meerva.sim.block: Simulation of meerva used to Analyze Data with Measurement...
In meerva: Analysis of Data with Measurement Error Using a Validation Subsample

Description Usage Arguments Value Author(s) See Also Examples

View source: R/meerva.sim.tools_211026.R

The meerva package is designed to analyze data with measurement error when there is a validation subsample randomly selected from the full sample. The method assumes surrogate variables measured with error are available for the full sample, and reference variables measured with little or no error are available for this randomly chosen subsample of the full sample. Measurement errors may be differential or non differential, in any or all predictors (simultaneously) as well as outcome.

The meerva.sim.block lets the user specify a model with measurement error, and then simulate and analyze many datasets to examine the model fits and judge how the method works. Data sets are generated according to 3 functions for simulating Cox PH, linear and logistic regression models. These functions generate data sets with 4 reference predictor variables and from 3 to 5 surrogate predictor variables. The user can consider, program and simulate data sets of greater complexity but these examples provided with the package should serve as a reasonable introduction to the robustness of the method.

meerva.sim.block(
  simfam = "gaussian",
  nsims = 100,
  seed = 0,
  n = 4000,
  m = 400,
  beta = c(-0.5, 0.5, 0.2, 1, 0.5),
  alpha1 = c(-0.05, 0.1, 0.05, 0.1),
  alpha2 = c(0.98, 0.98, 0.95, 0.95),
  bx3s1 = c(0.05, 0, 0, NA, NA),
  bx3s2 = c(0.95, NA, NA),
  bx12 = c(0.25, 0.15),
  sd = 1,
  fewer = 0,
  mncor = 0,
  sigma = NULL,
  vmethod = NA,
  jksize = 0,
  compare = 1,
  diffam = NA,
  simtime = 1
)

`simfam`	The family for the underlying regression model to be simulated, amongst "binomial", "gaussian" and "Cox".
`nsims`	Number of datasets to be simulated
`seed`	A seed for the R random number generator. The default is 0 in which case the program random selects and records the seed so one ca replicate simulation studies.
`n`	The full dataset size.
`m`	The validation subsample size (m < n).
`beta`	A vector of length 5 for the true regression parameter for the linear regression model with 5 predictors including the intercept. For the Cox model beta[0] is not estimated but determines a basal event rate.
`alpha1`	A vector of length four determining the measurement error or misclassification probabilities for the outcome surrogate ys. Usage is slightly different for the different simfam values "gaussian", "binomial" and "Cox". See the help pages for meerva.sim.brn, meerva.sim.cox and meerva.sim.nrm for clarification.
`alpha2`	A vector describing the correct classification probabilities for x1s, the surrogate for x1. Usage is slighlty different for the different simfam values "gaussian", "binomial" and "Cox". See the help pages for meerva.sim.brn, meerva.sim.cox and meerva.sim.nrm for clarification.
`bx3s1`	A vector of length 5 determining the relation between the reference variable x3 and the mean and SD of the surrogate x3s1. Roughly, bx3s1[1] determines a minimal measurement error SD, conditional on x3 bx3s1[2] determines a rate of increase in SD for values of x3 greater than bx3s1[3], bx3s1[4] is a value above which the relation between x3 and the mean of x3s is determined by the power bx3s1[5]. The mean values for x3s1 are rescaled to have mean 0 and variance 1.
`bx3s2`	A vector of length 3 determining scale in x3s and potentially x3s2, a second surrogate for xs. Roughly, bx3s2[1] takes the previously determined mean for x3s1 using bx3s1 and multiples by bx3s2[1]. Conditional on x3, x3s2 has mean bx3s2[2] * x3 and variance bx3s2[3].
`bx12`	Bernoulli probabilities for reference variables x1 and x2. A vector of length 2, default is c(0.25, 0.15). If mncor (see below) is positive the correlations between these Bernoulli and continuous predictors remains positive.
`sd`	In case of simfam == "gaussain" for linear regression, the sd of outcome y. In case of simfam == "Cox" for Cox PH regression, the multiplicative error term for ys, the surrogate for the time to event y (ys = log(sd * a (random variable) * y).
`fewer`	When set to 1 x3s1 and x4 will be collapsed to one variable in the surrogate set. This demonstrates how the method works when there are fewer surrogate variables than reference variables. If bx3s2 is specified such that there are duplicate surrogate variables for the reference variable x3 then the number of surrogate predictors will not be reduced.
`mncor`	Correlation of the columns in the x matrix before x1 and x2 are dichotomized to Bernoulli random variables. Default is 0.
`sigma`	A 4x4 varaince-covarniance matrix for the multivarite normal dsitribution used to derive the 4 reference predictor variables.
`vmethod`	Method for robust estimation of variance covariance matrices needed for calculation of the augmented estimates (beta aug). 0 for JK or jackknife (slowest but more accurate), 1 for IJK or the infinitesimal JK using the R default dfbeta's 2 for IJK using an alternate formula for the dfbeta, and 3 for all three of these methods to be used NA to let the program choose a stronger, faster method.
`jksize`	leave out number for grouped jackknife used for non validation data The default is 0 where the program chooses jksize so that the number of leave out groups is about validation subsample size.
`compare`	1 to compare gamma_val with gamma_ful (default) or 0 with gamma_non.
`diffam`	inidcates a cutoff if for a "guassian" family in surrogate a "binomial" famliy is to be similated for the refernce model. For example, the surrogate outcome could be an estimated probit (or logit) based upon a convolutional neural network. Normal data are simulated and y_val is repalced by 1*(y_val >= diffam). Default is NA and the surrogate and reference have the same model form. Only for use with vmethod of 0 or 1.
`simtime`	1 (default) to print out time duirng simulalation to inform user how long the simulation may run, 0 to not print out this information.

