randomSlopesMatrix {LPower}

Creates the xMatrix and zMatrix, and attrition rates for a two treatment clinical trial analyzed using the random slopes model.

Description

In the random slopes model each patient has a linear trajectory over time with a random intercept and slope. The intercepts are assumed to be the same for each of two treatment groups and the treatment effect is measured by the difference in average slopes.

Usage

randomSlopesMatrix(visit, vs, sigma2, dropPerMonth,baselineTreatment=FALSE)

Arguments

visit

A vector of visit times or a list of two visit time vectors if the treatments have different visit times.

vs

The variance covariance matrix of the intercept and slope random effects.

sigma2

The error variance.

dropPerMonth

Either a single number which is the attrition rate or a vector of attrition rates for each visit. Note this would have length one less than the number of visits since the attrition after the last visit would not be used.

baselineTreatment

A logical indicating whether their treatment is in the model as a main effect. In a random slopes model the effect or treatment is measured by the treatment-time interaction.

Details

This calculates the matrices for the random slopes model y_{t}=\mu+\beta_1 t+ \beta_2 t*I(\rm{rx}=1)+u+b t+\sigma^2 \epsilon, where u,b,\epsilon are random variables. Note that a treatment main effect is not included in the model by default, because in a randomized study the treatments should be the same at the baseline visit. This practice may vary.

Value

A list of xMatrix,vMatrix,attritionRates for input into LPower

Author(s)

David A. Schoenfeld

References

Q Yi and T. Panzarella. Estimating sample size for tests on trends across repeated measurements with missing data based on the interaction term in a mixed model. Control Clin Trials, 23(5):481–96, 2002.

See Also

LPower

Examples

vars=randomSlopesMatrix(list(c(0,1,2,4,6),c(0,1,2,4,6)),
                matrix(c(31.8,.8527,.8527,.6687),2,2),2.7085,.02)
LPower(sample_size=40,power=.8,xMatrix=vars$xMatrix,
vMatrix=vars$vMatrix,attritionRates=vars$attritionRates)