I'm working on a case-control study and I'm using VassarStats (http://vassarstats.net/odds2x2.html) to estimate the OR, 95% CI, and to perform the two-tailed Fisher's exact test. The problem is that, in some cases, I have a class of value zero. I know we can add 0.5 to each class to estimate the odds ratio and CI in these cases (I have an excel sheet with the formulas to calculate it "manually"). The problem then is that I believe there's no way to perform Fisher's exact test with non-integers. At least VassarStats (and many other tools I looked up) doesn't allow it. I believe that's because there's no point in doing this since Fisher's exact test is supposed to compare observations of some groups and you can't have half an observation. However, I believe I need to have a P value for the same values I used to estimate the OR, and I can't estimate the OR if I have a class of value zero.
I understand that if a class, let's say a genotype, is rare in both my samples (cases and controls), there's no need of estimating the OR. However, if I have a genotype that is frequent among cases and rare (even zero) among controls that may be extremely interesting! So, what do you suggest to estimate both OR (with 95% CI) and P values for this situation?
I send a numerical example just for the sake of clarity:
cases: 228 (reference genotype); 0 (test genotype)
controls: 148 (reference genotype); 4 (test genotype).
[One alternative I thought of was adding 1 to each class instead of 0.5, but I don't believe that solution is adequate, since it's a relevant change in the values]
Tagging zeros as missing is a hugely bad idea. The odds ratio is a problem here, but you can calculate the risk difference. In your case, it's -.026 with a 95% CI of -0.052 to -0.0009
The real problem is the lack of data, and you are correct to realise that adding a small 'start' to the zeros will allow you to calculate whatever odds ratio you like, but its numeric value will be the result of your start, not of the true value.
You can use chisq.test(x,simulate.p.value=TRUE) in R without adjusting the data. This will give you a correct p_value. There is no OR and CI that corresponds exactly to this p_value. However, the trick of adding .5 to each will give you something close. Another way, which wildly exaggerates the p_value but doesn't the OR, is to multiply the three other values by some number, but add 1 to the 0 value and calculate the OR and CI. The simulates having more data. If the population value represented by the 0 is close to 1/148, then a small multiplier will be most accurate. If the true value is closer to the 0/148, then a large multiplier will be most accurate. In the end, there is no correct way to do it other than to add more data.
Thank you very much for your contributions.
Mt concern was that I had to have a p value corresponding to the same values used to estimate the OR. I already calculated a p value without altering the values (which gives me (0,025) and an OR adding 0,5 (which gives an CI of 0-1.35, being non-significant), but these values refer to different entries. The suggestion for using the risk difference seemed interesting, however I read it shouldn't be used when we have small samples (more than 5 successes r failures in each group), like the chi-square.
I know enlarging the sample is the only really appropriate solution from the statistical point of view, but it is not really possible, since the disease is quite rare.
Maybe the way is to put all the numbers in the publication so that everyone can get their own conclusions...
Thanks! :)
Please ignore my suggestion of muliplying the non_zero entries. It was an untested thought. After testing, it does affect the OR's and CI's. Your, suggestion, Liana, of putting all the numbers in a publication is a good one. OR's and CI's are undefined in a case where there are 0 cells, so there is no expectation that they be included.
Interesting conversation. My understanding is Odds Ratios are used for Case Control studies while relative risks for cohort studies. However, if a disease is rare in a population, OR~RR. If there are zeroes in the 2X2 table that preclude calculating an OR, could one switch to doing a RR as an approximation of the OR? Then a single zero in one of the 4 cells would not interfere with calculation of RR and CI on that RR, as an approximation for the OR.
But it may just be simpler to add 1/2 to each number in a cell as a continuity correction and leave it at that.
Yachen Zhu, I think you mean that you want to compare two OR's. The standard null is OR = 1.0. There is another thread that discusses this. See Saduul Islam's question: How to compare odds ratios from one study to another. You need the CI's from both OR's (or RR's).
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