Package 'lbreg' reference manual

Title:	Log-Binomial Regression with Constrained Optimization
Description:	Maximum likelihood estimation of log-binomial regression with special functionality when the MLE is on the boundary of the parameter space.
Authors:	Bernardo B. Andrade
Maintainer:	Bernardo Andrade <[email protected]>
License:	GPL-2
Version:	1.3
Built:	2024-12-25 06:38:11 UTC
Source:	CRAN

Log-Binomial Regression with Constrained Optimization

Description

Maximum likelihood estimation of log-binomial regression with special functionality when the MLE is on the boundary of the parameter space.

Package lbreg performs maximum likelihood estimation of Log-Binomial Regression. The main functions are lbreg which provides a shortcut to constrOptim to estimate LBR coefficients and relrisk which takes lbreg results to produce estimated relative risks and associated confidence intervals and prediction. Results differ from glm when the MLE is on the boundary of the parameter space as explained in the reference below (Andrade, Andrade (2018)).

Details

The DESCRIPTION file:

Package:	lbreg
Type:	Package
Title:	Log-Binomial Regression with Constrained Optimization
Description:	Maximum likelihood estimation of log-binomial regression with special functionality when the MLE is on the boundary of the parameter space.
Version:	1.3
Date:	2019-12-13
Author:	Bernardo B. Andrade
Maintainer:	Bernardo Andrade <[email protected]>
License:	GPL-2
Depends:	R (>= 3.2.0)
Imports:	MASS
NeedsCompilation:	no
Packaged:	2019-12-13 13:57:19 UTC; root
Repository:	CRAN
Date/Publication:	2019-12-13 14:20:06 UTC

Index of help topics:

Birth                   Birth Weight Data
Caesarian               Caesarian Infection Dataset
Death                   Death Penalty Data
Evans                   Evans County dataset
HL_test                 Hosmer-Lemeshow Goodness of Fit Test
Heart                   Heart Dataset
PCS                     PCS Dataset
lbreg                   Log-Binomial regression
lbreg-package           Log-Binomial Regression with Constrained
                        Optimization
predict.lbreg           Predict method for Log-Binomial regression.
relrisk                 Regression Adjusted Relative Risks

Author(s)

Bernardo B. Andrade

Maintainer: Bernardo Andrade <[email protected]>

References

Andrade, BB; Andrade JML (2018) Some results for Maximum Likelihood Estimation of Adjusted Relative Risks. Communications in Statistics - Theory and Methods.

Birth Weight Data

Description

Data used by Wacholder (1986) to illustrate the use of log binomial regression for estimating adjusted relative risks of a low-birthweight baby.

Usage

data("Birth")data("Birth")

Format

A data frame with 900 observations on the following 5 variables.

lowbw: low birth weight delivery (1=yes)
alc: mother's alcohol drinking frequency (1=Light, 2=Moderate, 3=Heavy)
smo: mother smoked (1=no)
soc: mother's social status (1=I and II (lower), 2=III (middle), 3=IV and V (upper))

Source

Stata's online manual http://www.stata.com/manuals13/rbinreg.pdf

References

Wright JT, Waterson EJ, Barrison PJ, et al. (1983). Alcohol consumption, pregnancy and low birthweight. Lancet 1:663-665.

Examples

data(Birth)
dim(Birth)
names(Birth)

data(Birth)
dim(Birth)
names(Birth)

Caesarian Infection Dataset

Description

Adapted dataset from Fahrmeir et al (2013): grouped data on infections of 251 mothers after a C-section collected at the clinical center of the University of Munich.

Usage

data("Caesarian")data("Caesarian")

Format

A data frame with 7 rows and 5 variables.

n1: Caesarians with infections.
n0: Caesarians without infections.
NPLAN: = 1 if C-section was not planned.
RISK: = 1 if risk factors existed.
ANTIB: = 1 if antibiotics were administered as prophylaxis.

Source

http://www.uni-goettingen.de/de/551625.html

References

Fahrmeir, L., Kneib, Th., Lang, S., Marx, B. (2013) Regression - Models, Methods and Applications. Springer.

Examples

data(Caesarian)
Caesarian
# no observations for case (RISK=0, NPLAN=1, ANTIB=1)
y = Caesarian[,1:2]
cbind(Caesarian[,3:5], total=rowSums(y))
colSums(y)
data(Caesarian)
Caesarian
# no observations for case (RISK=0, NPLAN=1, ANTIB=1)
y = Caesarian[,1:2]
cbind(Caesarian[,3:5], total=rowSums(y))
colSums(y)

Death Penalty Data

Description

See references.

