Dose-Response Relationship Between Tissue Concentrations of UC781 and Explant Infectibility with HIV Type 1 in the RMP-01 Rectal Safety Study

Ex vivo infection endpoints

Ex vivo infection was measured using readouts of cumulative p24 (CUM), p24 at the soft endpoint (SOFT), slope (SLOPE), and area under the virus growth curve (AUC) using previously reported calculation formulas, ¹³ where the virus growth curve was the p24 supernatant (pg/ml), per time point, plotted against time. In brief, SLOPE was the slope parameter from a linear regression plotted between day 1 (first day of supernatant collection) and day 14 (last day of supernatant collection). The area under each virus growth curve (AUC) was approximated using the trapezoidal rule ¹⁴ applied to a second order polynomial curve. SOFT is the virus growth measurement (p24) at the last time point where the increase in virus concentration between two consecutive time points is greater than the square root of the sum of sequential changes in virus concentration for the entire assay (Eq. 1). SOFT is an estimation of the p24 level at the start of the stationary phase of virus growth, after exponential growth has been achieved and prior to the onset of the decline phase ^15,16 when virus growth may be less likely due to tissue deterioration. See www.alphastatconsult.com for examples of the SOFT calculation applied to virus growth curves and the numerical example given below. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}\begin{align*}\Delta {\rm p}24 \ ({\rm Time}_k - {\rm Time}_{k - 1}) > \sqrt{\Delta {\rm p}24 \ \Sigma \ {\rm ABS} ({\rm Time}_k - {\rm Time}_{k - 1})} \tag{1} \end{align*}\end{document}

Numerical example of SOFT calculation

Precision of explant infectibility endpoints

Tissue infectibility at the baseline visit (V2) was used to compare intrasubject and intersubject measurement precision across the four measures of tissue infection and to test the effect of biopsy location (10, 30 cm) on biopsy virus growth. AUC, CUM, SOFT, and SLOPE endpoint measures were tested for normality and log-normally distributed data were log transformed prior to the precision analyses. AUC, CUM, SOFT, and SLOPE measurements were each entered into a mixed model ANOVA where subject was a random factor and biopsy location (10 vs. 30 cm) was a fixed factor. The mixed model ANOVA was used to test the null hypothesis that there was no effect of biopsy location on AUC, CUM, SOFT, and SLOPE virus growth endpoints at V2. In addition, the mixed model ANOVA provided the variance components for within and between subjects variance. The percent relative standard deviation (%RSD; Eq. 2, when modeled with the base-10 logarithm), an estimate of the amount of variability in each ANOVA model, was calculated using the subject covariance parameter estimate as a measure of intersubject variability and the residual variance covariance estimate as a measure of intrasubject variability. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}\begin{align*} \% \ { \rm RSD} = 100 ( \sqrt{10^{variance}} - 1 ) \tag{2}\end{align*}\end{document}

In the mixed model ANOVA, variance is additive so that intersubject variability and intrasubject variability (residual variance) provide the total variance in each model. The percentage of total variance in each model attributed to intersubject and intrasubject sources can be determined as 100×(intersubject variance/total variance) and 100×(intrasubject variance/total variance), respectively. The relative proportion of measurement variability from intrasubject and intersubject sources was determined for each mixed model ANOVA. A mixed model ANOVA was run for each of the four endpoint measures (AUC, CUM, SOFT, and SLOPE) at each HIV inoculation condition (10² and 10⁴ TCID₅₀).

To determine the reproducibility of subject biopsy infectivity measurements over time, the placebo group log₁₀ transformed biopsy infectivity endpoints (n=12; AUC, CUM, SOFT, and SLOPE) at V3 and V5 were compared to the infectivity levels from the same subjects at V2. It was hypothesized that for the biopsy infectivity measurements to show within-subject reproducibility over the duration of the study, the 90% confidence interval for the ratio of V3:V2 and V5:V2 would be within 0.7–1.3. An endpoint measure would be considered reproducible when biopsy infectibilities at V3 and V5 were within±30% (i.e., 70–130% ¹⁸ ) of the infectibility for the same placebo subject, location, and virus titer at V2 90% of the time.

Tissue concentrations of UC781 in rectal biopsies

UC781 (ng/g) data were tested for normality and log-normally distributed data were log transformed. ANOVA models were used to test the main effects of treatment (0.1%, 0.25% UC781, and placebo) and location (10 versus 30 cm) on tissue UC781 levels at V3 and V5, where subject was a randomized block variable. Least squares means, adjusted for subject, were compared between treatment vs. placebo groups and 10 vs. 30 cm biopsy location by the Tukey pairwise comparison test, when indicated by statistically significant main effects of treatment, location, or the treatment×location interactions.

