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Andy Grieve, the first pharmaceutical statistician to be President of the Royal Statistical Society, practiced in the regulated world of drug development. With reduction in drug development costs as his motivation, Grieve advanced Bayesian methods for developing predictive methods for efficacy and toxicity - to be used as early as possible in the drug development process; and his presidential address exhorted statisticians to weigh-in wherever data are used to make decisions. Diagnostic tests for infectious diseases are less regulated than drugs and vaccines unless the blood supply is at risk. Unlike in the HIV and HCV pandemics of the late 20th century, even well-designed surveys linked to a volunteered biological sample (to be tested for SARS-CoV-2 antigen or antibodies) have had modest or low consent rates. Record-linkage, statistical design and reporting standards have seen triumph and tragedy. Among the triumphs are: Liverpool's insistence on dual testing (lateral flow device; polymerase chain reaction [PCR]) of some 6000 asymptomatic citizens who attended for SARS-CoV-2-screening; two tricky randomized controlled public-policy trials on daily contact testing for close contacts of index cases of SARS-CoV-2 infection versus self-isolation (with or without initial PCR); and among already-consented participants in surveillance, over 80% secondary consent for linkage to their health records, including the Immunization Management Service. Before the next pandemic we need to entrench better regulation of diagnostic tests, better informed consent (not via weblinks), better feedback to participants, and transparency about basic safety data., (© 2022 The Author. Pharmaceutical Statistics published by John Wiley & Sons Ltd.)

Objectives: Our objective was to present recent trends in the UK HIV epidemic (2007-2016) and the public health response., Methods: HIV diagnoses and clinical markers were extracted from the HIV and AIDS Reporting System; HIV testing data in sexual health services (SHS) were taken from GUMCAD STI Surveillance System. HIV data were modelled to estimate the incidence in men who have sex with men (MSM) and post-migration HIV acquisition in heterosexuals. Office for National Statistics (ONS) data enabled mortality rates to be calculated., Results: New HIV diagnoses have declined in heterosexuals as a result of decreasing numbers of migrants from high HIV prevalence countries entering the UK. Among MSM, the number of HIV diagnoses fell from 3570 in 2015 to 2810 in 2016 (and from 1554 to 1096 in London). Preceding the decline in HIV diagnoses, modelled estimates indicate that transmission began to fall in 2012, from 2800 [credible interval (CrI) 2300-3200] to 1700 (CrI 900-2700) in 2016. The crude mortality rate among people promptly diagnosed with HIV infection was comparable to that in the general population (1.22 vs. 1.39 per 1000 aged 15-59 years, respectively). The number of MSM tested for HIV at SHS increased annually; 28% of MSM who were tested in 2016 had been tested in the preceding year. In 2016, 76% of people started antiretroviral therapy within 90 days of diagnosis (33% in 2007)., Conclusions: The dual successes of the HIV transmission decline in MSM and reduced mortality are attributable to frequent HIV testing and prompt treatment (combination prevention). Progress towards the elimination of HIV transmission, AIDS and HIV-related deaths could be achieved if combination prevention, including pre-exposure prophylaxis, is replicated for all populations., (© 2018 British HIV Association.)

The modified method for random-effects meta-analysis, usually attributed to Hartung and Knapp and also proposed by Sidik and Jonkman, is easy to implement and is becoming advocated for general use. Here, we examine a range of potential concerns about the widespread adoption of this method. Motivated by these issues, a variety of different conventions can be adopted when using the modified method in practice. We describe and investigate the use of a variety of these conventions using a new taxonomy of meta-analysis datasets. We conclude that the Hartung and Knapp modification may be a suitable replacement for the standard method. Despite this, analysts who advocate the modified method should be ready to defend its use against the possible objections to it that we present. We further recommend that the results from more conventional approaches should be used as sensitivity analyses when using the modified method. It has previously been suggested that a common-effect analysis should be used for this purpose but we suggest amending this recommendation and argue that a standard random-effects analysis should be used instead., (© 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)

