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It has been reported that about half of biological discoveries are irreproducible. These irreproducible discoveries were partially attributed to poor statistical power. The poor powers are majorly owned to small sample sizes. However, in molecular biology and medicine, due to the limit of biological resources and budget, most molecular biological experiments have been conducted with small samples. Two-sample t -test controls bias by using a degree of freedom. However, this also implicates that t -test has low power in small samples. A discovery found with low statistical power suggests that it has a poor reproducibility. So, promotion of statistical power is not a feasible way to enhance reproducibility in small-sample experiments. An alternative way is to reduce type I error rate. For doing so, a so-called t α -test was developed. Both theoretical analysis and simulation study demonstrate that t α -test much outperforms t -test. However, t α -test is reduced to t -test when sample sizes are over 15. Large-scale simulation studies and real experiment data show that t α -test significantly reduced type I error rate compared to t -test and Wilcoxon test in small-sample experiments. t α -test had almost the same empirical power with t -test. Null p-value density distribution explains why t α -test had so lower type I error rate than t -test. One real experimental dataset provides a typical example to show that t α -test outperforms t -test and a microarray dataset showed that t α -test had the best performance among five statistical methods. In addition, the density distribution and probability cumulative function of t α -statistic were given in mathematics and the theoretical and observed distributions are well matched.

Meta-analysis of binary outcome data faces often a situation where studies with a rare event are part of the set of studies to be considered. These studies have low occurrence of event counts to the extreme that no events occur in one or both groups to be compared. This raises issues how to estimate validly the summary risk or rate ratio across studies. A preferred choice is the Mantel–Haenszel estimator, which is still defined in the situation of zero studies unless all studies have zeros in one of the groups to be compared. For this situation, a modified Mantel–Haenszel estimator is suggested and shown to perform well by means of simulation work. Also, confidence interval estimation is discussed and evaluated in a simulation study. In a second part, heterogeneity of relative risk across studies is investigated with a new chi-square type statistic which is based on a conditional binomial distribution where the conditioning is on the event margin for each study. This is necessary as the conventional Q -statistic is undefined in the occurrence of zero studies. The null-distribution of the proposed Q -statistic is obtained by means of a parametric bootstrap as a chi-square approximation is not valid for rare events meta-analysis, as bootstrapping of the null-distribution shows. In addition, for the effect heterogeneity situation, confidence interval estimation is considered using a nonparametric bootstrap procedure. The proposed techniques are illustrated at hand of three meta-analytic data sets.

The Cox regression model and its associated hazard ratio (HR) are frequently used for summarizing the effect of treatments on time to event outcomes. However, the HR’s interpretation strongly depends on the assumed underlying survival model. The challenge of interpreting the HR has been the focus of a number of recent papers. Several alternative measures have been proposed in order to deal with these concerns. The marginal Cox regression models include an identifiable hazard ratio without individual but populational causal interpretation. In this work, we study the properties of one particular marginal Cox regression model and consider its estimation in the presence of omitted confounder from an instrumental variable-based procedure. We prove the large sample consistency of an estimation score which allows non-binary treatments. Our Monte Carlo simulations suggest that finite sample behavior of the procedure is adequate. The studied estimator is more robust than its competitor (Wang et al.) for weak instruments although it is slightly more biased for large effects of the treatment. The practical use of the presented techniques is illustrated through a real practical example using data from the vascular quality initiative registry. The used R code is provided as Supplementary material.

Li and Greene (A weighting analogue to pair matching in propensity score analysis. Int J Biostat 2013;9:215–34) propose that estimates derived by the matching weight (MW) estimator are similar to those derived by the one-to-one propensity score matching estimator. The MW estimator has some useful properties, however, some regularity conditions need to be confirmed to derive an asymptotic distribution since the MW has a non-differentiable point. In this letter, we confirm the asymptotic distribution of the MW estimator and the sufficient conditions to achieve it.

Variable selection is needed and performed in almost every field and a large literature on it has been established, especially under the context of linear models or for complete data. Many authors have also investigated the variable selection problem for incomplete data such as right-censored failure time data. In this paper, we discuss variable selection when one faces bivariate interval-censored failure time data arising from a linear transformation model, for which it does not seem to exist an established procedure. For the problem, a penalized maximum likelihood approach is proposed and in particular, a novel Poisson-based EM algorithm is developed for the implementation. The oracle property of the proposed method is established, and the numerical studies suggest that the method works well for practical situations.

We describe an estimating equation that can be used to fit quantile regression models to interval-censored data. The proposed estimator presents important advantages over the existing methods, and can be applied when the data are a mixture of interval-censored, left-censored, and right-censored observations. We describe estimation and inference, report simulation results, and apply the proposed method to analyze the Signal Tandmobiel ® data. The necessary R code has been incorporated in the existing R package c t q r $\mathtt{c}\mathtt{t}\mathtt{q}\mathtt{r}$ .

