A clinical trial may have no subject (0%) or every subject (100%) developing the outcome of concern in either of the two comparison groups. This will cause a zero-cell in the four-cell (2x2) table of a trial using a binary outcome and make it impossible to estimate the odds ratio, a commonly used effect measure. A usual way to deal with this problem is to add 0.5 to each of the four cells in the 2x2 table. This is known as Haldane's approximation. In meta-analysis, Haldane's approximation can also be applied. Two approaches are possible: add 0.5 to only the trials with a zero cell or to all the trials in the meta-analysis. Little is known which approach is better when used in combination with different definitions of the odds ratio: the ordinary odds ratio, Peto's odds ratio and Mantel-Haenszel odds ratio. / A new formula is derived for converting Peto's odds ratio to the risk difference. The derived risk difference through the new method was then compared with the true risk difference and the risk difference derived by taking the Peto's odds ratio as the ordinary odds ratio. All simulations and analyses were conducted on the Statistical Analysis Software (SAS). / Conclusions. The estimated confidence interval of a meta-analysis would mostly exclude the truth if an inappropriate correction method is used to deal with zero cells. Counter-intuitively, the combined result of a meta-analysis will be worse as the number of studies included becomes larger. Mantel-Haenszel odds ratio without applying Haldane's approximation is recommended in general for dealing with sparse data in meta-analysis. The ordinary odds ratio with adding 0.5 to only the trials with a zero cell can be used when the trials are heterogeneous and the odds ratio is close to 1. Applying Haldane's approximation to all trials in a meta-analysis should always be avoided. Peto's odds ratio without Haldane's approximation can always be considered but the new formula should be used for converting Peto's odds ratio to the risk difference. / In addition, the odds ratio needs to be converted to a risk difference to aid decision making. Peto's odds ratio is preferable in some situations and the risk difference is derived by taking Peto's odds ratio as an ordinary odds ratio. It is unclear whether this is appropriate. / Methods. For studying the validity of Haldane's approximation, we defined 361 types of meta-analysis. Each type of meta-analysis is determined by a unique combination of the risk in the two compared groups and thus provides a unique true odds ratio. The number of trials in a meta-analysis is set at 5, 10 and 50 and the sample size of each trial in a meta-analysis varies at random but is made sufficiently small so that at least one trial in a meta-analysis will have a zero-cell. The number of outcome events in a comparison group of a trial is generated at random according to the pre-determined risk for that group. One thousand homogeneous meta-analyses and one thousand heterogeneous meta-analyses are simulated for each type of meta-analysis. Two Haldane's approximation approaches in addition to no approximation are evaluated for three definitions of the odds ratio. Thus, nine combined odds ratios are estimated for each type of meta-analysis and are all compared with the true odds ratio. The percentage of meta-analyses with the 95% confidence interval including the true odds ratio is estimated as the main index for validity of the correction methods. / Objectives. (1) We conducted a simulation study to examine the validity of Haldane's approximation as applied to meta-analysis, and (2) we derived and evaluated a new method to covert Peto's odds ratio to the risk difference, and compared it with the conventional conversion method. / Results. By using the true ordinary odds ratio, the percentage of meta-analyses with the confidence interval containing the truth was lowest (from 23.2% to 53.6%) when Haldane's approximation was applied to all the trials regardless the definition of the odds ratios used. The percentage was highest with Mantel-Haenszel odds ratio (95.0%) with no approximation applied. The validity of the corrections methods increases as the true odds ratio gets close to one, as the number of trials in a meta-analysis decreases, as the heterogeneity decreases and the trial size increases. / The proposed new formula performed better than the conventional method. The mean relative difference between the true risk difference and the risk difference obtained from the new formula is -0.006% while the mean relative difference between the true risk difference and the risk difference obtained from the conventional method is -10.9%. / The validity is relatively close (varying from 86.8% to 95.8%) when the true odds ratio is between 1/3 and 3 for all combinations of the correction methods and definitions of the odds ratio. However, Peto's odds ratio performed consistently best if the true Peto's odds ratio is used as the truth for comparison among the three definitions of the odds ratio regardless the correction method (varying from 88% to 98.7%). / Tam Wai-san Wilson. / "Jan 2006." / Adviser: J. L. Tang. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6488. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 151-157). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_343756 |
| Date | January 2006 |
| Contributors | Tam, Wai-san Wilson., Chinese University of Hong Kong Graduate School. Division of Medical Sciences. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, theses |
| Format | electronic resource, microform, microfiche, 1 online resource (xvii, 172 p. : ill.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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