dataset in matrix format and its corresponding sample information. For calculation purpose, we have considered the data of the samples that are common in all the subtypes and output training responses. For example, consider a dataset of 3 sub-types with different number of samples and features, with indices of samples in subtype 1, 2, 3 and output feature matrix is 1:10, 3:15, 5:16 and 5:11 respectively. Thus, features of sample index 5:10 (common to all subtypes and output feature matrix) of all subtypes and output feature matrix will be selected and considered for all calculations.

For M x N dataset, N number of bootstrap sampling sets are considered. For each bootstrap sampling set and each subtype, a Random Forest (RF) or, Multivariate Random Forest (MRF) model is generated, which is used for calculating the prediction performance for out-of-bag samples. The prediction performance for each subtype of the dataset is based on the averaging over different bootstrap training sets. The combination weights (regression coefficients) for each combination of subtypes are generated using least Square Regression from the individual subtype predictions and used later to calculate mean absolute error, mean square error and correlation coefficient between predicted and actual values.

For N-fold cross validation error estimation with M cell lines, N models are generated for each subtype of dataset, where for each partition (M/N)*(N-1) cell lines are used for training and the remaining cell lines are used to estimate errors and combination weights for different data subtype combinations.

In 0.632 Bootstrap error estimation, bootstrap and re-substitution error estimates are combined based on 0.632xBootstrap Error + 0.368xRe-substitution Error. While 0.632+ Bootstrap error estimation considers the overfitting of re-substitution error with no information error rate \gamma. An estimate of \gamma is obtained by permuting the responses y[i] and predictors x[j].

\gamma=sum(sum(error(x[j],y[i]),j=1,m),i=1,m)/m^2

The relative overfitting rate is defined as R=(Bootstrap Error-Resubstitution Error)/(\gamma-Resubstitution Error) and weight distribution between bootstrap error and Re-substitution Error is defined as w=0.632/(1-0.368*R). So, 0.632+ Bootstrap error is equal to (1-w)*Bootstrap Error+w*Resubstitution Error. These prediction results are then used to compute the errors and combination weights for different data subtype combinations.

Confidence Interval has been calculated using Jackkniffe-After-Bootstrap Approach and prediction result of bootstrap error estimation.

For leave-one-out error estimation using M cell lines, M models are generated for each subtype of dataset, which are then used to calculate the errors and combination weights for different data subtype combinations.

Value

List with the following components:

BSP_coeff

Combination weights using Bootstrap Error Estimation Model, where index is in list format. If the number of genomic characterizations or subtypes of dataset is 5, there will be 2^5-1=31 list of weights

Nfold_coeff

Combination weights using N fold cross validation Error Estimation Model, where index is in list format. If the number of genomic characterizations or subtypes of dataset is 5, there will be 2^5-1=31 list of weights

BSP632plus_coeff

Combination weights using 0.632+ Bootstrap Error Estimation Model, where index is in list format. If the number of genomic characterizations or subtypes of dataset is 5, there will be 2^5-1=31 list of weights

LOO_coeff

Combination weights using Leave-One-Out Error Estimation Model, where index is in list format. If the number of genomic characterizations or subtypes of dataset is 5, there will be 2^5-1=31 list of weights

Error

Matrix of Mean Absolute Error, Mean Square Error and correlation between actual and predicted responses for integrated model based on Bootstrap, N fold cross validation, 0.632+ Bootstrap and Leave-one-out error estimation sampling techniques for the integrated model containing all the data subtypes

Confidence Interval

Low and High confidence interval for a user defined confidence level for the drug using Jackknife-After-Bootstrap Approach in a list

BSP_error_all_mae

Bootstrap Mean Absolute Errors (MAE) for all combinations of the dataset subtypes. Size C x R, where C is the number of combinations and R is the number of output responses. C is in decreasing order, which means first value is combination of all subtypes and next ones are in decreasing order. For example, if a dataset has 3 subtypes, then C is equal to 2^3-1=7. The ordering of C is the combination of subtypes [1 2 3], [1 2], [1 3], [2 3], [1], [2], [3]

Nfold_error_all_mae

N fold cross validation Mean Absolute Errors (MAE) for all combinations of the dataset subtypes. Size C x R, where C is the number of combinations and R is the number of output responses. C is in decreasing order, which means first value is combination of all subtypes and next ones are in decreasing order. For example, if a dataset has 3 subtypes, then C is equal to 2^3-1=7. The ordering of C is the combination of subtypes [1 2 3], [1 2], [1 3], [2 3], [1], [2], [3]

BSP632plus_error_all_mae

0.632+ Bootstrap Mean Absolute Errors (MAE) for all combinations of the dataset subtypes. Size C x R, where C is the number of combinations and R is the number of output responses. C is in decreasing order, which means first value is combination of all subtypes and next ones are in decreasing order. For example, if a dataset has 3 subtypes, then C is equal to 2^3-1=7. The ordering of C is the combination of subtypes [1 2 3], [1 2], [1 3], [2 3], [1], [2], [3]

LOO_error_all_mae

Leave One Out Mean Absolute Errors (MAE) for all combinations of the dataset subtypes. Size C x R, where C is the number of combinations and R is the number of output responses. C is in decreasing order, which means first value is combination of all subtypes and next ones are in decreasing order. For example, if a dataset has 3 subtypes, then C is equal to 2^3-1=7. The ordering of C is the combination of subtypes [1 2 3], [1 2], [1 3], [2 3], [1], [2], [3]

The function also returns figures of different error estimations in .tiff format

References

Wan, Qian, and Ranadip Pal. "An ensemble based top performing approach for NCI-DREAM drug sensitivity prediction challenge." PloS one 9.6 (2014): e101183.

Rahman, Raziur, John Otridge, and Ranadip Pal. "IntegratedMRF: random forest-based framework for integrating prediction from different data types." Bioinformatics (Oxford, England) (2017).

Efron, Bradley, and Robert Tibshirani. "Improvements on cross-validation: the 632+ bootstrap method." Journal of the American Statistical Association 92.438 (1997): 548-560.

Examples

library(IntegratedMRF)
data(Dream_Dataset)
Tree=1
Feature=1
Leaf=5
Confidence=80
finalX=Dream_Dataset[[1]]
Cell=Dream_Dataset[[2]]
Y_train_Dream=Dream_Dataset[[3]]
Y_train_cell=Dream_Dataset[[4]]
Y_test=Dream_Dataset[[5]]
Y_test_cell=Dream_Dataset[[6]]
Drug=c(1,2,3)
Y_train_Drug=matrix(Y_train_Dream[,Drug],ncol=length(Drug))
Result=Combination(finalX,Y_train_Drug,Cell,Y_train_cell,Tree,Feature,Leaf,Confidence)