Package {ui}

Support function for ui_causal

Description

Divides the rho interval into a grid

Usage

gridrho_f(rho, gridn, rho_plotrange, plot)

Arguments

Gradient for the loglikelihood used by ui_probit

Description

This function derives the gradient in order for ui_probit to run faster.

Usage

grr(par, rho, Xz = Xz, Xy = Xy, y = y, z = z)

Arguments

Hessian for the loglikelihood used by ui_probit

Description

This function derives the hessian in order for ui_probit to run faster.

Usage

hess(par, rho, Xz = Xz, Xy = Xy, y = y, z = z)

Arguments

Print interval in parantesis

Description

This function allows you to print an interval (vector of two elements) in a parantesis single element.

Usage

interv_p(v, digits = 3)

Arguments

Inverse Mills rato

Description

This function allows you to calculate the inverse Mills ratio.

Usage

lambda0(x)

Arguments

Inverse Mills rato

Description

This function allows you to calculate the inverse Mills ratio.

Usage

lambda1(x)

Arguments

Loglikelihood used by ui_probit

Description

This function derives the Loglikelihood for ui_probit.

Usage

logl_probit(par, rho, Xz = Xz, Xy = Xy, y = y, z = z)

Arguments

Loglikelohood used in sandwich estimator of average causal effect on the treated for DR

Description

Loglikelohood used in sandwich estimator of average causal effect on the treated for DR, support function for ui_causal

Usage

logl_sand_act(x, X, z)

Arguments

Fit maximum likelihood for fixed values of rho

Description

This is a support function for ui_probit

Usage

ml_probit(out_formula, mis_formula, data, rho, progress = TRUE, method = "NR")

Arguments

Plot of UI and CI

Description

Plot function for objects returned from ui_ols. Plots confidence intervals, coefficients and significance assuming ignorability and the uncertainty interval under non-ignorability.

Usage

## S3 method for class 'uiols'
plot(
  x,
  plot.all = TRUE,
  which = NA,
  intercept = FALSE,
  ylab = NULL,
  col = c("black", "royalblue", "lightpink2"),
  ...
)

Arguments

Plot of UI and CI for partial correlation

Description

Plot function for objects returned from ui_pcor. Plots confidence intervals, coefficients and significans assuming ignorability and the uncertainty interval under non-ignorability.

Usage

## S3 method for class 'uipcor'
plot(x, col = c("black", "red"), ...)

Arguments

Plot of UI and CI

Description

Plot function for objects returned from ui_probit.Plots confidence intervals, coefficients and significance assuming ignorability and the uncertainty interval under non-ignorability.

Usage

## S3 method for class 'uiprobit'
plot(
  x,
  plot.all = TRUE,
  which = NA,
  intercept = FALSE,
  ylab = NULL,
  col = c("black", "royalblue", "lightpink2"),
  ...
)

Arguments

Print function for object of class uicausal

Description

Print function for object of class uicausal

Usage

## S3 method for class 'uicausal'
print(x, digits = 3, digitsci = digits, digitsui = digits, ...)

Arguments

Prints objects of class uiols

Description

Prints objects of class uiols

Usage

## S3 method for class 'uiols'
print(x, digits = 3, digitsci = digits, digitsui = digits, ...)

Arguments

Prints objects of class uipcor

Description

Prints objects of class uipcor

Usage

## S3 method for class 'uipcor'
print(x, digits = 3, digitsci = digits, digitsui = digits, ...)

Arguments

Prints objects of class uiprobit

Description

Prints objects of class uiprobit

Usage

## S3 method for class 'uiprobit'
print(x, digits = 3, digitsci = digits, digitsui = digits, ...)

Arguments

Profile method for ui objects

Description

Profile method for ui objects

Usage

profile(x, ...)

Arguments

Plot of UI and CI

Description

Plot function for objects returned from ui_causal. Plots confidence intervals for different values of rho and the uncertainty interval.

Usage

## S3 method for class 'uicausal'
profile(
  x,
  dr = TRUE,
  profile = "all",
  title = NULL,
  xlab = NULL,
  ylab = NULL,
  ...
)

Arguments

Plot of UI and CI

Description

Plot function for objects returned from ui_ols. Plots confidence intervals for different values of rho and the uncertainty interval.

Usage

## S3 method for class 'uiols'
profile(
  x,
  plot.all = TRUE,
  which = NA,
  intercept = FALSE,
  xlab = NULL,
  ylab = NULL,
  scales = "fixed",
  expand = 0.1,
  ...
)

Arguments

Plot of confidence intervals for partial correlation by values of the sensitivity parameter (s).

Description

Plots confidence intervals by values of sensitivity parameter (s) for objects returned from ui_pcor.

Usage

## S3 method for class 'uipcor'
profile(x, ...)

Arguments

Details

Plots estimated partial correlation, lower and upper bounds of confidence intervals for different values of rho (based on on values of the sensitivity parameter(s) in x$gridrho). Plots a 2D plot when missing data only in the outcome or the same missing in the outcome and the predictor of interest (missing data mechanisms A and B). Plots a 3D plot when different missing data in the outcome and the predictor of interest (missing data mechanism C).

