= Solution
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.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/iii/paper-32-funnel.png]
{title=Funnel plot of the ten transfusion trial estimates, with inverse-variance pooled effect and approximate sampling limits}
{height=600}
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.
\b[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.
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