Type: Package
Title: A Comprehensive Analysis of High Dimensional Longitudinal Data
Version: 0.2.2
Description: To provide a comprehensive analysis of high dimensional longitudinal data,this package provides analysis for any combination of 1) simultaneous variable selection and estimation, 2) mean regression or quantile regression for heterogeneous data, 3) cross-sectional or longitudinal data, 4) balanced or imbalanced data, 5) moderate, high or even ultra-high dimensional data, via computationally efficient implementations of penalized generalized estimating equations.
License: GPL-3
Encoding: UTF-8
LazyData: true
Depends: R (≥ 3.5.0)
Imports: mvtnorm, quantreg, Rcpp (≥ 0.10.2), doParallel, foreach
Suggests: methods
LinkingTo: Rcpp, RcppEigen
RoxygenNote: 7.3.2
NeedsCompilation: yes
Packaged: 2024-11-12 05:40:07 UTC; tianhaizu
Author: Tianhai Zu [aut, cre], Brittany Green [aut, ctb], Yan Yu [aut, ctb]
Maintainer: Tianhai Zu <zuti@mail.uc.edu>
Repository: CRAN
Date/Publication: 2024-11-12 10:20:02 UTC

Cross-Validation for Generalized Estimating Equations (GEE)

Description

This function performs k-fold cross-validation for model selection in the context of Generalized Estimating Equations (GEE). It is designed to evaluate the performance of different models specified by a range of lambda values, choosing the one that minimizes the cross-validation criterion.

Usage

CVfit(
  formula,
  id,
  data,
  family,
  scale.fix,
  scale.value,
  fold,
  lambda.vec,
  pindex,
  eps,
  maxiter,
  tol,
  corstr = "independence",
  ncore = 1
)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

id

a vector which identifies the cluster/group for each observation.

data

an optional data frame containing the variables in the model.

family

a description of the error distribution and link function to be used in the model.

scale.fix

logical; if TRUE, the scale parameter is fixed to scale.value.

scale.value

the value of the scale parameter when scale.fix is TRUE.

fold

the number of folds to be used in the cross-validation.

lambda.vec

a vector of lambda values for which the cross-validation error will be calculated.

pindex

an optional numeric vector specifying a parameter index.

eps

the threshold for convergence criteria.

maxiter

the maximum number of iterations for the convergence of the algorithm.

tol

the tolerance level for the convergence of the algorithm.

corstr

the correlation structure used.

ncore

if greater than 1, the function will use parallel computation.

Details

Note that this is a re-implemented version with parallel computing.

Value

An object of class "CVfit", which is a list containing:

fold

The number of folds used in the cross-validation.

lam.vect

The vector of lambda values tested.

cv.vect

The cross-validation error for each lambda.

lam.opt

The lambda value that resulted in the minimum cross-validation error.

cv.min

The minimum cross-validation error.

call

The matched call.

PGEE accelerated with RCpp

Description

A function to fit penalized generalized estimating equation model. This function was re-wrote partly with RCPP and RCPPEigen for better computation efficiency.

Usage

PGEE(
  formula,
  id,
  data,
  na.action = NULL,
  family = gaussian(link = "identity"),
  corstr = "independence",
  Mv = NULL,
  beta_int = NULL,
  R = NULL,
  scale.fix = TRUE,
  scale.value = 1,
  lambda,
  pindex = NULL,
  eps = 10^-6,
  maxiter = 30,
  tol = 10^-3,
  silent = TRUE
)

Arguments

formula

A formula expression response ~ predictors;

id

A vector for identifying subjects/clusters.

data

A data frame which stores the variables in formula with id variable.

na.action

A function to remove missing values from the data. Only na.omit is allowed here.

family

A family object: a list of functions and expressions for defining link and variance functions. Families supported in PGEE are binomial, gaussian, gamma and poisson. The links, which are not available in gee, is not available here. The default family is gaussian.

corstr

A character string, which specifies the correlation of correlation structure. Structures supported in PGEE are "AR-1","exchangeable", "fixed", "independence", "stat_M_dep","non_stat_M_dep", and "unstructured". The default corstr correlation is "independence".

Mv

If either "stat_M_dep", or "non_stat_M_dep" is specified in corstr, then this assigns a numeric value for Mv. Otherwise, the default value is NULL.

beta_int

User specified initial values for regression parameters. The default value is NULL.

