Title: Bias Reduction with Missing Binary Response
Version: 0.1.7
Date: 2019-09-09
Description: Provides two main functions, il() and fil(). The il() function implements the EM algorithm developed by Ibrahim and Lipsitz (1996) <doi:10.2307/2533068> to estimate the parameters of a logistic regression model with the missing response when the missing data mechanism is nonignorable. The fil() function implements the algorithm proposed by Maity et. al. (2017+) https://github.com/arnabkrmaity/brlrmr to reduce the bias produced by the method of Ibrahim and Lipsitz (1996) <doi:10.2307/2533068>.
Depends: R (≥ 2.10)
Imports: boot, brglm, MASS, profileModel, Rcpp, stats
License: GPL-3
Encoding: UTF-8
LazyData: true
RoxygenNote: 6.1.1
NeedsCompilation: no
Packaged: 2019-09-10 01:29:15 UTC; SUDESHNA
Author: Arnab Maity [aut, cre], Vivek Pradhan [aut], Ujjwal Das [aut]
Maintainer: Arnab Maity <arnab.maity@pfizer.com>
Repository: CRAN
Date/Publication: 2019-09-10 22:50:21 UTC

em.fil

Description

It is called by the main function fil and is for internal use.

Usage

em.fil(parameter, X, full.missing.data, observed.data, full.data, family)

Arguments

parameter

The starting values of the parameters as (\beta, \alpha) where \beta is the parameters of original model and \alpha is the for the missing data model.

X

The design matrix with the intercept column.

full.missing.data

The augmented response with design matrix and missing indicator 1 for missing data.

observed.data

The observed response with design matrix and missing indicator 0 for observed data.

full.data

The observed response, augmented response with corresponding design matrix and missing indicator 0 for observed data and 1 for missing data.

family

as in glm. brlrmr currently supports only the "binomial" family with links

References

Bias Reduction in Logistic Regression with Missing Responses when the Missing Data Mechanism is Nonignorable.

em.fil.interaction

Description

It is called by the main function fil and is for internal use.

Usage

em.fil.interaction(parameter, X, full.missing.data, observed.data, full.data, k, family)

Arguments

parameter

The starting values of the parameters as (\beta, \alpha) where \beta is the parameters of original model and \alpha is the for the missing data model.

X

The design matrix with the intercept column.

full.missing.data

The augmented response with design matrix and missing indicator 1 for missing data.

observed.data

The observed response with design matrix and missing indicator 0 for observed data.

full.data

The observed response, augmented response with corresponding design matrix and missing indicator 0 for observed data and 1 for missing data.

k

If interaction is present in the missing data model, then the k is the column number of covariate matrix which has interaction with the response.

family

as in glm. brlrmr currently supports only the "binomial" family with links

References

Bias Reduction in Logistic Regression with Missing Responses when the Missing Data Mechanism is Nonignorable.

em.il

Description

It is called by the main function fil and is for internal use.

Usage

em.il(parameter, X, full.missing.data, observed.data, full.data, family)

Arguments

parameter

The starting values of the parameters as (\beta, \alpha) where \beta is the parameters of original model and \alpha is the for the missing data model.

X

The design matrix with the intercept column.

full.missing.data

The augmented response with design matrix and missing indicator 1 for missing data.

observed.data

The observed response with design matrix and missing indicator 0 for observed data.

full.data

The observed response, augmented response with corresponding design matrix and missing indicator 0 for observed data and 1 for missing data.

family

as in glm. brlrmr currently supports only the "binomial" family with links

References

Bias Reduction in Logistic Regression with Missing Responses when the Missing Data Mechanism is Nonignorable.

em.il.interaction

Description

It is called by the main function fil and is for internal use.

Usage

em.il.interaction(parameter, X, full.missing.data, observed.data, full.data, k, family)

Arguments

parameter

The starting values of the parameters as (\beta, \alpha) where \beta is the parameters of original model and \alpha is the for the missing data model.

