Title:	Integrative Penalized Conditional Logistic Regression
Version:	2.0.0
Description:	Implements L1 and L2 penalized conditional logistic regression with penalty factors allowing for integration of multiple data sources. Implements stability selection for variable selection.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.2.3
Imports:	penalized, survival, clogitL1, stats
Suggests:	parallel, knitr, rmarkdown, tidyverse
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2023-07-20 17:25:05 UTC; veradj
Author:	Vera Djordjilovi'c [aut, cre], Erica Ponzi [aut]
Maintainer:	Vera Djordjilovi'c <vera.djordjilovic@unive.it>
Repository:	CRAN
Date/Publication:	2023-07-20 18:50:06 UTC

Default values for L1 penalty in conditional logistic regression

Description

Internal function that performs cross validation to determine reasonable default values for L1 penalty in a conditional logistic regression

Usage

default.lambda(X, Y, stratum, nfolds = 10, alpha = 1)

Arguments

Value

A numeric value for lambda minimizing cross validated deviance.

Data adaptive candidate vector of penalty factors for L1 penalty in conditional logistic regression with covariates divided in blocks

Description

Computes a data adaptive vector of penalty factors for blocks of covariates by fitting a tentative penalized conditional logistic regression model. The penalty for the ith block is obtained as the inverse of the arithmetic mean of coefficient estimates for its covariates.

Usage

default.pf(
  response,
  stratum,
  penalized,
  unpenalized = NULL,
  alpha = 1,
  p = NULL,
  standardize = TRUE,
  event,
  nfolds = 10,
  type.step1,
  verbose = FALSE
)

Arguments

Details

Blocks that contain covariates with large estimated coefficients will obtain a smaller penalty. If all estimated coefficients pertaining to a block are zero, the function returns a message. A tentative conditional logistic regression model is fit either to each covariates block separately (type.step1 = "sep") or jointly to all blocks (type.step1 = "comb"). Note that unpenalized = NULL is the only implemented option in this function as of now.

Value

The function returns a list containing the vector of penalty factors correspondng to different blocks.

References

Schulze G. (2017) Clinical Outcome Prediction based on Multi-Omics Data: Extension of IPF-LASSO. Master Thesis.

See Also

find.default.lambda

Default values for L1 penalty in conditional logistic regression

Description

Performs cross validation to determine reasonable values for L1 penalty in a conditional logistic regression.

Usage

find.default.lambda(
  response,
  stratum,
  penalized,
  unpenalized = NULL,
  alpha = 1,
  p = NULL,
  standardize = TRUE,
  event,
  pf.list = NULL,
  nfolds = 10
)

Arguments

Details

The function is based on cross-validation implemented in the clogitL1 package and returns the value of lambda that minimizes cross validated deviance. In the presence of blocks of covariates, a user specifies a list of candidate vectors of penalty factors. For each candidate vector of penalty factors a single lambda value is obtained. Note that cross-validation includes random data splitting, meaning that obtained values can vary significantly between different runs.

Value

A single numeric value if p and pf.list are missing, or a list of numeric values with L1 penalties for each vector of penalty factors supplied.

See Also

default.pf

Examples

set.seed(123)
# simulate covariates (pure noise in two blocks of 20 and 80 variables)
X <- cbind(matrix(rnorm(4000, 0, 1), ncol = 20), matrix(rnorm(16000, 2, 0.6), ncol = 80))
p <- c(20,80)
pf.list <- list(c(0.5, 1), c(2, 0.9))
# stratum membership
stratum <- sort(rep(1:100, 2))

# the response
Y <- rep(c(1, 0), 100)

# obtain a list with vectors of penalty factors

lambda.list <- find.default.lambda(response = Y,
                                   penalized = X, stratum = stratum, p = p, pf.list = pf.list)

# when `p` and `pf.list` are not provided all covariates are treated as a single block

lambda <- find.default.lambda(response = Y,
                                   penalized = X, stratum = stratum)

Penalized conditional logistic regression

Description

Fits conditional logistic regression models with L1 and L2 penalty allowing for different penalties for different blocks of covariates.

Usage

penalized.clr(
  response,
  stratum,
  penalized,
  unpenalized = NULL,
  lambda,
  alpha = 1,
  p = NULL,
  standardize = TRUE,
  event
)

Arguments

Details

The penalized.clr function fits a conditional logistic regression model for a given combination of L1 (lambda) and L2 penalties. L2 penalty is obtained from lambda and alpha as lambda*(1-alpha)/(2*alpha). Note that lambda is a single number if all covariates are to be penalized equally, and a vector of penatlies, if predictors are divided in blocks (of sizes provided in p) that are to be penalized differently. The penalized.clr function is based on the Cox model routine available in the penalized package.

Value

A list with the following elements:

• penalized - Regression coefficients for the penalized covariates.

