eqv.batch {PK}R Documentation

Establishing Bioequivalence in Batch Designs

Description

Confidence intervals for the ratio of independent or dependent area under the concentration versus time curves (AUCs) to the last time point in batch designs.

Usage

eqv.batch(conc, time, group, dependent=FALSE, 
           method=c("fieller", "z", "boott"),
           conf.level=0.90, nsample=1000, data)

Arguments

conc Levels of concentrations as a list.
time Time points of concentration assessment as a list. One time point for each concentration measured needs to be specified.
group A grouping variable as a list.
dependent Logical variable indicating if concentrations are measured on the same subjects for both AUCs (default=FALSE).
method A character string specifying the method for calculation of confidence intervals (default=c("fieller", "z", "boott")).
conf.level Confidence level (default=0.90).
nsample Number of bootstrap iterations for method boott (default=1000).
data Optional data frame containing variables named as id, conc, time and group.

Details

Calculation of confidence intervals for the ratio of (independent or dependent) AUCs (from 0 to the last time point) for batch designs. In a batch design multiple, but not necessarily all, time points are measured for each subject. The AUC (from 0 to the last time point) is calculated using the linear trapezoidal rule on the arithmetic means at the different time points.

dependent specifies if the AUCs are dependent, that is measured on the same subjects. If FALSE, the intervals are based on Jaki et al. (in press) for the batch design. For dependent AUCs the method of Wolfsegger and Jaki (in press), which assumes that subjects, batches and time points are equal for both AUCs, is used.

The fieller method is based on Fieller's theorem (1954) which uses the asymptotic standard errors of the individual AUCs and a critical value from a t-distribution with Satterthwaite's approximation (1946) to the degrees of freedom for calculation of confidence intervals. The z method is based on the limit distribution for the ratio using the critical value from a normal distribution for calculation of confidence intervals.

The boott method uses the asymptotic standard errors of the ratio of two AUCs while the critical value is obtained by the bootstrap-t approach and follows the idea discussed in the context of serial sampling designs in Jaki T. et al. (2009).

If data is specified the variable names id, conc, time and group are required and represent the corresponding variables as well as the subject id.

Value

An object of the class PK containing the following components:
est Point estimates.
CIs Point estimates, standard errors and confidence intervals.
conc Levels of concentrations.
conf.level Confidence level.
design Sampling design used.
group Grouping variable.
time Time points measured.

Author(s)

Thomas Jaki

References

Fieller E. C. (1954). Some problems in interval estimation. Journal of the Royal Statistical Society, Series B, 16:175-185.

Jaki T., Wolfsegger M. J. and Lawo J-P. (in press). Establishing bioequivalence in complete and incomplete data designs using AUCs. Journal of Biopharmaceutical Statistics.

Satterthwaite F. E. (1946). An approximate distribution of estimates of variance components. Biometrics Bulletin, 2:110-114.

Wolfsegger M. J. and Jaki T. (2009) Assessing systemic drug exposure in repeated dose toxicity studies in the case of complete and incomplete sampling. Biometrical Journal, 51(6):1017:1029.

Yeh, C. (1990). Estimation and significant tests of area under the curve derived from incomplete blood sampling. ASA Proceedings of the Biopharmaceutical Section, 74-81.

See Also

eqv, estimator, ci and test.

Examples

## Example of an independent batch design from Yeh (1990) 
conc <- list(batch1=c(0,0,0,0,0,0, 4.690,2.070,6.450,0.1,0.852,0.136, 
                      4.690,4.060,6.450,0.531,1.2,0.607),
           batch2=c(4,1.3,3.2,0.074,0.164,0.267, 6.68,3.83,6.08,0.669,1.21,0.878, 
                    8.13,9.54,6.29,0.923,1.65,1.04),
           batch3=c(9.360,13,5.48,1.090,1.370,1.430, 5.180,5.180,2.79,0.804,1.47,1.26, 
                    1.060,2.15,0.827,0.217,0.42,0.35))  
time <- list(batch1=c(rep(0,6),rep(1,6),rep(4,6)),
             batch2=c(rep(0.5,6),rep(2,6),rep(6,6)),
             batch3=c(rep(8,6),rep(12,6),rep(24,6)))
group <- list(batch1=rep(rep(c(1,2),each=3),3), batch2=rep(rep(c(1,2),each=3),3),
              batch3=rep(rep(c(1,2),each=3),3))

eqv.batch(conc=conc, time=time, group=group, dependent=FALSE, method=c("fieller"), 
    conf.level=0.90)


## example for a dependent batch data design from Wolfsegger and Jaki (2009)
conc <- list(batch1=c(0.46,0.2,0.1,0.1, 1.49,1.22,1.27,0.53, 0.51,0.36,0.44,0.28),
             batch2=c(1.51,1.80,2.52,1.91, 0.88,0.66,0.96,0.48),
             batch3=c(1.52,1.46,2.55,1.04, 0.54,0.61,0.55,0.27))
time <- list(batch1=c(0,0,0,0,1.5,1.5,1.5,1.5,10.5,10.5,10.5,10.5),
             batch2=c(5/60,5/60,5/60,5/60,4,4,4,4),
             batch3=c(0.5,0.5,0.5,0.5,7,7,7,7))
group <- list(batch1=c(1,1,2,2,1,1,2,2,1,1,2,2), batch2=c(1,1,2,2,1,1,2,2),
              batch3=c(1,1,2,2,1,1,2,2))

eqv.batch(conc=conc, time=time, group=group, dependent=TRUE, method=c("fieller"), 
     conf.level=0.90)

[Package PK version 1.2-1 Index]