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glmmrBase (version 0.3.1)

staircase_crt: Generate a staircase/diagonal trial design

Description

Generate a staircase/diagonal cluster randomised trial design model

Usage

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

Value

A Model object with MeanFunction and Covariance objects, or a ModelSpace holding several such Model objects.

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

beta

Vector of beta parameters to initialise the design, defaults to all zeros.

icc

Intraclass correlation coefficient.

cac

Cluster autocorrelation coefficient, optional

iac

Individual autocorrelation coefficient, optional

var

Assumed overall variance of the model, used to calculate the other covariance parameters, see details

family

a family object

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:

$$y_{ijt} \sim F(\mu_{ijt},\sigma)$$ $$\mu_{ijt} = h^-1(x_{ijt}\beta + \alpha_{1j} + \alpha_{2jt} + \alpha_{3i})$$ $$\alpha_{p.} \sim N(0,\sigma^2_p), p = 1,2,3$$

Defining \(\tau\) as the total model variance, then the intraclass correlation coefficient (ICC) is $$ICC = \frac{\sigma_1 + \sigma_2}{\tau}$$ the cluster autocorrelation coefficient (CAC) is : $$CAC = \frac{\sigma_1}{\sigma_1 + \sigma_2}$$ and the individual autocorrelation coefficient as: $$IAC = \frac{\sigma_3}{\tau(1-ICC)}$$

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 \(\alpha_{3i}\) 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` (\(\tau\) 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.

See Also

Model

Examples

Run this code
#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(5,0,0.1),-0.1),icc=0.05, iac = 0.1)

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