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Consequently, their estimates were consistently below the true values in the countries where alternative data sources were available.
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For all parameter sets considered, <5% of CIs had upper bounds below the true value of k.
The likelihood-based analyses showed less bias with mean estimates around or slightly above the true value of 0.2 and median estimates slightly below the true value.
This upward bias occurred even though many estimates were well below the true value λ = 0.5 kb, as shown in the histogram in Figure 4c.
Table 3 shows, for these three estimators, the proportion of times that their 95% confidence intervals are above or below the true value of μ1.
The bias was particularly severe when s = 0.5, with all of the 1000 MLEs falling below the true value for the standard and Gaussian diffusion approximations (median s ^ values of 0.397 and 0.406, respectively).
Because it tends, on average, to reduce the observable risk below the true value in cohort and case control studies, that is, to induce false-negative results, this effect can be substantial.
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