X

The design matrix with the intercept column.

full.missing.data

The augmented response with design matrix and missing indicator 1 for missing data.

observed.data

The observed response with design matrix and missing indicator 0 for observed data.

full.data

The observed response, augmented response with corresponding design matrix and missing indicator 0 for observed data and 1 for missing data.

k

If interaction is present in the missing data model, then the k is the column number of covariate matrix which has interaction with the response.

family

as in glm. brlrmr currently supports only the "binomial" family with links

References

Bias Reduction in Logistic Regression with Missing Responses when the Missing Data Mechanism is Nonignorable.

fil

Description

This provides the estimates using IL method and FIL method as described in the reference.

Usage

fil(formula, data, parameter = NULL, family = binomial, alpha = 0.05,
interaction = FALSE, k = NULL, na.action)

Arguments

formula

as in lm. The missing values of response are NA.

data

as in lm. The first column of data is binary missing response. The missing observations are denoted by NA. The rest of the columns are covariates or explanatory variables.

parameter

The starting values of the parameters as (\beta, \alpha) where \beta is the parameters of original model and \alpha is the for the missing data model.

family

as in glm. brlrmr currently supports only the "binomial" family with links.

alpha

This is used for upper 100(1 - alpha)% point of standard Normal distribution. The default is 1.96.

interaction

TRUE or FALSE, whether to consider interaction in the missing data model. Currenly only one intercation between response and covariates is supported. FALSE by default.

k

Which covariate has interaction with response. Takes integer values. User must assign a value if interaction = TRUE.

na.action

as in lm. Always set to na.pass. Note that setting any other value to na.action will remove the NA's from response and hence will break the code as this package is only intended for missing response data.

Value

n

number of observations.

nmissing

the number of missing observations.

missing.proportion

proportion of missing observations.

beta.hat

parameter estimate of logistic regression of y on x using FIL method.

beta.se.hat

standard error using FIL method.

z.value

Wald Z value using FIL method.

p.value

p value using FIL method.

significance.beta.firth

indicator output whether regressors are significant using FIL method, 1 if significant and 0 if not significant.

LCL

Lower Confidence Limits of 100(1 - alpha)% Confidence Intervals.

UCL

Upper Confidence Limits of 100(1 - alpha)% Confidence Intervals.

alpha.hat

parameter estimate due to missing model using FIL.

alpha.se.hat

standard error of the them.

z.value.alpha

Wald Z value for them.

p.value.alpha

p values for them.

References

Bias Reduction in Logistic Regression with Missing Responses when the Missing Data Mechanism is Nonignorable.

Examples

## Not run: 
#############################################
########### Simulated Example ###############
#############################################
data(simulated.data)  # load simulated data

# parameter definition
beta0 <- 1
beta1 <- 1
beta2 <- 1
beta3 <- 1
beta4 <- 1

# parameter definition for missing indicator
alpha0 <- -1.1
alpha1 <- -1
alpha2 <- 1
alpha3 <- 1
alpha4 <- 1
alpha5 <- -1

parameter <- c(beta0, beta1, beta2, beta3, beta4,
               alpha0, alpha1, alpha2, alpha3, alpha4, alpha5)

fil(y ~ x1 + x2 + x3 + x4, data = simulated.data, parameter,
family = binomial(link = "logit"), na.action = na.pass)

## End(Not run)

#############################################
##### Real data example with separation #####
#############################################
data(nhanes)  # load nhanes data
fil(hyp ~ age2 + age3, data = nhanes, family = binomial(link = "logit"), na.action = na.pass)

data(incontinence)  # load nhanes data
fil(y ~ x1 + x2 + x3, data = incontinence, family = binomial(link = "logit"), na.action = na.pass)

il

Description

This provides the estimates using IL method as described in the reference.

