staircase_crt: Generate a staircase/diagonal trial design

In samuel-watson/glmmr: Design and analysis for generalised linear mixed models in R

Generate a staircase/diagonal trial design

Description

Generate a staircase/diagonal cluster randomised trial design in glmmr

Usage

staircase_crt(
  J,
  M,
  beta = c(rep(0, J + 1), 0),
  icc,
  cac = NULL,
  iac = NULL,
  var = 1,
  family = gaussian()
)

Arguments

J	Integer indicating the number of sequences such that there are J time periods
M	Integer. The number of individual observations per cluster-period, assumed equal across all clusters
icc	Intraclass correlation coefficient. User may specify more than one value, see details.
cac	Cluster autocorrelation coefficient, optional and user may specify more than one value, see details
iac	Individual autocorrelation coefficient, optional and user may specify more than one value, see details
var	Assumed overall variance of the model, used to calculate the other covariance, see details
family	a family object
nper	Integer. The number of clusters per sequence, default is one.
beta.	Vector of beta parameters to initialise the design, defaults to all zeros.

Details

The staircase/diagonal cluster randomised trial design has J sequences of clusters observed over J time periods, each sequence has 'nper' clusters. The first cluster is observed only once, in the first period in the treatment state. All the remaining clusters are observed twice, once in the control and once in the treatment state staggered over the course of the trial. In each time period there is therefore one cluster/sequence in the control state and one in the treatment state, so that the design produces a "staircase".

The assumed generalised linear mixed model for the staircase/diagonal cluster trial is, for individual i, in cluster j, at time t:

y_{ijt} \sim F(μ_{ijt},σ)

μ_{ijt} = h^-1(x_{ijt}β + α_{1j} + α_{2jt} + α_{3i})

α_{p.} \sim N(0,σ^2_p), p = 1,2,3

Defining τ as the total model variance, then the intraclass correlation coefficient (ICC) is

ICC = \frac{σ_1 + σ_2}{τ}

the cluster autocorrelation coefficient (CAC) is :

CAC = \frac{σ_1}{σ_1 + σ_2}

and the individual autocorrelation coefficient as:

IAC = \frac{σ_3}{τ(1-ICC)}

When CAC and/or IAC are not specified in the call, then the respective random effects terms are assumed to be zero. For example, if IAC is not specified then α_{3i} does not appear in the model, and we have a cross-sectional sampling design; if IAC were specified then we would have a cohort.

For non-linear models, such as Poisson or Binomial models, there is no single obvious choice for 'var_par' (τ in the above formulae), as the models are heteroskedastic. Choices might include the variance at the mean values of the parameters or a reasonable choice based on the variance of the respective distribution.

If the user specifies more than one value for icc, cac, or iac, then a DesignSpace is returned with Designs with every combination of parameters. This can be used in particular to generate a design space for optimal design analyses.

Value

A Design object with MeanFunction and Covariance objects, or a DesignSpace holding several such Design objects.

See Also

Design, DesignSpace

Examples

#generate a simple design with only cluster random effects and 6 clusters with 10
#individuals in each cluster-period
des <- staircase_crt(6,10,icc=0.05)
# same design but with a cohort of individuals
des <- staircase_crt(6,10,icc=0.05, iac = 0.1)
# same design, but with two clusters per sequence and specifying the initial parameters
des <- staircase_crt(6,10,beta = c(rnorm(7,0,0.1),-0.1),icc=0.05, iac = 0.1)
# specifying multiple values of the variance parameters will return a design space 
# with all designs with all the combinations of the variance parameter
des <- staircase_crt(6,10,icc=c(0.01,0.05), cac = c(0.5,0.7,0.9), iac = 0.1)

samuel-watson/glmmr documentation built on July 27, 2022, 10:30 p.m.