[R] Confidence interval for relative risk
Michael Dewey [EMAIL PROTECTED] wrote Subject: [R] Confidence interval for relative risk 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 === Since RR = p1 +1 p1=a/(a+b), p2=c/(c+d) -- p2 1 - + --- 1-p2OR you can backsolve for the RR CI. x - function(p1, p2, oddsr) p1 + 1/(p2/(1-p2) + 1/oddsr) 1/x(8/508, 0, 1/1.694792) [1] 1.650734 Another approach is the Cornfield method -- which is a profile likelihood based CI using the Gibbs Chi-square (LRTS), but IIRC originally used the Pearson chi-square. I don't think there are R implementations. David Duffy. -- | David Duffy (MBBS PhD) ,-_|\ | email: [EMAIL PROTECTED] ph: INT+61+7+3362-0217 fax: -0101 / * | Epidemiology Unit, Queensland Institute of Medical Research \_,-._/ | 300 Herston Rd, Brisbane, Queensland 4029, Australia GPG 4D0B994A v __ R-help@stat.math.ethz.ch 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.
Re: [R] Confidence interval for relative risk
At 15:54 10/11/2006, Viechtbauer Wolfgang (STAT) wrote: Thanks for the suggestion Wolfgang, but whatever the original authors did that is not it. Hello, A common way to calculate the CI for a relative risk is the following. Given a 2x2 table of the form: a b c d the log of the risk ratio is given by: lrr = log[ a/(a+b) / ( c/(c+d) ) ] which is asymptotically normal with variance: vlrr = 1/a - 1/(a+b) + 1/c - 1/(c+d). So an approximate 95% CI for the risk ratio is given by: exp[ lrr - 1.96*sqrt(vlrr) ], exp[ lrr + 1.96*sqrt(vlrr) ]. A common convention is to add 1/2 to each cell when there are zeros. So, for the table: Col 1 Col 2 Row 1 8 500 Row 2 0 500 lrr = log[ 8.5/509 / ( 0.5/501 ) ] = 2.817 vllr = 1/8.5 - 1/509 + 1/0.5 - 1/501 = 2.1137 exp[ 2.817-1.96*sqrt(2.1137) ] = .97 exp[ 2.817+1.96*sqrt(2.1137) ] = 289.04 Maybe that is what the authors did. Best, -- Wolfgang Viechtbauer Department of Methodology and Statistics University of Maastricht, The Netherlands http://www.wvbauer.com/ -Original Message- From: [EMAIL PROTECTED] [mailto:r-help- [EMAIL PROTECTED] On Behalf Of Michael Dewey Sent: Friday, November 10, 2006 15:43 To: r-help@stat.math.ethz.ch Subject: [R] Confidence interval for relative risk 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 2P(Col 1) 95% conf. interval Row 1 8 500 0.01570.0079 0.0312 Row 2 0 500 0.0. NaN 95% conf. interval Relative Risk:Inf NaN Inf Sample Odds Ratio:Inf NaN Inf Conditional MLE Odds Ratio:Inf1.6948 Inf Probability difference: 0.01570.0027 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 5000 500 Exposed2 5008 508 Total10008 1008 $measure risk ratio with 95% C.I. Predictor estimate lower upper Exposed11NANA 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 Michael Dewey http://www.aghmed.fsnet.co.uk __ R-help@stat.math.ethz.ch 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.
