Choice of estimand and analysis methods in diabetes trials with rescue medication

The analysis of clinical trials aiming to show symptomatic benefits is often complicated by the ethical requirement for rescue medication when the disease state of patients worsens. In type 2 diabetes trials, patients receive glucose‐lowering rescue medications continuously for the remaining trial duration, if one of several markers of glycemic control exceeds pre‐specified thresholds. This may mask differences in glycemic values between treatment groups, because it will occur more frequently in less effective treatment groups. Traditionally, the last pre‐rescue medication value was carried forward and analyzed as the end‐of‐trial value. The deficits of such simplistic single imputation approaches are increasingly recognized by regulatory authorities and trialists. We discuss alternative approaches and evaluate them through a simulation study. When the estimand of interest is the effect attributable to the treatments initially assigned at randomization, then our recommendation for estimation and hypothesis testing is to treat data after meeting rescue criteria as deterministically ‘missing’ at random, because initiation of rescue medication is determined by observed in‐trial values. An appropriate imputation of values after meeting rescue criteria is then possible either directly through multiple imputation or implicitly with a repeated measures model. Crucially, one needs to jointly impute or model all markers of glycemic control that can lead to the initiation of rescue medication. An alternative for hypothesis testing only are rank tests with outcomes from patients ‘requiring rescue medication’ ranked worst, and non‐rescued patients ranked according to final visit values. However, an appropriate ranking of not observed values may be controversial. Copyright © 2015 John Wiley & Sons, Ltd.     

Clinical utility estimation for assay cutoffs in early phase oncology enrichment trials

Predictive enrichment strategies use biomarkers to selectively enroll oncology patients into clinical trials to more efficiently demonstrate therapeutic benefit. Because the enriched population differs from the patient population eligible for screening with the biomarker assay, there is potential for bias when estimating clinical utility for the screening eligible population if the selection process is ignored. We write estimators of clinical utility as integrals averaging regression model predictions over the conditional distribution of the biomarker scores defined by the assay cutoff and discuss the conditions under which consistent estimation can be achieved while accounting for some nuances that may arise as the biomarker assay progresses toward a companion diagnostic. We outline and implement a Bayesian approach in estimating these clinical utility measures and use simulations to illustrate performance and the potential biases when estimation naively ignores enrichment. Results suggest that the proposed integral representation of clinical utility in combination with Bayesian methods provide a practical strategy to facilitate cutoff decision‐making in this setting. Copyright © 2015 John Wiley & Sons, Ltd.     

Application of a predictive distribution formula to Bayesian computation for incomplete data models

We consider exact and approximate Bayesian computation in the presence of latent variables or missing data. Specifically we explore the application of a posterior predictive distribution formula derived in Sweeting And Kharroubi (2003), which is a particular form of Laplace approximation, both as an importance function and a proposal distribution. We show that this formula provides a stable importance function for use within poor man’s data augmentation schemes and that it can also be used as a proposal distribution within a Metropolis-Hastings algorithm for models that are not analytically tractable. We illustrate both uses in the case of a censored regression model and a normal hierarchical model, with both normal and Student t distributed random effects. Although the predictive distribution formula is motivated by regular asymptotic theory, it is not necessary that the likelihood has a closed form or that it possesses a local maximum.     

Impact of selection bias on the evaluation of clusters of chemical compounds in the drug discovery process

Expert opinion plays an important role when selecting promising clusters of chemical compounds in the drug discovery process. Indeed, experts can qualitatively assess the potential of each cluster, and with appropriate statistical methods, these qualitative assessments can be quantified into a success probability for each of them. However, one crucial element often overlooked is the procedure by which the clusters are assigned to/selected by the experts for evaluation. In the present work, the impact such a procedure may have on the statistical analysis and the entire evaluation process is studied. It has been shown that some implementations of the selection procedure may seriously compromise the validity of the evaluation even when the rating and selection processes are independent. Consequently, the fully random allocation of the clusters to the experts is strongly advocated. Copyright © 2014 John Wiley & Sons, Ltd.     