Correlating ex vivo HIV tissue infectibility with in vivo tissue UC781 drug concentrations

Linear regression analyses were used to correlate AUC, CUM, SOFT, and SLOPE endpoints with log transformed tissue concentrations of UC781 (ng/ml). A statistically significant (p<0.05) linear dose-response relationship between drug and endpoint was followed by the application of an infection/noninfection categorization. The infected/noninfected Boolean categorization of linear, continuous virus growth endpoint measurements was performed by imposing a cut-point where an assay virus growth endpoint less than or equal to the cut-point was categorized as a “noninfected” explant assay and an endpoint greater than the cut-point was categorized as an “infected” explant assay. A range of cut-points was tested, for example 200, 300, 400 etc. to 1300 (pg/ml) SOFT. For each cut-point, an assay result at or below the cut-point would be categorized as “noninfected,” depending on the virus growth endpoints that were progressed into this stage of the analysis.

Calculation of EC_50,90,95

The infected/noninfected categorized explant results were entered into a series of logistical dose-response regression analyses where the dose of drug predicted to achieve noninfection in 50, 90, and 95% (EC₅₀, EC₉₀, and EC₉₅) of explants was calculated. An ROC (receiver operating characteristic) curve was used to compare the “goodness of fit” of each of the logistical regression models. The ROC is a plot of the sensitivity (true positive rate) and 1 – specificity (true negative rate). The area under the ROC curve (C) was used as a measure of goodness of fit for each logistical regression model.

Statistical analyses were performed with SAS^® version 9.2 and an α=0.05.

Variability greater for SLOPE infectibility measure

The total model variances for SLOPE were 5- to 10-fold higher for both 10² (0.3361) and 10⁴ (0.1660) TCID₅₀ viral titers (“Variance”; Table 1), compared to the AUC, CUM, and SOFT endpoint variances. Although there was a slightly larger proportion of variance from the intersubject compared to intrasubject sources of variances for the SLOPE measure [“Variance Proportion”; Table 1], the %RSD values [“RSD”; Table 1] were extremely high for both intersubject and intrasubject sources of measurement variation for SLOPE. Overall, 31% of virus growth curves had a zero slope value between day 0 and day 14.

Similar variance for AUC, CUM and SOFT infectibility measures

Total model variance for AUC, CUM, and SOFT ranged from 0.0168 to 0.0600 (“Variance”; Table 1), that is, total variance for all three endpoint measures were within a 2- to 3-fold range. There was a similar pattern in the relative proportion of variance attributed to intrasubject and intersubject sources for the AUC, CUM, and SOFT endpoints. A larger relative proportion of total variance was found from intrasubject sources after 10² infection [AUC=57.7%, CUM=57.4%, SOFT=56.7%; “Variance Proportion”; Table 1] and from intersubject sources after 10⁴ infection (AUC=56.6%, CUM=57%, SOFT=56.6%).

Total measurement variance greater for 10² titer

The total variance explained by each model was increased by approximately 2- to 3-fold following the 10² viral titer compared to the 10⁴ viral titer (“Variance”; Table 1). Intrasubject and intersubject variability was lower following the 10⁴ infection (21.7–98.7; “%RSD,” Table 1) than the 10² infection (34.5–191.9% RSD; Table 1).

Intersubject variance was greater than intrasubject variance for 10⁴ titer

The expectation was that multiple biopsy samples taken from the same subject (i.e., intrasubject) would be more consistently infectible than biopsy samples taken from multiple subjects (i.e., intersubject). This was found to be the case for the 10⁴ titer, where the relative proportion of variance (“Variance Proportion”; Table 1) attributed to intersubject sources was consistently higher than intrasubject sources (Table 1).

No statistical impact of biopsy location

There was no effect of biopsy location on measurements of CUM, SOFT, AUC, and SLOPE at either 10² or 10⁴ TCID₅₀ infection (“Location,” Table 1).

Reproducibility of infectivity measures across visits for the 10⁴ titer

It was expected that the biopsy infectivity results for subjects in the placebo group (n=12) would be reproducible across V2, V3, and V5 testing times as these measurements were made following either no gel application (V2) or HEC gel application (V3 and V5) where neither condition was expected to affect biopsy infectibility. Reproducibility was found for CUM, SOFT, and AUC endpoints for the 10⁴ titer at 10 cm, where the 90% confidence interval (CI) for the ratio of V3:V2 and V5:V2 was within 0.7–1.3, an acceptable level of bioequivalence for data showing large interindividual variation ¹⁸ (bolded values in Table 2), where the 90% CI for measures at V3:V2 were within 0.8–1.25. ¹⁹ That is, the measures in the placebo group at V3 and V5 were within 30% of the baseline measures at V2 following the 10⁴ infection and at 10 cm. A greater than±30% difference to baseline infectibility measures was found for CUM and SOFT following the 10² infection (Table 2) at both locations (10 and 30 cm) and at both visits (V3 and V5).

