MC.Xdc.statistics function

Size and Power for the Several-Sample DM Parameter Test Comparison

This Monte-Carlo simulation procedure provides the power and size of the several sample Dirichlet-Multinomial parameter test comparison, using the likelihood-ratio-test statistics.

MC.Xdc.statistics(group.Nrs, numMC = 10, alphap, type = "ha", 
                siglev = 0.05, est = "mom")

Arguments

• group.Nrs: A list specifying the number of reads/sequence depth for each sample in a group with one group per list entry.

• numMC: Number of Monte-Carlo experiments. In practice this should be at least 1,000.

• alphap: If "hnull": A matrix where rows are vectors of alpha parameters for the reference group.

  If "ha": A matrix consisting of vectors of alpha parameters for each taxa in each group.

• type: If "hnull": Computes the size of the test.

  If "ha": Computes the power of the test. (default)

• siglev: Significance level for size of the test / power calculation. The default is 0.05.

• est: The type of parameter estimator to be used with the Likelihood-ratio-test statistics, 'mle' or 'mom'. Default value is 'mom'. (See Note 2 in details)

Returns

Size of the test statistics (under "hnull") or power (under "ha") of the test.

Details

1. Note 1: Though the test statistic supports an unequal number of reads across samples, the performance has not yet been fully tested.
2. Note 2: 'mle' will take significantly longer time and may not be optimal for small sample sizes; 'mom' will provide a more conservative result in such a case.
3. Note 3: All components of alphap should be non-zero or it may result in errors and/or invalid results.

Examples

data(saliva)
        data(throat)
        data(tonsils)
        
        ### Get a list of dirichlet-multinomial parameters for the data
        fit.saliva <- DM.MoM(saliva) 
        fit.throat <- DM.MoM(throat)
        fit.tonsils <- DM.MoM(tonsils)
        
        ### Set up the number of Monte-Carlo experiments
        ### We use 1 for speed, should be at least 1,000
        numMC <- 1
        
        ### Generate the number of reads per sample
        ### The first number is the number of reads and the second is the number of subjects
        nrsGrp1 <- rep(12000, 9)
        nrsGrp2 <- rep(12000, 11)
        nrsGrp3 <- rep(12000, 12)
        group.Nrs <- list(nrsGrp1, nrsGrp2, nrsGrp3)
        
        ### Computing size of the test statistics (Type I error)
        alphap <- fit.saliva$gamma
        pval1 <- MC.Xdc.statistics(group.Nrs, numMC, alphap, "hnull")
        pval1
        
        ### Computing Power of the test statistics (Type II error)
        alphap <- rbind(fit.saliva$gamma, fit.throat$gamma, fit.tonsils$gamma)
        pval2 <- MC.Xdc.statistics(group.Nrs, numMC, alphap)
        pval2