p_gdfa_nonconstant {pooling}

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

Description

See p_gdfa.

Usage

p_gdfa_nonconstant(g, y, xtilde, c = NULL, errors = "processing",
  estimate_var = TRUE, start_nonvar_var = c(0.01, 1),
  lower_nonvar_var = c(-Inf, 1e-04), upper_nonvar_var = c(Inf, Inf),
  jitter_start = 0.01, hcubature_list = list(tol = 1e-08),
  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 with pool sizes, i.e. number of members in each pool.

y

Numeric vector with poolwise Y values, coded 0 if all members are controls and 1 if all members are cases.

xtilde

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

c

List where each element is a numeric matrix containing the C values for members of a particular pool (1 row for each member).

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".

estimate_var

Logical value for whether to return variance-covariance matrix for parameter estimates.

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.

hcubature_list

List of arguments to pass to hcubature for numerical integration.

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.

Mitchell, E.M, Lyles, R.H., and Schisterman, E.F. (2015) "Positing, fitting, and selecting regression models for pooled biomarker data." Stat. Med 34(17): 2544–2558.

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.

Whitcomb, B.W., Perkins, N.J., Zhang, Z., Ye, A., and Lyles, R. H. (2012) "Assessment of skewed exposure in case-control studies with pooling." Stat. Med. 31: 2461–2472.