In trials comparing the rate of chronic obstructive pulmonary disease exacerbation between treatment arms, the rate is typically calculated on the basis of the whole of each patient's follow-up period. However, the true time a patient is at risk should exclude periods in which an exacerbation episode is occurring, because a patient cannot be at risk of another exacerbation episode until recovered. We used data from two chronic obstructive pulmonary disease randomized controlled trials and compared treatment effect estimates and confidence intervals when using two different definitions of the at-risk period. Using a simulation study we examined the bias in the estimated treatment effect and the coverage of the confidence interval, using these two definitions of the at-risk period. We investigated how the sample size required for a given power changes on the basis of the definition of at-risk period used. Our results showed that treatment efficacy is underestimated when the at-risk period does not take account of exacerbation duration, and the power to detect a statistically significant result is slightly diminished. Correspondingly, using the correct at-risk period, some modest savings in required sample size can be achieved. Using the proposed at-risk period that excludes recovery times requires formal definitions of the beginning and end of an exacerbation episode, and we recommend these be always predefined in a trial protocol., (Copyright © 2016 The Authors. Pharmaceutical Statistics Published by John Wiley & Sons Ltd.)

Network meta-analysis is becoming more popular as a way to compare multiple treatments simultaneously. Here, we develop a new estimation method for fitting models for network meta-analysis with random inconsistency effects. This method is an extension of the procedure originally proposed by DerSimonian and Laird. Our methodology allows for inconsistency within the network. The proposed procedure is semi-parametric, non-iterative, fast and highly accessible to applied researchers. The methodology is found to perform satisfactorily in a simulation study provided that the sample size is large enough and the extent of the inconsistency is not very severe. We apply our approach to two real examples., (© 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)

In this paper, we review the adaptive design methodology of Li et al. (Biostatistics 3:277-287) for two-stage trials with mid-trial sample size adjustment. We argue that it is closer in principle to a group sequential design, in spite of its obvious adaptive element. Several extensions are proposed that aim to make it even more attractive and transparent alternative to a standard (fixed sample size) trial for funding bodies to consider. These enable a cap to be put on the maximum sample size and for the trial data to be analysed using standard methods at its conclusion. The regulatory view of trials incorporating unblinded sample size re-estimation is also discussed., (© 2014 The Authors. Pharmaceutical Statistics published by John Wiley & Sons, Ltd.)

The process of undertaking a meta-analysis involves a sequence of decisions, one of which is deciding which measure of treatment effect to use. In particular, for comparative binary data from randomised controlled trials, a wide variety of measures are available such as the odds ratio and the risk difference. It is often of interest to know whether important conclusions would have been substantively different if an alternative measure had been used. Here we develop a new type of sensitivity analysis that incorporates standard measures of treatment effect. Thus, rather than examining the implications of a variety of measures in an ad hoc manner, we can simultaneously examine an entire family of possibilities, including the odds ratio, the arcsine difference and the risk difference., (Copyright © 2012 John Wiley & Sons, Ltd.)

Methods for individual participant data meta-analysis of survival outcomes commonly focus on the hazard ratio as a measure of treatment effect. Recently, Siannis et al. (2010, Statistics in Medicine 29:3030-3045) proposed the use of percentile ratios as an alternative to hazard ratios. We describe a novel two-stage method for the meta-analysis of percentile ratios that avoids distributional assumptions at the study level., (Copyright © 2012 John Wiley & Sons, Ltd.)

In drug development, there is often uncertainty about the most promising among a set of different treatments. Multi-arm multi-stage (MAMS) trials provide large gains in efficiency over separate randomised trials of each treatment. They allow a shared control group, dropping of ineffective treatments before the end of the trial and stopping the trial early if sufficient evidence of a treatment being superior to control is found. In this paper, we discuss optimal design of MAMS trials. An optimal design has the required type I error rate and power but minimises the expected sample size at some set of treatment effects. Finding an optimal design requires searching over stopping boundaries and sample size, potentially a large number of parameters. We propose a method that combines quick evaluation of specific designs and an efficient stochastic search to find the optimal design parameters. We compare various potential designs motivated by the design of a phase II MAMS trial. We also consider allocating more patients to the control group, as has been carried out in real MAMS studies. We show that the optimal allocation to the control group, although greater than a 1:1 ratio, is smaller than previously advocated and that the gain in efficiency is generally small., (Copyright © 2012 John Wiley & Sons, Ltd.)

