Publication bias is a major problem, perhaps the major problem, in meta-analysis (or systematic reviews). Small studies are more likely to be published if their results are 'significant' than if their results are negative or inconclusive, and so the studies available for review are biased in favour of those with positive outcomes. Correcting for this bias is not possible without making untestable assumptions. In this paper, a sensitivity analysis is suggested which is based on fitting a model to the funnel plot. Some examples are discussed.

Periodontal disease, which includes gingivitis and periodontitis, is highly prevalent in adults and disease severity increases with age. The relationship between periodontal disease and oral cancer has been examined for several decades, but there is increasing interest in the link between periodontal disease and overall cancer risk, with systemic inflammation serving as the main focus for biological plausibility. Numerous case-control studies have addressed the role of oral health in head and neck cancer, and several cohort studies have examined associations with other types of cancers over the past decade. For this review, we included studies that were identified from either 11 published reviews on this topic or an updated literature search on PubMed (between 2011 and July 2016). A total of 50 studies from 46 publications were included in this review. Meta-analyses were conducted on cohort and case-control studies separately when at least 4 studies could be included to determine summary estimates of the risk of cancer in relation to 1) periodontal disease or 2) tooth number (a surrogate marker of periodontal disease) with adjustment for smoking. Existing data provide support for a positive association between periodontal disease and risk of oral, lung, and pancreatic cancers; however, additional prospective studies are needed to better inform on the strength of these associations and to determine whether other cancers are associated with periodontal disease. Future studies should include sufficiently large sample sizes, improved measurements for periodontal disease, and thorough adjustment for smoking and other risk factors.

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There is no simple method of correcting for publication bias in systematic reviews. We suggest a sensitivity analysis in which different patterns of selection bias can be tested against the fit to the funnel plot. Publication bias leads to lower values, and greater uncertainty, in treatment effect estimates. Two examples are discussed. An appendix lists the S-plus code needed for carrying out the analysis.