Adjusted point parameter estimates, maximum log-likelihoods, and risk of mortality attributable to <i>Onchocerca volvulus</i> infection.

a<p>Dose-response models were fitted assuming microfilarial loads were measured with error. MLL: Maximum Log Likelihood; AR: Attributable Risk.</p>b<p>The degree of measurement error is summarized by parameter <i>k</i> of the negative binomial distribution, which is an inverse measure of extra-Poisson variation in the distribution of microfilarial counts measured per individual.</p>c<p>Evaluated at the posterior means of the estimated parameters; analogous to the maximum log-likelihood of the model.</p>d<p>Naïve: Point parameter estimates assuming no measurement error in microfilarial loads (see <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0001578#pntd-0001578-t003" target="_blank">Table 3</a>);</p>e<p>Poisson measurement errors;</p>f<p>Measurement error estimated from published data <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0001578#pntd.0001578-Picq1" target="_blank">[43]</a>;</p>g<p>Arbitrarily large measurement error.</p>h<p>Parameter value fixed, not estimated.</p

Definitions of parameters and variables.

<p>Definitions of parameters and variables.</p

Summary of mortality data collected by the onchocerciasis control programme in West Africa From 1974 through 2001.

a<p>Inclusion criteria comprise all the consistency checks described in the text plus participation in at least two surveys.</p

Relative mortality risk with increasing <i>Onchocerca volvulus</i> microfilarial load in the Onchocerciasis Control Programme cohort.

<p>Observed (open squares) and fitted (solid line) relative risk of mortality, with fitted (log-)sigmoid dose-response model adjusted to the average age of individuals within the cohort. Shaded (grey) area represents the 95% Bayesian credible interval around the fitted line; vertical error bars are 95% confidence intervals around observations. Inset permits visual inspection of the mortality relative risk at parasite loads ≤40 microfilariae per skin snip.</p

Measurement error-adjusted microfilarial loads plotted against their observed values.

<p>Each panel corresponds to an adjustment for a different assumed magnitude of measurement error as defined by parameter <i>k</i> of the negative binomial measurement error model (see <i>Measurement Error</i> section in the main text). In panel A, <i>k</i>→∞ which corresponds to Poisson measurement error. In panel B, <i>k</i> = 15 as estimated from published data <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0001578#pntd.0001578-Picq1" target="_blank">[43]</a> (see <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0001578#pntd.0001578.s003" target="_blank">Protocol S3</a>). In panel C, <i>k</i> = 1, which corresponds to an arbitrarily large degree of measurement error. In each panel the solid red line is the diagonal representing perfect agreement between observed and adjusted microfilarial loads.</p

Measurement error-adjusted and fitted relative mortality risk in the Onchocerciasis Control Programme cohort.

<p>Panels from top to bottom correspond to adjustments for increasing assumed magnitudes of measurement error as defined by parameter <i>k</i> of the negative binomial measurement error model (see <i>Measurement Error</i> section in the main text). In panel A, <i>k</i>→∞, corresponding to Poisson measurement error. In panel B, <i>k</i> = 15, as estimated from published data <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0001578#pntd.0001578-Picq1" target="_blank">[43]</a> (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0001578#pntd.0001578.s003" target="_blank">Protocol S3</a>). In panel C, <i>k</i> = 1. In all panels the solid and dashed lines represent, respectively, the fitted (log-)sigmoid and (log-)linear dose-response models. Note the absence of error bars around the model-derived point estimates of relative risk (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0001578#pntd.0001578.s001" target="_blank">Protocol S1</a>) and around the fitted dose-response. This is because regression calibration cannot account fully for the uncertainty introduced by adjusting the observed data for measurement error (see <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0001578#s4" target="_blank">Discussion</a>).</p