Measures that quantify the impact of heterogeneity in univariate meta-analysis, including the very popular I(2) statistic, are now well established. Multivariate meta-analysis, where studies provide multiple outcomes that are pooled in a single analysis, is also becoming more commonly used. The question of how to quantify heterogeneity in the multivariate setting is therefore raised. It is the univariate R(2) statistic, the ratio of the variance of the estimated treatment effect under the random and fixed effects models, that generalises most naturally, so this statistic provides our basis. This statistic is then used to derive a multivariate analogue of I(2), which we call I(R)(2). We also provide a multivariate H(2) statistic, the ratio of a generalisation of Cochran's heterogeneity statistic and its associated degrees of freedom, with an accompanying generalisation of the usual I(2) statistic, I(H)(2). Our proposed heterogeneity statistics can be used alongside all the usual estimates and inferential procedures used in multivariate meta-analysis. We apply our methods to some real datasets and show how our statistics are equally appropriate in the context of multivariate meta-regression, where study level covariate effects are included in the model. Our heterogeneity statistics may be used when applying any procedure for fitting the multivariate random effects model., (Copyright © 2012 John Wiley & Sons, Ltd.)

Two-stage trial designs provide the flexibility to stop early for efficacy or futility and are popular because they have a smaller sample size on average than a traditional trial has with the same type I and II error rates. This makes them financially attractive but also has the ethical benefit of reducing, in the long run, the number of patients who are given ineffective treatments. Designs that minimise the expected sample size are often referred to as 'optimal'. However, two-stage designs can impart a substantial bias into the parameter estimate at the end of the trial. In this paper, we argue that the expected performance of one's chosen estimation method should also be considered when deciding on a two-stage trial design. We review the properties of standard and bias-adjusted maximum likelihood estimators as well as mean and median unbiased estimators. We then identify optimal two-stage design and analysis procedures that balance projected sample size considerations with those of estimator performance. We make available software to implement this new methodology., (Copyright © 2012 John Wiley & Sons, Ltd.)

In statistical modelling, it is often important to know how much parameter estimates are influenced by particular observations. An attractive approach is to re-estimate the parameters with each observation deleted in turn, but this is computationally demanding when fitting models by using Markov chain Monte Carlo (MCMC), as obtaining complete sample estimates is often in itself a very time-consuming task. Here we propose two efficient ways to approximate the case-deleted estimates by using output from MCMC estimation. Our first proposal, which directly approximates the usual influence statistics in maximum likelihood analyses of generalised linear models (GLMs), is easy to implement and avoids any further evaluation of the likelihood. Hence, unlike the existing alternatives, it does not become more computationally intensive as the model complexity increases. Our second proposal, which utilises model perturbations, also has this advantage and does not require the form of the GLM to be specified. We show how our two proposed methods are related and evaluate them against the existing method of importance sampling and case deletion in a logistic regression analysis with missing covariates. We also provide practical advice for those implementing our procedures, so that they may be used in many situations where MCMC is used to fit statistical models., (Copyright © 2011 John Wiley & Sons, Ltd.)

Multistage designs allow considerable reductions in the expected sample size of a trial. When stopping for futility or efficacy is allowed at each stage, the expected sample size under different possible true treatment effects (δ) is of interest. The δ-minimax design is the one for which the maximum expected sample size is minimised amongst all designs that meet the types I and II error constraints. Previous work has compared a two-stage δ-minimax design with other optimal two-stage designs. Applying the δ-minimax design to designs with more than two stages was not previously considered because of computational issues. In this paper, we identify the δ-minimax designs with more than two stages through use of a novel application of simulated annealing. We compare them with other optimal multistage designs and the triangular design. We show that, as for two-stage designs, the δ-minimax design has good expected sample size properties across a broad range of treatment effects but generally has a higher maximum sample size. To overcome this drawback, we use the concept of admissible designs to find trials which balance the maximum expected sample size and maximum sample size. We show that such designs have good expected sample size properties and a reasonable maximum sample size and, thus, are very appealing for use in clinical trials., (Copyright © 2011 John Wiley & Sons, Ltd.)

