p_gdfa_nonconstant function

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)

See p_gdfa.

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.

Returns

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.