Multiple inference

Description

Compute adjusted p-values and simultaneous confidence intervals for given bi- and trifactorial design data.

Usage

mintest(C,test=NULL,method="bootstrap",nboot=NULL,simerror=NULL,...)
margint(C,test=NULL,method="bootstrap",nboot=NULL,simerror=NULL,
        alpha=0.05,...)

Arguments

Details

The generic functions mintest and margint calculate adjusted p-values and simultaneous confidence intervals for the test of parametric differences between prespecified treatment groups on bi- or trifactorial design clinical trials. If an object of class carpet is commited, mintest will return adjusted p-values for the min-test on combination superiority in bifactorial clinical trial designs (Laska and Meisner, 1989). The alternative hypothesis of this test is that the detected effect size for the combination treatment is better than for both single component groups; i.e. the test results in only one p-value for each combination. The generic function margint will, when applied to carpet objects, return simultaneous confidence intervals for the parametric differences between each combination treatment group and its respective components. Depending on the type of data, the calculations can be based on Student's t-test for metric data or the Z-statistic for binary applications.

By default, the calculations are performed by a resampling-based approach. The desired simulation accuracy always needs to be specified by the number nboot of bootstrap iterations to perform or an upper bound simerror for the simulation standard error. If both are given, the two constraints will be held simultaneously. On the other hand, the multivariate normal approach for unbalanced designs from Hung (2000) is available when the argument method is set to the value "hung". For the trifactorial case, no such approach is available and thus the calculations are based on the bootstrap approach, performing a generalized min-test on the data, if an object of class cube is commited. The interval calculations are based on the multivariate t-distribution if "tdistr" is specified.

In the classical approach to the min-test, a normality assumption for the data is used and the desired critical values are calculated using quantiles of the multivariate t-distribution. However, this method fails when handling with data that are skewed or heteroscedastic over the treatment groups. When using the bootstrap, only the empirical distribution of the data is used and thus the results are always valid, provided that a sufficiently large samples are available. When handling with data from bifactorial clinical trial designs, bootstrap methods need much less analytical framework on the distributional properties of the tests than if the approach given by Hung (2000) is used. In particular, the restriction to only two compounds is not needed and binary data applications can be handled analogously. The theory of resampling-based multiple testing has been extensively discussed by Westfall and Young (1993).

The calculation of simultaneous confidence intervals is much easier because the c.d.f. of the min-statistic is not needed. Hence this is leading to an ordinary multiple contrast problem.

Value

An object of class mintest or margint with the following slots.

Note

Performance of the implemented methods has been evaluated and compared. The min-test performs very conservative if the means in the marginal treatment groups are close for a combination.

Author(s)

Peter Frommolt, University of Cologne peter.frommolt@uni-koeln.de
http://portal.ccg.uni-koeln.de

References

Frommolt P, Hellmich M (2009): Resampling in multiple-dose factorial designs. Biometrical J 51(6), pp. 915-31

Hung HMJ, Chi GYH, Lipicky RJ (1993): Testing for the existence of a desirable dose combination. Biometrics 49, pp. 85-94

Hung HMJ, Wang SJ (1997): Large-sample tests for binary outcomes in fixed-dose combination drug studies. Biometrics 53, pp. 498-503

Hung HMJ (2000): Evaluation of a combination drug with multiple doses in unbalanced factorial design clinical trials. Statist Med 19, pp. 2079-2087

Hellmich M, Lehmacher W (2005): Closure procedures for monotone bi-factorial dose-response designs. Biometrics 61, pp. 269-276

Laska EM, Meisner MJ (1989): Testing whether an identified treatment is best. Biometrics 45, pp. 1139-1151

Snapinn SM (1987): Evaluating the efficacy of a combination therapy. Statist Med 6, pp. 657-665

Westfall PH, Young SS (1993): Resampling-based multiple testing. John Wiley & Sons, Inc., New York

See Also

bifactorial, carpet, cube, avetest, maxtest,

Examples

#AML example from Huang et al. (2007) with data from
#Issa et al. (2004) and Petersdorf et al. (2007)
n<-c(10,31,17,100,50,50,101,50,50)
p<-c(0.00,0.45,0.65,0.30,0.71,0.70,0.59,0.64,0.75)
y<-list()
for(i in 1:9){
  y[[i]]<-0
  while((sum(y[[i]])!=round(n[i]*p[i]))||(length(y[[i]])==1)){
    y[[i]]<-rbinom(n[i],1,p[i])
  }
}

aml<-carpet(data=y,D=c(2,2))
mintest(aml,test="ztest",nboot=25000)
margint(aml,test="ztest",nboot=25000)

Results