R

If corstr = "fixed" is specified, then R is a square matrix of dimension maximum cluster size containing the user specified correlation. Otherwise, the default value is NULL.

scale.fix

A logical variable; if true, the scale parameter is fixed at the value of scale.value. The default value is TRUE.

scale.value

If scale.fix = TRUE, this assigns a numeric value to which the scale parameter should be fixed. The default value is 1.

lambda

A numerical value for the penalization parameter of the scad function, which is estimated via cross-validation.

pindex

An index vector showing the parameters which are not subject to penalization. The default value is NULL. However, in case of a model with intercept, the intercept parameter should be never penalized.

eps

A numerical value for the epsilon used in minorization-maximization algorithm. The default value is 10^-6.

maxiter

The number of iterations that is used in the estimation algorithm. The default value is 25.

tol

The tolerance level that is used in the estimation algorithm. The default value is 10^-3.

silent

A logical variable; if false, the regression parameter estimates at each iteration are printed. The default value is TRUE.

Value

a PGEE object, which includes: fitted coefficients - the fitted single index coefficients with unit norm and first component being non negative

Examples

#generate data
set.seed(2021)
sim_data <- generateData(nsub = 100, nobs = rep(10, 100),  p = 100,
                         c(rep(1,7),rep(0,93)), rho = 0.6, correlation = "AR1",
                          dis = "normal", ka = 1)

X=sim_data$X
y=sim_data$y
id = rep(1:100, each = 10)
data = data.frame(X,y,id)

PGEE_fit = PGEE("y ~.-id-1",id = id, data = data,corstr = "exchangeable",lambda=0.01)
PGEE_fit$coefficients

Generate Covariance Matrix

Description

This function generates a covariance matrix based on the specified correlation structure. The function supports "compound symmetry" (cs) and "autoregressive" (ar) correlation structures, as well as an identity matrix as the default option when neither "cs" nor "AR1" is specified.

Usage

Siga_cov(rho, correlation, nt)

Arguments

rho

Numeric, the correlation coefficient used for generating the covariance matrix. For "cs" or "exchangeable", it represents the common correlation between any two observations. For "AR1", it represents the correlation between two consecutive observations, with the correlation decreasing for observations further apart.

correlation

Character, specifies the correlation of correlation structure for the covariance matrix. Options are "cs" or "exchangeable" for compound symmetry, "AR1" for autoregressive, and any other input will result in an identity matrix.

nt

Integer, the dimension of the square covariance matrix (number of time points or observations).

Value

A square matrix of dimension 'nt' representing the specified covariance structure.

Compile Results from qpgee()

Description

This function reports correct percentage, TP, FP, MSE and MAD from a (list of) fitted qpgee model comparing to the true betas.

Usage

compile_result(qpgee_results, beta0, threshold = 10^-3)

Arguments

qpgee_results

A (list of) fitted qpgee model.

beta0

True beta used in true data generation process.

threshold

Integer, the threshold to determine whether a esimated beta should be consider as 0.

Value

a vector contains correct percentage, TP, FP, MSE and MAD and its standard error if Monte Carlo simulations.

Generate Data for Simulation

Description

This function generates simulated data including the predictor matrix 'X' and the response vector 'y', based on the specified parameters. The function allows for the simulation of data under different settings of correlation, distribution, and the number of observations and subjects.

Usage

generateData(
  nsub,
  nobs,
  p,
  beta0,
  rho,
  correlation = "AR1",
  dis = "normal",
  ka = 0,
  SNPs = NULL
)

Arguments

nsub

Integer, the number of subjects.

nobs

Integer or numeric vector, the number of observations per subject.

p

Integer, the number of predictors.

beta0

Numeric vector, initial coefficients for the first few predictors.

rho

Numeric, the correlation coefficient used in generating correlated errors.

correlation

Character, the correlation of correlation structure (default is autoregressive).

dis

Character, the distribution of errors ("normal" or "t").

ka

1 for heterogeneous errors and 0 for homogeneous errors.

SNPs

User can provide simulated or real SNPs for genetic data simulation.

Value

A list containing two elements: 'X', the matrix of predictors, and 'y', the response vector.

