Can I calculate the % of people positive for an outcome from an odds ratio?


New Member
Thanks for looking at my question.


I am doing a systematic reveiw and metanalysis, essentially on diagnostic test accuracy and particularly on the accuracy of 'tests' alone or in combination. Some studies do not report sensitivity and specificity or the % or no. of people with the symptom/s who have the disease/outcome or people with the symptom/s who don't have the disease/outcome. These studies report only the odds ratio i.e. the odds that people with the symptom will have the disease.


Can I calculate the % or no. of people with symptom/s A who had the disease/outcome in a (published) study, and,
the % or no. of people who did not have symptom/s A who had the disease/outcome, if,
the only information I have is the odds ratio (95% CI and p value) and the total number of people in the study/including in the analysis?

If so I would really appreciate it if someone could tell me the formula or name of analysis in r/stats software.

Many thanks

PS I tried to search the threads here for this but it keeps coming up with a 'page not found' so apologies if this is a duplicate.


Less is more. Stay pure. Stay poor.
I am not doubting you, but I find it had to believe the published study does have more info than that, say prevalence of exposure or outcome. ORs come from a contingency table and Accuracy comes from a classification/confusion table/matrix. So you think the exposure is the same thing as a screening in this setting. How was the OR calculated (e.g., 2x2 table or multiple logistic regression)?

Can you provide a link to the paper? I enjoy diagnostic stats, so I am happy to try and help. In a meta-analysis for diagnostics, are differences in prevalence between studies an issue and considered heterogeneity?


New Member
Thanks hlsmith

You're right of course, true diagnostic test accuracy studies do report that information. However the topic I am working on is slightly different - mortality is used in place of the reference standard as there is no diagnostic test for this condition and sensitivity specificity etc of tests are based on prediction of mortality. Some studies report the information you mentioned for some clinical criteria/tests and some do not. I am including studies that were not primarily DTA studies but include relevant information, for eg this study reports the odds ratio of mortality for people with a respiratory rate > than a certain number ( I would like to analyse respiratory rate alone as a screening criteria (the test is the same as a DTA test i.e. sensitivity and specificity) but they only report the odds ratio. Thus my original question.

If anyone is able to tell me please if it is possible to caluclate % or number of people with symptom A who had outcome B, and people with symptom A who did not have outcome B from an odds ratio (with confidence intervals and p value), when you know the total number of people including in the calculation of the odds ratio, I'd really appreciate it.



New Member
I posted a reply but it isn't here (new to this forum unsure what I did wrong)

Briefly again. Thanks for your reply. Yes you are right true DTA studies report that information. However my study is of a cinditon that dosn't have a reference diagnostic test and mortality is used in place of this to identifiy people at risk of poor outcomes. Screening or clinical criteria are used and analysed the same i.e. sensitivity and specificity etc but I am including info from studies that are not primarily DTA studis but include the relevant information. However some of these report odds ratio only rather than the two by two table e.g. respiratory rate is a symptom of interest by itself as a predictor and this study reports the odds raton for mortality but not other information

Thus my original question. If anyone is able to tell me please if you can calculate the % or number of peple ina group who had symptom A and had outcome B, and % or number who did not have symptom A and had outcome B, from an odds ratio that is the odds ratio of having outcome B if you have symptom A (other info you have is Confidence interval and p value for odds ratio and total nuber of people included in calculation of odds ratio.

Many thanks


New Member
Addit, sorry I typed that quickly and didn't address the last part of your comment (or my multiple typos!). I'd definately appreciate your input on this as I haven't done this type of analysis before so it's all new to me.

I haven't got to looking at what will be factored into heterogeneity, I'm guessing it's based on differences in sensitivity and specificity if that is the metanalysis I am doing (plotting different tests on the ROC and or plotting different studies analysing the same test on the ROC).

Any tips really appreciate, thanks again.


Less is more. Stay pure. Stay poor.
Not by an actual computer but collected the following:

Said they used multivariate (probably multiple) logistic regression for in hospital mortality for shock patients.

n=122, outcome prevalence = 32%.

Model looks like it controlled for 7 variables, none representing more degrees of freedom.

Resp rate beta coefficient: 0.989
95% CI: 0.943-1.037
P-value: 0.653

This is an adjusted estimate control for other covariates.

SO, it is a continuous variable, not dichotomized, so you have no values to put in 2x2 table. Coefficient interpretation is odds ratio for a one unit increase in resp rate.

I will think about it but you are probably out of luck.


New Member
Thanks so much hlsmith, that's what I needed to know. An additional question, how strong do you think conlcusions basd on metanalyis of odds ratios are? I can probably convert all my 2x2 table studies to odds ratio results from the information provided in the studies but I don't want to end up doing a metanalysis that is plagued with potential error and doubt as the results are then not useful to answer the question.
I haven't read this whole paper but it talks about how commonly used methods for metanalyss of odds ratios are bad
Please don't feel obliged to answer this, I think it's something I'm going to have to spend a bit of time figuring out.
Thaks again


Less is more. Stay pure. Stay poor.
I will check out that paper if I get a chance. Meta-analyses are conducted with ORs all of the time and to my current knowledge there isn't any issue.

