LP function

Sensitivity analysis for misspecification of standardized model parameters

Calculates the loss in power associated with misspecification of the standardized model parameters for a specific model.

LP(models, model, type = c("both", "LP1", "LP2"), paramRange,
   doses, base, maxEff, sigma, n, len = c(10, 1), nr = 1,
   alpha = 0.025, twoSide = FALSE, off = 0.1 * max(doses),
   scal = 1.2 * max(doses), control = mvtnorm.control())

Arguments

• models: A list specifying the candidate models. This can also be a fullMod object, then the arguments base, maxEff, off and scal are ignored
• model: Character string giving the model for which the sensitivity should be investigated.
• type: Character string: One of "LP1", "LP2" or "both".
• paramRange: Numeric of length two, giving lower and upper limits for standardized model parameter values when the model has just one standardized model parameter. For models with two standardized model parameters a 2x2 matrix with the boundaries for each standardized model parameter in the rows. See examples for details.
• doses: Dose levels to be administered
• base: Baseline effect
• maxEff: Maximum change from baseline
• sigma: Standard deviation
• n: Numeric vector of sample sizes per group. In case just one number is specified, it is assumed that all group sample sizes are equal to this number.
• len: Number of points in the standardized model parameter range on which LP is calculated. Has to be of length 2 in case of models with 2 standardized model parameters.
• nr: Numeric giving the number of the model (in the order given in the model argument) in case there is more than one model from one model class in the candidate set (e.g. two emax models).
• alpha: Level of significance (default: 0.025)
• twoSide: Logical indicating whether a two sided or a one sided test is performed (defaults to one-sided).
• off: Offset parameter for the linear in log model (default 10 perc. of maximum dose).
• scal: Scale parameter for the beta model (default 20 perc. larger than maximum dose).
• control: A list of options for the pmvt and qmvt functions as produced by mvtnorm.control

Details

For a given set of candidate models the power-sensitivity of the multiple contrast test with respect to misspecification of the guesstimates is investigated. Two measures to measure loss in power ("LP1" or "LP2") can be used. Roughly LP1 can be interpretated as the difference between the power that "was intended" (nominal power), when designing the study and "what one actually gets" (actual power).

LP2 can be interpreted as the difference between "what could be achieved knowing the true value of the parameter in advance" (potential power) and "what one actually gets". For a detailed definition see the reference below. The power values are calculated on a number of points specified by the len argument. The calculation of LP2 is computationally more demanding as the optimal contrasts and the critical value need to be recalculated for each point in the standardized model parameter space.

Returns

An object of class LP, i.e. a matrix containing the different alternative standardized model parameters, associated potential/actual power values and the loss in power values.

References

Bornkamp B., Pinheiro J. C., Bretz, F. (2009). MCPMod: An R Package for the Design and Analysis of Dose-Finding Studies, Journal of Statistical Software, 29 (7), 1--23

Pinheiro, J. C., Bornkamp, B. and Bretz, F. (2006). Design and analysis of dose finding studies combining multiple comparisons and modeling procedures, Journal of Biopharmaceutical Statistics, 16 , 639--656

See Also

plot.LP, guesst

Examples

## Not run:

doses <- c(0,10,25,50,100,150)
models <- list(linear=NULL, emax=c(25),
           logistic=c(50,10.88111), exponential=c(85),
           betaMod=matrix(c(0.33,2.31,1.39,1.39),byrow=TRUE,nrow=2))

# Examples from JBS paper, p.654
LPobj <- LP(models, model = "emax", type = "both", paramRange = c(10,70),
          doses = doses, base = 0, maxEff = 0.4, sigma = 1, n = 60,
          alpha = 0.05, len = 15, scal = 200)
print(LPobj)
plot(LPobj)

# for exponential model with fullMod and LP1:
fMod <- fullMod(models, doses, base = 0, maxEff = 0.4, scal=200)
LPobj <- LP(fMod, "exponential", "LP1", c(50, 120), sigma = 1,
            alpha = 0.05, len = 20, n = 60)
plot(LPobj)

# Examples for models with two standardized model parameters
LP(models, "betaMod", "LP1", 
   paramRange = matrix(c(0.3,1.9,0.4,2.5),nrow=2),
   doses, 0, 0.4, 1, 60, alpha=0.05, len=c(10,4), scal=200)
#  Time consuming example
LPobj <- LP(models, "logistic", "both",
            paramRange = matrix(c(40,5,60,15),nrow=2),    
            doses, 0, 0.4, 1, 60, alpha=0.05, len=c(10,4), scal=200)
plot(LPobj)
## End(Not run)