Examples

sim_data <- generateData(nsub = 100, nobs = rep(10, 100),  p = 200,
                         beta0 = c(rep(1,7),rep(0,193)), rho = 0.6, correlation = "AR1",
                          dis = "normal", ka = 1)

Predict method for qpgee model objects

Description

This function makes predictions from a "qpgee" model object. When 'newdata' is not provided, it returns predictions using the original data the model was fitted on. If 'newdata' is supplied (through '...'), it uses this new data for prediction.

Usage

## S3 method for class 'qpgee'
predict(object, ...)

Arguments

object

A "qpgee" model object.

...

Additional arguments to the function. Can include 'newdata', a dataframe containing the new data to predict on. The structure of 'newdata' should match that of the data the model was originally fitted with, specifically in terms of the variables it contains. Additional arguments are ignored.

Value

If 'newdata' is not supplied, returns a vector of predictions based on the fitted values and handling of NAs specified in the model object. If 'newdata' is supplied, returns a vector of predictions for the new data.

Examples

# Example usage:
sim_data <- generateData(nsub = 100, nobs = rep(10, 100),  p = 100,
                         beta0 = c(rep(1,7),rep(0,93)), rho = 0.6, correlation = "AR1",
                          dis = "normal", ka = 1)

X=sim_data$X
y=sim_data$y

#fit qpgee
qpgee.fit = qpgee(X,y,tau=0.5,nobs=rep(10, 100),lambda = 0.1)
predict(qpgee.fit)

Quantile Penalized Generalized Estimating Equations with Auto Selected Penalty level

Description

This function automatically select the penalty level by going through a list of lambdas, and select the best level of penalty with high-dimensional BIC (HBIC) or cross-validation (CV).

Usage

qpgee(
  x,
  y,
  tau = 0.5,
  method = "HBIC",
  ncore = 1,
  nobs = rep(1, length(y)),
  correlation = "exchangeable",
  lambda = NULL,
  intercept = FALSE,
  f0 = NULL,
  betaint = NULL,
  max_it = 100,
  cutoff = 10^-4
)

Arguments

x

A matrix of predictors.

y

A numeric vector of response variables.

tau

The quantile to be estimated (default is 0.5, the median).

method

The criterion to select level of penalty. Currently it only supports "HBIC".

ncore

A numeric value specifying how many core to use.

nobs

A numeric vector indicating the number of observations per subject.

correlation

A string specifying the working correlation structure. Options include "exchangeable" (Exchangeable), "AR1" (Autoregressive), "Tri" (Tri-diagonal), and "exchangeable" (Independent).

lambda

A vector of penalty parameter for regularization. If not provided, a grid will be provided by this function.

intercept

Whether to include an intercept when estimating.

f0

estimated conditional error distributions.

betaint

Initial values for the beta coefficients. If NULL, non-longitudinal quantile regression is used for initialization.

max_it

Maximum number of iterations (default is 100).

cutoff

Threshold for coefficient shrinkage (default is 0.1).

Value

A list containing the following components:

beta

Estimated beta coefficients.

g

Fitted values of the linear predictor.

R

Estimated working correlation matrix.

X_selected

Indices of selected predictors.

mcl

Mean check loss.

hbic

Hannan-Quinn Information Criterion value.

converge

Boolean indicating whether the algorithm converged.

Examples

# Example usage:

sim_data <- generateData(nsub = 20, nobs = rep(10, 20),  p = 20,
                         beta0 = c(rep(1,5),rep(0,15)), rho = 0.1, correlation = "AR1",
                          dis = "normal", ka = 1)

X=sim_data$X
y=sim_data$y

#fit qpgee with auto selected lambda
qpgee.fit = qpgee(X,y,tau=0.5,nobs=rep(10, 20),ncore=1)
qpgee.fit$beta

Quantile Penalized Generalized Estimating Equations (QPGEE) Estimation Function

Description

This function implements Quantile Penalized Generalized Estimating Equations (QPGEE) for longitudinal data analysis. It estimates parameters using a penalized quantile regression approach within a GEE framework, allowing for different working correlation structures.

