Compute Winner’s Curse Correction

Zachary McCaw
Updated: 2020-09-15

Description

This package calculates the winner’s curse correction using the model proposed by Turley et al (2018), implemented via the Expectation-Maximization algorithm. Also see MGMM for fitting Gaussian Mixture Models more generally.

Installation

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

Model

See the model specification here. The parameters estimated by this package are the probability of membership to the null component (pi) and the variance component (tau^2) of the non-null component.

Examples

Data

Example may be loaded via:

library(WinCurse)
data(wc_data)
head(wc_data)

##   non_null        theta         se
## 1        0  0.266490285 0.09712859
## 2        1 -0.013344779 0.10425721
## 3        0 -0.199862356 0.10540926
## 4        0  0.125285959 0.09901475
## 5        1  0.072490809 0.10000000
## 6        0 -0.007482795 0.09950372

Here:

• non_null is the generative component, 1 if non-null, 0 if null.
• theta is the estimated parameter.
• se is the standard error of the estimated parameter.

The true pi = 0.75 and the true tau^2 = 0.05.

Estimation

To fit the winner’s curse model:

fit <- fit.WinCurse(
  theta = wc_data$theta,
  se = wc_data$se,
  pi = 0.5,
  tau2 = 1,
  eps = 1e-12
)
show(fit)

## Estimated null proportion:
## [1] 0.766
## 
## 
## Estimated non-null variance component:
## [1] 0.048

Outputs

The output of fit.WinCurse is an object of class winCurse with these slots.

• @Assignments containing the component assignments and normalized (0,1) assignment entropy. Higher entropy means the assignment is less certain.

head(fit@Assignments)

##   non_null    entroy
## 1        1 0.8230338
## 2        0 0.5203778
## 3        0 0.9455816
## 4        0 0.7154702
## 5        0 0.5747059
## 6        0 0.5075906

• @Estimates containing the final parameter estimates:

fit@Estimates

## $pi
## [1] 0.7656391
## 
## $tau2
## [1] 0.04803447

• @Expectations containing the posterior expected effect size given the observed effect size. The posterior expectations are shrunk towards zero.

head(fit@Expectations)

## [1]  0.165374887 -0.001272114 -0.059008241  0.020476311  0.008183376
## [6] -0.000698325

• @Responsibilities containing the posterior probabilities of membership to the null and non-null components.

head(fit@Responsibilities)

##        null  non_null
## 1 0.2575546 0.7424454
## 2 0.8831021 0.1168979
## 3 0.6364610 0.3635390
## 4 0.8032057 0.1967943
## 5 0.8636100 0.1363900
## 6 0.8874397 0.1125603

Posterior Expectations

For pre-computed pi and tau^2, the posterior expected effect size may be calculated via:

post_exp <- PostExp(
  theta = wc_data$theta,
  se = wc_data$se,
  pi = 0.75,
  tau2 = 0.05
)