Meta-analyses of clinical trials with continuous outcome data typically report the effect of an intervention as either a mean difference or a standardized mean difference. These results can be difficult to interpret, and re-expressing the effect size in terms of risk may facilitate understanding and applicability. We describe three methods for obtaining risks in such situations. Two of these methods involve direct transformation of a standardized mean difference to an odds ratio. The third entails estimation of risks in the two groups for a specific cut point. We extend this third approach to a completed meta-analysis by expressing the finding in the format of a single 'meta-study'. We compare the methods in two examples of meta-analyses and in a series of simulation studies that examine their properties in individual studies and in meta-analyses. These simulations show that the methods for expressing meta-analysis results from continuous outcomes are sensitive to underlying distributions, sample sizes and cut points but are remarkably robust to the presence of heterogeneity across studies. We offer suggestions of situations in which the various methods may safely be applied. In particular, if the underlying distribution is approximately normal, then estimation of risks for a specific cut point may be used for large sample sizes; direct transformations may be preferable otherwise. However, if the standard deviations in the two groups are notably different, then none of the methods have good properties. Furthermore, absolute risks are safely estimated after direct transformation only if they are in the region of 20% to 80%., (Copyright © 2011 John Wiley & Sons, Ltd.)

The development of a new drug is a major undertaking and it is important to consider carefully the key decisions in the development process. Decisions are made in the presence of uncertainty and outcomes such as the probability of successful drug registration depend on the clinical development programmme.The Rheumatoid Arthritis Drug Development Model was developed to support key decisions for drugs in development for the treatment of rheumatoid arthritis. It is configured to simulate Phase 2b and 3 trials based on the efficacy of new drugs at the end of Phase 2a, evidence about the efficacy of existing treatments, and expert opinion regarding key safety criteria.The model evaluates the performance of different development programmes with respect to the duration of disease of the target population, Phase 2b and 3 sample sizes, the dose(s) of the experimental treatment, the choice of comparator, the duration of the Phase 2b clinical trial, the primary efficacy outcome and decision criteria for successfully passing Phases 2b and 3. It uses Bayesian clinical trial simulation to calculate the probability of successful drug registration based on the uncertainty about parameters of interest, thereby providing a more realistic assessment of the likely outcomes of individual trials and sequences of trials for the purpose of decision making.In this case study, the results show that, depending on the trial design, the new treatment has assurances of successful drug registration in the range 0.044-0.142 for an ACR20 outcome and 0.057-0.213 for an ACR50 outcome., (Copyright (c) 2009 John Wiley & Sons, Ltd.)

Violation of Hardy-Weinberg equilibrium (HWE) can raise doubts about the validity of the conclusions from genetic association studies. However, for most currently performed gene-disease association studies, the available tests have low power to detect deviations from HWE. We consider this issue from a meta-analysis perspective, and suggest an approach to estimate the deviation and investigate its relationship with the observed genetic effects. Different degrees of deviation from HWE have previously been proposed as a potential source of heterogeneity across studies. We present a hierarchical meta-regression model that can be applied to test this assumption, using the concept of the fixation coefficient. We re-analyse seven meta-analyses to illustrate these methods. The uncertainty in the genetic effect estimate tended to increase once the fixation coefficient was taken into account. Dependence of the genetic effect size on the deviation from HWE was found in one meta-analysis, while in the other six examples, deviations from HWE did not clearly explain between-study heterogeneity in the genetic effects. The proposed hierarchical models allow the synthesis of data across gene-disease association studies with appropriate consideration of HWE issues., (2006 John Wiley & Sons, Ltd.)