Usage

qpgee.est(
  x,
  y,
  tau = 0.5,
  nobs = rep(1, length(y)),
  correlation = "exchangeable",
  lambda = 0.1,
  intercept = FALSE,
  betaint = NULL,
  f0 = NULL,
  max_it = 100,
  cutoff = 10^-4
)

Arguments

x

A matrix of predictors.

y

A numeric vector of response variables.

tau

The quantile to be estimated (default is 0.5, the median).

nobs

A numeric vector indicating the number of observations per subject.

correlation

A string specifying the working correlation structure. Options include "exchangeable" (Exchangeable), "AR1" (Autoregressive), "Tri" (Tri-diagonal), "independence" (Independent), and "unstructured".

lambda

The penalty parameter for regularization (default is 0.1).

intercept

Whether to include an intercept when estimating.

betaint

Initial values for the beta coefficients. If NULL, non-longitudinal quantile regression is used for initialization.

f0

estimated conditional error distributions.

max_it

Maximum number of iterations (default is 100).

cutoff

Threshold for coefficient shrinkage (default is 0.1).

Value

A list containing the following components:

beta

Estimated beta coefficients.

g

Fitted values of the linear predictor.

R

Estimated working correlation matrix.

X_selected

Indices of selected predictors.

mcl

Mean check loss.

hbic

Hannan-Quinn Information Criterion value.

converge

Boolean indicating whether the algorithm converged.

Examples

# Example usage:
sim_data <- generateData(nsub = 100, nobs = rep(10, 100),  p = 100,
                         beta0 = c(rep(1,7),rep(0,93)), rho = 0.6, correlation = "AR1",
                          dis = "normal", ka = 1)

X=sim_data$X
y=sim_data$y

#fit qpgee
qpgee.fit = qpgee.est(X,y,tau=0.5,nobs=rep(10, 100))
qpgee.fit$beta

A Simulated Genetic Data from HapGen2

Description

The 'simuGene' dataset contains 500 SNPs simulated data from a commonly used tool for genetic data, HapGen2. We re-sampled existing genotype data to create this simulated data. The genotype data we resample from is the publicly available 1000 Genomes Project data. More specifically, we use resampled from chromosome 14.

Usage

simuGene

Format

A data frame with 1000 rows (subjects) and 500 columns (SNPs).

Examples

data(simuGene)
head(simuGene)

A Subset of Yeast Cell Cycle Gene Expression Data (G1 Phase)

Description

The 'yeastG1' dataset contains gene expression data from the yeast cell cycle during the G1 phase. The original dataset (Spellman et al. 1998) includes expression levels for 6178 genes measured at 18 time points. And this is a subset of 283 cell-cycled-regularized genes observed over 4 time points at G1 stage and the standardized binding probabilities of a total of 96 TFs obtained from

Usage

yeastG1

Format

A data frame with 1132 rows and 99 columns.

The dataset contains gene expression levels for the following transcription factors: ABF1, ACE2, ADR1, ARG80, ARG81, ARO80, ASH1, BAS1, CAD1, CBF1, CIN5, CRZ1, CUP9, DAL81, DAL82, DIG1, DOT6, FHL1, FKH1, FKH2, FZF1, GAL4, GAT1, GAT3, GCN4, GCR1, GCR2, GLN3, GRF10.Pho2., GTS1, HAL9, HAP2, HAP3, HAP4, HAP5, HIR1, HIR2, HMS1, HSF1, IME4, INO2, INO4, IXR1, LEU3, MAC1, MAL13, MATa1, MBP1, MCM1, MET31, MET4, MIG1, MOT3, MSN1, MSN4, MSS11, MTH1, NDD1, NRG1, PDR1, PHD1, PHO4, PUT3, RAP1, RCS1, REB1, RFX1, RGM1, RLM1, RME1, ROX1, RPH1, RTG1, RTG3, SFP1, SIG1, SIP4, SKN7, SMP1, SOK2, SRD1, STB1, STE12, STP1, STP2, SUM1, SWI4, SWI5, SWI6, YAP1, YAP5, YAP6, YFL044C, YJL206C, ZAP1, ZMS1

Source

Spellman, P. T., Sherlock, G., Zhang, M. Q., Iyer, V. R., Anders, K., Eisen, M. B., ... & Futcher, B. (1998). Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Molecular biology of the cell, 9(12), 3273-3297.

Wang, L., Zhou, J., and Qu, A. (2012). Penalized generalized estimating equations for high-dimensional longitudinal data anaysis. Biometrics, 68, 353–360.

Examples

data(yeastG1)
head(yeastG1)