pkci2.flowcytest {rflowcyt} | R Documentation

## Testing the difference of upper-tail distributions of two samples

### Description

This function calculates a cut-off value designating the lower bound of the upper tail as k.hat.pkci2, the given percentile of the control sample, and a 95% confidence interval to test for a significant difference in proportion of stimulated cells and control cells above the threshold, k.hat.pkci2.

### Usage

    pkci2.flowcytest(controldata, stimuldata, crit = 0.999, alpha = 0.05)

### Arguments

`controldata` | vector of data for control cells
`stimuldata` | vector of data for stimulated cells
`crit` | the percent of control sample below the threshold, k.hat.pkci2
`alpha` | The Type I error rate for construction of (1-alpha)% confidence interval

### Details

Sometimes the difference in two sample distributions (control and stimulated) lies in the upper tail (usually at k.hat.pkci2 threshold which is the 99.9th percentile of the control sample). This function applies a standard normal test of the difference of two proportions (One proportion is obtained from the control sample, and one proportion is obtained from the stimulated sample. Both proportions are defined as the proportion of cells within that particular sample that are above the k.hat.pkci2 threhold value.) Please note that the standard normal approximation is used because it is assumed that the control and the stimulated samples are large in size (over 100 observations).

The null hypothesis of the test is that the proportion of the control sample above the k.hat.pkci2 threshold is the same as the proportion of the stimulated sample above the k.hat.pkci2 (ie, the distribution of cells in the tails of both the control and the stimulated samples are the same.)

Two alternative hypotheses are investigated. The one-sided alternative hypothesis states that the stimulated proportion is greater than the control proportion. The two-sided alternative hypothesis is that the stimulated proportion is not equal to the control proportion.

The respective p-values and a 95% confidence interval is obtained from the Z statistic (standard normal statistic).

### Value

`k.hat.pkci2` | the threshold which is the 100*crit-th percentile of the control sample, where crit is the user input value
`pc.hat.pkci2` | the proportion of control cells/data above the k.hat.pkci2 threshold
`ps.hat.pkci2` | the proportion of stimulated cells/data above the k.hat.pkci2 threshold
`lb.pkci2` | The numeric lower bound of the 95% confidence interval from the Z statistic of the test
`up.pkci2` | The numeric upper bound of the 95% confidence interval from the Z statistic of the test
`test.1pkci2` | 0,1 indicator for the one-sided test: 1= reject the null hypothesis, 0=cannot reject the null hypothesis
`pval1.pkci2` | p-value of the one-sided test; Pr(Z > z.statistic)
`test.2pkci2` | 0,1 indicator for the two-sided test: 1= reject the null hypothesis, 0=cannot reject the null hypothesis
`pval2.pkci2` | p-value of the two-sided test; Pr(|Z| > z.statistic )= Pr(Z > z.statistic) + Pr(Z <-z.statistic)

### WARNING

Usually the FCS object is gated and subset prior to this testing and analysis.

### Note

Other flowcytests are available such as `WLR.flowcytest`, `ProbBin.flowcytest`, `KS.flowcytest`, which test the equivalence of two sample distributions. Generally, comparing the control and stimulated samples of the interferon gamma variable is of interest.

### Author(s)

Zoe Moodie and A.J. Rossini and J.Y. Wan

### References

Zoe Moodie, PhD Statistical Center for HIV/AIDS Research and Prevention (SCHARP) Fred Hutchison Cancer Research Center Seattle, WA 98109-1024

### See Also

`WLR.flowcytest`, `ProbBin.flowcytest`, `KS.flowcytest`, `runflowcytests`, `qnorm`, `pnorm`

### Examples

    if (require(rfcdmin)){
    data.there<-is.element(c("st.1829", "unst.1829", "st.DRT", "unst.DRT"),objects())
    if ( ( sum(data.there) != length(data.there) )){
    ## obtaining the FCS objects from VRC data
    data(VRCmin)
    }

    ## This only serves as an example.  Usually the FCS object is
    ## gated and then subset

    ## HIV negative individual 1829
      IFN.control<-unst.1829@data[1:2000,4]
      IFN.stimul<-st.1829@data[1:2000,4]

      output1.pkci2<-pkci2.flowcytest(IFN.control, IFN.stimul, crit=.9999)

    ## HIV positive individual DRT
      IFN.control2<-unst.DRT@data[1:2000,4]
      IFN.stimul2<-st.DRT@data[1:2000,4]
      output2.pkci2<-pkci2.flowcytest(IFN.control2, IFN.stimul2, crit=.9999)

    ## This is an artifical example, but one would expect the
    ## distributions of the stimulated and control samples
    ## to be the same in the HIV negative individual 1829
    ## and to be different in the HIV positive individual DRT
    ## The test in this example is a bit contrived but
    ## the bigger picture is achieved.
    }

[Package rflowcyt version 1.8.0 Index]