Asymmetric limbs of Confidence Interval - clarification
Please see below the table generated in Epidata analysis and note the confidence interval in the first row
HIV results Total 1539 108 7.0 (5.8-8.4)
This is the proportion of HIV infected among a group of TB suspects which is 7% with 95% CI being 5.8 - 8.4.
It can be deduced that the upper limb of confidence interval(which is 1.96 times Standard error) is 8.4 minus 7 = 1.4
Similarly, it can be deduced that the lower limb of confidence interval(which is 1.96 times Standard error) is 7 minus 5.8 = 1.2
*Query - why are the two limbs of the confidence interval different?* the same observation can be noted in all CIs noted above in the table. The asymmetry of limbs of CI are expected in case of non-linear measures like Odds Ratio, Relative risk, Hazard Ratio etc, but not in case of simple proportions. I am given to understand (from Dr Hans Reider, from whom I learnt Epidata) that EpiData Analysis is purported to follow the recommendations by the BMJ in the calculation of most confidence intervals and this would indeed suggest that the CI around a proportion should be symmetric on a linear scale.
Would be grateful if you could clarify.
Regards, Ajay
To the extent that users can influence the direction of the software, I would vote to keep the CI about a proportion as they are (or provide the user an option to choose between "exact" method and the simple test-based, or Wald approximation). OpenEpi provides 6 different CI about a proportion, one of which is symmetric, while the others are various approximations to the exact (asymmetric) CI.
In most situations, the differences will not be important. However, when working with small numbers as in many outbreaks, the "exact" CI may be preferred.
Certainly, a short document on statistical methods employed will be useful. I'm happy to help write that.
Jamie
On 2011-02-16, Ajay wrote:
Query - why are the two limbs of the confidence interval [about a proportion] different?
The statistical principles for Confidence intervals for proportions are several as Jamie Hockin indicated. The strategy of Openepi (and formerly in Epi6 also created by Andrew Dean) was in several commands to show a number of these such that it is up to the user to decide which of the principles is the optimal for a given estimation.
Usually the methods will in a simplified manner be one of these three: a. Some sort of normal approximation method - these tend to give symmetrical intervals around the point estimate b. Exact ones based on resampling and cut off point's for probabilities among the sampled estimates. c. Enhanced approximative methods often based on non-parametric principles, that is some sort of ranking.
Current implementation in EpiData can be any of a b c, but for small samples would either be b (tables, life tables) or c (proportions).
My intention would be to include all of the estimations for simple situations as described by Altman et al, currently this has been done for proportions and life tables. I suggest that users read the book: Altman et al. Statistics with confidence, London, BMJ books. ISBN 0 7279 1375 1, 2nd edition,2005. For proportions this is given on p 47 and life table methods on p 94. This is also found in the documentation for Analysis (press F1 when analysis is running).
In the book Altman et al compares for several measures the standard approximative methods (a above) with the enhanced ones (c above). For proportions the problem is that the symmetrical (standard) methods can give proportions below 0 or above one, whereas the enhanced one implemented will not do so.
In papers the reference for the CI would be Altman et al as implemented in EpiData Analysis.
Jamie's offer to assist in writing guidance on this is definetely welcomed and encouraged.
Regards Jens Lauritsen
In most situations, the differences will not be important. However, when working with small numbers as in many outbreaks, the "exact" CI may be preferred. Certainly, a short document on statistical methods employed will be useful. I'm happy to help write that.
Jamie
On 2011-02-16, Ajay wrote:
Query - why are the two limbs of the confidence interval [about a proportion] different?
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