Though, issues can arise from using observational data, many issues. Most of the time you would use relative risks, but if the study is not prospective and incidence can't be established, then ORs and retrospective/cross-sectional studies get used. Also, some people default to logistic regression due to its ease and then use ORs.

So what is suspect in observational studies is heterogeneity between studies (designs, methods, etc.). In addition, since treatment is not randomized, covariates need to be controlled for and each model may control for different covariates. This runs the risk of the models between the studies not being exchangeable. In addition, probably a risk for Table 2 fallacy, meaning you can't always treat covariates as primary study outcomes, since the modeling may not have been designed to controlling for its confounders. So big picture, if you have a bunch of well designed studies pooling ORs in random or fixed effects models can be fine, though in observational studies you need to weigh the quality of studies more vigorously. There are criteria to help, I am thinking one is MOOSE. Feel free to keep posting, I will help where I can as my schedule allows. But this solar eclipse thing with be consuming my time tomorrow!!!


New Member
Thank you so much, I cannot tell you how much I appreciate you taking the time to give me your thoughts (an obviously considerable knowledge!) on this.

I’m thinking from what you have said, that I will only be able to meta-analyse unadjusted (rather than adjusted based on regression factoring in other things) odds ratios based on equivalent populations and test thresholds? Which would be ok if the studies report this. I’m thinking if the studies predominantly report sensitivity and specificity and there are a few that report odds ratios I will try contacting authors to see if I can get the sensitivity and specificity info and meta- analyse that. If most report odds ratios I will have to look at metanalysing them as odds ratios. But as these are not intervention studies I’m thinking most of them will be reporting unadjusted odds ratios so I don’t need to worry about differences in covariates (?) e.g. they will calculate the odds ratio for mortality in people with a respiratory rate of 30 based on the 2x2 table. As long as the populations and test threshold (RR 30) are equivalent. Mind you I am not at all familiar with these statistical methods so I may be over simplifying or misunderstanding?

To make it all a bit clearer, the systematic review is on the accuracy of screening tools/diagnostic criteria (which are essentially combinations of clinical criteria and sometimes biomarkers) and any clinical criteria including biomarkers alone or in combination, that identify patients who will have poor sepsis outcomes in sub-Saharan Africa. At this stage I’m still looking at whether I can include septic shock as a poor outcome or have to limit it to mortality (no gold standard diagnostic test/criteria for septic shock and clinical criteria are not often reported in the studies I’ll be including). I am at the protocol writing stage now.

If I find enough studies with comparable enough populations I will likely need to do a few separate meta-analyses. From what I know of the literature there are potentially a lot of published results that can be included depending on how many analyses I’m going to do. That’s really the drive behind decisions about the analyses, I want to find out how I can validly get as much data out of the published studies as possible. For example say 20 studies, only 3 which are DTA/screening test studies, happen to have published what the respiratory rate was in patents who died (and didn’t die), if I can make that information comparable (extract the comparable info) and group particular respiratory rates (RR) there could be a good amount of data behind the sensitivity/specificity of RR or odds ratio-> risk ratio if that’s what I can do. Or perhaps I might find that any tachypnoea is an excellent predictor, if I can analyse it properly.. (I’m not actually expecting RR to be great in itself but just using to illustrate).

Some aspects of the topic mean that heterogeneity may not be a big issue regardless of the study designs. Particularly, the population is only defined as “confirmed or suspected infection”, mostly, comorbidities don’t matter and the ‘assessment’ data can be at any time point during their admission. And with the “reference standard” being mortality there is no (little) room for issues on that end (maybe an issue around time period but unlikely). I’m thinking as long as the methods have included conducting the test (collecting the clinical criteria) in all people in the set population and they haven’t excluded certain groups or lost people (not able to report mortality or lost data) there shouldn’t be too many potential differences based in study design. If I’m only using mortality then there’s no chance of an issue with the reference test being conducted before the index test (which can influence/bias timing, selection for or subjective assessment of the reference test). Prevalence could theoretically be important but I’m not expecting it to be as sepsis is one of the most common presentations in SS-Africa and mortality isn’t near 100%. Most what would be heterogeneity will be dealt with by categories, e.g. neonates, infants, children, adolescents, adults, HIV positive patients, setting clinic, setting tertiary hospital etc. The age categories need to be separately analysed anyway and some other categories might be looked at in sensitivity analyses if they don’t look like a big issue.

To put this into context the main sepsis guidelines’ clinical criteria is based on retrospective analyses of huge patient datasets from a number of hospitals where the guideline authors applied different criteria, e.g. the Sequential Organ Failure Assessment (SOFA), to the patient observations and looked at mortality, i.e. the population was very broadly defined (confirmed or suspected infection) and comorbidities weren’t looked at (maybe a couple of groups were excluded from memory). The prevalence and comorbidities would have been similar across sites but this will also be the case in SS-Africa.

The above doesn’t really go to the statistical methods issues you have mentioned, which to be honest I have only a thin grasp of currently (only stats I have worked on previously has been factor analysis and structural equation modelling). But it might make my questions and issues a bit clearer.
I’ll be nutting this out over the next couple of weeks and if you have time I might run some things by you, but please don’t feel obliged. I really appreciate your help so far.

I’m intrigued by what the implications of a solar eclipse are for a statistics person?? Do you work in astronomy?
I’m a PhD student in Australia.

Thanks so much again