Usage

data("Death")data("Death")

Format

A data frame with 147 observations on the following 6 variables.

death: death = 1, life in prison = 0
blackd: black defendant = 1
whitvic: white victim = 1
serious: a measure of crime seriousness
culp: a measure of culpability
serious2: another measure of crime seriousness

Source

SAS Institute Inc. (2006). Logistic regression using the SAS system: Theory and application. SAS Publishing, Cary, NC: SAS Institute Inc; http://ftp.sas.com/~samples/A55770

References

Petersen MR, Deddens JA (2010). Maximum Likelihood Estimation of the Log-Binomial Model. Communications in Statistics: Theory and Methods, 39, 874-883.

Examples

data(Death)
dim(Death)
names(Death)
data(Death)
dim(Death)
names(Death)

Evans County dataset

Description

Data from cohort study in which white males in Evans County were followed for 7 years, with coronary heart disease as the outcome of interest.

Usage

data("Evans")data("Evans")

Format

A data frame with 609 observations on the following 9 variables.

CDH: outcome variable; 1 = coronary heart disease
CAT: 1 = high, 0 = normal catecholamine level
AGE: age (in years)
CHL: cholesterol, mg/dl
SMK: 1 = subject has ever smoked
ECG: 1 = presence of electrocardiogram abnormality
DBP: diastolic blood pressure, mmHg
SBP: systolic blood pressure, mmHg
HPT: 1 = SBP greater than or equal to 160 or DBP greater than or equal to 95

Source

http://web1.sph.emory.edu/dkleinb/logreg3.htm#data

References

D. Kleinbaum and M. Klein (2010) Survival Analysis: A Self-Learning Text. 3rd ed. Springer.

Examples

data(Evans)
dim(Evans)
names(Evans)

data(Evans)
dim(Evans)
names(Evans)

Heart Dataset

Description

Heart attack data from the ASSENT-2 study.

Usage

data("Heart")data("Heart")

Format

A data frame with 16,949 observations on the following 5 variables.

Heart: binary response; 1 = death
age: categorized into <65, 65-75 or >75 years
severity: Killip class I, II, or III/IV
region: code for three USA regions
onset: treatment delay categorized into <2, 2-4 or >4 hours

Source

http://biostatistics.oxfordjournals.org/content/13/1/179/suppl/DC1

References

ASSENT-2 INVESTIGATORS (1999). Single-bolus tenecteplase compared with front-loaded alteplase in acute myocardial infarction: the ASSENT-2 double-blind randomised trial. Lancet 354, 716-722.

Ian C. Marschner and Alexandra C. Gillett (2012) Relative risk regression: reliable and flexible methods for log-binomial models. Biostatistics 13, 179-192

Examples

data(Heart)
dim(Heart)
names(Heart)

data(Heart)
dim(Heart)
names(Heart)

Hosmer-Lemeshow Goodness of Fit Test

Description

The HL decile-of-risk test. Validity of the test assumes that the number of covariate patterns is close to the number of observations which is violated when many observations have the same covariate pattern and several ties will impact the required ordering and grouping (by deciles) of observations. This is less likely when there is at least one continuous covariate. Not valid for grouped data.

Usage

 HL_test(object, g = 10) HL_test(object, g = 10)

Arguments

`object`	object of class 'lbreg'.
`g`	number of groups

Value

A list with elements

`X2`	HL statistic
`pvalue`	p-value for the test from Chi Squared with df = g-2

Author(s)

Bernardo B. Andrade

References

Hosmer D W, Lemeshow S 2000. Applied Logistic Regression. New York, USA: John Wiley and Sons.

Examples

require(lbreg)

# data preparation
data(PCS)
w <- PCS
w <- w[,-1]
w$race <- factor(w$race)
w$dpros <- factor(w$dpros)
w$dcaps <- factor(w$dcaps)

fm <- lbreg(tumor ~ ., data=w)

HL_test(fm)
require(lbreg)

# data preparation
data(PCS)
w <- PCS
w <- w[,-1]
w$race <- factor(w$race)
w$dpros <- factor(w$dpros)
w$dcaps <- factor(w$dcaps)

fm <- lbreg(tumor ~ ., data=w)

HL_test(fm)

Log-Binomial regression

Description

Fitting a Log-Binomial Regression Model

Usage

lbreg(formula, data, start.beta, tol=0.9999, delta=1, ...)
lbreg(formula, data, start.beta, tol=0.9999, delta=1, ...)

Arguments

`formula`	an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
`data`	an optional data frame containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lbreg is called.
`start.beta`	starting values for the parameters in the linear predictor. If missing, the default value explained in Andrade and Andrade (2018) is used according to the choice of `delta`.
`tol`	defaults to 0.9999; threshold for declaring a probability on the boundary (p = 1).
`delta`	defaults to 1. See reference below.
`...`	not used.

