Arthritis1 Dataset

Description

This dataset contains binary response data from a longitudinal study on rheumatoid arthritis. The data include repeated measurements on 38 individuals, each with 5 time points.

Usage

Arthritis1

Format

A data frame with 190 rows and 6 variables:

Ind

Subject identifier (integer from 1 to 38)

y

Binary response variable (0 or 1)

Sex

Sex indicator (0 = Female, 1 = Male)

Age

Age indicator (0 = <=55 years 1 = > 55 uears)

Treatment

Treatment group (0 = Placebo, 1 = Auranofin)

Time

Time indicator (0 = baseline, 1 = follow-up)

Details

The original data was collected to evaluate the effect of a treatment over time on arthritis severity. Covariates include demographic and clinical variables, and the response is binary (presence/absence of symptoms).

Source

Derived from the original dataset included in:
Arthritis.txt an internal clinical dataset used in Bernoulli-GLG modeling study.

References

Fitzmaurice, G. M. and Lipsitz, S. (1995). A model for binary time series data with serial odds ratio patterns. Journal of the Royal Statistical Society: Series B, 44, 51–61.

Examples

data(Arthritis1)
head(Arthritis1)

# Fit the Bernoulli-LGG model
fit <- MRMfit(y ~ Sex + Age + Treatment + Time, data = Arthritis1)
summary(fit)

Fit Mixed Regression Model with Log-Gamma Random Effects

Description

This function fits a mixed regression model for binary outcomes with random effects following a generalized log-gamma distribution. The estimation is performed by maximizing a custom log-likelihood using numerical optimization via optim.

Usage

MRMfit(formula, data, hessian = TRUE, method = "BFGS", ...)

Arguments

Value

An object of class "MRM" containing:

Examples

# Simulated data
data1 <- rMRM(n = 50, m = rep(3, 50),
              theta = c(0.8, 1, -1, 1),
              X = cbind(x1 = rnorm(150), x2 = rnorm(150)))

# Fit using BFGS (default)
fit1 <- MRMfit(y ~ x1 + x2, data = data1)
summary(fit1)

# Fit using L-BFGS-B with bounds
fit2 <- MRMfit(y ~ x1 + x2, data = data1,
               method = "L-BFGS-B",
               lower = c(1e-5, rep(-Inf, 3)),
               upper = rep(Inf, 4),
               control = list(factr = 1e7))
summary(fit2)

Compute simulation envelopes for MRM model

Description

This function computes the envelopes simulation of the randomized quantile residuals for objects of class MRM.

Usage

envelope.MRM(object, R = 100, ...)

Arguments

Value

A QQ-plot with envelope.

Examples

data(Arthritis1)
fit <- MRMfit(y ~ Sex + Age + Treatment + Time, data = Arthritis1)
envelope.MRM(fit)

Simulate Data from a Mixed Regression Model with GLG Random Effects

Description

This function simulates clustered binary response data from a mixed regression model with random effects. The model allows for different link functions and random effect distributions.

Usage

rMRM(n, m, theta, X)

Arguments

Value

A tibble containing the simulated dataset with the following columns:

Ind

Cluster or subject ID (integer from 1 to n).

y

Binary response variable (0 or 1).

x1, x2, ...

Covariates as defined in X, repeated according to cluster size.

The output also has an attribute "proportions" indicating the proportions of 0's and 1's in y.

Examples

set.seed(123)
n <- 500
m <- rep(3,n)
theta <- c(0.5,1,-2,1)
set.seed(123)
x1 <- runif(sum(m))
x2 <- rnorm(sum(m))
X <- cbind(x1,x2)
set.seed(456)
data1 <- rMRM(n,m,theta,X)
head(data1)

Compute the randomized quantile residuals for MRM model

Description

This function computes the randomized quantile residuals for objects of class MRM.

Usage

## S3 method for class 'MRM'
residuals(object, ...)

Arguments

Value

A numeric vector of randomized quantile residuals.

Examples

data(Arthritis1)
fit <- MRMfit(y ~ Sex + Age + Treatment + Time, data = Arthritis1)
summary(residuals(fit))

toenail Dataset

Description

A data frame with 1908 observations on the following 5 variables.

Usage

toenail

Format

A data frame with 1908 rows and 4 variables:

Ind

Subject identifier (integer from 1 to 38)

y

Binary response is the severity of infection, 0 (not severe) and 1(severe).

treatment

Treatment group (0 = Treatment A, 1 = Treatment B)

month

a numeric vector giving the time of the visit (not exactly monthly intervals hence not round numbers)

visit

a numeric vector giving the number of the visit

Details

The Toenail data discussed in Molenberghs and Verbeke (2010) and Lesaffre and Spiessens (2001 come from a multicenter study comparing two oral treatments (coded as A and B) for toenail (Dermatophyte Onychomycosis - TDO) infection, involved patients evaluated at seven visits, i.e. on weeks 0, 4, 8, 12, 24, 36 and 48. This study was evaluated on 294 patients comprising 1908 measurements. The binary outcome was infection severity, coded as 0 (no and mild) and 1 (moderate and severe). The patients have not been treated prior to the first visit so this should be regarded as the baseline.

References

Molenberghs G, Verbeke G (2010). Models for Discrete Longitudinal data. Springer, New York.

Lesaffre, E. and Spiessens, B. (2001). On the effect of the number of quadrature points in a logistic random-effects model: An example. Journal of the Royal Statistical Society, Series C, 50, 325-335.

Examples

data(toenail)
head(toenail)

# Fit the Bernoulli-LGG model
fit <- MRMfit(y ~ treatment + month + treatment:month, data = toenail)
summary(fit)