LOD_bootstrap_fit {lodr}

Rcpp Code for Computing Standard Errors When Fitting Linear Models with Covariates Subject to a Limit of Detection (LOD)

Description

LOD_bootstrap_fit calls Rcpp code to compute linear model regression parameter standard errors in C++, taking into account covariates with limits of detection per the method detailed in May et al. (2011).

Usage

LOD_bootstrap_fit(num_of_boots, y_data, x_data, no_of_samples, threshold, 
max_iterations, LOD_u_l)

Arguments

num_of_boots

number denoting the number of bootstrap resamples to use to compute the regression parameter standard errors.

y_data

numeric vector consisting of data of the model's outcome variable.

x_data

column-named matrix consisting of data of the model's covariates with each column representing one covariate, with values outside of the limit(s) of detection marked as NA. A columns of ones must be included if the model has an intercept term. Note that for valid inference, order of the covariates/columns in the matrix must be as follows from left to right: those with no LOD followed by those with an LOD.

no_of_samples

an integer specifying the number of samples to generate for each subject with covariate values outside of their limits of detection. For more details, see May et al. (2011).

threshold

number denoting the minimum difference in the regression parameter estimates needed for convergence of the model fitting procedure.

max_iterations

number denoting the maximum number of iterations allowed in the model fitting procedure.

LOD_u_l

numeric matrix consisting of the lower and upper limits of detection for all covariates in the model as the columns, with each covariate containing its own row, in the same order as the covariates in x_data. If no limit of detection exists, the corresponding matrix entry is marked with an NA. An entry for the intercept (NA in each column) must be included if applicable.

Details

This function is used to complete the standard error computations done when fitting a linear model by calling lod_lm; the standard error computations are done in C++ to minimize computation time.

Value

LOD_bootstrap_fit returns a list which each component being a numeric vector consisting of the last iteration's regression parameter estimates when fitting the model on a bootstrap resample of the input data.

Author(s)

Kevin Donovan, [e-mail].

Maintainer: Kevin Donovan <[e-mail]>

References

May RC, Ibrahim JG, Chu H (2011). “Maximum likelihood estimation in generalized linear models with multiple covariates subject to detection limits.” Statistics in medicine, 30(20), 2551–2561.

See Also

lod_lm is the recommended function for fitting a linear model with covariates subject to limits of detection, which uses LOD_fit. LOD_fit is used to compute the regression parameter estimates.

Examples

library(lodr)
## Using example dataset provided in lodr package: lod_data_ex
## 3 covariates: x1, x2, x3 with x2 and x3 subject to a lower limit of
## detection of 0

# Replace values marked as under limit of detection using 0 with NA,
# add column of ones for intercept
lod_data_with_int <-
  as.matrix(cbind("Intercept"=rep(1, dim(lod_data_ex)[1]), lod_data_ex))

lod_data_ex_edit <-
  apply(lod_data_with_int, MARGIN = 2, FUN=function(x){ifelse(x==0, NA, x)})

# Fit model with bootstrap procedure, report regression parameter estimate standard errors
LOD_matrix <- cbind(c(NA, NA, -100, -100), c(NA, NA, 0, 0))

## no_of_samples set to 50 for computational speed/illustration purposes only.  
## At least 250 is recommended.  
## Same for num_of_boots=5; at least 25 is recommended
 
bootstrap_fit_object <-
  LOD_bootstrap_fit(num_of_boots=5, y_data=lod_data_ex_edit[,2],
                    x_data=lod_data_ex_edit[,-2],
                    no_of_samples=50,
                    threshold=0.001, max_iterations=100, LOD_u_l=LOD_matrix)

boot_SEs <- apply(do.call("rbind", bootstrap_fit_object), 2, sd)
names(boot_SEs) <- names(lod_data_with_int[,-2])

boot_SEs