SimLongiMix: Simultaneous Inference for Longitudinal Data Using Linear...

In PhilipPallmann/SimLongi: Simultaneous Inference in Longitudinal Data Settings

Description

Simultaneous inference for a set of contrasts (linear combinations) of means in longitudinal scenarios. Computes multiplicity-adjusted p-values and simultaneous confidence intervals for comparing groups at multiple time points, or comparing time points in multiple groups.

Usage

SimLongiMix(data, response, group, time, id, covariates=NULL,
            rand=list("1|id", "time|id", "group|id", "timegroup|id"),
            contrasts=NULL, type="Dunnett", base=1, direction="gpt",
            alternative="two.sided", level=0.95, df="kr")

Arguments

data	A data frame.
response	A character string giving the name of the response variable in data.
group	A character string giving the name of the (treatment) group variable in data.
time	A character string giving the name of the time variable in data.
id	A character string giving the name of the subject variable in data.
covariates	ccc
rand	A list containing the random effects structures to be employed. There are four options of increasing complexity: 1|id for random subject effects; time|id for time-point-specific random subject effects; group|id for treatment-specific random subject effects; and timegroup|id for time-point- and treatment-specific random subject effects. Note that for the latter option the correlation between time-point- and group-specific random effects is (modelled as) zero. Also note that complex models can cause instabilities when being fitted.
contrasts	An optional matrix of appropriate dimensions defining the contrasts to be applied. Default to NULL. See examples.
type	A character string defining the type of contrast matrix (i.e., the set of comparisons); ignored unless contrasts=NULL. Two widespread and often useful choices are Dunnett (many-to-one i.e., compare each group against a common reference) and Tukey (all-pairs i.e., pairwise comparisons of all groups). Further options are Sequen, AVE, Changepoint, Williams, Marcus, McDermott, UmbrellaWilliams, and GrandMean.
base	An integer specifying the reference group with many-to-one comparisons; ignored unless contrasts=NULL and type="Dunnett".
direction	Defines which factor's levels are to be compared at each level of the other factor; ignored unless contrasts=NULL. gpt ("groups per time") invokes comparisons among groups separately and simultaneously for each time point. By contrast, tpg ("times per group") compares time points separately and simultaneously for each group.
alternative	The direction of the alternative to be tested against. Default is two.sided. Options for one-sided testing are greater or less.
level	A numeric value giving the simultaneous confidence level (1 - alpha).
df	A character string specifying the approximation to the degrees of freedom for the multivariate t-distribution. Must be one of kr (Kenward-Roger), pb (Pinheiro-Bates), ess (effective sample size), adj (adjusted), naive (naive), res (residual), or normal (multivariate normal instead of t). See details.

Details

The function performs time-point-wise comparisons of treatment groups, or treatment-group-wise comparisons of points in time, using multiple contrast as described by Hothorn et al. (2008). Test statistics are built with fixed-effects and covariance estimates from an appropriately parameterized linear mixed-effects model (e.g., Verbeke & Molenberghs 2000). If rand contains more than one element, AICc model selection (Burnham & Anderson 2002) is employed for selecting a "best-fitting" model to base further inferences on. Both multiplicity-adjusted p-values and simultaneous confidence intervals are provided.

Several approximations to the degrees of freedom for the multivariate t-distribution can be chosen. kr computes the approximation of Kenward & Roger (1997) as implemented in package pbkrtest. pb invokes the containment degrees of freedom as described by Pinheiro & Bates (2000, p. 91) and implemented in their nlme package. naive calculates the number of independent units minus the number of cell means; it is prone to make results conservative (i.e., not exploit their type I error level). In contrast, residual compute the total number of observations minus the number of cell means and is therefore likely cause anticonservatism. normal uses a critical point from a multivariate normal distribution (i.e., a multivariate t-distribution at "infinite" degrees of freedom).

Value

A list of class silo with elements

Results	A table listing comparisonwise the estimated difference with standard error, lower and upper simultaneous confidence bounds, value of the test statistic, and multiplicity-adjusted p-value.
CovStat	The covariance matrix of test statistics.
CritValue	The critical value (equicoordinate quantile from a multivariate t-distribution).
Alternative	The direction of the alternative.
ConfLevel	The confidence level as specified via level.
DFMethod	The approximation to the degrees of freedom.
DF	The degrees of freedom used for the multivariate t-distribution (zero if multivariate normal).
ContMat	The contrast matrix.
BestMod	The formula (in R syntax) of the AICc-chosen model.
ModSelTab	A model selection table.
AWBest	The Akaike weight of the AICc-chosen model (with respect to the set of models considered).
CovBest	The estimated covariance matrix of the AICc-chosen model.
Model	The fit of the AICc-chosen model.

Author(s)

Philip Pallmann [e-mail]

References

Burnham, K. P. & Anderson, D. R. (2002) Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. Second Edition. Springer, New York, NY.

Hothorn, T., Bretz, F., Westfall, P. (2008) Simultaneous inference in general parametric models. Biometrical Journal, 50(3), 346–363.

Kenward, M. G. & Roger, J. H. (1997) Small sample inference for fixed effects from restricted maximum likelihood. Biometrics, 53(3), 983–997.

Pinheiro, J. C. & Bates, D. M. (2000) Mixed-Effects Models in S and S-PLUS. Springer, New York, NY.

Verbeke, G. & Molenberghs, G. (2000) Linear Mixed Models for Longitudinal Data. Springer, New York, NY.

See Also

SimLongi, SimLongiMMM

Examples

data(heart)

# Many-to-one comparisons of groups per time point
# taking the third group ("control") as reference

Mix <- SimLongiMix(data=heart, response="heartrate", group="drug",
                   time="time", id="person", rand=list("1|id", "time|id"), 
                   direction="gpt", type="Dunnett", base=3)

Mix$Results

# The simplest model was chosen:
Mix$BestMod

# Kenward-Roger-approximated denominator degrees of freedom:
Mix$DF

# A graphical display of simultaneous confidence intervals:
PlotCI(Mix)

PhilipPallmann/SimLongi documentation built on May 8, 2019, 1:34 a.m.