cond_logreg {pooling}

Conditional Logistic Regression with Measurement Error in One Covariate

Description

Compatible with individual or pooled measurements. Assumes a normal linear model for exposure given other covariates, and additive normal errors.

Usage

cond_logreg(g = rep(1, length(xtilde1)), xtilde1, xtilde0, c1 = NULL,
  c0 = NULL, errors = "processing", approx_integral = TRUE,
  estimate_var = FALSE, 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.

xtilde1

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

xtilde0

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

c1

Numeric matrix with precisely measured covariates for cases.

c0

Numeric matrix with precisely measured covariates for controls.

errors

Character string specifying the errors that X is subject to. Choices are "none", "measurement" for measurement error, "processing" for processing error (only relevant for pooled data), and "both".

approx_integral

Logical value for whether to use the probit approximation for the logistic-normal integral, to avoid numerically integrating X's out of the likelihood function.

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. Only used if approx_integral = FALSE.

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 (if estimate_var = TRUE).

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

4. Akaike information criterion (AIC).

References

Saha-Chaudhuri, P., Umbach, D.M. and Weinberg, C.R. (2011) "Pooled exposure assessment for matched case-control studies." Epidemiology 22(5): 704–712.

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.

Weinberg, C.R. and Umbach, D.M. (1999) "Using pooled exposure assessment to improve efficiency in case-control studies." Biometrics 55: 718–726.

Weinberg, C.R. and Umbach, D.M. (2014) "Correction to 'Using pooled exposure assessment to improve efficiency in case-control studies' by Clarice R. Weinberg and David M. Umbach; 55, 718–726, September 1999." Biometrics 70: 1061.

Examples

# Load simulated data for 150 case pools and 150 control pools
data(dat_cond_logreg)
dat <- dat_cond_logreg$dat
xtilde1 <- dat_cond_logreg$xtilde1
xtilde0 <- dat_cond_logreg$xtilde0

# Fit conditional logistic regression to estimate log-odds ratio for X and Y
# adjusted for C, using the precise poolwise summed exposure X. True log-OR
# for X is 0.5.
truth <- cond_logreg(
  g = dat$g,
  xtilde1 = dat$x1,
  xtilde0 = dat$x0,
  c1 = dat$c1.model,
  c0 = dat$c0.model,
  errors = "neither"
)
truth$theta.hat

# Suppose X is subject to additive measurement error and processing error,
# and we observe Xtilde1 and Xtilde0 rather than X1 and X0. Fit model with
# Xtilde's, accounting for errors (numerical integration avoided by using
# probit approximation).
## Not run: 
corrected <- cond_logreg(
  g = dat$g,
  xtilde1 = xtilde1,
  xtilde0 = xtilde0,
  c1 = dat$c1.model,
  c0 = dat$c0.model,
  errors = "both",
  approx_integral = TRUE
)
corrected$theta.hat

## End(Not run)