README.md

In zrmacc/BNEM: Surrogate Outcome Regression Analysis

Surrogate Outcome Regression Analsyis

Zachary McCaw Updated: 2024-03-30

Description

This package performs regression analysis on a partially missing target outcome while borrowing information from a correlated surrogate outcome. Rather than regarding the surrogate outcome as a proxy for the target outcome, the target and surrogate outcomes are jointly modeled within a bivariate regression framework. Unobserved values of either outcome are treated as missing data. In contrast to imputation-based inference, surrogate regression is robust, requiring no assumptions regarding the relationship between the target and surrogate outcomes. However, in order for surrogate inference to improve efficiency, the target and surrogate outcomes must be correlated, and the target outcome must be partially missing. When both the target and the surrogate outcomes both contain missing values, estimation is performed via an expectation conditional maximization either (ECME) algorithm. When missingness is confined to the target outcome, estimation is performed using an accelerated least squares procedure. A flexible association test is provided for evaluating hypotheses about the target regression parameters. For additional details, see the following:

• For the case where the target and surrogate outcomes both contain missing values: McCaw ZR, Gaynor SM, Sun R, Lin X: Leveraging a surrogate outcome to improve inference on a partially missing target outcome (bioRxiv).

• For the case where only the target outcome contains missing values: McCaw ZR, Gao J, Lin X, Gronsbell J: Leveraging a machine learning derived surrogate phenotype to improve power for genome-wide association studies of partially missing phenotypes in population biobanks.

• For the related problem of fitting Gaussian mixture models on data with missing values: McCaw ZR, Aschard H, Julienne H: Fitting Gaussian mixture models on incomplete data, and the accompanying R package MGMM.

Installation

devtools::install_github(repo = 'zrmacc/SurrogateRegression')

Vignette

Model specification, parameter estimation, and inference on target regression coefficients are discussed in the package vignette, available here.

Compact Example

In the following, target and surrogate outcome data are generated for 1000 subjects. Each outcome depends on a design matrix with an intercept and a single standard normal covariate. The true target regression coefficient is $\beta = (1, 1)'$ and the true surrogate regression coefficient is $\alpha = (-1, -1)'$; 20% of target outcomes are missing, and 10% of surrogate outcomes are missing.

library(SurrogateRegression)
set.seed(100)

# Data generation.
## Observations.
n <- 1e3

## Target design matrix.
X <- cbind(1, rnorm(n))

## Surrogate design matrix.
Z <- cbind(1, rnorm(n))

## Outcome data.
Y <- rBNR(
  X = X, 
  Z = Z,
  b = c(1, 1), 
  a = c(-1, -1),
  t_miss = 0.2,
  s_miss = 0.1
  )

# Fit bivariate outcome model.
fit <- FitBNR(
  t = Y[, "Target"],
  s = Y[, "Surrogate"],
  X = X,
  Z = Z
)

## Objective increment:  0.166 
## Objective increment:  0.00497 
## Objective increment:  0.000183 
## Objective increment:  7.15e-06 
## Objective increment:  2.85e-07 
## 4 update(s) performed before tolerance limit.

show(fit)

##     Outcome Coefficient  Point     SE      L      U         p
## 1    Target          x1  0.961 0.0368  0.889  1.030 2.10e-150
## 2    Target          x2  0.952 0.0360  0.882  1.020 1.40e-154
## 3 Surrogate          z1 -1.020 0.0318 -1.080 -0.954 9.53e-225
## 4 Surrogate          z2 -1.100 0.0321 -1.160 -1.040 1.26e-258
## 
##         Covariance    Point     SE       L      U
## 1           Target  1.08000 0.0542  0.9820 1.2000
## 2 Target-Surrogate -0.00478 0.0375 -0.0423 0.0327
## 3        Surrogate  0.90800 0.0428  0.8280 0.9960

zrmacc/BNEM documentation built on March 31, 2024, 12:20 a.m.