censIndCR: Conditional independence test for survival data

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

Conditional independence test for survival data

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. This test can based on the Cox (semi-parametric) regression or on the Weibull (parametric) regression.

Usage

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

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

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

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

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

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

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

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

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

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

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

Arguments

target	A Survival object (class Surv from package survival) containing the time to event data (time) and the status indicator vector (event). View Surv documentation for more information.
dataset	A numeric matrix or data frame, in case of categorical predictors (factors), containing the variables for performing the test. Rows as samples and columns as features. In the cases of "waldCR", "waldWR", "waldER", "waldCR", "permWR", "permER" and "permLLR" this is strictly a matrix.
xIndex	The index of the variable whose association with the target we want to test.
csIndex	The indices of the variables to condition on.
wei	A vector of weights to be used for weighted regression. The default value is NULL. An example where weights are used is surveys when stratified sampling has occured.
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 the 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 (in this example case), 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

The censIndCR implies the Cox (semiparametric) regression, the censIndWR the Weibull (parametric) regression and the censIndER the exponential (parametric) regression, which is a special case of the Weibull regression (when shape parameter is 1). Note: When there are observations with zero values (time=0) the Weibull and Exponential regressions will not work. Only Cox regression will run. The censIndLLR is the log-logistic regression. This is a pure AFT model, unlike Weibull which is either a proportional hazards model or and AFT.

If hash = TRUE, censIndCR, censIndWR, censIndER and censIndLLR require 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".

The log-likelihood ratio test used in "censIndCR", "censIndWR" and "censIndER" requires the fitting of two models. The Wald tests used in "waldCR", "waldWR" and "waldER" requires fitting of only one model, the full one. The significance of the variable is examined only. Only continuous (or binary) predictor variables are currently accepted in this test.

Value

A list including:

pvalue	A numeric value that represents the logarithm of the generated p-value.
stat	A numeric value that represents the generated statistic.
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.

Note

This test uses the functions coxph and Surv of the package survival and the function anova (analysis of variance) of the package stats.

Author(s)

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

References

V. Lagani and I. Tsamardinos (2010). Structure-based variable selection for survival data. Bioinformatics Journal 16(15): 1887-1894.

Cox,D.R. (1972) Regression models and life-tables. J. R. Stat. Soc., 34, 187-220.

Scholz, F. W. (2001). Maximum likelihood estimation for type I censored Weibull data including covariates. ISSTECH-96-022, Boeing Information & Support Services.

Smith, R. L. (1991). Weibull regression models for reliability data. Reliability Engineering & System Safety, 34(1), 55-76.

See Also

SES, censIndWR, testIndFisher, gSquare, testIndLogistic, Surv, anova, CondIndTests

Examples

#create a survival simulated dataset
dataset <- matrix(runif(400 * 20, 1, 100), nrow = 400 , ncol = 20)
dataset <- as.data.frame(dataset);
timeToEvent <- numeric(400)
event <- numeric(400)
ca <- numeric(400)
for(i in 1:400) {
  timeToEvent[i] <- dataset[i, 1] + 0.5 * dataset[i, 10] + 2 * dataset[i, 15] + runif(1, 0, 3);
  event[i] <- sample( c(0, 1), 1)
  ca[i] <- runif(1, 0, timeToEvent[i] - 0.5)
  if(event[i] == 0)   timeToEvent[i] = timeToEvent[i] - ca[i]
}

require(survival, quietly = TRUE)

#init the Surv object class feature
target <- Surv(time = timeToEvent, event = event)
#run the censIndCR   conditional independence test
censIndCR( target, dataset, xIndex = 12, csIndex = c(5, 7, 4) )
# run the SESC algorithm 
## Not run: 
ses1 <- SES(target, dataset, max_k = 1, threshold = 0.05, test = "censIndCR");
ses2 <- SES(target, dataset, max_k = 1, threshold = 0.05, test = "censIndWR");

## End(Not run)

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