Dose and location effects of 0.1% and 0.25% UC781 gel application at V3

At V3, after the single rectal microbicide application, differences in UC781 tissue concentration were found across treatments (p<0.0001) and locations (p=0.0013). The treatment×location interaction did not reach significance at alpha=0.05, but could be considered to be “marginally” significant (p=0.0506; Fig. 1a). At V3, tissue drug concentrations for 0.1% and 0.25% UC781 groups and at both locations (10 cm and 30 cm) were higher compared to the placebo (“Treatment vs. Placebo”; embedded table in Fig. 1a.). Additionally, there was a higher tissue concentration at the 10 cm biopsy location compared to the 30 cm biopsy location for the 0.10% UC781 treatment group (p=0.0166, “Treatment 10 cm vs. 30 cm”; embedded table in Fig. 1a.).

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FIG. 1.

UC781 rectal tissue drug concentrations. Visit 3 (a), after single application of rectal microbicide gel and Visit 5 (b), after seven daily doses of rectal microbicide gel. The mean is displayed as a horizontal solid line. The horizontal dashed line indicates the lower limit of quantification for this assay (5 ng/g). Embedded tables show the probability values for the main effects of treatment (placebo, 0.1% and 0.25% UC781) and biopsy location (10, 30 cm) in the headers and the Tukey pairwise comparisons between each drug treated groups (0.1 and 0.25% UC781) and the placebo (treatment vs. placebo) and the effect of location (treatment at 10 cm vs. 30 cm) on log transformed UC781 tissue drug concentrations in the table. The treatment×location interaction for visits 3 and 5 are given as footnotes below each embedded table.

Dose and location effects of 0.25% UC781 gel application at V5

At V5, after the seven-daily rectal microbicide gel applications, there was an effect of treatment (p=0.0465, embedded Table in Fig. 1b) but no effect of biopsy location on tissue UC781 levels for the 0.1% gel. The treatment×location interaction was significant (p=0.0173; Fig. 1b). UC781 levels for the 0.25% gel treatment group were higher than the placebo at 10 cm (p=0.0247; embedded table in Fig. 1b). There was also an effect of location for the 0.25% treatment group at V5 where the 10 cm location provided a higher tissue concentration than the 30 cm location (p=0.00115; embedded table in Fig. 1b).

Candidate infectibility measures for “infected/noninfected” categorization

SOFT and CUM measures were considered candidate endpoints for the Boolean infection/noninfection categorization due to both the fit of the linear relationship with tissue UC781 and relatively high measurement precision (above). Specifically, SOFT and CUM measures presented clear, statistically significant, linear dose-response relationships (Fig. 2b and d), intersubject and intrasubject %RSDs <35% (Table 1), and evidence for measurement reproducibility over time (Table 2) for infectibility measured after a 10⁴ titer. However, the CUM endpoint provided a difficult conceptualization for a cut-point intended to enable comparison of the same drug efficacy between different laboratories and explant models of different duration and tissue source. Without other confounders, a longer assay duration would increase this cumulative p24 measure and a shorter assay duration would reduce cumulative p24. A 14-day explant assay duration was used here whereas explant assay durations ranging from 10 to 21 days have been reported elsewhere. ^6,20 As long as an explant assay has been designed to allow the system to reach the SOFT endpoint, SOFT will be identical irrespective of the duration of the assay beyond that point. Cumulative p24 (CUM) is the sum of p24 across assay days so that the cumulative p24 will increase with increasing length of the assay assuming measurable virus is found at all time points. For example, a mean cumulative p24 of 1567.34 pg/ml would have been reduced to 712.35 pg/ml if the assays presented here had extended to only 10 days instead of 14 (p<0.001; paired t-test). As one of the aims of this study was to present a cut-point that could be used to compare drug efficacy across laboratories using a variety of explant protocols (e.g., assay durations between 6 and 16 days), CUM was not used in the logistic regression analyses. SOFT is reached at a time point after exponential virus growth has been achieved and before cell death occurs, so providing an endpoint that is, theoretically, less affected by assay duration assuming that the explant protocol captures the kinetics of HIV virus growth.

SOFT “infected/noninfected” categorization

For the Boolean categorization, the SOFT endpoint was used and provided 12 cut-points ranging from 200 to 1300 p24 pg/ml, increasing in increments of 100. Explant assay SOFT values at or lower than each cut-point level were categorized as “noninfected” and explant assay SOFT values higher than the cut-point were categorized as “infected.”