Simulate a dataframe containing replicate measurements on the same items using different methods.

Simulates a dataframe representing data from a method comparison study. It is returned as a Meth object.

Meth.sim(
  Ni = 100,
  Nm = 2,
  Nr = 3,
  nr = Nr,
  alpha = rep(0, Nm),
  beta = rep(1, Nm),
  mu.range = c(0, 100),
  sigma.mi = rep(5, Nm),
  sigma.ir = 2.5,
  sigma.mir = rep(5, Nm),
  m.thin = 1,
  i.thin = 1
)

Arguments

Ni: The number of items (patient, animal, sample, unit etc.)
Nm: The number of methods of measurement.
Nr: The (maximal) number of replicate measurements for each (item,method) pair.
nr: The minimal number of replicate measurements for each (item,method) pair. If nr<Nr, the number of replicates for each (meth,item) pair is uniformly distributed on the points nr:Nr, otherwise nr is ignored. Different number of replicates is only meaningful if replicates are not linked, hence nr is also ignored when sigma.ir>0.
alpha: A vector of method-specific intercepts for the linear equation relating the "true" underlying item mean measurement to the mean measurement on each method.
beta: A vector of method-specific slopes for the linear equation relating the "true" underlying item mean measurement to the mean measurement on each method.
mu.range: The range across items of the "true" mean measurement. Item means are uniformly spaced across the range. If a vector length Ni is given, the values of that vector will be used as "true" means.
sigma.mi: A vector of method-specific standard deviations for a method by item random effect. Some or all components can be zero.
sigma.ir: Method-specific standard deviations for the item by replicate random effect.
sigma.mir: A vector of method-specific residual standard deviations for a method by item by replicate random effect (residual variation). All components must be greater than zero.
m.thin: Fraction of the observations from each method to keep.
i.thin: Fraction of the observations from each item to keep. If both m.thin and i.thin are given the thinning is by their componentwise product.

Value

A Meth object, i.e. dataframe with columns meth, item, repl and y, representing results from a method comparison study.

Details

Data are simulated according to the following model for an observation $y_{mir}$: $$y_{mir} = \alpha_m + \beta_m(\mu_i+b_{ir} + c_{mi}) + e_{mir}$$ where $b_{ir}$ is a random item by repl interaction (with standard deviation for method $m$ the corresponding component of the vector $\sigma_ir$), $c_{mi}$ is a random meth by item interaction (with standard deviation for method $m$ the corresponding component of the vector $\sigma_mi$) and $e_{mir}$ is a residual error term (with standard deviation for method $m$ the corresponding component of the vector $\sigma_mir$). The $\mu_i$'s are uniformly spaced in a range specified by mu.range.

Author

Lyle Gurrin, University of Melbourne, https://mspgh.unimelb.edu.au/centres-institutes/centre-for-epidemiology-and-biostatistics

Bendix Carstensen, Steno Diabetes Center, https://BendixCarstensen.com

Examples


  Meth.sim( Ni=4, Nr=3 )
  xx <- Meth.sim( Nm=3, Nr=5, nr=2, alpha=1:3, beta=c(0.7,0.9,1.2), m.thin=0.7 )
  summary( xx )
#>        #Replicates
#> Method  1  2  3  4  5 #Items #Obs: 1040 Values:  min      med       max
#>      1  2 14 31 32 21    100        356   -15.609748 34.97557  84.29873
#>      2  4 16 28 35 17    100        345    -6.933551 46.86464 100.62993
#>      3  1 20 31 35 13    100        339   -15.230222 67.02680 140.47183
  plot( xx )