Quantifying uncertainty in method of moments estimates of the heterogeneity variance in random effects meta-analysis.

The between-study variance or heterogeneity variance is an important parameter in random effects meta-analysis. This paper uses an M-estimation framework to introduce and discuss variance estimators for quantifying the uncertainty in estimates of the heterogeneity variance using the noniterative generalized method of moments estimator and some related method of moments estimators. An example is used to further illustrate the variance estimators, and simulation results are presented for assessing the empirical properties of the proposed variance estimators.

A note on the empirical Bayes heterogeneity variance estimator in meta-analysis.

This paper focuses on the empirical Bayes (EB) or Mandel-Paule estimator of the heterogeneity variance in meta-analysis, which was discussed by Morris and proposed in earlier publications by Mandel and Paule in an inter-laboratory context. The relationship of the EB estimator to other heterogeneity variance estimators typically used in meta-analysis is explored, and approximate variance estimators for the EB estimate of the heterogeneity variance are proposed based on the M-estimation method. Statistical inference for the overall treatment effect using the EB estimator and the proposed standard errors is discussed using two example data sets from meta-analysis applications.

An Evaluation of the Collagen Fragments Related to Fibrogenesis and Fibrolysis in Nonalcoholic Steatohepatitis.

Fibrosis, resulted from the imbalance of fibrogenesis and fibrolysis, is a key readout of disease progression in nonalcoholic steatohepatitis (NASH) and reflects mortality risk. Non-invasive biomarkers capable of diagnosing fibrosis stages and monitoring fibrosis changes in NASH patients are urgently needed. This study is to evaluate collagen formation and degradation biomarkers, reflective of fibrogenesis or fibrolysis, in patients with biopsy proven NASH. Collagen formation biomarker PRO-C3 and PRO-C6 levels were significantly higher in patients with advanced fibrosis stage 3-4 than those with fibrosis stage 0-2. Elevated PRO-C3 levels were also associated with severe lobular inflammation and ballooning, but not with steatosis. Multivariate logistic regression analysis identified PRO-C3 and PRO-C6 to be independently related to fibrosis stage. PRO-C3 showed similar performance to identify patients with advanced fibrosis in discovery and validation cohorts. Furthermore, in a longitudinal study cohort with paired biopsies, mean PRO-C3 increased with worsening of fibrosis and decreased with fibrosis improvement. The results suggest that PRO-C3 may be a potentially useful biomarker in identifying patients with advanced fibrosis and active fibrogenesis, as well as in assessing changes in fibrosis over time. It is worthy of further evaluation to confirm its diagnostic value and clinical utility.

Mapping the central effects of (±)-ketamine and traxoprodil using pharmacological magnetic resonance imaging in awake rats.

Major depressive disorder is a leading cause of disability globally. Improvements in the efficacy of antidepressant therapy are needed as a high proportion (>40%) of individuals with major depressive disorder fail to respond adequately to current treatments. The non-selective N-methyl-D-aspartate receptor channel blocker, (±)-ketamine, has been reported to produce a rapid and long-lasting antidepressant response in treatment-resistant major depressive disorder patients, which provides a unique opportunity for investigation of mechanisms that mediate its therapeutic effect. Efforts have also focused on the development of selective N-methyl-D-aspartate receptor subtype 2B antagonists which may retain antidepressant activity but have lower potential for dissociative/psychotomimetic effects. In the present study, we examined the central nervous system effects of acute, intravenous administration of (±)-ketamine or the N-methyl-D-aspartate receptor subtype 2B antagonist, traxoprodil, in awake rats using pharmacological magnetic resonance imaging. The study contained five treatment groups: vehicle, 3 mg/kg (±)-ketamine, and three doses of traxoprodil (0.3 mg/kg, 5 mg/kg, and 15 mg/kg). Non-linear model fitting was performed on the temporal hemodynamic pharmacological magnetic resonance imaging data to generate brain activation maps as well as regional responses based on blood oxygen level dependent signal changes for group analysis. Traxoprodil at 5 mg/kg and 15 mg/kg produced a dose-dependent pharmacological magnetic resonance imaging signal in rat forebrain regions with both doses achieving >80% N-methyl-D-aspartate receptor subtype 2B occupancy determined by ex vivo [3H]Ro 25-6981 binding. The middle dose of traxoprodil (5 mg/kg) generated region-specific activations in medial prefrontal cortex, ventral orbital cortex, and anterior cingulate cortex whereas the high dose (15 mg/kg) produced a widespread pharmacological magnetic resonance imaging response in both cortical and subcortical brain regions which was similar to that produced by (±)-ketamine (3 mg/kg, intravenous).

