SAMBA (version 0.9.0)

approxdist: Estimate parameters in the disease model approximating the observed data distribution

Description

approxdist estimates parameters in the disease model given a previously-estimated marginal sensitivity. This estimation is based on approximating the distribution of D* given Z.

Usage

approxdist(Dstar, Z, c_marg, weights = NULL)

Arguments

Dstar

Numeric vector containing observed disease status. Should be coded as 0/1

Z

Numeric matrix of covariates in disease model

c_marg

marginal sensitivity, P(D* = 1 | D = 1, S = 1)

weights

Optional numeric vector of patient-specific weights used for selection bias adjustment. Default is NULL

Value

a list with two elements: (1) 'param', a vector with parameter estimates for disease model (logOR of Z), and (2) 'variance', a vector of variance estimates for disease model parameters. Results do not include intercept.

Details

We are interested in modeling the relationship between binary disease status and covariates Z using a logistic regression model. However, D may be misclassified, and our observed data may not well-represent the population of interest. In this setting, we estimate parameters from the disease model using the following modeling framework.

Notation:

D

Binary disease status of interest.

D*

Observed binary disease status. Potentially a misclassified version of D. We assume D = 0 implies D* = 0.

S

Indicator for whether patient from population of interest is included in the analytical dataset.

Z

Covariates in disease model of interest.

W

Covariates in model for patient inclusion in analytical dataset (selection model).

X

Covariates in model for probability of observing disease given patient has disease (sensitivity model).

Model Structure:

Disease Model

$$logit(P(D=1|X)) = theta_0 + theta_Z Z$$

Selection Model

$$P(S=1|W,D)$$

Sensitivity Model

$$logit(P(D* = 1| D = 1, S = 1, X)) = beta_0 + beta_X X$$

References

Statistical inference for association studies using electronic health records: handling both selection bias and outcome misclassification Lauren J Beesley and Bhramar Mukherjee medRxiv 2019.12.26.19015859

Examples

# NOT RUN {
library(SAMBA)
# These examples are generated from the vignette. See it for more details.

# Generate IPW weights from the true model
expit <- function(x) exp(x) / (1 + exp(x))
prob.WD <- expit(-0.6 + 1 * samba.df$D + 0.5 * samba.df$W)
weights <- nrow(samba.df) * (1  / prob.WD) / (sum(1 / prob.WD))

# Estimate sensitivity by using inverse probability of selection weights
# and P(D=1)
sens <- sensitivity(samba.df$Dstar, samba.df$X, prev = mean(samba.df$D),
                    weights = weights)

approx1 <- approxdist(samba.df$Dstar, samba.df$Z, sens$c_marg,
                     weights = weights)
# }