Re: [R] Confidence interval for relative risk
Michael Dewey [EMAIL PROTECTED] writes: At 15:54 10/11/2006, Viechtbauer Wolfgang (STAT) wrote: Thanks for the suggestion Wolfgang, but whatever the original authors did that is not it. Did you ever say what result they got? -p Hello, A common way to calculate the CI for a relative risk is the following. Given a 2x2 table of the form: a b c d the log of the risk ratio is given by: lrr = log[ a/(a+b) / ( c/(c+d) ) ] which is asymptotically normal with variance: vlrr = 1/a - 1/(a+b) + 1/c - 1/(c+d). So an approximate 95% CI for the risk ratio is given by: exp[ lrr - 1.96*sqrt(vlrr) ], exp[ lrr + 1.96*sqrt(vlrr) ]. A common convention is to add 1/2 to each cell when there are zeros. So, for the table: Col 1 Col 2 Row 1 8 500 Row 2 0 500 lrr = log[ 8.5/509 / ( 0.5/501 ) ] = 2.817 vllr = 1/8.5 - 1/509 + 1/0.5 - 1/501 = 2.1137 exp[ 2.817-1.96*sqrt(2.1137) ] = .97 exp[ 2.817+1.96*sqrt(2.1137) ] = 289.04 Maybe that is what the authors did. Best, -- Wolfgang Viechtbauer Department of Methodology and Statistics University of Maastricht, The Netherlands http://www.wvbauer.com/ -Original Message- From: [EMAIL PROTECTED] [mailto:r-help- [EMAIL PROTECTED] On Behalf Of Michael Dewey Sent: Friday, November 10, 2006 15:43 To: r-help@stat.math.ethz.ch Subject: [R] Confidence interval for relative risk 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 2P(Col 1) 95% conf. interval Row 1 8 500 0.01570.0079 0.0312 Row 2 0 500 0.0. NaN 95% conf. interval Relative Risk:Inf NaN Inf Sample Odds Ratio:Inf NaN Inf Conditional MLE Odds Ratio:Inf1.6948 Inf Probability difference: 0.01570.0027 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 5000 500 Exposed2 5008 508 Total10008 1008 $measure risk ratio with 95% C.I. Predictor estimate lower upper Exposed11NANA 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 Michael Dewey http://www.aghmed.fsnet.co.uk __ R-help@stat.math.ethz.ch 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
Re: [R] Confidence interval for relative risk
At 12:35 12/11/2006, Peter Dalgaard wrote: Michael Dewey [EMAIL PROTECTED] writes: At 15:54 10/11/2006, Viechtbauer Wolfgang (STAT) wrote: Thanks for the suggestion Wolfgang, but whatever the original authors did that is not it. Did you ever say what result they got? -p No, because I did not want to use the original numbers in the request. So as the snippet below indicates I changed the numbers. If I apply Wolfgang's suggestion (which I had already thought of but discarded) I get about 13 for the real example where the authors quote about 5. My question still remains though as to how I can get a confidence interval for the risk ratio without adding a constant to each cell. it credible. I show below my attempts to do this in R. The example is slightly changed from the authors'. Michael Dewey http://www.aghmed.fsnet.co.uk __ R-help@stat.math.ethz.ch 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.
Re: [R] Confidence interval for relative risk
When I have refereed manuscripts for publication and have been unable to get their answers, I have told the authors they need more explanation of their methodology -- while summarizing what I tried in a few lines. I've even told some that it would make it vastly easier for the referees and increase the potential readership for their article if they make R code available -- at least downloadable somewhere and preferably in a contributed R package, where it could attract interest in the article from audiences who would not likely find it any other way. I've done this for articles that were NOT written to specifically describe statistical software. I have not followed all of this thread. However, one suggestion I saw looked like it used the delta method, if I understood correctly from skimming without studying the details carefully. Have you also considered 2*log(likelihood ratio) being approximately chi-square? Just my 2e-9 Euros (or 2e-7 Yen or Yuan). Spencer Graves Michael Dewey wrote: At 12:35 12/11/2006, Peter Dalgaard wrote: Michael Dewey [EMAIL PROTECTED] writes: At 15:54 10/11/2006, Viechtbauer Wolfgang (STAT) wrote: Thanks for the suggestion Wolfgang, but whatever the original authors did that is not it. Did you ever say what result they got? -p No, because I did not want to use the original numbers in the request. So as the snippet below indicates I changed the numbers. If I apply Wolfgang's suggestion (which I had already thought of but discarded) I get about 13 for the real example where the authors quote about 5. My question still remains though as to how I can get a confidence interval for the risk ratio without adding a constant to each cell. it credible. I show below my attempts to do this in R. The example is slightly changed from the authors'. Michael Dewey http://www.aghmed.fsnet.co.uk __ R-help@stat.math.ethz.ch 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. __ R-help@stat.math.ethz.ch 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.
[R] Confidence interval for relative risk
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 2P(Col 1) 95% conf. interval Row 1 8 500 0.01570.0079 0.0312 Row 2 0 500 0.0. NaN 95% conf. interval Relative Risk:Inf NaN Inf Sample Odds Ratio:Inf NaN Inf Conditional MLE Odds Ratio:Inf1.6948 Inf Probability difference: 0.01570.0027 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 5000 500 Exposed2 5008 508 Total10008 1008 $measure risk ratio with 95% C.I. Predictor estimate lower upper Exposed11NANA 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 __ R-help@stat.math.ethz.ch 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.
