Statistical Methods for Standard Membrane-Feeding Assays to Measure Transmission Blocking or Reducing Activity in Malaria

<p>Transmission blocking vaccines for malaria are not designed to directly protect vaccinated people from malaria disease, but to reduce the probability of infecting other people by interfering with the growth of the malaria parasite in mosquitoes. Standard membrane-feeding assays compare the growth of parasites in mosquitoes from a test sample (using antibodies from a vaccinated person) compared to a control sample. There is debate about whether to estimate the transmission reducing activity (TRA) which compares the mean number of parasites between test and control samples, or transmission blocking activity (TBA) which compares the proportion of infected mosquitoes. TBA appears biologically more important since each mosquito with any parasites is potentially infective; however, TBA is less reproducible and may be an overly strict criterion for screening vaccine candidates. Through a statistical model, we show that the TBA estimand depends on μ_<i>c</i>, the mean number of parasites in the control mosquitoes, a parameter not easily experimentally controlled. We develop a standardized TBA estimator based on the model and a given target value for μ_<i>c</i> which has better mean squared error than alternative methods. We discuss types of statistical inference needed for using these assays for vaccine development. Supplementary materials for this article are available online.</p

Qualification of Standard Membrane-Feeding Assay with <em>Plasmodium falciparum</em> Malaria and Potential Improvements for Future Assays

<div><p>Vaccines that interrupt malaria transmission are of increasing interest and a robust functional assay to measure this activity would promote their development by providing a biologically relevant means of evaluating potential vaccine candidates. Therefore, we aimed to qualify the standard membrane-feeding assay (SMFA). The assay measures the transmission-blocking activity of antibodies by feeding cultured <i>P. falciparum</i> gametocytes to <i>Anopheles</i> mosquitoes in the presence of the test antibodies and measuring subsequent mosquito infection. The International Conference on Harmonisation (ICH) Harmonised Tripartite Guideline Q2(R1) details characteristics considered in assay validation. Of these characteristics, we decided to qualify the SMFA for Precision, Linearity, Range and Specificity. The transmission-blocking 4B7 monoclonal antibody was tested over 6 feeding experiments at several concentrations to determine four suitable concentrations that were tested in triplicate in the qualification experiments (3 additional feeds) to evaluate Precision, Linearity and Range. For Specificity, 4B7 was tested in the presence of normal mouse IgG. We determined intra- and inter-assay variability of % inhibition of mean oocyst intensity at each concentration of 4B7 (lower concentrations showed higher variability). We also showed that % inhibition was dependent on 4B7 concentration and the activity is specific to 4B7. Since obtaining empirical data is time-consuming, we generated a model using data from all 9 feeds and simulated the effects of different parameters on final readouts to improve the assay procedure and analytical methods for future studies. For example, we estimated the effect of number of mosquitoes dissected on variability of % inhibition, and simulated the relationship between % inhibition in oocyst intensity and % inhibition of prevalence of infected mosquitos at different mean oocysts in the control. SMFA is one of the few biological assays used in preclinical and early clinical development of transmission-blocking vaccines, and this study strongly supports its further development and application.</p> </div

Effect of modifications of assay on the sensitivity of SMFA.

<p>In this simulation, we assumed there were two test samples (T₁ and T₂), and true PIm of T₁ (50 or 70% inhibition compared to control) was higher than the true PIm of T₂ (0, 10, 20, 30, 40 or 50%). Three different dissection conditions were simulated; 1) total of 20 mosquitoes were dissected from a single COM (m = 20), 2) total of 60 from a single COM (m = 60), and 3) total of 60, but from three COM (m = 20×3). In addition, we stimulated either: 1) T₁ and T₂ were tested in the same feeding experiment (SF), or 2) tested in different feeding experiments (DF). We assumed the mean number of oocysts in the control was 20. For each test condition, 10,000 data were generated to calculate the probability of feeds in which T₁ showed higher PIm (i.e., lower mean oocyst number) than that T₂.</p

Repeatability (intra-feed variance) and Intermediate Precision (inter-feed variance) of SMFA.

a<p>Concentration of 4B7 mAb in a feeder [µg/ml].</p>b<p>Intra-feed variance estimates the variability between three PIm values (each one using one test COM and one control COM) where the test samples have the same 4B7 concentration and both PIm are measured on the same feed. We use U-statistics to estimate the intra-feed variance for each of the 3 feeds, as well as to estimate the overall estimate that combines the 3 feeds.</p>c<p>Inter-feed variance is similar to the intra-feed variance, except that the variability is between two PIm values from identically concentrated test samples where one value is measured on one feed and the other value is measured on a second feed. Again we use U-statistics. We give the pairwise estimates and an overall estimate of inter-feed variance.</p

Sample mean of oocyst counts by proportion of mosquitoes with any infection.

<p>Each point represents one COM. Black line is the fit from the zero-inflated negative binomial model. The blue dotted line is a nonparametric moving window average (specifically, a kernel smoother with a normal kernel with bandwidth 0.5 log₁₀ chosen to be slightly overfit).</p

Dose dependent % inhibition in mean oocyst intensity by 4B7 mAb.

<p>Various concentrations of 4B7 mAbs (ranging from 1 to 375 µg/ml) were tested over 6 independent feeding experiments (Feed 1–6). Different symbols represent data from different feeding experiments.</p

Effect of mean number of oocysts in the control on the two % inhibitions.

<p>The % inhibition of prevalence (PIp) is plotted against % inhibition in mean oocyst intensity (PIm) at different mean number of oocysts in the control.</p

Intra- and inter-feed variability in PIm of 4B7 mAb.

<p>Four concentrations (1, 6, 23 and 94 µg/ml) of 4B7 mAb were tested in triplicate in each feed, and three independent feeds were performed (Feed 7, 8 and 9). Since there were 3 COM of negative control and 3 COM of 4B7 mAb at each concentration, 9 different numbers of PIm were calculated (individual dots) at each concentration in each feed. Bar represents the mean of the 9 calculated data.</p

Relationship between 4B7 concentration and PIm.

<p>Various concentrations of 4B7 mAb were tested in the qualification experiments (Feed 7–9). For these data the first COM negative control is matched with the first COM of the 4B7 mAb at each concentration, the second with the second, etc. The square root of 4B7 concentration is shown on the x-axis, and the ratio of mean oocyst (mean of oocysts in control divided by mean of oocysts in test) is plotted on a log scale (shown on left side of y-axis, the associated PIm value is shown on the right side of the y-axis). Points with the same symbol use the same control, and points with the same color are from the same feed. Dotted line represents the best-fit line.</p

Relationship between mean number of oocysts and the standard deviation.

<p>For each COM, mean number of oocysts and standard deviation were calculated. Data from all COM tested in 9 independent feeding experiments are shown. Different symbols represent data from different feeding experiments and the line represents the best-fit curve from the zero-inflated negative binomial model. The R² value for the fit is 0.94. Gray lines represent 95% confidence intervals calculated using the t-distribution (for the means) or chi square distribution (for the standard deviations).</p