This paper focuses on detecting the existence of a treatment effect when comparing multiple treatments using discrete observational data. A new test statistic, based on a divergence measure, is introduced, and its theoretical properties are obtained. Stochastic dominance tests are also proposed, illustrating relevant practical cases of treatment-level effects ordering patterns. Numerical simulations show the effectiveness of the proposed tests, in terms of both significance level and power. A clinical application indicates that our methods can significantly enhance the evaluation of multitreatments in real-world scenarios using observational data.

Clinical audits are essential for monitoring and improving the quality of healthcare with statistical outlier detection used to identify healthcare units whose performance deviates from expected standards. Two commonly used outlier-detection approaches are Common Mean Model (CMM) and Random Effects Logistic Regression (RELR). However, these methods can identify different healthcare units as outliers when applied to the same dataset. Incorrectly flagging a unit as an outlier can have serious consequences, including reputational harm, decreased staff morale, unnecessary regulatory scrutiny, diversion of resources, and loss of public trust. This article investigates the reasons for these discrepancies through a simulation study evaluating the performance of the CMM and RELR under a range of scenarios. The results show that differences in outlier detection are primarily driven by the degree to which a normality assumption holds for each method. When these assumptions are violated, for one or both methods, the two approaches may produce markedly different outlier detection. To choose the most appropriate approach for a given dataset, we recommend assessing each normality assumption, by combining visual diagnostics, such as QQ plots, with quantitative measures, such as Lin's concordance correlation coefficient (CCC).

The multi-arm two-stage (MATS) design combines proof-of-concept and dose optimization in a single study, which starts from parallel enrollments of participants across multiple cohorts (indications) at a dose selected from the dose-escalation study, which is usually the maximum tolerable dose (MTD) in traditional oncology dose-escalation studies, followed by randomizing subjects into two dose levels only for those "efficaciously promising" cohorts at the second stage. Here, we communicate a variant of the MATS design by "reversing" the two stages so that randomization to two dose levels for each indication-specific cohort precedes potential further enrollment at the dose selected for optimal efficacy/safety profile based on the randomization stage. This "Reversed MATS" (RevMATS) design fits into certain situations when prior data evidence indicates two doses may result in similar activities or there is not enough evidence to favor one dose over the other in terms of preliminary activities, thus justifying earlier randomization of two doses instead of delaying to the second stage. It also fits when one dose has revealed promising early efficacy signals in a heterogenous population and there is reasonable belief of effectiveness across indications (so that a larger upfront investment is justified so that the second stage of MATS may be skipped). The RevMATS design further improves the underlying Bayesian hierarchical model in the MATS design by accounting for broader (potential) efficacy profiles of candidate doses and explicitly incorporating collective data evidence, such as estimated dose-response curves (from dose escalation), to boost efficiency in decision-making.

In crossover designs, multiple outcomes are often collected to assess treatment effectiveness in a comprehensive manner. Also, interest has grown in comparing intra-subject variability between treatments in such designs. We present three distinct multivariate linear mixed-effects models, with the choice of the model depending on the design and assumptions regarding carryover effects. We discuss maximum likelihood (ML) and restricted ML (REML) approaches for parameter estimation. For a special case that a crossover design is uniform within sequences, we derive the closed-form expressions for the ML and REML estimators of the variance components. We propose general hypothesis testing methods for the treatment effects and the intra-subject variance matrices. The latter situation has not received much attention in the statistical literature. For the special case, we derive the exact test statistics for treatment means comparisons and for testing the null hypothesis of homogeneous intra-subject variance matrices. Simulation studies are conducted to validate the superior performance of the proposed multivariate approach compared with the usual univariate approach in testing treatment effects. Finally, we apply the methodologies to two data examples.

R. A. Fisher was one of the greatest scientists of the last century. He made many groundbreaking contributions, so many indeed that it seems almost impossible to list all of them. His revolutionary contributions to the design of experiments can mostly be traced back to the early part of his academic career, and they are inextricably linked to his involvement with agricultural field experiments at Rothamsted Experiment Station. In this talk, I will review Fisher's key ideas on experimental design and relate them to some of the work I am involved in, most of which directly focuses on field experiments in agriculture. Topics covered include systematic designs, row-column designs, augmented row-column designs, multi-environment trials, partially replicated designs, optimal allocation of trials to zones in subdivided target populations of environments, and the connection of trialing systems across countries.

