cond_logreg function

Conditional Logistic Regression with Measurement Error in One Covariate

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

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.

Returns

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).

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)

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.