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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 09:55:50 -0500 |

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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