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From |
"Steichen, Thomas" <STEICHT@rjrt.com> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: META with confidence intervals |

Date |
Tue, 29 Oct 2002 15:35:35 -0500 |

In my earlier reply to Paul O'Brien I slipped in a typographical error... Charles Poole (forwarded via Jay Kaufman) privately pointed it out for me, thus this follow-up. I claimed: Data that follows log symmetry has the characteristic that the following are all equal: rr/ll = (ul-ll)/2 = ul/rr This is not true. A correct form (and the one I used in my calculations) is: rr/ll = exp((ln(ul)-ln(ll))/2) = ul/rr Charles pointed out that a simpler form is: rr/ll = sqrt(ul/ll) = ul/rr (I once knew this...) My apologies to Paul for the error and my thanks to Charles for the correction and to Jay for forwarding Charles' comment. Tom Steichen > Paul O'Brien writes: > > > I am combining two studies: > > > > Study RR LCI UCI > > Study 1 0.7 0.1 8.2 > > Study 2 0.6 0.1 6.4 > > > > With the command: > > > > . meta rr ll ul, ci eform gr(f) print id(study) > > > > However, the confidence intervals listed in the print are > > different from what I have entered: > > > > Meta-analysis (exponential form) > > | Pooled 95% CI Asymptotic No. of > > Method | Est Lower Upper z_value p_value studies > > -------+---------------------------------------------------- > > Fixed | 0.645 0.142 2.927 -0.568 0.570 2 > > Random | 0.645 0.142 2.927 -0.568 0.570 > > Test for heterogeneity: Q= 0.010 on 1 degrees of freedom (p= 0.921) > > Moment-based estimate of between studies variance = 0.000 > > | Weights Study 95% CI > > Study | Fixed Random Est Lower Upper > > ----------+---------------------------------------- > > Study 1 | 0.79 0.79 0.70 0.08 6.34 > > Study 2| 0.89 0.89 0.60 0.08 4.80 > > > > What is the problem? > > The problem is that your input data do not follow the expected > ratios for log-based confidence intervals (probably because > too few digits were retained). -meta- uses your input CI to > compute the standard error (se), assuming log symmetry, then > later recalculates the proper log-symmetric CI endpoints about > the point estimate using this standard error. > > Data that follows log symmetry has the characteristic that the > following are all equal: > > rr/ll = (ul-ll)/2 = ul/rr > > For your input data I get: > > rr/ll = (ul-ll)/2 = ul/rr > study 1 7 9.06 11.71 > study 2 6 8 10.67 > > For the (rounded) recalculated values I get: > > study 1 8.75 8.90 9.06 > study 2 7.50 7.75 8.00 > > These values are not exactly equal because the two-digit > representation of the recalculated ll, .08, is not > accurate enough. > > For a more accurate value, note that -meta- uses the > following calculation to get the se: > > se = ( ln(ul) - ln(ll) ) / 2 / z > > (where z is an appropriate Normal value) > > For your study 1 data this generates: > > se = ( ln(8.2) - ln(.1) ) / 2 / 1.96 > = ( 2.1041342 - -2.3025851 ) / 2 / 1.96 > = 4.4067192 / 2 / 1.96 > = 1.1241631 > > Later, -meta- spits back the recalculated CI endpoints as: > > ll = exp( ln(rr) - z * se ) > ul = exp( ln(rr) + z * se ) > > Or, for study 1: > > ll = exp( ln(rr) - z * se ) > = exp( ln(.7) - 1.96 * 1.1241631 ) > = exp( -.35667494 - 1.96 * 1.1241631 ) > = exp( -2.5600346 ) > = .07730206 (displayed as .08) > > ul = exp( ln(rr) + z * se) > = exp( ln(.7) + 1.96 * 1.1241631 ) > = exp( -.35667494 + 1.96 * 1.1241631 ) > = exp( 1.8466847 ) > = 6.3387699 (displayed as 6.34) > > Thus, using the exact ll and ul in the ratio calculations: > > rr/ll = (ul-ll)/2 = ul/rr = 9.06 > > > This suggests to me that more digits are required from your > original data in order to properly meta-analyze the data. > > Tom >

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