p_ndfa_nonconstant {pooling}

Normal Discriminant Function Approach for Estimating Odds Ratio with Exposure Measured in Pools and Potentially Subject to Additive Normal Errors (Non-constant Odds Ratio Version)

Description

Assumes exposure given covariates and outcome is a normal-errors linear regression. Pooled exposure measurements can be assumed precise or subject to additive normal processing error and/or measurement error. Parameters are estimated using maximum likelihood.

Usage

p_ndfa_nonconstant(g, y, xtilde, c = NULL, errors = "processing",
  start_nonvar_var = c(0.01, 1), lower_nonvar_var = c(-Inf, 1e-04),
  upper_nonvar_var = c(Inf, Inf), jitter_start = 0.01,
  nlminb_list = list(control = list(trace = 1, eval.max = 500, iter.max =
  500)), hessian_list = list(method.args = list(r = 4)),
  nlminb_object = NULL)

Arguments

g

Numeric vector of pool sizes, i.e. number of members in each pool.

y

Numeric vector of poolwise Y values (number of cases in each pool).

xtilde

Numeric vector (or list of numeric vectors, if some pools have replicates) with Xtilde values.

c

Numeric matrix with poolwise C values (if any), with one row for each pool. Can be a vector if there is only 1 covariate.

errors

Character string specifying the errors that X is subject to. Choices are "neither", "processing" for processing error only, "measurement" for measurement error only, and "both".

start_nonvar_var

Numeric vector of length 2 specifying starting value for non-variance terms and variance terms, respectively.

lower_nonvar_var

Numeric vector of length 2 specifying lower bound for non-variance terms and variance terms, respectively.

upper_nonvar_var

Numeric vector of length 2 specifying upper bound for non-variance terms and variance terms, respectively.

jitter_start

Numeric value specifying standard deviation for mean-0 normal jitters to add to starting values for a second try at maximizing the log-likelihood, should the initial call to nlminb result in non-convergence. Set to NULL for no second try.

nlminb_list

List of arguments to pass to nlminb for log-likelihood maximization.

hessian_list

List of arguments to pass to hessian for approximating the Hessian matrix. Only used if estimate_var = TRUE.

nlminb_object

Object returned from nlminb in a prior call. Useful for bypassing log-likelihood maximization if you just want to re-estimate the Hessian matrix with different options.

Value

List containing:

1. Numeric vector of parameter estimates.

2. Variance-covariance matrix.

3. Returned nlminb object from maximizing the log-likelihood function.

4. Akaike information criterion (AIC).

References

Lyles, R.H., Van Domelen, D.R., Mitchell, E.M. and Schisterman, E.F. (2015) "A discriminant function approach to adjust for processing and measurement error When a biomarker is assayed in pooled samples." Int. J. Environ. Res. Public Health 12(11): 14723–14740.

Schisterman, E.F., Vexler, A., Mumford, S.L. and Perkins, N.J. (2010) "Hybrid pooled-unpooled design for cost-efficient measurement of biomarkers." Stat. Med. 29(5): 597–613.