[R] How to test frequency independence (in a 2 by 2 table) with many missing values

[Robert A LaBudde]

1. Drop all subjects where both test results are not present. These 
are uninformative on the difference.

2. Perform McNemar test on the remaining table. (Only the different 
pairs are informative.)

This will give you a p-value on the data that actually contrasts the 
two tests. (For your example, the p-value is

 > X2<- data.frame(x1.m, x2.m)
 > tX2<- table(X2)
 > tX2
     x2.m
x1.m  0  1
    0  6  5
    1 15  4
 > mcnemar.test(tX2)

         McNemar's Chi-squared test with continuity correction

data:  tX2
McNemar's chi-squared = 4.05, df = 1, p-value = 0.04417


The low power is a consequence of the data not being informative. 
You'll have to live with it.

If you want to squeeze any more out this data, I'd guess about the 
only way to do it would be via a maximum likelihood approach with 
marginals for the one test only data, an assumption of, e.g., a 
binomial distribution for each test, and then use a likelihood ratio 
test for p1=p2 vs. p1!=p2.

If you really feel up to it, you could program a randomization or 
bootstrap test equivalent to the ML approach, maintaining the 
marginal totals involved.

At 01:23 PM 7/24/2009, Tal Galili wrote:
>Hello dear R help group.
>
>My question is statistical and not R specific, yet I hope some of you might
>be willing to help.
>
>*Experiment settings*:  We have a list of subjects. each of them went
>through two tests with the answer to each can be either 0 or 1.
>*Goal*: We want to know if the two experiments yielded different results in
>the subjects answers.
>*Statistical test (and why it won't work)*: Naturally we would turn to
>performing a mcnemar test. But here is the twist: we have missing values in
>our data.
>For our purpose, let's assume the missingnes is completely at random, and we
>also have no data to use for imputation. Also, we have much more missing
>data for experiment number 2 then in experiment number 1.
>
>So the question is, under these settings, how do we test for experiment
>effect on the outcome?
>
>So far I have thought of two options:
>1) To perform the test only for subjects that has both values. But they are
>too scarce and will yield low power.
>2) To treat the data as independent and do a pearson's chi square test
>(well, an exact fisher test that is) on all the non-missing data that we
>have. The problem with this is that our data is not fully independent (which
>is a prerequisite to chi test, if I understood it correctly). So I am not
>sure if that is a valid procedure or not.
>
>Any insights will be warmly welcomed.
>
>
>p.s: here is an example code producing this scenario.
>
>set.seed(102)
>
>x1 <- rbinom(100, 1, .5)
>x2 <- rbinom(100, 1, .3)
>
>X <- data.frame(x1,x2)
>tX <- table(X)
>margin.table(tX,1)
>margin.table(tX,2)
>mcnemar.test(tX)
>
>put.missings <- function(x.vector, na.percent)
>{
>turn.na <- rbinom(length(x.vector), 1, na.percent)
>  x.vector[turn.na == 1] <- NA
>return(x.vector)
>}
>
>
>x1.m <- put.missings(x1, .3)
>x2.m <- put.missings(x2, .6)
>
>tX.m <- rbind(table(na.omit(x1.m)), table(na.omit(x2.m)))
>fisher.test(tX.m)
>
>
>
>
>With regards,
>Tal
>
>
>
>
>
>
>
>
>
>--
>----------------------------------------------
>
>
>My contact information:
>Tal Galili
>Phone number: 972-50-3373767
>FaceBook: Tal Galili
>My Blogs:
>http://www.r-statistics.com/
>http://www.talgalili.com
>http://www.biostatistics.co.il
>
>         [[alternative HTML version deleted]]
>
>______________________________________________
>R-help at r-project.org mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>and provide commented, minimal, self-contained, reproducible code.

================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

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