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A funnel plot displays study effect estimates against a measure of their precision, often standard error increasing down the vertical axis. Under a common-effect model, imprecise estimates spread more widely around the effect. Asymmetry is evidence of a small-study effect and can be consistent with publication bias, but it has other possible explanations.

Publication bias occurs when the availability or publication of a study depends on its results, for example their direction or statistical significance. The published studies then need not represent all studies meeting the review's eligibility criteria. This is different from unbiased studies simply having large sampling errors.

If mortality reductions favouring transfusion are more likely to be published than null or unfavourable findings, the observed log risk ratios will tend to be too negative and the pooled risk ratio too small. The apparent benefit will then be exaggerated. An ordinary meta-analysis interval ignores uncertainty about the missing evidence and may have poor coverage even if its sampling-variance calculation is correct for the studies included. The direction of bias depends on which results are preferentially made available; publication bias does not invariably favour a particular treatment.

A funnel plot places each estimated log risk ratio horizontally and its standard error vertically, with the most precise studies at the top. Under a common-effect model without selective availability, less precise estimates should spread approximately symmetrically around the underlying effect. The plotted dashed limits are the pooled estimate plus or minus twice the standard error; they illustrate the expected sampling spread, not a test of publication bias by themselves.

The least precise estimates are mostly far to the left, whereas the most precise estimates are close to zero. The reported regression slope means that increasing the standard error by one unit is associated with a decrease of about $1.99$ in the estimated log risk ratio. Its 95% confidence interval $(-3.40,-0.59)$ excludes zero, and $P=0.01$ gives evidence against a zero slope under that regression model. This is evidence of a small-study effect: less precise trials report stronger apparent benefit.

There is evidence consistent with publication bias, but asymmetry does not identify its cause. Selective availability of favourable small studies is a plausible explanation. Genuine differences in patient populations, trial quality, interventions or effect modification could also generate the pattern, and there are only ten trials. The given outcome-on-error regression should be interpreted as specified; it is not automatically the original standardized-effect-on-precision form of an Egger test. The plot and slope justify investigating missing studies and sensitivity to selection, rather than concluding that publication bias has been proved.

One method is trim and fill. Estimate the direction and extent of funnel asymmetry, temporarily trim the extreme studies on the overrepresented side to estimate a centre, and fill in mirror-image studies on the underrepresented side. Recompute the pooled effect using the observed and imputed studies. This estimates what the summary might be under a symmetry-based missing-study model. It can move an exaggerated effect towards the null, but genuine heterogeneity can violate its symmetry assumptions.

A second method is a selection model for publication bias. Specify how the probability of a result being available depends on quantities such as its $P$ value, direction or precision, and combine that mechanism with a model for the underlying study effects. If a study estimate has density $f(y)$ and availability probability $\pi (y)$, its observed density is proportional to $f(y)\pi (y)$, with a normalizing factor accounting for unobserved results. Fit the model, or vary the selection probabilities over plausible scenarios, to obtain selection-adjusted effects. Such models make assumptions about evidence that is missing, so their results are particularly useful as sensitivity analyses. Neither method removes publication bias without assumptions about the missing studies.

Trim and fill estimates missing studies from funnel plot asymmetry by trimming extreme studies to locate a centre and filling in counterparts on the less represented side. The adjusted meta-analysis includes these imputed estimates. Its interpretation depends on a symmetry model for missing evidence; it is not a guarantee that genuine publication bias has been removed.