[R] Summary, was Re: Confidence interval for relative risk

[Michael Dewey]

At 14:43 10/11/2006, Michael Dewey wrote:

After considerable help from list members and some digging of my own
I have prepared a summary of the findings which I have posted (see
link below). Broadly there were four suggestions
1 - Wald-type intervals,
2 - transforming the odds ratio confidence interval,
3 - method based on score test,
4 - method based on likelihood.

Method 3 was communicated to me off-list
  ===========================
I haven't followed all of the thread either but has someone already 
pointed out to you confidence intervals that use the score method? 
For example Agresti (Categorical Data Analysis 2nd edition, p. 77-78) 
note that 'although computationally more complex, these methods often 
perform better'. However, they also note that 'currently they are not 
available in standard software'.

But then again, R is not standard software: the code (riskscoreci) 
can be found from here: 
http://www.stat.ufl.edu/~aa/cda/R/two_sample/R2/index.html

best regards,
Jukka Jokinen

================================================
and so I reproduce it here. Almost a candidate for the fortunes package there.
The other three can be found from the archive
under the same subject although not all in the same thread.

Methods 3 and 4 seem to have more going for them as far
as I can judge.

Thanks to David Duffy, Spencer Graves,
Jukka Jokinen, Terry Therneau, and Wolfgan Viechtbauer.
The views and calculations presented here and in the summary
are my own and
any errors are my responsibility not theirs.

The summary document is available from here

http://www.zen103156.zen.co.uk/rr.pdf


Original post follows.

====================================
>The concrete problem is that I am refereeing
>a paper where a confidence interval is
>presented for the risk ratio and I do not find
>it credible. I show below my attempts to
>do this in R. The example is slightly changed
>from the authors'.
>
>I can obtain a confidence interval for
>the odds ratio from fisher.test of
>course
>
>=== fisher.test example ===
>
> > outcome <- matrix(c(500, 0, 500, 8), ncol = 2, byrow = TRUE)
> > fisher.test(outcome)
>
>         Fisher's Exact Test for Count Data
>
>data:  outcome
>p-value = 0.00761
>alternative hypothesis: true odds ratio is not equal to 1
>95 percent confidence interval:
>  1.694792      Inf
>sample estimates:
>odds ratio
>        Inf
>
>=== end example ===
>
>but in epidemiology authors often
>prefer to present risk ratios.
>
>Using the facility on CRAN to search
>the site I find packages epitools and Epi
>which both offer confidence intervals
>for the risk ratio
>
>=== Epi example ===
>
> > library(Epi)
> > twoby2(outcome[c(2,1),c(2,1)])
>2 by 2 table analysis:
>------------------------------------------------------
>Outcome   : Col 1
>Comparing : Row 1 vs. Row 2
>
>       Col 1 Col 2    P(Col 1) 95% conf. interval
>Row 1     8   500      0.0157    0.0079   0.0312
>Row 2     0   500      0.0000    0.0000      NaN
>
>                                    95% conf. interval
>              Relative Risk:    Inf       NaN      Inf
>          Sample Odds Ratio:    Inf       NaN      Inf
>Conditional MLE Odds Ratio:    Inf    1.6948      Inf
>     Probability difference: 0.0157    0.0027   0.0337
>
>              Exact P-value: 0.0076
>         Asymptotic P-value: NaN
>------------------------------------------------------
>
>=== end example ===
>
>So Epi gives me a lower limit of NaN but the same confidence
>interval and p-value as fisher.test
>
>=== epitools example ===
>
> > library(epitools)
> > riskratio(outcome)
>$data
>           Outcome
>Predictor  Disease1 Disease2 Total
>   Exposed1      500        0   500
>   Exposed2      500        8   508
>   Total        1000        8  1008
>
>$measure
>           risk ratio with 95% C.I.
>Predictor  estimate lower upper
>   Exposed1        1    NA    NA
>   Exposed2      Inf   NaN   Inf
>
>$p.value
>           two-sided
>Predictor  midp.exact fisher.exact  chi.square
>   Exposed1         NA           NA          NA
>   Exposed2 0.00404821  0.007610478 0.004843385
>
>$correction
>[1] FALSE
>
>attr(,"method")
>[1] "Unconditional MLE & normal approximation (Wald) CI"
>Warning message:
>Chi-squared approximation may be incorrect in: chisq.test(xx, correct =
>correction)
>
>=== end example ===
>
>And epitools also gives a lower limit
>of NaN.
>
>=== end all examples ===
>
>I would prefer not to have to tell the authors of the
>paper I am refereeing that
>I think they are wrong unless I can help them with what they
>should have done.
>
>Is there another package I should have tried?
>
>Is there some other way of doing this?
>
>Am I doing something fundamentally wrong-headed?
>
>
>

Michael Dewey
http://www.aghmed.fsnet.co.uk