Plot of UI and CI

Description

Plot function for objects returned from ui_probit. Plots confidence intervals for different values of rho and the uncertainty interval.

Usage

## S3 method for class 'uiprobit'
profile(
  x,
  plot.all = TRUE,
  which = NA,
  intercept = FALSE,
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  scales = "fixed",
  expand = 0.1,
  ...
)

Arguments

Calculates standard error of Average causal effect on the treated

Description

This is a support function for ui_causal and calculates standard error of Average causal effect on the treated for the doubly robust estimator.

Usage

sand_dr_act(
  deltasigma1,
  X,
  Xz,
  y,
  z,
  u,
  BetaOLSy0,
  phat,
  NaivEst,
  n1,
  n0,
  N,
  p,
  pz
)

Arguments

Calculates standard error of Average causal effect

Description

This is a support function for ui_causal and calculates standard error of Average causal effect for the outcome regression estimator.

Usage

sand_or_ace(X, y, z, BetaOLSy0, BetaOLSy1, NaivEst, N, p)

Arguments

Calculates standard error of Average causal effect on the treated

Description

This is a support function for ui_causal and calculates standard error of Average causal effect on the treated for the outcome regression estimator.

Usage

sand_or_act(X, y, z, BetaOLSy0, NaivEst, n1, N, p)

Arguments

Calculation of se for OLS

Description

This function calculates the se for UI based on OLS when we have MNAR data, for ui_ols.

Usage

se_ols(X, sigma_ols_cor, u, gridrho)

Arguments

Correction of OLS sigma for causal effects

Description

This function is a bias correction of the residual standard deviation under MNAR, for ui_causal.

Usage

sigma_ols_cor0(X, sigma_ols, n, p, u, gridrho)

Arguments

Correction of OLS sigma

Description

This function is a bias correction of the residual standard deviation under MNAR, used by ui_causal and ui_ols.

Usage

sigma_ols_cor1(X, sigma_ols, n, p, u, gridrho)

Arguments

Uncertainty intervals for Average Causal Effects

Description

This function allows you to derive uncertainty intervals for the average causal effect (ACE) or the average causal effect on the treated (ACT). The function uses a regression imputation estimator and a doubly robust estimator. The uncertainty intervals can be used as a sensitivity analysis to unconfoundedness. Note that rho=0 render the same results as assuming no unobserved confounding.

Usage

ui_causal(
  out_formula,
  treat_formula,
  data,
  rho = c(-0.3, 0.3),
  rho0 = NULL,
  rho1 = NULL,
  ACT = FALSE,
  sand = TRUE,
  gridn = 21,
  plot = TRUE,
  rho_plotrange = c(-0.5, 0.5),
  alpha = 0.05
)

Arguments

Details

In order to visualize the results, you can use profile.uicausal. Details about estimators can be found in Genbäck and de Luna (2018)

The standard errors are calculated with the following estimators:

DR ACE - simplified sandwich estimator

DR ACT - sandwich estimator

OR ACE - if sand=TRUE sandwich estimator (default and recommended), if sand=FALSE large sample variance

OR ACT - if sand=TRUE sandwich estimator (default and recommended), if sand=FALSE large sample variance

Value

A list containing:

Author(s)

Minna Genbäck

References

Genbäck, M., de Luna, X. (2018). Causal Inference Accounting for Unobserved Confounding after Outcome Regression and Doubly Robust Estimation. Biometrics. DOI: 10.1111/biom.13001

Examples

library(MASS)
n<-500
delta<-c(-0.3,0.65)
rho<-0.3
X<-cbind(rep(1,n),rnorm(n))
x<-X[,-1]
s0<-2
s1<-3
error<-mvrnorm(n, c(0,0,0), matrix(c(1,0.6,0.9,0.6,4,0.54,0.9,0.54,9), ncol=3))
zstar<-X%*%delta+error[,1]
z<- zstar>0
y1<-ifelse(x< (-1),0.2*x-0.1*x^2, ifelse(x< 1,0.3*x, ifelse(x<3,0.4-0.1*x^2,-0.2-0.1*x)))+error[,3]
y0<-ifelse(x<1.5, x-0.4*x^2, ifelse(x<2, -0.15-0.25*x+0.5*x^2, 1.85-0.25*x))+error[,2]
y<-y0
y[z==1]<-y1[z==1]
data<-data.frame(y,z,x)


ui<-ui_causal(y~x, z~x, data=data, rho=c(0,0.3), ACT=FALSE)
ui
profile(ui)
mean(y1-y0)

ui<-ui_causal(y~x, z~x, data=data, rho=c(0,0.3), ACT=TRUE)
ui
profile(ui)
profile(ui,profile="ui")
mean(y1[z==1]-y0[z==1])

Uncertainty intervals for OLS regression

Description

This function allows you to derive uncertainty intervals for OLS regression when there is missing data in the continuous outcome. The uncertainty intervals can be used as a sensitivity analysis to ignorability (missing at random). Note that rho=0 render the same results as a complete case analysis.

