James H. Roger

Small Sample Inference for Fixed Effects from Restricted Maximum Likelihood

Restricted maximum likelihood (REML) is now well established as a method for estimating the parameters of the general Gaussian linear model with a structured covariance matrix, in particular for mixed linear models. Conventionally, estimates of precision and inference for fixed effects are based on their asymptotic distribution, which is known to be inadequate for some small-sample problems. In this paper, we present a scaled Wald statistic, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings. The statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias. This approach has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact, namely for Hotelling T2 type statistics and for analysis of variance F-ratios. The performance of the modified statistics is assessed through simulation studies of four different REML analyses and the methods are illustrated using three examples.

An improved approximation to the precision of fixed effects from restricted maximum likelihood

An approximate small sample variance estimator for fixed effects from the multivariate normal linear model, together with appropriate inference tools based on a scaled F pivot, is now well established in practice and there is a growing literature on its properties in a variety of settings. Although effective under linear covariance structures, there are examples of nonlinear structures for which it does not perform as well. The cause of this problem is shown to be a missing term in the underlying Taylor series expansion which accommodates the bias in the estimators of the parameters of the covariance structure. The form of this missing term is derived, and then used to adjust the small sample variance estimator. The behaviour of the resulting estimator is explored in terms of invariance under transformation of the covariance parameters and also using a simulation study. It is seen to perform successfully in the way predicted from its derivation.

A Statistical Assessment of QT Data Following Placebo and Moxifloxacin Dosing in Thorough QT Studies

The ICH guidelines indicate that a single “thorough QT study” should be conducted to evaluate the effects of new drugs on cardiac repolarization. A positive control, such as moxifloxacin, is required to be assessed as part of the thorough QT study to validate the assay sensitivity of each study. In order to better understand the effect of moxifloxacin, a meta-analysis of nine thorough QT studies has been undertaken to assess the overall moxifloxacin effect. The data was analyzed using a repeated measures mixed model to test various covariance structures to identify the most suitable model for this and future meta-analyses of thorough QT studies.

Platelet Aggregation Unchanged by Lipoprotein-Associated Phospholipase A2 Inhibition: Results from an In Vitro Study and Two Randomized Phase I Trials

Background We explored the theorized upregulation of platelet-activating factor (PAF)– mediated biologic responses following lipoprotein-associated phospholipase A2 (Lp-PLA2) inhibition using human platelet aggregation studies in an in vitro experiment and in 2 clinical trials. Methods and Results Full platelet aggregation concentration response curves were generated in vitro to several platelet agonists in human plasma samples pretreated with rilapladib (selective Lp-PLA2 inhibitor) or vehicle. This was followed by a randomized, double-blind crossover study in healthy adult men (n = 26) employing a single-agonist dose assay of platelet aggregation, after treatment of subjects with 250 mg oral rilapladib or placebo once daily for 14 days. This study was followed by a second randomized, double-blind parallel-group trial in healthy adult men (n = 58) also treated with 250 mg oral rilapladib or placebo once daily for 14 days using a full range of 10 collagen concentrations (0–10 µg/ml) for characterizing EC50 values for platelet aggregation for each subject. Both clinical studies were conducted at the GlaxoSmithKline Medicines Research Unit in the Prince of Wales Hospital, Sydney, Australia. EC50 values derived from multiple agonist concentrations were compared and no pro-aggregant signals were observed during exposure to rilapladib in any of these platelet studies, despite Lp-PLA2 inhibition exceeding 90%. An increase in collagen-mediated aggregation was observed 3 weeks post drug termination in the crossover study (15.4% vs baseline; 95% confidence interval [CI], 3.9–27.0), which was not observed during the treatment phase and was not observed in the parallel-group study employing a more robust EC50 examination. Conclusions Lp-PLA2 inhibition does not enhance platelet aggregation. Trial Registration 1) Study 1: ClinicalTrials.gov NCT01745458 2) Study 2: ClinicalTrials.gov NCT00387257

Evaluations of Bayesian and maximum likelihood methods in PK models with below-quantification-limit data.

Pharmacokinetic (PK) data often contain concentration measurements below the quantification limit (BQL). While specific values cannot be assigned to these observations, nevertheless these observed BQL data are informative and generally known to be lower than the lower limit of quantification (LLQ). Setting BQLs as missing data violates the usual missing at random (MAR) assumption applied to the statistical methods, and therefore leads to biased or less precise parameter estimation. By definition, these data lie within the interval [0, LLQ], and can be considered as censored observations. Statistical methods that handle censored data, such as maximum likelihood and Bayesian methods, are thus useful in the modelling of such data sets. The main aim of this work was to investigate the impact of the amount of BQL observations on the bias and precision of parameter estimates in population PK models (non-linear mixed effects models in general) under maximum likelihood method as implemented in SAS and NONMEM, and a Bayesian approach using Markov chain Monte Carlo (MCMC) as applied in WinBUGS. A second aim was to compare these different methods in dealing with BQL or censored data in a practical situation. The evaluation was illustrated by simulation based on a simple PK model, where a number of data sets were simulated from a one-compartment first-order elimination PK model. Several quantification limits were applied to each of the simulated data to generate data sets with certain amounts of BQL data. The average percentage of BQL ranged from 25% to 75%. Their influence on the bias and precision of all population PK model parameters such as clearance and volume distribution under each estimation approach was explored and compared.