# [R] Correlation adjusted Bonferroni? (was: Multiple tests on repeated measurements)

R Heberto Ghezzo, Dr heberto.ghezzo at mcgill.ca
Wed Aug 2 19:48:33 CEST 2006

```HI, just my 2 cents. Bonferroni et al, assume independent tests, thus p ~ p*k with k the number of tests, in repeated measures, each measure is correlated with the previous, so k is not 2 but 2-q. I do not know q but it should be a function of the correlation between measures, ie the Sigma in gee.
A long time ago, in my days as a student i remember, vagely, I saw a paper in Biometics on a correction to apply to Fisher method for pooling several tests to take into account the correlation between the variables.
Heberto Ghezzo
McGill University

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch on behalf of Spencer Graves
Sent: Wed 8/2/2006 4:25 AM
To: Grathwohl, Dominik, LAUSANNE, NRC-BAS
Cc: r-help at stat.math.ethz.ch; Torsten Hothorn
Subject: Re: [R] Correlation adjusted Bonferroni? (was: Multiple tests on repeated measurements)

I'm not familiar with the correlation adjustment to Bonferroni you
mention below, though it sounds interesting.  However, I think there is
code produced the following for me:

= raw.p      = bon.p   =multcomp.p "bon.cor.p"
diff/v=0 0.028572509 0.057145019 0.054951102 0.034934913
diff/v=1 0.001727993 0.003455987 0.003415545 0.002119276

In the absence of other information, I'd be inclined to believe

Hope this helps.
Spencer Graves

Grathwohl, Dominik, LAUSANNE, NRC-BAS wrote:
> Dear R-helpers:
>
> My question is how do I efficient and valid correct for multiple tests in a repeated measurement design:
> Suppose we measure at two distinct visits with repeated subjects a treatment difference on the same variable.
> The treatment differences are assessed with a mixed model and adjusted by two methods for multiple tests:
>
> # 1. Method: Adjustment with library(multcomp)
>
> library(nlme)
> library(multcomp)
>
> n <- 30 # number of subjects
> sd1 <- 0.5 # Standard deviation of the random intercept
> sd2 <- 0.8 # Standard deviation of the residuals
> id <- rep(1:n,times=2); v <- rep(0:1, each=n); trt <- rep(sample(rep(0:1, each=n/2), n), times=2)
> df <- data.frame(id, v, trt,
> y=2 + rep(rnorm(10,0,sd1), times=2) + 0.5*v + 0.7*trt + 0.2*v*trt + rnorm(2*n, 0, sd2))
> m1 <- lme(y ~ v + trt + v*trt, data=df, random= ~ 1|id)
> summary(m1)
> par4 <- m1\$coef\$fixed
> cov4 <- vcov(m1)
> cm4 <- matrix(c(0, 0, 1, 0, 0, 0, 1, 1), nrow = 2, ncol=4, byrow=TRUE,
> 	dimnames = list(c("diff/v=0", "diff/v=1"), c("C.1", "C.2", "C.3", "C.4")))
> v4 <- csimint(estpar=par4, df=n-6, # I'm not sure whether I found
>      # the correct degrees of freedom
> 	covm=cov4,
> 	cmatrix=cm4, conf.level=0.95)
> sv4 <- summary(v4)
>
> # 2. Method: I found in Handbook of Statistics Vol 13, p.616,
> # same can be found in http://home.clara.net/sisa/bonhlp.htm
> # Bonferroni on correlated outcomes:
>
> raw.p <- sv4\$p.value.raw
> co4 <- cor(df\$y[df\$v==0],df\$y[df\$v==1])
> rho <- mean(c(1,co4,co4,1))
> pai <- 1-(1-raw.p)^2^(1-rho)
>
> # The results of two methods are presented in the following lines:
> out <- cbind(raw.p, sv4\$p.value.bon, sv4\$p.value.adj, pai)
> colnames(out) <- c("raw.p", "bon.p", "multcomp.p", "bon.cor.p")
> out
>
> As you can see there are quite big differences
> between the two ways adjusting for multiple tests on repeated measurements.
> I guess that the multcomp library is not appropriate for this kind of hypotheses.
> However I could not find an explanation in the help files.
> May be one of the experts can point me in the right direction?
>
> Kind regards,
>
> Dominik
>
> platform i386-pc-mingw32
> arch     i386
> os       mingw32
> system   i386, mingw32
> status
> major    2
> minor    2.1
> year     2005
> month    12
> day      20
> svn rev  36812
> language R
>
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>
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