Estimates of national immunization coverage (ENIC) are crucial for guiding policy and decision-making in national immunization programs and setting the global immunization agenda. World Health Organization (WHO) and UNICEF estimates of national immunization coverage (WUENIC) are produced annually for various vaccine-dose combinations and all WHO Member States using information from multiple data sources and a deterministic computational logic approach. This approach, however, is incapable of characterizing the uncertainties inherent in coverage measurement and estimation. It also provides no statistically principled way of exploiting and accounting for the interdependence in immunization coverage data collected for multiple vaccines, countries, and time points. Here, we develop Bayesian hierarchical modeling approaches for producing accurate ENIC and associated uncertainties. We propose and explore two candidate models: a base single likelihood (BSL) model and an irregular data multiple likelihood (IDML) model, both of which differ in their handling of missing data and characterization of the uncertainties associated with the multiple input data sources. We provide a simulation study that demonstrates a high degree of accuracy of the estimates produced by the proposed models, and which also shows that the IDML model generally outperformed the BSL model in most cases we considered. We apply the methodology to produce coverage estimates for select vaccine-dose combinations for the period 2000-2019. A contributed R package, imcover, implementing the No-U-Turn Sampler in the Stan programming language enhances the utility and reproducibility of the methodology.

The cure model extends standard survival models to analyze survival data with a cure or nonsusceptible fraction. Numerous methods have been developed to infer such data using the mixture cure model, which separately models and interprets the cure rate and the failure time of uncured subjects. Most of these methods assume that all covariates are measured precisely. Cure models that account for mismeasured covariates are scarce in the literature, largely due to the challenges they pose for estimation, inference, and asymptotic theory. This article considers a logistic-proportional odds mixture cure model for right-censored survival data with mismeasured covariates and proposes a functional modeling approach to correct measurement errors. We develop a two-stage estimation method with extensively corrected scores to sequentially infer the cure rate and failure time of uncured subjects. The computational algorithm is straightforward to implement, and its large sample properties are established. We conduct simulation studies to assess the approach's performance and apply it to a real dataset for illustration.

In this short communication, we describe the recent debate on whether the hazard function should be used for causal inference in time-to-event studies and consider three different potential outcomes frameworks (by Rubin, Robins, and Pearl, respectively), as well as use the single-world intervention graph to show mathematically that the hazard function has causal interpretations under all three frameworks. In addition, we argue that the hazard ratio over time can provide a useful interpretation in practical settings.

Interval estimation of a proportion estimated from testing of pooled samples has been studied by a variety of researchers, who have examined both exact and asymptotic methods. Recent work in point estimation has seen the use of Firth's correction to maximum likelihood estimation to reduce bias effectively. We consider the Firth-corrected score statistic, using either expected or observed information, as the first derivative function of a penalized likelihood and develop score-based confidence intervals wholly within this framework. We evaluate their performance, comparing them by information type and to the existing, recommended asymptotic method of Gart. The methods are illustrated using data on West Nile virus infection in field-collected mosquitoes and on yellow fever virus infection in mosquitoes reported in Walter et al. The penalized likelihood approach using expected information is found to unify previously recommended point and interval estimates under one inferential framework. Detailed evaluation of coverage properties of the intervals over a range of pooling designs show improved performance for the intervals using observed information and skewness-correction to the score. We derive simple, interpretable expressions for the score and skewness-corrected score statistics, and give a quadratic formula for the skewness-corrected score interval for the case that all pools are the same size, which reduces to a skewness-correction for the standard Wilson interval in the standard binomial case.

We consider the optimal design problem for identifying effective dose combinations within drug combination studies where the effect of the combination of two drugs is investigated. Drug combination studies are becoming increasingly important as they investigate potential interaction effects rather than the individual impacts of the drugs. In this situation, identifying effective dose combinations that yield a prespecified effect is of special interest. If nonlinear surface models are used to describe the dose combination-response relationship, these effective dose combinations, also called isoboles, result in specific contour lines of the fitted response model. Consequently, accurately estimating these effective dose combinations is crucial. We propose a novel design criterion that targets the precise estimation of these effective dose combinations. In particular, an optimal design minimizes the width of the confidence band of the contour lines of interest. Optimal design theory is developed for this problem, including equivalence theorems and efficiency bounds. The performance of the optimal design is illustrated in different examples modeling dose combination data by various nonlinear surface models. It is demonstrated that the proposed optimal design for identifying effective dose combinations yields a more precise estimation of the effective dose combinations than ray or factorial designs, which are commonly used in practice. This particularly holds true for a case study motivated by data from an oncological dose combination study.

The Cox proportional hazards model is often used to analyze data from randomized controlled trials (RCTs) with time-to-event outcomes. Random survival forest (RSF) is a machine-learning algorithm known for its high predictive performance. We conduct a comprehensive neutral comparison study to compare the performance of Cox regression and RSF in various simulation scenarios based on two reference datasets from RCTs. The motivation is to identify settings in which one method is preferable over the other when comparing different aspects of performance using measures according to the TRIPOD (Transparent Reporting of a multivariable prediction model for Individual Prognosis or Diagnosis) recommendations. Our results show that conclusions solely based on the C index, a performance measure that has been predominantly used in previous studies comparing predictive accuracy of the Cox-PH and RSF model based on real-world observational time-to-event data and that has been criticized by methodologists, may not be generalizable to other aspects of predictive performance. We found that measures of overall performance may generally give more reasonable results, and that the standard log-rank splitting rule used for the RSF may be outperformed by alternative splitting rules, in particular in nonproportional hazards settings. In our simulations, the performance of the RSF suffers less in data with treatment-covariate interactions compared to data where these are absent. The performance of the Cox-PH model is affected by the violation of the proportional hazards assumption.

In oncology, clinical trials are a cornerstone of evaluating new treatments. However, traditional designs face significant challenges, particularly when assessing multiple treatment options. The emergence of multi-arm multi-stage (MAMS) designs, such as the drop-the-losers (DtL) approach, offers innovative solutions by combining multiple hypotheses within a single trial. This work evaluates the DtL approach. We extend the design to binary and survival endpoints. The statistical performance (Type I error control, statistical power, and biases) of the DtL design was assessed using a simulation study. Results demonstrated that the DtL design effectively balances statistical rigor and efficiency. The design strongly controls Type I error while ensuring high power in detecting drug effects. Scenarios with ineffective treatments highlighted the advantage of eliminating suboptimal options early. One limitation identified is that long-term survival endpoints may not be mature enough to support early treatment selection. Early decision-making is a key aspect of adaptive designs to support futility analysis or early efficacy analysis. It is critical to define properly the decision thresholds for such early analyses. Updating the endpoint of interest over time also aligns with clinical practices, starting with ORR, transitioning to benefit-risk scores or progression-free survival (PFS), and concluding with overall survival (OS) at the final analysis. Such an approach requires handling of correlations between drug effects across these endpoints. This work provides a comprehensive framework for implementing DtL design, demonstrating its potential to accelerate treatment evaluation in oncology.

Row-column designs play an important role in applications where two orthogonal sources of error need to be controlled for by blocking. Field or greenhouse experiments, in which experimental units are arranged as a rectangular array of experimental units, are a prominent example. In plant breeding, the amount of seed available for the treatments to be tested may be so limited that only one experimental unit per treatment can be accommodated. In such settings, augmented designs become an interesting option, where a small set of treatments, for which sufficient seed is available, is replicated across the rectangular layout so that row and column effects, as well as the error variance, can be estimated. Here, we consider the use of an auxiliary design, also known as a contraction, to generate an augmented row-column design. We make use of the fact that the efficiency factors of the contraction and the associated augmented design are closely interlinked. A major advantage of this approach is that an efficient contraction can be found by computer search at much higher computational speed than is required for direct search for an efficient augmented design. Two examples are used to illustrate the proposed method. Furthermore, we contrast the usage of our approach when the array dimensions are fixed, as is the case with microplates, to settings with more flexibility regarding the number of rows and columns of the layout, as in greenhouse and field trials.