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Fit a logistic regression model with an interval-censored covariate

Source: R/fit_joint_model.R
fit_joint_model.Rd

This function fits a logistic regression model for a binary outcome Y with an interval-censored covariate T, using an EM algorithm, as described in Morrison et al (2021); doi:10.1111/biom.13472 .

Usage

fit_joint_model(
  participant_level_data,
  obs_level_data,
  model_formula = stats::formula(Y ~ T),
  mu_function = compute_mu,
  bin_width = 1,
  denom_offset = 0.1,
  EM_toler_loglik = 0.1,
  EM_toler_est = 1e-04,
  EM_max_iterations = Inf,
  glm_tolerance = 1e-07,
  glm_maxit = 20,
  initial_S_estimate_location = 0.25,
  coef_change_metric = "max abs rel diff coefs",
  verbose = FALSE
)

Arguments

participant_level_data

a data.frame or tibble with the following variables:

  • ID: participant ID

  • E: study enrollment date

  • L: date of last negative test for seroconversion

  • R: date of first positive test for seroconversion

  • Cohort` (optional): this variable can be used to stratify the modeling of the seroconversion distribution.

obs_level_data

a data.frame or tibble with the following variables:

  • ID: participant ID

  • O: biomarker sample collection dates

  • Y: MAA classifications (binary outcomes)

model_formula

the functional form for the regression model for p(y|t) (as a formula() object)

mu_function

a function taking a vector of regression coefficient estimates as input and outputting an estimate of mu (mean duration of MAA-positive infection).

bin_width

the number of days between possible seroconversion dates (should be an integer)

denom_offset

an offset value added to the denominator of the hazard estimates to improve numerical stability

EM_toler_loglik

the convergence cutoff for the log-likelihood criterion ("Delta_L" in the paper)

EM_toler_est

the convergence cutoff for the parameter estimate criterion ("Delta_theta" in the paper)

EM_max_iterations

the number of EM iterations to perform before giving up if still not converged.

glm_tolerance

the convergence cutoff for the glm fit in the M step

glm_maxit

the iterations cutoff for the glm fit in the M step

initial_S_estimate_location

determines how seroconversion date is guessed to initialize the algorithm; can be any decimal between 0 and 1; 0.5 = midpoint imputation, 0.25 = 1st quartile, 0 = last negative, etc.

coef_change_metric

a string indicating the type of parameter estimate criterion to use:

  • "max abs rel diff coefs" is the "Delta_theta" criterion described in the paper.

  • "max abs diff coefs" is the maximum absolute change in the coefficients (not divided by the old values); this criterion can be useful when some parameters are close to 0.

  • "diff mu" is the absolute change in mu, which may be helpful in the incidence estimate calibration setting but not elsewhere.

verbose

whether to print algorithm progress details to the console

Value

a list with the following elements:

  • Theta: the estimated regression coefficients for the model of p(Y|T)

  • Mu: the estimated mean window period (a transformation of Theta)

  • Omega: a table with the estimated parameters for the model of p(S|E).

  • converged: indicator of whether the algorithm reached its cutoff criteria before reaching the specified maximum iterations. 1 = reached cutoffs, 0 = not.

  • iterations: the number of EM iterations completed before the algorithm stopped.

  • convergence_metrics: the four convergence metrics

References

Morrison, Laeyendecker, and Brookmeyer (2021). "Regression with interval-censored covariates: Application to cross-sectional incidence estimation". Biometrics. doi:10.1111/biom.13472 .

Examples

if (FALSE) {

# simulate data:
study_data <- simulate_interval_censoring()

# fit model:
EM_algorithm_outputs <- fit_joint_model(
  obs_level_data = study_data$obs_data,
  participant_level_data = study_data$pt_data
)
}