Package 'MBRM'

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)

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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

object	An object of class MRM, typically returned from MRMfit.
R	Integer. Number of replications to simulate the envelopes (default is 100).
...	Additional arguments passed to MRMfit when envelope = TRUE.

Value

A QQ-plot with envelope.

Examples

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

formula	A symbolic description of the model to be fitted, e.g., y ~ x1 + x2. The response variable must be binary (0/1).
data	A data frame containing the variables in the model. The data must include an Ind column indicating cluster or subject IDs for the random effects.
hessian	Logical. Should a numerically differentiated Hessian matrix be returned?
method	Optimization method to be used in optim. One of "Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", or "Brent". Default is "BFGS".
...	Additional arguments passed to optim, such as control, lower, or upper (when supported by the chosen method).

Value

An object of class "MRM" containing:

call	The matched function call.
formula	The model formula.
coefficients	Estimated fixed effects coefficients.
scale	Estimated scale parameter for the random effects distribution.
loglik	Maximized log-likelihood value.
n	Number of clusters or subjects.
m	Vector with the number of observations per cluster.
ep	Estimated standard errors of the parameters.
iter	Number of iterations used by the optimizer.
method	Optimization method used.
data	The original data frame used.

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 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

object	An object of class MRM, typically returned from MRMfit.
...	Additional arguments passed to MRMfit.

Value

A numeric vector of randomized quantile residuals.

Examples

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

n	Integer. Number of clusters or subjects.
m	Integer vector of length n. Each element indicates the number of observations per cluster.
theta	Numeric vector. The first element is the scale or dispersion parameter for the random effects, and the remaining values are the fixed effects coefficients, including the intercept.
X	A data frame or matrix of covariates with n rows (one per cluster). Should not include the intercept.

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)

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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)

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