• unpenalized - Regression coefficients for the unpenalized covariates.

• converged - Whether the fitting process was judged to have converged.

• lambda - The tuning parameter for L1 used.

• alpha - The elastic net mixing parameter used.

See Also

stable.clr and stable.clr.g for variable selection through stability selection in penalized conditional logistic regression with a single penalty factor and multiple penalty factors, respectively.

Examples

set.seed(123)
# simulate covariates (pure noise in two blocks of 20 and 80 variables)
X <- cbind(matrix(rnorm(4000, 0, 1), ncol = 20), matrix(rnorm(16000, 2, 0.6), ncol = 80))

# stratum membership
stratum <- sort(rep(1:100, 2))

# the response
Y <- rep(c(1, 0), 100)

fit <- penalized.clr( response = Y, stratum = stratum,
  penalized = X, lambda = c(1, 0.3),
  p = c(20, 80), standardize = TRUE)
fit$penalized
fit$converged
fit$lambda

Stability selection based on penalized conditional logistic regression

Description

Performs stability selection for conditional logistic regression models with L1 and L2 penalty.

Usage

stable.clr(
  response,
  stratum,
  penalized,
  unpenalized = NULL,
  lambda.seq,
  alpha = 1,
  B = 100,
  parallel = TRUE,
  standardize = TRUE,
  event
)

Arguments

Value

A list with a numeric vector Pistab giving selection probabilities for each penalized covariate, and a sequence lambda.seq used.

See Also

stable.clr.g for stability selection in penalized conditional logistic regression with multiple penalties for block structured covariates.

Examples

 set.seed(123)

# simulate covariates (pure noise in two blocks of 20 and 80 variables)
X <- cbind(matrix(rnorm(4000, 0, 1), ncol = 20), matrix(rnorm(16000, 2, 0.6), ncol = 80))

# stratum membership
stratum <- sort(rep(1:100, 2))

# the response
Y <- rep(c(1, 0), 100)

# default L1 penalty
lambda <- find.default.lambda(response = Y,
                                   penalized = X,
                                   stratum = stratum)

# perform stability selection

stable1 <- stable.clr(response = Y, penalized = X, stratum = stratum,
                         lambda.seq = lambda)

Stability selection based on penalized conditional logistic regression

Description

Performs stability selection for conditional logistic regression models with L1 and L2 penalty allowing for different penalties for different blocks (groups) of covariates (different data sources).

Usage

stable.clr.g(
  response,
  stratum,
  penalized,
  unpenalized = NULL,
  p = NULL,
  lambda.list,
  alpha = 1,
  B = 100,
  parallel = TRUE,
  standardize = TRUE,
  event
)

Arguments

Details

This function implements stability selection (Meinshausen and Bühlmann, 2010) in a conditional logistic regression. The implementation is based on the modification of Shah and Samworth (2013) featuring complementary subsamples. Note that this means that the number of subsamples will be ⁠2B⁠ instead of B. Subsampling procedure is repeated ⁠2B⁠ times for each vector of per-block penalties resulting each time in a vector of selection frequencies (frequency of non-zero coefficient estimate of each covariate). The final selection probability Pistab is obtained by taking the maximum over all considered vectors of penalties.

Value

A list containing a numeric vector Pistab, giving selection probabilities for all penalized covariates, lambda.list and p provided as input arguments.

References

1. Meinshausen, N., & Bühlmann, P. (2010). Stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72(4), 417-473.

2. Shah, R. D., & Samworth, R. J. (2013). Variable selection with error control: another look at stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75(1), 55-80.

Examples

set.seed(123)

# simulate covariates (pure noise in two blocks of 20 and 80 variables)
X <- cbind(matrix(rnorm(4000, 0, 1), ncol = 20), matrix(rnorm(16000, 2, 0.6), ncol = 80))
p <- c(20,80)

# stratum membership
stratum <- sort(rep(1:100, 2))

# the response
Y <- rep(c(1, 0), 100)

# list of L1 penalties

lambda.list = list(c(0.5,1), c(2,0.9))

# perform stability selection

stable.g1 <- stable.clr.g(response = Y, penalized = X, stratum = stratum,
                         p = p, lambda.list = lambda.list)

Stability selection for penalized conditional logistic regression

Description

Internal function used by stable.clr and stable.clr.g.

Usage

subsample.clr(
  response,
  stratum,
  penalized,
  unpenalized = NULL,
  lambda,
  alpha = 1,
  B = 100,
  matB = NULL,
  return.matB = FALSE,
  parallel = TRUE,
  standardize = TRUE
)

Arguments

Value

If return.matB is TRUE, a list with two elements, a numeric vector Pistab, giving selection probabilities for each covariate and a matrix matB; otheriwise only Pistab.