Comparative Evaluation of Plasma Bile Acids, Dehydroepiandrosterone Sulfate, Hexadecanedioate, and Tetradecanedioate with Coproporphyrins I and III as Markers of OATP Inhibition in Healthy Subjects.

Multiple endogenous compounds have been proposed as candidate biomarkers to monitor organic anion transporting polypeptide (OATP) function in preclinical species or humans. Previously, we demonstrated that coproporphyrins (CPs) I and III are appropriate clinical markers to evaluate OATP inhibition and recapitulate clinical drug-drug interactions (DDIs). In the present study, we investigated bile acids (BAs) dehydroepiandrosterone sulfate (DHEAS), hexadecanedioate (HDA), and tetradecanedioate (TDA) in plasma as endogenous probes for OATP inhibition and compared these candidate probes to CPs. All probes were determined in samples from a single study that examined their behavior and their association with rosuvastatin (RSV) pharmacokinetics after administration of an OATP inhibitor rifampin (RIF) in healthy subjects. Among endogenous probes examined, RIF significantly increased maximum plasma concentration (Cmax) and area under the concentration-time curve (AUC)(0-24h) of fatty acids HDA and TDA by 2.2- to 3.2-fold. For the 13 bile acids in plasma examined, no statistically significant changes were detected between treatments. Changes in plasma DHEAS did not correlate with OATP1B inhibition by RIF. On the basis of the magnitude of effects for the endogenous compounds that demonstrated significant changes from baseline over interindividual variations, the overall rank order for the AUC change was found to be CP I > CP III > HDA ≈ TDA ≈ RSV > > BAs. Collectively, these results reconfirmed that CPs are novel biomarkers suitable for clinical use. In addition, HDA and TDA are useful for OATP functional assessment. Since these endogenous markers can be monitored in conjunction with pharmacokinetics analysis, the CPs and fatty acid dicarboxylates, either alone or in combination, offer promise of earlier diagnosis and risk stratification for OATP-mediated DDIs.

Novel platens to measure the hardness of a pentagonal shaped tablet.

Tablet hardness, a measure of the breaking force of a tablet, is based on numerous factors. These include the shape of the tablet and the mode of the application of force. For instance, when a pentagonal-shaped tablet was tested with a traditional hardness tester with flat platens, there was a large variation in hardness measurements. This was due to the propensity of vertices of the tablet to crush, referred to as an "improper break". This article describes a novel approach to measure the hardness of pentagonal-shaped tablets using modified platens. The modified platens have more uniform loading than flat platens. This is because they reduce loading on the vertex of the pentagon and apply forces on tablet edges to generate reproducible tablet fracture. The robustness of modified platens was assessed using a series of studies, which included feasibility and Gauge Repeatability & Reproducibility (R&R) studies. A key finding was that improper breaks, generated frequently with a traditional hardness tester using flat platens, were eliminated. The Gauge R&R study revealed that the tablets tested with novel platens generated consistent values in hardness measurements, independent of batch, hardness level, and day of testing, operator and tablet dosage strength.

A comparison of the variance estimation methods for heteroscedastic nonlinear models.

