PwrTime: _A Priori_ Synergy Power Analysis Based on Time

In SynergyLMM: Statistical Framework for in Vivo Drug Combination Studies

A Priori Synergy Power Analysis Based on Time

Description

A priori power calculation for a hypothetical two-drugs combination study of synergy depending on the time of follow-up or the frequency of measurements.

Usage

PwrTime(
  npg = 5,
  time = list(seq(0, 9, 3), seq(0, 21, 3), seq(0, 30, 3)),
  type = "max",
  grwrControl = 0.08,
  grwrA = 0.07,
  grwrB = 0.06,
  grwrComb = 0.03,
  sd_ranef = 0.01,
  sgma = 0.1,
  method = "Bliss",
  ...
)

Arguments

npg	Number of mouse per group.
time	A list in which each element is a vector with the times at which the tumor volume measurements have been performed. If type is set to "max", each vector in the list should represent measurements taken at the same interval and differ in the final time of follow-up. If type is set to "freq", each vector in the list should have the same final time of follow-up and differ in the intervals at which the measurements have been taken.
type	String indicating whether to calculate the power depending on the time of follow-up ("max"), or the frequency of measurements ("freq").
grwrControl	Coefficient for Control treatment group tumor growth rate.
grwrA	Coefficient for Drug A treatment group tumor growth rate.
grwrB	Coefficient for Drug B treatment group tumor growth rate.
grwrComb	Coefficient for Combination (Drug A + Drug B) treatment group tumor growth rate.
sd_ranef	Random effects standard deviation for the model.
sgma	Residuals standard deviation for the model.
method	String indicating the method for synergy calculation. Possible methods are "Bliss" and "HSA", corresponding to Bliss and highest single agent, respectively.
...	Additional parameters to be passed to nlmeU::Pwr.lme method.

Details

PwrTime allows the user to define an hypothetical drug combination study, customizing several experimental parameters, such as the sample size, time of measurements, or drug effect, for the power evaluation of synergy for Bliss and HSA reference models. The power calculation is based on F-tests of the fixed effects of the model as previously described (Helms, R. W. (1992), Verbeke and Molenberghs (2009), Gałecki and Burzykowski (2013)).

The focus the power analysis with PwrTime is on the time at which the measurements are done. The function allows for the evaluation of how the statistical power changes when the time of follow-up varies while the frequency of measurements is keep constant. It also allows to how the statistical power changes when the time of follow-up is kept constant, but the frequency of measurements varies.

For other a priori power analysis see also APrioriPwr() and PwrSampleSize().

• npg, grwrControl, grwrA, grwrB, grwrComb, sd_ranef and sgma are parameters referring to the initial exemplary data set and corresponding fitted model. These values can be obtained from a fitted model, using lmmModel_estimates(), or be defined by the user.

• time is a list in which each element is a vector with the times at which the tumor volume measurements have been performed, and for which the statistical power is going to be evaluated, keeping the rest of parameters fixed.

Value

The functions returns two plots:

• A plot representing the hypothetical data, with the regression lines for each treatment group according to grwrControl, grwrA, grwrB and grwrComb values. The values assigned to sd_ranef and sgma are also shown.

• A plot showing the values of the power calculation depending on the values assigned to Time. If type is set to "max", the plot shows how the power varies depending on the maximum time of follow-up. If type is set to "freq", the plot shows how the power varies depending on how frequently the measurements have been performed.

The function also returns the data frame with the power for the analysis for each value specified in Time.

References

• Helms, R. W. (1992). Intentionally incomplete longitudinal designs: I. Methodology and comparison of some full span designs. Statistics in Medicine, 11(14–15), 1889–1913. https://doi.org/10.1002/sim.4780111411

• Verbeke, G. & Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. Springer New York. https://doi.org/10.1007/978-1-4419-0300-6

• Andrzej Galecki & Tomasz Burzykowski (2013) Linear Mixed-Effects Models Using R: A Step-by-Step Approach First Edition. Springer, New York. ISBN 978-1-4614-3899-1

See Also

PostHocPwr, APrioriPwr(), PwrSampleSize().

Examples

# Power analysis maintaining the frequency of measurements 
# and varying the time of follow-up ('type = "max"')
PwrTime(time = list(seq(0, 9, 3), 
                    seq(0, 12, 3), 
                    seq(0, 15, 3), 
                    seq(0, 21, 3), 
                    seq(0, 30, 3)), 
                    type = "max")

# Power analysis maintaining the time of follow-up 
# and varying the frequency of measurements ('type = "freq"')
PwrTime(time = list(seq(0, 10, 1), 
                    seq(0, 10, 2), 
                    seq(0, 10, 5), 
                    seq(0, 10, 10)), 
                    type = "freq")

SynergyLMM documentation built on April 4, 2025, 4:13 a.m.