Usage

ui_ols(
  out_formula,
  mis_formula = NULL,
  data,
  rho = c(-0.3, 0.3),
  alpha = 0.05,
  gridn = 101
)

Arguments

Details

In order to visualize the results, you can use plot.uiols, or profile.uiols.

Value

A list containing:

Author(s)

Minna Genbäck

References

Genbäck, M., Stanghellini, E., de Luna, X. (2015). Uncertainty Intervals for Regression Parameters with Non-ignorable Missingness in the Outcome. Statistical Papers, 56(3), 829-847.

Examples

library(MASS)
n<-500
delta<-c(0.5,0.3,0.1)
beta<-c(0.8,-0.2,0.3)
X<-cbind(rep(1,n),rnorm(n),rbinom(n,1,0.5))
x<-X[,-1]
rho=0.4
error<-mvrnorm(n,c(0,0),matrix(c(1,rho*2,rho*2,4),2))
zstar<-X%*%delta+error[,1]
z<-as.numeric(zstar>0)
y<-X%*%beta+error[,2]
y[z==0]<-NA
data<-data.frame(y,x,z)
ui<-ui_ols(y~X1+X2,data=data,rho=c(-0.5,0.5))
ui
plot(ui)

Uncertainty intervals for partial correlation

Description

This function is used to calculate uncertainty intervals for partial correlation between two variables adjusting for a set of other variables. The two variables of interest might have missing data according to the three missing data mechanisms (see reference). Data for the variables in the adjustment set should be completely observed.

Usage

ui_pcor(
  out_formula,
  data,
  rho = c(-0.3, 0.3),
  rho2 = rho,
  alpha = 0.05,
  gridn = 101,
  gridn2 = 11
)

Arguments

Details

In order to visualize the results, you can use plot.uipcor. In the initial publication (see reference), the sensitivity parameter is called gamma, while the function denote the sensitivity paramter as rho for the corespondence with other functions in the package.

Value

A list containing:

Author(s)

Tetiana Gorbach

References

Gorbach, T., de Luna, X. (2018). Inference for partial correlation when data are missing not at random. Statistics & Probability Letters, 141, 82-89.

Examples

library(MASS)
n <- 1000
rho <- 0.1
error <- mvrnorm(n, mu = c(0, 0, 0), Sigma = diag(c(1.16, 0.028^2 * (1 - rho^2), 1)))
X3 <- rnorm(n, mean = 67, sd = 7)
X4 <- rbinom(n, 1, prob = 0.3)
X2 <- 2.313 - 0.042 * X3 - 0.216 * X4 + error[, 1]
X1 <- 1.092 + 0.01 * X2 - 0.002 * X3 - 0.006 * X4 + 0.028 * rho * error[, 3] + error[, 2]
Z <- as.numeric(2.708 + 0.548 * X2 - 0.036 * X3 - 0.042 * X4 + error[, 3] > 0)
X1[Z == 0] <- NA
data <- data.frame(X1, X2, X3, X4)
ui <-  ui_pcor(
 out_formula = X1 ~ X2 + X3 + X4,
 data = data,
 rho = c(0.1, 0.5),
 alpha = 0.05,
 gridn = 10
)
 ui

Uncertainty intervals for probit regression

Description

This function allows you to derive uncertainty intervals for probit regression when there is missing data in the binary outcome. The uncertainty intervals can be used as a sensitivity analysis to ignorability (missing at random), and are derived by maximum likelihood. Note that rho=0 render the same results as a complete case analysis.

Usage

ui_probit(
  out_formula,
  mis_formula = NULL,
  data,
  rho = c(-0.3, 0.3),
  progress = TRUE,
  max_grid = 0.1,
  alpha = 0.05,
  method = "NR"
)

Arguments

Details

In order to visualize the results, you can use plot.uiprobit or profile.uiprobit.

Value

A list containing:

Author(s)

Minna Genbäck

References

Genbäck, M., Ng, N., Stanghellini, E., de Luna, X. (2018). Predictors of Decline in Self-reported Health: Addressing Non-ignorable Dropout in Longitudinal Studies of Aging. European journal of ageing, 15(2), 211-220.

Examples

library(MASS)
n<-500

delta<-c(0.5,0.6,0.1,-1,1)
beta<-c(-0.3,-0.5,0,-0.4,-0.3)

X<-cbind(rep(1,n),rnorm(n),runif(n),rbinom(n,2,0.5),rbinom(n,1,0.5))
x<-X[,-1]
rho=0.4
error<-mvrnorm(n,c(0,0),matrix(c(1,rho,rho,1),2))

zstar<-X%*%delta+error[,1]
z<-as.numeric(zstar>0)

ystar<-X%*%beta+error[,2]
y<-as.integer(ystar>0)
y[z==0]<-NA
data=data.frame(y=y,x1=x[,1],x2=x[,2],x3=x[,3],x4=x[,4])

m<-ui_probit(y~x1+x2+x3+x4,data=data,rho=c(0,0.4))
m
plot(m)
profile(m)