Heteroscedasticity is commonly encountered when fitting nonlinear regression models in practice. We discuss eight different variance estimation methods for nonlinear regression models with heterogeneous response variances, and present a simulation study to compare the performance of the eight methods in terms of estimating the standard errors of the fitted model parameters. The simulation study suggests that when the true variance is a function of the mean model, the power of the mean variance function estimation method and the transform-both-sides method are the best choices for estimating the standard errors of the estimated model parameters. In general, the wild bootstrap estimator and two modified versions of the standard sandwich variance estimator are reasonably accurate with relatively small bias, especially when the heterogeneity is nonsystematic across values of the covariate. Furthermore, we note that the two modified sandwich estimators are appealing choices in practice, considering the computational advantage of these two estimation methods relative to the variance function estimation method and the transform-both-sides approach. Copyright © 2016 John Wiley & Sons, Ltd.

Testing for parallelism in the heteroscedastic four-parameter logistic model.

For bioassay data in drug discovery and development, it is often important to test for parallelism of the mean response curves for two preparations, such as a test sample and a reference sample in determining the potency of the test preparation relative to the reference standard. For assessing parallelism under a four-parameter logistic model, tests of the parallelism hypothesis may be conducted based on the equivalence t-test or the traditional F-test. However, bioassay data often have heterogeneous variance across dose levels. Specifically, the variance of the response may be a function of the mean, frequently modeled as a power of the mean. Therefore, in this article we discuss estimation and tests for parallelism under the power variance function. Two examples are considered to illustrate the estimation and testing approaches described. A simulation study is also presented to compare the empirical properties of the tests under the power variance function in comparison to the results from ordinary least squares fits, which ignore the non-constant variance pattern.

Multiplex transcriptional analysis of paraffin-embedded liver needle biopsy from patients with liver fibrosis.

BACKGROUND: The possibility of extracting RNA and measuring RNA expression from paraffin sections can allow extensive investigations on stored paraffin samples obtained from diseased livers and could help with studies of the natural history of liver fibrosis and inflammation, and in particular, correlate basic mechanisms to clinical outcomes. RESULTS: To address this issue, a pilot study of multiplex gene expression using branched-chain DNA technology was conducted to directly measure mRNA expression in formalin-fixed paraffin-embedded needle biopsy samples of human liver. Twenty-five genes were selected for evaluation based on evidence obtained from human fibrotic liver, a rat BDL model and in vitro cultures of immortalized human hepatic stellate cells. The expression levels of these 25 genes were then correlated with liver fibrosis and inflammation activity scores. Statistical analysis revealed that three genes (COL3A1, KRT18, and TUBB) could separate fibrotic from non-fibrotic samples and that the expression of ten genes (ANXA2, TIMP1, CTGF, COL4A1, KRT18, COL1A1, COL3A1, ACTA2, TGFB1, LOXL2) were positively correlated with the level of liver inflammation activity. CONCLUSION: This is the first report describing this multiplex technique for liver fibrosis and has provided the proof of concept of the suitability of RNA extracted from paraffin sections for investigating the modulation of a panel of proinflammatory and profibrogenic genes. This pilot study suggests that this technique will allow extensive investigations on paraffin samples from diseased livers and possibly from any other tissue. Using identical or other genes, this multiplex expression technique could be applied to samples obtained from extensive patient cohorts with stored paraffin samples in order to correlate gene expression with valuable clinically relevant information. This method could be used to provide a better understanding of the mechanisms of liver fibrosis and inflammation, its progression, and help development of new therapeutic approaches for this indication.

Equivalence testing for parallelism in the four-parameter logistic model.

