Pharmaceutical Statistics最新文献

Most published applications of the estimand framework have focused on superiority trials. However, non-inferiority trials present specific challenges compared to superiority trials. The International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use notes in their addendum on estimands and sensitivity analysis in clinical trials that there may be special considerations to the implementation of estimands in clinical trials with a non-inferiority objective yet provides little guidance. This paper discusses considerations that trial teams should make when defining estimands for a clinical trial with a non-inferiority objective. We discuss how the pre-addendum way of establishing non-inferiority can be embraced by the estimand framework including a discussion of the role of the Per Protocol analysis set. We examine what clinical questions of interest can be formulated in the context of non-inferiority trials and outline why we do not think it is sensible to describe an estimand as 'conservative'. The impact of the estimand framework on key considerations in non-inferiority trials such as whether trials should have more than one primary estimand, the choice of non-inferiority margin, assay sensitivity, switching from non-inferiority to superiority and estimation are discussed. We conclude by providing a list of recommendations, and important considerations for defining estimands for trials with a non-inferiority objective.

Preclinical studies are broad and can encompass cellular research, animal trials, and small human trials. Preclinical studies tend to be exploratory and have smaller datasets that often consist of biomarker data. Logistic regression is typically the model of choice for modeling a binary outcome with explanatory variables such as genetic, imaging, and clinical data. Small preclinical studies can have challenging data that may include a complete separation or quasi-complete separation issue that will result in logistic regression inflated coefficient estimates and standard errors. Penalized regression approaches such as Firth's logistic regression are a solution to reduce the bias in the estimates. In this tutorial, a number of examples with separation (complete or quasi-complete) are illustrated and the results from both logistic regression and Firth's logistic regression are compared to demonstrate the inflated estimates from the standard logistic regression model and bias-reduction of the estimates from the penalized Firth's approach. R code and datasets are provided in the supplement.

Mixture experimentation is commonly seen in pharmaceutical formulation studies, where the relative proportions of the individual components are modeled for effects on product attributes. The requirement that the sum of the component proportions equals 1 has given rise to the class of designs, known as mixture designs. The first mixture designs were published by Quenouille in 1953 but it took nearly 40 years for the earliest mixture design applications to be published in the pharmaceutical sciences literature by Kettaneh-Wold in 1991 and Waaler in 1992. Since then, the advent of efficient computer algorithms to generate designs has made this class of designs easily accessible to pharmaceutical statisticians, although the use of these designs appears to be an underutilized experimental strategy even today. One goal of this tutorial is to draw the attention of experimental statisticians to this class of designs and their advantages in pursuing formulation studies such as excipient compatibility studies. We present sufficient materials to introduce the novice practitioner to this class of design, associated models, and analysis strategies. An example of a mixture-process variable design is given as a case study.

The estimands framework outlined in ICH E9 (R1) describes the components needed to precisely define the effects to be estimated in clinical trials, which includes how post-baseline 'intercurrent' events (IEs) are to be handled. In late-stage clinical trials, it is common to handle IEs like 'treatment discontinuation' using the treatment policy strategy and target the treatment effect on outcomes regardless of treatment discontinuation. For continuous repeated measures, this type of effect is often estimated using all observed data before and after discontinuation using either a mixed model for repeated measures (MMRM) or multiple imputation (MI) to handle any missing data. In basic form, both these estimation methods ignore treatment discontinuation in the analysis and therefore may be biased if there are differences in patient outcomes after treatment discontinuation compared with patients still assigned to treatment, and missing data being more common for patients who have discontinued treatment. We therefore propose and evaluate a set of MI models that can accommodate differences between outcomes before and after treatment discontinuation. The models are evaluated in the context of planning a Phase 3 trial for a respiratory disease. We show that analyses ignoring treatment discontinuation can introduce substantial bias and can sometimes underestimate variability. We also show that some of the MI models proposed can successfully correct the bias, but inevitably lead to increases in variance. We conclude that some of the proposed MI models are preferable to the traditional analysis ignoring treatment discontinuation, but the precise choice of MI model will likely depend on the trial design, disease of interest and amount of observed and missing data following treatment discontinuation.

Correctly characterising the dose-response relationship and taking the correct dose forward for further study is a critical part of the drug development process. We use optimal design theory to compare different designs and show that using longitudinal data from all available timepoints in a continuous-time dose-response model can substantially increase the efficiency of estimation of the dose-response compared to a single timepoint model. We give theoretical results to calculate the efficiency gains for a large class of these models. For example, a linearly growing Emax dose-response in a population with a between/within-patient variance ratio ranging from 0.1 to 1 measured at six visits can be estimated with between 1.43 and 2.22 times relative efficiency gain, or equivalently, with 30% to a 55% reduced sample size, compared to a single model of the final timepoint. Fractional polynomials are a flexible way to incorporate data from repeated measurements, increasing precision without imposing strong constraints. Longitudinal dose-response models using two fractional polynomial terms are robust to mis-specification of the true longitudinal process while maintaining, often large, efficiency gains. These models have applications for characterising the dose-response at interim or final analyses.