Quantile regression permits describing how quantiles of a scalar response variable depend on a set of predictors. Because a unique definition of multivariate quantiles is lacking, extending quantile regression to multivariate responses is somewhat complicated. In this paper, we describe a simple approach based on a two-step procedure: in the first step, quantile regression is applied to each response separately; in the second step, the joint distribution of the signs of the residuals is modeled through multinomial regression. The described approach does not require a multidimensional definition of quantiles, and can be used to capture important features of a multivariate response and assess the effects of covariates on the correlation structure. We apply the proposed method to analyze two different datasets.

We combine robust loss functions with statistical boosting algorithms in an adaptive way to perform variable selection and predictive modelling for potentially high-dimensional biomedical data. To achieve robustness against outliers in the outcome variable (vertical outliers), we consider different composite robust loss functions together with base-learners for linear regression. For composite loss functions, such as the Huber loss and the Bisquare loss, a threshold parameter has to be specified that controls the robustness. In the context of boosting algorithms, we propose an approach that adapts the threshold parameter of composite robust losses in each iteration to the current sizes of residuals, based on a fixed quantile level. We compared the performance of our approach to classical M-regression, boosting with standard loss functions or the lasso regarding prediction accuracy and variable selection in different simulated settings: the adaptive Huber and Bisquare losses led to a better performance when the outcome contained outliers or was affected by specific types of corruption. For non-corrupted data, our approach yielded a similar performance to boosting with the efficient L 2 loss or the lasso. Also in the analysis of skewed KRT19 protein expression data based on gene expression measurements from human cancer cell lines (NCI-60 cell line panel), boosting with the new adaptive loss functions performed favourably compared to standard loss functions or competing robust approaches regarding prediction accuracy and resulted in very sparse models.

Prevalent cohort studies in medical research often give rise to length-biased survival data that require special treatments. The recently proposed varying-coefficient partially linear transformation (VCPLT) model has the virtue of providing a more dynamic content of the effects of the covariates on survival times than the well-known partially linear transformation (PLT) model by allowing flexible interactions between the covariates. However, no existing analysis of the VCPLT model has considered length-biased sampling. In this paper, we consider the VCPLT model when the data are length-biased and right censored, thereby extending the reach of this flexible and powerful tool. We develop a martingale estimating function-based approach to the estimation of this model, provide theoretical underpinnings, evaluate finite sample performance via simulations, and showcase its practical appeal via an empirical application using data from two HIV vaccine clinical trials conducted by the U.S. National Institute of Allergy and Infectious Diseases.

This article considers the concept of designing Phase I clinical trials using both clinician- and patient-reported outcomes to adaptively allocate study participants to tolerable doses and determine the maximum tolerated dose (MTD) at the study conclusion. We describe an application of a Bayesian form of the patient-reported outcomes continual reassessment method (PRO-CRMB) in an ongoing Phase I study of adjuvant hypofractionated whole pelvis radiation therapy (WPRT) in endometrial cancer (NCT04458402). The study’s primary objective is to determine the MTD per fraction of WPRT, defined by acceptable clinician- and patient-reported DLT rates. We conduct simulation studies of the operating characteristics of the design and compared them to a rule-based approach. We illustrate that the PRO-CRMB makes appropriate dose assignments during the study to give investigators and reviewers an idea of how the method behaves. In simulation studies, the PRO-CRMB demonstrates superior performance to a 5 + 2 stepwise design in terms of recommending target treatment courses and allocating patients to these courses. The design is accompanied by an easy-to-use R shiny web application to simulate operating characteristics at the design stage and sequentially update dose assignments throughout the trial’s conduct.

Non-inferiority vaccine trials compare new candidates to active controls that provide clinically significant protection against a disease. Bayesian statistics allows to exploit pre-experimental information available from previous studies to increase precision and reduce costs. Here, historical knowledge is incorporated into the analysis through a power prior that dynamically regulates the degree of information-borrowing. We examine non-inferiority tests based on credible intervals for the unknown effects-difference between two vaccines on the log odds ratio scale, with an application to new Covid-19 vaccines. We explore the frequentist properties of the method and we address the sample size determination problem.