Usage

il(formula, data, parameter = NULL, family = binomial, alpha = 0.05,
interaction = FALSE, k = NULL, na.action)

Arguments

formula

as in lm. The missing values of response are NA.

data

as in lm. The first column of data is binary missing response. The missing observations are denoted by NA. The rest of the columns are covariates or explanatory variables.

parameter

The starting values of the parameters as (\beta, \alpha) where \beta is the parameters of original model and \alpha is the for the missing data model.

family

as in glm. brlrmr currently supports only the "binomial" family with links.

alpha

This is used for upper 100(1 - alpha)% point of standard Normal distribution. The default is 1.96.

interaction

TRUE or FALSE, whether to consider interaction in the missing data model. Currenly only one intercation between response and covariates is supported. FALSE by default.

k

Which covariate has interaction with response. Takes integer values. User must assign a value if interaction = TRUE.

na.action

as in lm. Always set to na.pass. Note that setting any other value to na.action will remove the NA's from response and hence will break the code as this package is only intended for missing response data.

Value

n

number of observations.

nmissing

the number of missing observations.

missing.proportion

proportion of missing observations.

beta.hat

parameter estimate of logsitic regression of y on x using IL method.

beta.se.hat

standard error using IL method.

z.value

Wald Z value using IL method.

p.value

p value using IL method.

significance.beta

is indicator output whether regressors are significant using IL method, 1 if significant and 0 if not significant.

LCL

Lower Confidence Limits of 100(1 - alpha)% Confidence Intervals.

UCL

Upper Confidence Limits of 100(1 - alpha)% Confidence Intervals.

alpha.hat

parameter estimate due to missing model using IL.

alpha.se.hat

standard error of the them.

z.value.alpha

Wald Z value for them.

p.value.alpha

p values for them.

sep

separation indicator = 1 if separation, = 0 otherwise

References

Ibrahim, J. G. and Lipsitz, S. R. (1996). Parameter estimation from incomplete data in binomial regression when the missing data mechanism is nonignorable. Biometrics, 52:1071–1078.

Examples

## Not run: 
#############################################
########### Simulated Example ###############
#############################################
data(simulated.data)  # load simulated data

# parameter definition
beta0 <- 1
beta1 <- 1
beta2 <- 1
beta3 <- 1
beta4 <- 1

# parameter definition for missing indicator
alpha0 <- -1.1
alpha1 <- -1
alpha2 <- 1
alpha3 <- 1
alpha4 <- 1
alpha5 <- -1

parameter <- c(beta0, beta1, beta2, beta3, beta4,
               alpha0, alpha1, alpha2, alpha3, alpha4, alpha5)

il(y ~ x1 + x2 + x3 + x4, data = simulated.data, parameter,
family = binomial(link = "logit"), na.action = na.pass)

## End(Not run)

## Not run: 
#############################################
##### Real data example with separation #####
#############################################
data(nhanes)  # load nhanes data
il(hyp ~ age2 + age3, data = nhanes, family = binomial(link = "logit"), na.action = na.pass)
# IL method encounters separation

## End(Not run)

Incontinence example.

Description

A urinary incontinence study.

Usage

incontinence

Format

A data frame with 21 observations on the following 4 variables:

y

Response (1 = continent, 0 = otherwise)

x1

Lower urinary tract measure

x2

Lower urinary tract measure

x3

Lower urinary tract measure

Source

Heinze, G. (2006). A comparative investigation of methods for logistic regression with seperated or nearly separated data. Statistics in Medicine, 25:4216–4226.

Subset of original NHANES data used in mice package.

Description

A small data set with missing values.

Usage

nhanes

Format

A data frame with 25 observations on the following 2 variables:

hyp

Hypertensive (0 = no, 1 = yes)

age2

Age group (1 = 40-59, 0 = otherwise)

age3

Age group (1 = 60+, 0 = otherwise)

Source

Schafer, J.L. (1997). Analysis of Incomplete Multivariate Data. London: Chapman & Hall. Table 6.14.

We simulate this data for the purpose of illustration of the package

Description

A dataset containing the 100 observations and 4 covariates. The covariates are generated from standard normal distribution. The missing binary response is generated using the simulation process as described in the reference.

Usage

simulated.data

Format

A data frame with 100 observations with 28 missing responses: