A comparison of statistical methods for animal oncology studies.

In pre-clinical oncology studies, tumor-bearing animals are treated and observed over a period of time in order to measure and compare the efficacy of one or more cancer-intervention therapies along with a placebo/standard of care group. A data analysis is typically carried out by modeling and comparing tumor volumes, functions of tumor volumes, or survival. Data analysis on tumor volumes is complicated because animals under observation may be euthanized prior to the end of the study for one or more reasons, such as when an animal's tumor volume exceeds an upper threshold. In such a case, the tumor volume is missing not-at-random for the time remaining in the study. To work around the non-random missingness issue, several statistical methods have been proposed in the literature, including the rate of change in log tumor volume and partial area under the curve. In this work, an examination and comparison of the test size and statistical power of these and other popular methods for the analysis of tumor volume data is performed through realistic Monte Carlo computer simulations. The performance, advantages, and drawbacks of popular statistical methods for animal oncology studies are reported. The recommended methods are applied to a real data set.

A Bayesian Statistical Approach to Continuous Qualification of a Bioassay.

A validated bioassay is used to measure the potency of commercial lots, and as such, must be accurate, precise, and fit for its intended purpose. Regulatory expectations for a bioassay include a characterization of features, such as accuracy, precision, linearity, and range. The journey of a bioassay typically starts in a development lab, where it is initially qualified and used to support the release and stability testing of clinical lots. As a program moves through the different clinical phases, it may be optimized further, used to support process development, or transferred to new laboratories, with each activity generating additional bioassay data. Finally, the bioassay is fully validated as part of the transfer to the commercial quality control testing laboratories. In this work, rather than capturing the data from each study as a separate, independent report, it is proposed that, beginning with the qualification study, the accuracy and precision of the bioassay be continuously characterized, with each subsequent study result building upon the preceding ones. We call this approach continuous qualification Such a proposition is naturally carried out using Bayesian statistical methods in which the historical study data is used to construct prior knowledge that is blended with the current study data. By doing so, the bioassay accuracy and precision may be assessed with high confidence well ahead of commercial manufacturing. Further, by following the total-variance approach, the method also allows for a robust construction of system suitability and control limits for potency.

Setting Alert and Action Limits in the Presence of Significant Amount of Censoring in Data.

In manufacturing settings, control limits are often set using a three-sigma rule (i.e., three estimated standard deviations above and below the estimated mean). More sophisticated statistical methods might include the use of confidence, prediction, or tolerance intervals. However, in environmental monitoring of microbial excursions in aseptic manufacturing operations, most of the assayed measurements fall below the limit of quantitation. In such circumstances, it is inappropriate to directly calculate control limits with a mean plus two or three standard deviations to represent the center and spread of the data. The system under consideration assumes that microbial assayed values stem from a log-normal distribution with two sources of variability to account for testing occasions and measurements made within a testing occasion. Bayesian statistical methods and a Tobit likelihood are used to model the observed and left-censored data in order to predict the distribution of new data. Control limits are generated from quantiles of the posterior predictive distribution. LAY ABSTRACT: In manufacturing settings, control limits are used to ensure either the manufacturing process or environment is in a state of control. These limits can be set using a three-sigma rule (i.e., three estimated standard deviations above and below the estimated mean) or via more sophisticated statistical methods. In this paper, we consider setting the control limits for a clean room setting in which microbial excursions are rare. Under such circumstance, the measurements of microbial counts are often below the limit of quantification. We develop methods based on Bayesian analysis and a Tobit regression to more accurately estimate control limits.

A new PK equivalence test for a bridging study.

In a bridging study, the plasma drug concentration-time curve is generally used to assess bioequivalence between the two formulations. Selected pharmacokinetic (PK) parameters including the area under the concentration-time curve, the maximum plasma concentration or peak exposure (Cmax), and drug half-life (T1/2) are compared to ensure comparable bioavailability of the two formulations. Comparability in these PK parameters, however, does not necessarily imply equivalence of the entire concentration-time profile. In this article, we propose an alternative metric of equivalence based on the maximum difference between PK profiles of the two formulations. A test procedure based on Bayesian analysis and accounting for uncertainties in model parameters is developed. Through both theoretical derivation and empirical simulation, it is shown that the new method provides better control over consumer's risk.

Pharmacokinetics/Pharmacodynamics of Peptide Deformylase Inhibitor GSK1322322 against Streptococcus pneumoniae, Haemophilus influenzae, and Staphylococcus aureus in Rodent Models of Infection.

GSK1322322 is a novel inhibitor of peptide deformylase (PDF) with good in vitro activity against bacteria associated with community-acquired pneumonia and skin infections. We have characterized the in vivo pharmacodynamics (PD) of GSK1322322 in immunocompetent animal models of infection with Streptococcus pneumoniae and Haemophilus influenzae (mouse lung model) and with Staphylococcus aureus (rat abscess model) and determined the pharmacokinetic (PK)/PD index that best correlates with efficacy and its magnitude. Oral PK studies with both models showed slightly higher-than-dose-proportional exposure, with 3-fold increases in area under the concentration-time curve (AUC) with doubling doses. GSK1322322 exhibited dose-dependent in vivo efficacy against multiple isolates of S. pneumoniae, H. influenzae, and S. aureus. Dose fractionation studies with two S. pneumoniae and S. aureus isolates showed that therapeutic outcome correlated best with the free AUC/MIC (fAUC/MIC) index in S. pneumoniae (R(2), 0.83), whereas fAUC/MIC and free maximum drug concentration (fCmax)/MIC were the best efficacy predictors for S. aureus (R(2), 0.9 and 0.91, respectively). Median daily fAUC/MIC values required for stasis and for a 1-log10 reduction in bacterial burden were 8.1 and 14.4 for 11 S. pneumoniae isolates (R(2), 0.62) and 7.2 and 13.0 for five H. influenzae isolates (R(2), 0.93). The data showed that for eight S. aureus isolates, fAUC correlated better with efficacy than fAUC/MIC (R(2), 0.91 and 0.76, respectively), as efficacious AUCs were similar for all isolates, independent of their GSK1322322 MIC (range, 0.5 to 4 µg/ml). Median fAUCs of 2.1 and 6.3 µg · h/ml were associated with stasis and 1-log10 reductions, respectively, for S. aureus.

Testing drug additivity based on monotherapies.

Under the Loewe additivity, constant relative potency between two drugs is a sufficient condition for the two drugs to be additive. Implicit in this condition is that one drug acts like a dilution of the other. Geometrically, it means that the dose-response curve of one drug is a copy of another that is shifted horizontally by a constant over the log-dose axis. Such phenomenon is often referred to as parallelism. Thus, testing drug additivity is equivalent to the demonstration of parallelism between two dose-response curves. Current methods used for testing parallelism are usually based on significance tests for differences between parameters in the dose-response curves of the monotherapies. A p-value of less than 0.05 is indicative of non-parallelism. The p-value-based methods, however, may be fundamentally flawed because an increase in either sample size or precision of the assay used to measure drug effect may result in more frequent rejection of parallel lines for a trivial difference. Moreover, similarity (difference) between model parameters does not necessarily translate into the similarity (difference) between the two response curves. As a result, a test may conclude that the model parameters are similar (different), yet there is little assurance on the similarity between the two dose-response curves. In this paper, we introduce a Bayesian approach to directly test the hypothesis that the two drugs have a constant relative potency. An important utility of our proposed method is in aiding go/no-go decisions concerning two drug combination studies. It is illustrated with both a simulated example and a real-life example.

The acute extracellular flux (XF) assay to assess compound effects on mitochondrial function.

Numerous investigations have linked mitochondrial dysfunction to adverse health outcomes and drug-induced toxicity. The pharmaceutical industry is challenged with identifying mitochondrial liabilities earlier in drug development and thereby reducing late-stage attrition. Consequently, there is a demand for reliable, higher-throughput screening methods for assessing the impact of drug candidates on mitochondrial function. The extracellular flux (XF) assay described here is a plate-based method in which galactose-conditioned HepG2 cells were acutely exposed to test compounds, then real-time changes in the oxygen consumption rate and extracellular acidification rate were simultaneously measured using a Seahorse Bioscience XF-96 analyzer. The acute XF assay was validated using marketed drugs known to modulate mitochondrial function, and data analysis was automated using a spline curve fitting model developed at GlaxoSmithKline. We demonstrate that the acute XF assay is a robust, sensitive screening platform for evaluating drug-induced effects on mitochondrial activity in whole cells.

Testing assay linearity over a pre-specified range.

Validation of linearity is a regulatory requirement. Although many methods are proposed, they suffer from several deficiencies including difficulties of setting fit-for-purpose acceptable limits, dependency on concentration levels used in linearity experiment, and challenges in implementation for statistically lay users. In this article, a statistical procedure for testing linearity is proposed. The method uses a two one-sided test (TOST) of equivalence to evaluate the bias that can result from approximating a higher-order polynomial response with a linear function. By using orthogonal polynomials and generalized pivotal quantity analysis, the method provides a closed-form solution, thus making linearity testing easy to implement.

A simple test for synergy for a small number of combinations.

A method for detecting deviations from the Loewe additive drug combination reference model for in vitro drug combination experimentation is described. It is often difficult to fit a response surface model to drug combination data, especially in situations where the experimental design contains a sparse set of combinations. The literature does contain good response surface modeling approaches, but they tend to be complex and can be difficult to execute. It is especially difficult to check model quality when fitting to more than two combined agents. A simple method based on sound statistical principles is proposed that examines the mean response deviation of each combination from the predicted response under Loewe additivity. The method can readily handle any number of combined agents, does not require sophisticated modeling, and can even be programmed into Microsoft Excel without the use of macros. Several potential extensions to the method are discussed in detail. Computer-generated simulations demonstrate the statistical capabilities of the approach, and a real-data example is given to illustrate the method.

Development of a high-throughput electrophysiological assay for the human ether-à-go-go related potassium channel hERG.

INTRODUCTION: Drug-induced prolongation of the QT interval via block of the hERG potassium channel is a major cause of attrition in drug development. The advent of automated electrophysiology systems has enabled the detection of hERG block earlier in drug discovery. In this study, we have evaluated the suitability of a second generation automated patch clamp instrument, the IonWorks Barracuda, for the characterization of hERG biophysics and pharmacology. METHODS: All experiments were conducted with cells stably expressing hERG. Recordings were made in perforated patch mode either on a conventional patch clamp setup or on the IonWorks Barracuda. On the latter, all recordings were population recordings in 384-well patch plates. RESULTS: HERG channels activated with a V(1/2)=-3.2±1.6mV (n=178) on the IonWorks Barracuda versus -11.2±6.1mV (n=9) by manual patch clamp. On the IonWorks Barracuda, seal resistances and currents were stable (<30% change) with up to six cumulative drug additions and 1-min incubations per addition. Over 27 experiments, an average of 338 concentration-response curves were obtained per experiment (96% of the 352 test wells on each plate). HERG pharmacology was examined with a set of 353 compounds that included well-characterized hERG blockers. Astemizole, terfenadine and quinidine inhibited hERG currents with IC(50) values of 159nM, 224nM and 2µM, respectively (n=51, 10 and 18). This set of compounds was also tested on the PatchXpress automated electrophysiology system. We determined through statistical methods that the two automated systems provided equivalent results. DISCUSSION: Evaluating drug effects on hERG channels is best performed by electrophysiological methods. HERG activation and pharmacology on the IonWorks Barracuda automated electrophysiology platform were in good agreement with published electrophysiology results. Therefore, the IonWorks Barracuda provides an efficient way to study hERG biophysics and pharmacology.

Pharmacovirological impact of an integrase inhibitor on human immunodeficiency virus type 1 cDNA species in vivo.

Clinical trials of the first approved integrase inhibitor (INI), raltegravir, have demonstrated a drop in the human immunodeficiency virus type 1 (HIV-1) RNA loads of infected patients that was unexpectedly more rapid than that with a potent reverse transcriptase inhibitor, and apparently dose independent. These clinical outcomes are not understood. In tissue culture, although their inhibition of integration is well documented, the effects of INIs on levels of unintegrated HIV-1 cDNAs have been variable. Furthermore, there has been no report to date on an INI's effect on these episomal species in vivo. Here, we show that prophylactic treatment of transgenic rats with the strand transfer INI GSK501015 reduced levels of viral integrants in the spleen by up to 99.7%. Episomal two-long-terminal-repeat (LTR) circles accumulated up to sevenfold in this secondary lymphoid organ, and this inversely correlated with the impact on the proviral burden. Contrasting raltegravir's dose-ranging study with HIV patients, titration of GSK501015 in HIV-infected animals demonstrated dependence of the INI's antiviral effect on its serum concentration. Furthermore, the in vivo 50% effective concentration calculated from these data best matched GSK501015's in vitro potency when serum protein binding was accounted for. Collectively, this study demonstrates a titratable, antipodal impact of an INI on integrated and episomal HIV-1 cDNAs in vivo. Based on these findings and known biological characteristics of viral episomes, we discuss how integrase inhibition may result in additional indirect antiviral effects that contribute to more rapid HIV-1 decay in HIV/AIDS patients.

Nonlinear blending: a useful general concept for the assessment of combination drug synergy.

Human diseases may involve cellular signaling networks that contain redundant pathways, so that blocking a single pathway in the system cannot achieve the desired effect. As such, the use of drugs in combination are particularly effective interventions in networked systems. However, common synergy measures are often inadequate to quantify the effect of two different drugs in complex cellular systems. This article proposes a general approach to quantifying the synergy of two drugs in combination. This approach is called strong nonlinear blending. Drugs with different relative potencies, different effect maxima, or situations of potentiation or coalism pose no problem for strong nonlinear blending as a way to assess the increased response benefit to be gained by combining two drugs. This is important as testing drug combinations in complex biological systems are likely to produce a wide variety of possible response surfaces. It is also shown that for monotone increasing (or decreasing) dose response surfaces that strong nonlinear blending is equivalent to improved potency along a ray of constant dose ratio. This is important because fixed dose ratios form the basis for many preclinical and clinical combination drug experiments. Two examples are given involving HIV and cancer chemotherapy combination drug experiments.