Details

This function uses constrOptim with the BFGS method in order to perform maximum likelihood estimation of the log-binomial regression model as described in the reference below. When the MLE is the interior of the parameter space results should agree with glm(...,family=binomial(link='log')). lbreg uses the adaptive logarithimic barrier algorithm rather than iteratively weighted least squares (glm).

Value

`Active`	matrix of active constraints.
`barrier.value`	same as in `constrOptim`.
`coefficients`	named vector of estimated regression coefficients.
`convergence`	same as in `constrOptim`.
`call`	the matched call.
`cook.distance`	Cook's distance.
`data`	the data argument.
`deviance`	residual deviance.
`dev.resid`	deviance residuals.
`fitted.values`	fitted probabilities.
`formula`	the formula supplied.
`hat.matrix`	hat matrix for GLMs (whose diagonal contains leverage values).
`loglik`	maximized loglikelihood.
`outer.iterations`	same as in `constrOptim`.
`residuals`	Pearson residuals.
`se`	standard errors of estimated coefficients.
`start.beta`	starting values used by `constrOptim`.
`vcov`	variance-covariance matrix of estimates.
`vcov0`	inverse of observed Fisher information; should be equal to vcov if there are no active constraints (Active = NULL).
`X2`	sum of squared residuals (variance-inflation estimate (dispersion) = X2/df).

Author(s)

Bernardo B. Andrade

References

Andrade, BB; Andrade JML (2018) Some results for Maximum Likelihood Estimation of Adjusted Relative Risks. Communications in Statistics - Theory and Methods.

Examples

require(lbreg)

# data preparation
data(PCS)  # ungrouped data
w <- PCS
w <- w[,-1]
w$race <- factor(w$race)
w$dpros <- factor(w$dpros)
w$dcaps <- factor(w$dcaps)

# log-binomial regression
fm <- lbreg(tumor ~ ., data=w)
fm
coef(fm)
summary(fm)


# grouped data
require(lbreg)
data(Caesarian)
m1 <- lbreg( cbind(n1, n0) ~ RISK + NPLAN + ANTIB, data=Caesarian)
summary(m1)

# dispersion estimate based on deviance residuals
sum(m1$dev.res^2)  
# dispersion estimate based on Pearson residuals (reported in the summary above)
sum(m1$residuals^2)/(8-4)  

predict(m1, newdata=data.frame(RISK=0, NPLAN=1, ANTIB=1))

# m0 <- glm( cbind(n1, n0) ~ RISK + NPLAN + ANTIB, data=Dat, family=binomial(link='log'))
# summary(m0)


require(lbreg)

# data preparation
data(PCS)  # ungrouped data
w <- PCS
w <- w[,-1]
w$race <- factor(w$race)
w$dpros <- factor(w$dpros)
w$dcaps <- factor(w$dcaps)

# log-binomial regression
fm <- lbreg(tumor ~ ., data=w)
fm
coef(fm)
summary(fm)


# grouped data
require(lbreg)
data(Caesarian)
m1 <- lbreg( cbind(n1, n0) ~ RISK + NPLAN + ANTIB, data=Caesarian)
summary(m1)

# dispersion estimate based on deviance residuals
sum(m1$dev.res^2)  
# dispersion estimate based on Pearson residuals (reported in the summary above)
sum(m1$residuals^2)/(8-4)  

predict(m1, newdata=data.frame(RISK=0, NPLAN=1, ANTIB=1))

# m0 <- glm( cbind(n1, n0) ~ RISK + NPLAN + ANTIB, data=Dat, family=binomial(link='log'))
# summary(m0)

PCS Dataset

Description

Prostate Cancer Study

Usage

data("PCS")data("PCS")

Format

A data frame with 380 observations on the following 9 variables.

id: Identification Code; 1 - 380
tumor: Tumor Penetration of Prostatic Capsule, 0 = No Penetration
age: in years
race: Race; 1= White, 2 = Black
dpros: Results of the Digital Rectal Exam, 4 levels
dcaps: Detection of Capsular Involvement in Rectal Exam; 1 = No, 2 = Yes
psa: antigen mg/ml
vol: Tumor Volume Obtained from Ultrasound, cm3
gleason: Total Gleason Score; 0 - 10

Source

https://www.umass.edu/statdata/statdata/data/pros.txt

References

Hosmer and Lemeshow (2000) Applied Logistic Regression, Wiley.

Examples

data(PCS)
## View(PCS)
## str(PCS) ; plot(PCS) ...
data(PCS)
## View(PCS)
## str(PCS) ; plot(PCS) ...

Predict method for Log-Binomial regression.

Description

Predicted values based on 'lbreg' object.

Usage

## S3 method for class 'lbreg'
predict(object, newdata, ...)
## S3 method for class 'lbreg'
predict(object, newdata, ...)

