Density-Dependent Mortality of the Human Host in Onchocerciasis: Relationships between Microfilarial Load and Excess Mortality

Human onchocerciasis (River Blindness) is a parasitic disease leading to visual impairment including blindness. Blindness may lead to premature death, but infection with the parasite itself (Onchocerca volvulus) may also cause excess mortality in sighted individuals. The excess risk of mortality may not be directly (linearly) proportional to the intensity of infection (a measure of how many parasites an individual harbours). We analyze cohort data from the Onchocerciasis Control Programme in West Africa, collected between 1974 and 2001, by fitting a suite of quantitative models (including a ‘null’ model of no relationship between infection intensity and mortality, a (log-) linear function, and two plateauing curves), and choosing the one that is the most statistically adequate. The risk of human mortality initially increases with parasite density but saturates at high densities (following an S-shape curve), and such risk is greater in younger individuals for a given infection intensity. Our results have important repercussions for programmes aiming to control onchocerciasis (in terms of how the benefits of the programme are calculated), for measuring the burden of disease and mortality caused by the infection, and for a better understanding of the processes that govern the density of parasite populations among human hosts

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