[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]

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 >

CONFIDENTIALITY NOTE: This e-mail message, including any attachment(s), contains information that may be confidential, protected by the attorney-client or other legal privileges, and/or proprietary non-public information. If you are not an intended recipient of this message or an authorized assistant to an intended recipient, please notify the sender by replying to this message and then delete it from your system. Use, dissemination, distribution, or reproduction of this message and/or any of its attachments (if any) by unintended recipients is not authorized and may be unlawful.

- Prev by Date:
**st: Re: RE: Re: RE: Utility for Changing Directories** - Next by Date:
**st: help with record length problem** - Previous by thread:
**st: RE: META with confidence intervals** - Next by thread:
**st: gmm estimation** - Index(es):

© Copyright 1996–2015 StataCorp LP | Terms of use | Privacy | Contact us | What's new | Site index |