Goodness-of-fit tests for general linear models with covariates missed at random

In this paper, we consider a model checking problem for general linear models with randomly missing covariates. Two types of score type tests with inverse probability weight, which is estimated by parameter and nonparameter methods respectively, are proposed to this goodness of fit problem. The asymptotic properties of the test statistics are developed under the null and local alternative hypothesis. Simulation study is carried out to present the performance of the sizes and powers of the tests. We illustrate the proposed method with a data set on monozygotic twins.     

A SEMIPARAMETRIC REGRESSION MODEL WITH MISSING COVARIATES IN CONTINUOUS-TIME CAPTURE-RECAPTURE STUDIES

Covariate data were missing when a semiparametric regression model was used to study bird abundance in the Mai Po Sanctuary, Hong Kong. This paper proposes an EM‐type algorithm to estimate the regression parameters for that study. Analytical calculation of the expectation in the EM method is difficult, or even impossible, especially when missing covariates are continuous. A Monte Carlo method is used in the EM algorithm to ease the calculation complexity. Asymptotic variances of the parameter estimates are also derived. Properties of the proposed estimators are assessed through numerical simulations and a real example.     

Two-step and likelihood methods for HIV viral dynamic models with covariate measurement errors and missing data

HIV viral dynamic models have received much attention in the literature. Long-term viral dynamics may be modelled by semiparametric nonlinear mixed-effect models, which incorporate large variation between subjects and autocorrelation within subjects and are flexible in modelling complex viral load trajectories. Time-dependent covariates may be introduced in the dynamic models to partially explain the between-individual variations. In the presence of measurement errors and missing data in time-dependent covariates, we show that the commonly used two-step method may give approximately unbiased estimates but may under-estimate standard errors. We propose a two-stage bootstrap method to adjust the standard errors in the two-step method and a likelihood method.     

Imputation by power transformation

In this paper, a new power transformation estimator of population mean in the presence of non-response has been suggested. The estimator of mean obtained from proposed technique remains better than the estimators obtained from ratio or mean methods of imputation. The mean squared error of the resultant estimator is less than that of the estimator obtained on the basis of ratio method of imputation for the optinum choice of parameters. An estimator for estimating a parameter involved in the process of new method of imputation has been discussed. The MSE expressions for the proposed estimators have been derived analytically and compared empirically. Product method of imputation for negatively correlated variables has also been introduced. The work has been extended to the case of multi-auxiliary information to be used for imputation.     

Birnbaum–Saunders sample selection model

The sample selection bias problem occurs when the outcome of interest is only observed according to some selection rule, where there is a dependence structure between the outcome and the selection rule. In a pioneering work, J. Heckman proposed a sample selection model based on a bivariate normal distribution for dealing with this problem. Due to the non-robustness of the normal distribution, many alternatives have been introduced in the literature by assuming extensions of the normal distribution like the Student-t and skew-normal models. One common limitation of the existent sample selection models is that they require a transformation of the outcome of interest, which is common R+-valued, such as income and wage. With this, data are analyzed on a non-original scale which complicates the interpretation of the parameters. In this paper, we propose a sample selection model based on the bivariate Birnbaum–Saunders distribution, which has the same number of parameters that the classical Heckman model. Further, our associated outcome equation is R+-valued. We discuss estimation by maximum likelihood and present some Monte Carlo simulation studies. An empirical application to the ambulatory expenditures data from the 2001 Medical Expenditure Panel Survey is presented.     

Statistical methods for handling missing data to align with treatment policy strategy

The International Council for Harmonization (ICH) E9(R1) addendum recommends choosing an appropriate estimand based on the study objectives in advance of trial design. One defining attribute of an estimand is the intercurrent event, specifically what is considered an intercurrent event and how it should be handled. The primary objective of a clinical study is usually to assess a product's effectiveness and safety based on the planned treatment regimen instead of the actual treatment received. The estimand using the treatment policy strategy, which collects and analyzes data regardless of the occurrence of intercurrent events, is usually utilized. In this article, we explain how missing data can be handled using the treatment policy strategy from the authors' viewpoint in connection with antihyperglycemic product development programs. The article discusses five statistical methods to impute missing data occurring after intercurrent events. All five methods are applied within the framework of the treatment policy strategy. The article compares the five methods via Markov Chain Monte Carlo simulations and showcases how three of these five methods have been applied to estimate the treatment effects published in the labels for three antihyperglycemic agents currently on the market.