bcmarg function

Marginal Model of the Mixed Effect Model with the Box-Cox Transformation.

bcmarg returns the inference results the parameters of the marginal model of the linear mixed effect model with the Box-Cox transformation proposed by Maruo et al. (2017). If time and id are not specified, inference results reduce to the results for the context of linear regression model provided by Maruo et al. (2015).

bcmarg(
  formula,
  data,
  time = NULL,
  id = NULL,
  structure = "UN",
  lmdint = c(-3, 3)
)

Arguments

• formula: a two-sided linear formula object describing the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right.
• data: a data frame containing the variables used in the model.
• time: time variable name for repeated measurements. The default is NULL.
• id: subject id variable name for repeated measurements. The default is NULL.
• structure: specify the covariance structure from c("UN", "CS", "AR(1)"). The default is "UN".
• lmdint: a vector containing the end-points of the interval to be searched for a transformation parameter. The default is c(-3, 3).

Returns

an object of class "bcmarg". Objects of this class have methods for the generic functions coef, logLik, print, and summary. The object includes following components for the marginal model parameter inference:

• lambda: a numeric value of the estimate of the transformation parameter.
• beta: a vector with the estimates of the regression parameters.
• alpha: a vector with the estimates of the covariance parameters.
• V: variance-covariance matrix for any subject with no missing values.
• betainf: a matrix containing the inference results for beta under the assumption that lambda is known. Note that standard errors might be underestimated although statistical tests would be asymptotically valid.
• Vtheta.mod: model-based variance-covariance matrix for MLE of the vector of all parameters: c(lambda, beta, alpha).
• Vtheta.rob: robust variance-covariance matrix for MLE of the vector of all parameters.
• logLik: a numeric value of the maximized likelihood.
• adj.prm: a vector with parameters used for the empirical small sample adjustment in bcmmrm: c(number of subjects, number of completed subjects, number of outcome observations, number of missing observations).
• glsObject: an object of "gls" (or "lm" when time and id are not specified) containing results of gls (or lm) function on the transformed scale.

Examples

data(aidscd4)
 bcmarg(cd4 ~ as.factor(treatment) * as.factor(weekc) + age,
        data = aidscd4, time = weekc, id = id, structure = "AR(1)")

References

• Maruo, K., Isogawa, N., Gosho, M. (2015). Inference of median difference based on the Box-Cox model in randomized clinical trials. Statistics in Medicine, 34, 1634-1644, tools:::Rd_expr_doi("10.1002/sim.6408") .
• Maruo, K., Yamaguchi, Y., Noma, H., Gosho, M. (2017). Interpretable inference on the mixed effect model with the Box-Cox transformation. Statistics in Medicine, 36, 2420-2434, tools:::Rd_expr_doi("10.1002/sim.7279") .

See Also

bcmmrm gls