We conducted an age and sex matched case control study (84 cases, 174 controls). The outcome was cancer X and the exposure of interest was Y. Sample size was calculated based on the prevalence of Y in the general population of province Z.
Prevalance of Y among cases was 79.7 % and among controls 27.5 %. With a conditional logistic regression, I get an OR of 21.2 (95%CI, 8.4-53.8) , for the risk of Cancer X associated with ever exposure to Y. While smoking tobacco which is a co-exposure has an OR of 2.2 (1.4-4.5), with a prevalence of 33.3 and 15.5 among the cases and controls respectively.
It may also be noted that exposures similar to Y studies previously in similar settings have produced similarly large risk estimates and wide C.I. What could be the possible reasons for this wide C.I for the main exposure , while a narrow CI for a co exposure whose prevalence is clearly much lower than Y. We tried simple Log regression as well, and it yields similar results.
If these were your results, what would be your interpretation.
P.S. just to add to the above, In step wise log regression the risk estimates are low as well as the CI are comparatively precise, until you add "Sex", which almost doubles the risk and the CI. There is no plausible explanation for this other than that among men only 5 % of the cases are never users of Y, and among women only 6 % of the controls are exposed to Y. (Simpsons paradox ?)
Thank you, everyone, for taking time out to reply to my query. @Rohit, yes the problem is indeed sparse data. In simple logistic regression, the estimates are pretty precise with smokeless tobacco use, Smoking, alcohol use, age, and socioeconomic status as the predictors of oral cancer, but the moment "sex" is added as a predictor variable, it just doubles the effect estimate and the imprecise CI. I think the reason is the very small number of unexposed male cases 3/52, while in females it is 14/32.
I really put in a lot of effort into this project (my PhD project), doing all the field research by myself amid threats of terrorism and 50-degree temperatures, and now these results are such a dampener...I just feel that everyone who looks at them, just see the wide intervals and the elevated risk estimate and think of some error, but what can I do, it is how it is. I could not have asked cases to have a lesser exposure, nor the controls to use more tobacco....I just wish statistics was kinder to me :)
@ all any pointers for the defence of such results ?
You might try using different methods for calculating the confidence intervals. eg Cornfeld, Logit and Test based. With large very RRs like the 21.2, and big differences between case and referent numbers, you can get big alterations in variance estimates.
See Breslow and Day Statistical Methods in Cancer Research 1980 vol 1 p 133-136
I don't think it's at all unusual for a larger OR to have a wider confidence interval, because odds ratios are non-linear: the difference between an odds ratio of 1 and an odds ratio of 2 is really not the same as the difference between an odds ratio of 21 and an odds ratio of 22.
In fact if you convert your odds ratios into proportions, the CI widths totally shift. Your exposure effect has a CI of [8.4, 53.8] when expressed as an odds ratio, but [89%, 98%] when expressed as a percentage likelihood of getting cancer. On the other hand, your co-exposure has a CI of [1.4, 4.5] when expressed as an odds ratio, but [58%, 81%] when expressed as a percentage likelihood. Long story short, I don't think it makes much sense to compare the widths of the CIs when they're in very different ranges (one close to chance level and the other close to 100% level).
[EDIT: these numbers are mistaken, see below]
Thank you James and Stephen for your prompt responses. They are indeed helpful. @ Stephen would you be kind enough to direct me to a resource from which you have concluded your response, please. I will need a resource to cite in my explanation of the CI. Thank you again sirs.
Actually I just realized my earlier comment was mistaken; to translate the odds ratios into proportions you need to look at the regression coefficient plus the intercept, not just the regression coefficient itself. (Or you can convert the log odds ratio into marginal effects.) So without knowing what the intercept was, I can't be sure what those CIs correspond to in terms of proportions.
Thank you, everyone, for taking time out to reply to my query. @Rohit, yes the problem is indeed sparse data. In simple logistic regression, the estimates are pretty precise with smokeless tobacco use, Smoking, alcohol use, age, and socioeconomic status as the predictors of oral cancer, but the moment "sex" is added as a predictor variable, it just doubles the effect estimate and the imprecise CI. I think the reason is the very small number of unexposed male cases 3/52, while in females it is 14/32.
I really put in a lot of effort into this project (my PhD project), doing all the field research by myself amid threats of terrorism and 50-degree temperatures, and now these results are such a dampener...I just feel that everyone who looks at them, just see the wide intervals and the elevated risk estimate and think of some error, but what can I do, it is how it is. I could not have asked cases to have a lesser exposure, nor the controls to use more tobacco....I just wish statistics was kinder to me :)
@ all any pointers for the defence of such results ?
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Sampling Design
- Sample Size