[R-sig-Epi] [epitools] Risk Difference

[BXC (Bendix Carstensen)]

Hi Will,

> -----Original Message-----
> From: epitools at yahoogroups.com 
> [mailto:epitools at yahoogroups.com] On Behalf Of wleephd
> Sent: 25. august 2010 21:23
> To: epitools at yahoogroups.com
> Subject: [epitools] Risk Difference
> 
>   
> 
> Hello,
> 
> I am very new to R and I am trying to find a way to calculate 
> risk differece and the associated CI. What is method used to 
> calculate CI?
> 
> Thanks for you help.
> 
> Will

You can compute rate-ratios using a Poisson model with log-link.
Rate differences comes from using a Poisson model with identity link.

Here is an illustration of how it goes; it requires small trick in specification of the glm. The following R-code also produces confidence intervals etc. using the function ci.lin() from the Epi package, www.biostat.ku.dk/~bxc/Epi.

Best regards,
Bendix Carstensen
_______________________________________________

Bendix Carstensen 
Senior Statistician
Steno Diabetes Center
Niels Steensens Vej 2-4
DK-2820 Gentofte
Denmark
+45 44 43 87 38 (direct)
+45 30 75 87 38 (mobile)
bxc at steno.dk   http://www.biostat.ku.dk/~bxc
www.steno.dk

###################################################
### Define some events and person-years and do the 
### traditional RR calculation
###################################################
D0 <- 15   ; D1 <- 28
Y0 <- 5532 ; Y1 <- 4783
RR <- (D1/Y1)/(D0/Y0)
erf <- exp( 1.96 * sqrt(1/D0+1/D1) )
c( RR, RR/erf, RR*erf )
exp( c( log(RR), sqrt(1/D0+1/D1) ) %*% ci.mat() )

###################################################
### Stack the data and fit a model that gives the RR 
###################################################
D <- c(D0,D1) ; Y <- c(Y0,Y1); xpos <- 0:1
mm <- glm( D ~ factor(xpos), offset=log(Y), family=poisson )
exp( coef( mm ) )

###################################################
### The ci.lin function is in the Epi package
###################################################
library( Epi )
ci.lin( mm, E=T)[,5:7]

###################################################
### The same model can be fitted using the observed 
### rate as response and the person-years as weight 
###################################################
mr <- glm( D/Y ~ factor(xpos), weight=Y, 
                 family=poisson )
### Note the results are exactly the same
summary(mm)$coef
summary(mr)$coef

###################################################
### This specification gives the possibility of an
### identity link to give rate and rate difference
###################################################
ma <- glm( D/Y ~ factor(xpos), weight=Y, 
                 family=poisson(link=identity) )
summary( ma )$coef
ci.lin( ma )[,c(1,5,6)]

###################################################
### The ci.lin function in Epi have nice facilities 
### that can be used to produce nice output
###################################################
# Scale person-years to get reasonable rates (per 1000)
Y <- Y/1000
rownames( CM ) <- c("rate 0","rate 1","RD 1 vs. 0")
ma <- glm( D/Y ~ factor(xpos), weight=Y, 
                 family=poisson(link=identity) )
ci.lin( ma, ctr.mat=CM )