For assay or dose-response data in drug discovery, it is often important to test for parallelism of the response curves for two preparations, such as a test drug and a standard drug, in order to determine the potency of the test preparation relative to the standard preparation. A typical approach is to perform a three-degree of freedom approximate F test of the null hypothesis that the relevant parameters are equal for the two preparations. We argue that this problem may be more appropriately viewed as a practical equivalence testing problem, and present an alternative method for testing parallelism in the four-parameter logistic response curve, based on the theory of intersection-union tests. The approach is intuitively appealing and simple to implement using commonly available software, and may provide more appropriate inference for the problem of interest. Two examples are discussed to illustrate the testing approach outlined in this article, and to compare it with the typical approach to testing parallelism. A simulation study is also presented to compare the empirical properties of the two different testing approaches for a set of cases based approximately on one of the examples.

A comparison of heterogeneity variance estimators in combining results of studies.

For random effects meta-analysis, seven different estimators of the heterogeneity variance are compared and assessed using a simulation study. The seven estimators are the variance component type estimator (VC), the method of moments estimator (MM), the maximum likelihood estimator (ML), the restricted maximum likelihood estimator (REML), the empirical Bayes estimator (EB), the model error variance type estimator (MV), and a variation of the MV estimator (MVvc). The performance of the estimators is compared in terms of both bias and mean squared error, using Monte Carlo simulation. The results show that the REML and especially the ML and MM estimators are not accurate, having large biases unless the true heterogeneity variance is small. The VC estimator tends to overestimate the heterogeneity variance in general, but is quite accurate when the number of studies is large. The MV estimator is not a good estimator when the heterogeneity variance is small to moderate, but it is reasonably accurate when the heterogeneity variance is large. The MVvc estimator is an improved estimator compared to the MV estimator, especially for small to moderate values of the heterogeneity variance. The two estimators MVvc and EB are found to be the most accurate in general, particularly when the heterogeneity variance is moderate to large.

A note on variance estimation in random effects meta-regression.

For random effects meta-regression inference, variance estimation for the parameter estimates is discussed. Because estimated weights are used for meta-regression analysis in practice, the assumed or estimated covariance matrix used in meta-regression is not strictly correct, due to possible errors in estimating the weights. Therefore, this note investigates the use of a robust variance estimation approach for obtaining variances of the parameter estimates in random effects meta-regression inference. This method treats the assumed covariance matrix of the effect measure variables as a working covariance matrix. Using an example of meta-analysis data from clinical trials of a vaccine, the robust variance estimation approach is illustrated in comparison with two other methods of variance estimation. A simulation study is presented, comparing the three methods of variance estimation in terms of bias and coverage probability. We find that, despite the seeming suitability of the robust estimator for random effects meta-regression, the improved variance estimator of Knapp and Hartung (2003) yields the best performance among the three estimators, and thus may provide the best protection against errors in the estimated weights.

Exact unconditional tests for testing non-inferiority in matched-pairs design.

The problem of testing non-inferiority in a 2 x 2 matched-pairs sample is considered. Two exact unconditional tests based on the standard and the confidence interval p-values are proposed. Although tests of non-inferiority have two nuisance parameters under the null hypothesis, the exact tests are defined by reducing the dimension of nuisance parameter space from two to one using the monotonicity of the distribution. The exact sizes and powers of these tests and the existing asymptotic test are considered. The exact tests are found to be accurate in view of their size property. In addition, the exact test based on the confidence interval p-value is more powerful than the other exact test. It is shown that the asymptotic test is inaccurate, that is, its size exceeds the claimed nominal level alpha. Therefore, it recommends a cautious approach in use of the asymptotic test for the problem of testing non-inferiority, particularly when sample sizes are small or moderately large.

A simple confidence interval for meta-analysis.

In the context of a random effects model for meta-analysis, a number of methods are available to estimate confidence limits for the overall mean effect. A simple and commonly used method is the DerSimonian and Laird approach. This paper discusses an alternative simple approach for constructing the confidence interval, based on the t-distribution. This approach has improved coverage probability compared to the DerSimonian and Laird method. Moreover, it is easy to calculate, and unlike some methods suggested in the statistical literature, no iterative computation is required.