testIndClogit: Conditional independence test based on conditional logistic...

In MXM: Feature Selection (Including Multiple Solutions) and Bayesian Networks

Conditional independence test based on conditional logistic regression for case control studies

Description

The main task of this test is to provide a p-value PVALUE for the null hypothesis: feature 'X' is independent from 'TARGET' given a conditioning set CS. The pvalue is calculated by comparing a conditional logistic regression model based on the conditioning set CS against a model whose regressors are both X and CS. The comparison is performed through a chi-square test with the appropriate degrees of freedom on the difference between the deviances of the two models. This is suitable for a case control design

Usage

testIndClogit(target, dataset, xIndex, csIndex, wei = NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL)

permClogit(target, dataset, xIndex, csIndex, wei = NULL,  
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
threshold = 0.05, R = 999)

Arguments

target	A matrix with two columns, the first one must be 0 and 1, standing for 0 = control and 1 = case. The second column is the id of the patients. A numerical variable, for example c(1,2,3,4,5,6,7,1,2,3,4,5,6,7).
dataset	A numeric matrix or a data.frame in case of categorical predictors (factors), containing the variables for performing the test. Rows as samples and columns as features.
xIndex	The index of the variable whose association with the target we want to test.
csIndex	The indices of the variables to condition on. If you have no variables set this equal to 0.
wei	A vector of weights to be used for weighted regression. The default value is NULL and it should stay NULL as weights are ignored at the conditional logistic regression. See the survival package for more information about conditional logistic regression.
univariateModels	Fast alternative to the hash object for univariate test. List with vectors "pvalues" (p-values), "stats" (statistics) and "flags" (flag = TRUE if the test was succesful) representing the univariate association of each variable with the target. Default value is NULL.
hash	A boolean variable which indicates whether (TRUE) or not (FALSE) to use tha hash-based implementation of the statistics of SES. Default value is FALSE. If TRUE you have to specify the stat_hash argument and the pvalue_hash argument.
stat_hash	A hash object which contains the cached generated statistics of a SES run in the current dataset, using the current test.
pvalue_hash	A hash object which contains the cached generated p-values of a SES run in the current dataset, using the current test.
threshold	Threshold (suitable values in (0, 1)) for assessing p-values significance.
R	The number of permutations, set to 999 by default. There is a trick to avoind doing all permutations. As soon as the number of times the permuted test statistic is more than the observed test statistic is more than 50 (if threshold = 0.05 and R = 999), the p-value has exceeded the signifiance level (threshold value) and hence the predictor variable is not significant. There is no need to continue do the extra permutations, as a decision has already been made.

Details

If hash = TRUE, testIndClogit requires the arguments 'stat_hash' and 'pvalue_hash' for the hash-based implementation of the statistic test. These hash Objects are produced or updated by each run of SES (if hash == TRUE) and they can be reused in order to speed up next runs of the current statistic test. If "SESoutput" is the output of a SES run, then these objects can be retrieved by SESoutput@hashObject$stat_hash and the SESoutput@hashObject$pvalue_hash.

Important: Use these arguments only with the same dataset that was used at initialization. For all the available conditional independence tests that are currently included on the package, please see "?CondIndTests".

This is for case control studies. The log-likelihood for a conditional logistic regression model equals the log-likelihood from a Cox model with a particular data structure. When a well tested Cox model routine is available many packages use this "trick" rather than writing a new software routine from scratch, and this is what the "clogit" function in the "survival" package does. In detail, a stratified Cox model with each case/control group assigned to its own stratum, time set to a constant, status of 1=case 0=control, and using the exact partial likelihood has the same likelihood formula as a conditional logistic regression. The "clogit" routine creates the necessary dummy variable of times (all 1) and the strata, then calls the function "coxph".

Note that this function is a bit sensitive and prone to breaking down for some reason which I have not yet figured out. In case of singular design matrix it will work, it identifies the problem and handles it internally like most regression functions do. However, problems can still occur.

Value

A list including:

pvalue	A numeric value that represents the logarithm of the generated p-value due to the conditional logistic regression (see reference below).
stat	A numeric value that represents the generated statistic due to the conditional logistic regression (see reference below).
stat_hash	The current hash object used for the statistics. See argument stat_hash and details. If argument hash = FALSE this is NULL.
pvalue_hash	The current hash object used for the p-values. See argument stat_hash and details. If argument hash = FALSE this is NULL.

Author(s)

Vincenzo Lagani, Ioannis Tsamardinos, Giorgos Athineou and Michail Tsagris

R implementation and documentation: Giorgos Athineou <[e-mail]>, Vincenzo Lagani <[e-mail]> and Michail Tsagris [e-mail]

References

Michell H. Gail, Jay H. Lubin and Lawrence V. Rubinstein (1980). Likelihood calculations for matched case-control studies and survival studies with tied death times. Biometrika 68:703-707.

See Also

SES, testIndLogistic, censIndCR, censIndWR

Examples

#simulate a dataset with continuous data
dataset <- matrix( rnorm(100 * 7), nrow = 100 ) 
#the target feature is the last column of the dataset as a vector
case <- rbinom(100, 1, 0.6)
ina <- which(case == 1)
ina <- sample(ina, 50)
case[-ina] = 0 
id <- rep(1:50, 2)
target <- cbind(case, id)

results <- testIndClogit(target, dataset, xIndex = 4, csIndex = 1)
results

#run the SES algorithm using the testIndClogit conditional independence test
a <- MMPC(target, dataset, max_k = 3, threshold = 0.01, test = "testIndClogit")

MXM documentation built on Aug. 25, 2022, 9:05 a.m.