In preclinical drug discovery, at the step of lead optimization of a compound, in vivo experimentation can differentiate several compounds in terms of efficacy and potency in a biological system of whole living organisms. For the lead optimization study, it may be desirable to implement a dose-response design so that compound comparisons can be made from nonlinear curves fitted to the data. A dose-response design requires more thought relative to a simpler study design, needing parameters for the number of doses, the dose values, and the sample size per dose. This tutorial illustrates how to calculate statistical power, choose doses, and determine sample size per dose for a comparison of two or more dose-response curves for a future in vivo study.

Finding an adequate dose of the drug by revealing the dose-response relationship is very crucial and a challenging problem in the clinical development. The main concerns in dose-finding study are to identify a minimum effective dose (MED) in anesthesia studies and maximum tolerated dose (MTD) in oncology clinical trials. For the estimation of MED and MTD, we propose two modifications of Firth's logistic regression using reparametrization, called reparametrized Firth's logistic regression (rFLR) and ridge-penalized reparametrized Firth's logistic regression (RrFLR). The proposed methods are designed by directly reducing the small-sample bias of the maximum likelihood estimate for the parameter of interest. In addition, we develop a method on how to construct confidence intervals for rFLR and RrFLR using profile penalized likelihood. In the up-and-down biased-coin design, numerical studies confirm the superior performance of the proposed methods in terms of the mean squared error, bias, and coverage accuracy of confidence intervals.

Biomarker-guided therapy is a growing area of research in medicine. To optimize the use of biomarkers, several study designs including the biomarker-strategy design (BSD) have been proposed. Unlike traditional designs, the emphasis here is on comparing treatment strategies and not on treatment molecules as such. Patients are assigned to either a biomarker-based strategy (BBS) arm, in which biomarker-positive patients receive an experimental treatment that targets the identified biomarker, or a non-biomarker-based strategy (NBBS) arm, in which patients receive treatment regardless of their biomarker status. We proposed a simulation method based on a partially clustered frailty model (PCFM) as well as an extension of Freidlin formula to estimate the sample size required for BSD with multiple targeted treatments. The sample size was mainly influenced by the heterogeneity of treatment effect, the proportion of biomarker-negative patients, and the randomization ratio. The PCFM is well suited for the data structure and offers an alternative to traditional methodologies.

The ICH E9(R1) Addendum (International Council for Harmonization 2019) suggests treatment-policy as one of several strategies for addressing intercurrent events such as treatment withdrawal when defining an estimand. This strategy requires the monitoring of patients and collection of primary outcome data following termination of randomised treatment. However, when patients withdraw from a study early before completion this creates true missing data complicating the analysis. One possible way forward uses multiple imputation to replace the missing data based on a model for outcome on- and off-treatment prior to study withdrawal, often referred to as retrieved dropout multiple imputation. This article introduces a novel approach to parameterising this imputation model so that those parameters which may be difficult to estimate have mildly informative Bayesian priors applied during the imputation stage. A core reference-based model is combined with a retrieved dropout compliance model, using both on- and off-treatment data, to form an extended model for the purposes of imputation. This alleviates the problem of specifying a complex set of analysis rules to accommodate situations where parameters which influence the estimated value are not estimable, or are poorly estimated leading to unrealistically large standard errors in the resulting analysis. We refer to this new approach as retrieved dropout reference-base centred multiple imputation.

In conventional subgroup analyses, subgroup treatment effects are estimated using data from each subgroup separately without considering data from other subgroups in the same study. The subgroup treatment effects estimated this way may be heterogenous with high variability due to small sample sizes in some subgroups and much different from the treatment effect in the overall population. A Bayesian hierarchical model (BHM) can be used to derive more precise, and less heterogenous estimates of subgroup treatment effects that are closer to the treatment effect in the overall population. BHM assumes exchangeability in treatment effect across subgroups after adjusting for effect modifiers and other relevant covariates. In this article, we will discuss the technical details for applying one-way and multi-way BHM using summary-level statistics, and patient-level data for subgroup analysis. Four case studies based on four new drug applications are used to illustrate the application of these models in subgroup analyses for continuous, dichotomous, time-to-event, and count endpoints.