meerva.sim.block returns a list object of class meerva.sim. The list will contain summary information used to simulate the data, and for each data set simulated with measurement error, the augmented estimates based upon the full data set accounting for measurement error, estimates based upon reference variables from the validation subsample, estimates based upon the surrogate variables from the whole sample, along with estimated variances for these estimates. These can be inspected by the user directly or by as shown in the example.

Walter Kremers (kremers.walter@mayo.edu)

meerva.fit , meerva.sim.brn , meerva.sim.cox , meerva.sim.nrm

# Simulation study for logistic reg data with 
# differential misclassification in outcome 
# and a predictor and measurement error in 
# another predictor.  nsims=10 is as an 
# example only.  Try running nsims=100 or 
# 1000, but be prepared to wait a little while. 
sim.binomial = meerva.sim.block(simfam="binomial", 
    nsims=10, seed=0, n=4000, m=400, 
    beta = c(-0.5, 0.5, 0.2, 1, 0.5) , 
    alpha1 = c(0.95, 0.90, 0.90, 0.95), 
    alpha2 = c(0.98,0.98,0.95,0.95), 
    bx3s1=c(0.05, 0, 0, NA, NA) , 
    bx3s2 = c(NA,NA,NA) , 
    vmethod=2, jksize=0, compare=1) 
    
plot(sim.binomial) 
summary(sim.binomial, 1) 

# Simulation study for linear reg data.   
# For this example there are more surrogate 
# predictors than reference predictors.  
# nsims=10 is as an example only.  Try 
# running nsims=100 or 1000, but be 
# prepared to wait a little while.   
sim.gaussianm = meerva.sim.block(simfam="gaussian", 
    nsims=10, seed=0, n=4000, m=400, 
    beta = c(-0.5, 0.5, 0.2, 1, 0.5) , 
    alpha1 = c(-0.05, 0.1, 0.05, 0.1) , 
    alpha2 = c(0.98,0.94,0.95,0.95) , 
    bx3s1=c(0.05, 0, 0, NA, NA) , 
    bx3s2  = c(1.1,0.9,0.05) ,  
    sd=1, fewer=0, 
    vmethod=1, jksize=0, compare=1) 

plot(sim.gaussianm)
summary(sim.gaussianm)
 
# Simulation study for Cox PH data.  
# For this example there are fewer surrogates 
# than reference variables yet they provide 
# information to decrease the variance in the 
# augmented estimate.  nsims=10 is as an 
# example only.  Try running nsims=100 or 
# 1000, but be prepared to wait a little 
# while.   
sim.coxphf = meerva.sim.block(simfam="Cox", 
    nsims=10, seed=0, n=4000, m=400, 
    beta   = c(-0.5, 0.5, 0.2, 1, 0.5) , 
    alpha1 = c(0.95,0.90,0.90,0.95)  , 
    alpha2 = c(0.98,0.94,0.94,0.98) , 
    bx3s1  = c(0.05,0,0,NA,NA) , 
    bx3s2  = c(1.1, NA, NA) , 
    sd=0.1, fewer=1, 
    vmethod=1, jksize=0, compare=1 ) 

plot(sim.coxphf)
summary(sim.coxphf)