[R] mcnemar.test odds ratios, CI, etc.

[Peter Dalgaard]

"Bliese, Paul D LTC USAMH" <paul.bliese at us.army.mil> writes:

> Does anyone know of another version of the Mcnemar test that provides:
> 
>  
> 
> 1.  Odds Ratios
> 
> 2.  95% Confidence intervals of the Odds Ratios
> 
> 3.  Sample probability 
> 
> 4.  95% Confidence intervals of the sample probability
> 
>  
> 
> Obviously the Odds Ratios and Sample probabilities are easy to calculate
> from the contingency table, but I would appreciate any help on how to
> calculate the confidence intervals.
> 
>  
> 
> Below is a simple example of the test, and the corresponding output with
> the function mcnemar.test.
> 
>  
> 
> > xtabs(~PLC50.T1+PLC50.T2,data=LANCET.DAT)
> 
>         PLC50.T2
> 
> PLC50.T1 0   1  
> 
>        0 464  22
> 
>        1   6   1
> 
> > mcnemar.test(xtabs(~PLC50.T1+PLC50.T2,data=LANCET.DAT))
> 
>  
> 
>         McNemar's Chi-squared test with continuity correction
> 
>  
> 
> data:  xtabs(~PLC50.T1 + PLC50.T2, data = LANCET.DAT) 
> 
> McNemar's chi-squared = 8.0357, df = 1, p-value = 0.004586


What is the "sample probability" in this context? The odds ratio is a
simple functional of the off-diagonal elements, and the conditional
distribution of those given their sum is just a binomial, so you can
use prop.test or binom.test to get estimate and confidence intervals
for the probability parameter and convert that to odds.

E.g.

> prop.test(6,28)

        1-sample proportions test with continuity correction

data:  6 out of 28, null probability 0.5
X-squared = 8.0357, df = 1, p-value = 0.004586
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
 0.09027927 0.41462210
sample estimates:
        p
0.2142857


> ci.p <- prop.test(22,28)$conf
> ci.odds <- ci.p/(1-ci.p)
> ci.odds
[1]  1.411835 10.076740
attr(,"conf.level")
[1] 0.95
> ci.p <- binom.test(22,28)$conf
> ci.odds <- ci.p/(1-ci.p)
> ci.odds
[1]  1.441817 11.053913
attr(,"conf.level")
[1] 0.95



-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907