Arguments

`object`	Object of class inheriting from "lbreg"
`newdata`	a data frame with covariate values with which to predict. If omitted, the fitted probabilities are returned.
`...`	not used

Details

If newdata is omitted the predictions are simply the fitted values stored in the object supplied.

Value

`Active`	active restrictions (taking newdata into account).
`coef.pred`	regression coefficients re-estimated to satisfy possibly new restrictions imposed by newdata. See reference below.
`convergence`	same as in the object supplied.
`se.pred`	estimated standard errors of predictions.
`tol`	same as in the object supplied.
`ypred`	predicted probabilities for newdata.

Author(s)

Bernardo B. Andrade

References

Andrade, BB; Andrade JML (2018) Some results for Maximum Likelihood Estimation of Adjusted Relative Risks. Communications in Statistics - Theory and Methods.

Examples

require(lbreg)

# data preparation
data(PCS)
w <- PCS
w <- w[,-1]
w$race <- factor(w$race)
w$dpros <- factor(w$dpros)
w$dcaps <- factor(w$dcaps)

# log-binomial regression
fm <- lbreg(tumor ~ ., data=w)
novo <- data.frame(age=c(41, 32), race=c(1,2), dpros=c(2,4), 
                   dcaps=c(1,1), psa=c(7.24,3.25), vol=c(4.3,5.6), 
                   gleason=c(2,8))
predict(fm, newdata=novo)
require(lbreg)

# data preparation
data(PCS)
w <- PCS
w <- w[,-1]
w$race <- factor(w$race)
w$dpros <- factor(w$dpros)
w$dcaps <- factor(w$dcaps)

# log-binomial regression
fm <- lbreg(tumor ~ ., data=w)
novo <- data.frame(age=c(41, 32), race=c(1,2), dpros=c(2,4), 
                   dcaps=c(1,1), psa=c(7.24,3.25), vol=c(4.3,5.6), 
                   gleason=c(2,8))
predict(fm, newdata=novo)

Regression Adjusted Relative Risks

Description

This function calculates the relative risks RR adjusted for covariates (acting on a previous log-binomial regression fit) and confidence intervals (by default 95 percent) for the estimated RR. The confidence interval is calculated from the log(RR) and backtransformed.

Usage

relrisk(object, alpha = 0.05, dispersion = FALSE)
relrisk(object, alpha = 0.05, dispersion = FALSE)

Arguments

`object`	object of class 'lbreg'.
`alpha`	1 - desired confidence level.
`dispersion`	logical. `TRUE` if standard errors should be adjusted for dispersion estimate based on Pearson residuals.

Value

value

table with estimated relative risks, lower and upper bounds of condifidence intervals.

Author(s)

Bernardo B. Andrade

References

Andrade, BB; Andrade JML (2018) Some results for Maximum Likelihood Estimation of Adjusted Relative Risks. Communications in Statistics - Theory and Methods.

Examples

require(lbreg)

# ungrouped data
# data preparation
data(PCS)
w <- PCS
w <- w[,-1]
w$race <- factor(w$race)
w$dpros <- factor(w$dpros)
w$dcaps <- factor(w$dcaps)

# log-binomial regression
fm <- lbreg(tumor ~ ., data=w)

# relative risks
relrisk(fm)
relrisk(fm, alpha=.10)

# grouped data 
require(lbreg)
data(Caesarian)
m1 <- lbreg( cbind(n1, n0) ~ RISK + NPLAN + ANTIB, data=Caesarian)
relrisk(m1)
relrisk(m1, dispersion=TRUE)


require(lbreg)

# ungrouped data
# data preparation
data(PCS)
w <- PCS
w <- w[,-1]
w$race <- factor(w$race)
w$dpros <- factor(w$dpros)
w$dcaps <- factor(w$dcaps)

# log-binomial regression
fm <- lbreg(tumor ~ ., data=w)

# relative risks
relrisk(fm)
relrisk(fm, alpha=.10)

# grouped data 
require(lbreg)
data(Caesarian)
m1 <- lbreg( cbind(n1, n0) ~ RISK + NPLAN + ANTIB, data=Caesarian)
relrisk(m1)
relrisk(m1, dispersion=TRUE)

Package 'lbreg'

Help Index

Log-Binomial Regression with Constrained Optimization

Description

Details

Author(s)

References

Birth Weight Data

Description

Usage

Format

Source

References

Examples

Caesarian Infection Dataset

Description

Usage

Format

Source

References

Examples

Death Penalty Data

Description

Usage

Format

Source

References

Examples

Evans County dataset

Description

Usage

Format

Source

References

Examples

Heart Dataset

Description

Usage

Format

Source

References

Examples

Hosmer-Lemeshow Goodness of Fit Test

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Log-Binomial regression

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

PCS Dataset

Description

Usage

Format

Source

References

Examples

Predict method for Log-Binomial regression.

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Regression Adjusted Relative Risks

Description

Usage