District-representative data are rarely collected in the surveys for identifying localised disparities in Bangladesh, and so district-level estimates of undernutrition indicators – stunting, wasting and underweight – have remained largely unexplored. This study aims to estimate district-level prevalence of these indicators by employing a multivariate Fay–Herriot (MFH) model which accounts for the underlying correlation among the undernutrition indicators. Direct estimates (DIR) of the target indicators and their variance–covariance matrices calculated from the 2019 Bangladesh Multiple Indicator Cluster Survey microdata have been used as input for developing univariate Fay–Herriot (UFH), bivariate Fay–Herriot (BFH) and MFH models. The comparison of the various model-based estimates and their relative standard errors with the corresponding direct estimates reveals that the MFH estimator provides unbiased estimates with more accuracy than the DIR, UFH and BFH estimators. The MFH model-based district level estimates of stunting, wasting and underweight range between 16 and 43%, 15 and 36%, and 6 and 13% respectively. District level bivariate maps of undernutrition indicators show that districts in north-eastern and south-eastern parts are highly exposed to either form of undernutrition, than the districts in south-western and central parts of the country. In terms of the number of undernourished children, millions of children affected by either form of undernutrition are living in densely populated districts like the capital district Dhaka, though undernutrition indicators (as a proportion) are comparatively lower. These findings can be used to target districts with a concurrence of multiple forms of undernutrition, and in the design of urgent intervention programs to reduce the inequality in child undernutrition at the localised district level.

The optimal dynamic treatment rule (ODTR) framework offers an approach for understanding which kinds of patients respond best to specific treatments – in other words, treatment effect heterogeneity. Recently, there has been a proliferation of methods for estimating the ODTR. One such method is an extension of the SuperLearner algorithm – an ensemble method to optimally combine candidate algorithms extensively used in prediction problems – to ODTRs. Following the ``causal roadmap,” we causally and statistically define the ODTR and provide an introduction to estimating it using the ODTR SuperLearner. Additionally, we highlight practical choices when implementing the algorithm, including choice of candidate algorithms, metalearners to combine the candidates, and risk functions to select the best combination of algorithms. Using simulations, we illustrate how estimating the ODTR using this SuperLearner approach can uncover treatment effect heterogeneity more effectively than traditional approaches based on fitting a parametric regression of the outcome on the treatment, covariates and treatment-covariate interactions. We investigate the implications of choices in implementing an ODTR SuperLearner at various sample sizes. Our results show the advantages of: (1) including a combination of both flexible machine learning algorithms and simple parametric estimators in the library of candidate algorithms; (2) using an ensemble metalearner to combine candidates rather than selecting only the best-performing candidate; (3) using the mean outcome under the rule as a risk function. Finally, we apply the ODTR SuperLearner to the ``Interventions” study, an ongoing randomized controlled trial, to identify which justice-involved adults with mental illness benefit most from cognitive behavioral therapy to reduce criminal re-offending.

Given an (optimal) dynamic treatment rule, it may be of interest to evaluate that rule – that is, to ask the causal question: what is the expected outcome had every subject received treatment according to that rule? In this paper, we study the performance of estimators that approximate the true value of: (1) an a priori known dynamic treatment rule (2) the true, unknown optimal dynamic treatment rule (ODTR); (3) an estimated ODTR, a so-called “data-adaptive parameter,” whose true value depends on the sample. Using simulations of point-treatment data, we specifically investigate: (1) the impact of increasingly data-adaptive estimation of nuisance parameters and/or of the ODTR on performance; (2) the potential for improved efficiency and bias reduction through the use of semiparametric efficient estimators; and, (3) the importance of sample splitting based on the cross-validated targeted maximum likelihood estimator (CV-TMLE) for accurate inference. In the simulations considered, there was very little cost and many benefits to using CV-TMLE to estimate the value of the true and estimated ODTR; importantly, and in contrast to non cross-validated estimators, the performance of CV-TMLE was maintained even when highly data-adaptive algorithms were used to estimate both nuisance parameters and the ODTR. In addition, we apply these estimators for the value of the rule to the “Interventions” study, an ongoing randomized controlled trial, to identify whether assigning cognitive behavioral therapy (CBT) to criminal justice-involved adults with mental illness using an ODTR significantly reduces the probability of recidivism, compared to assigning CBT in a non-individualized way.

We consider estimation of a functional parameter of a realistically modeled data distribution based on observing independent and identically distributed observations. The highly adaptive lasso estimator of the functional parameter is defined as the minimizer of the empirical risk over a class of cadlag functions with finite sectional variation norm, where the functional parameter is parametrized in terms of such a class of functions. In this article we establish that this HAL estimator yields an asymptotically efficient estimator of any smooth feature of the functional parameter under a global undersmoothing condition. It is formally shown that the L 1 -restriction in HAL does not obstruct it from solving the score equations along paths that do not enforce this condition. Therefore, from an asymptotic point of view, the only reason for undersmoothing is that the true target function might not be complex so that the HAL-fit leaves out key basis functions that are needed to span the desired efficient influence curve of the smooth target parameter. Nonetheless, in practice undersmoothing appears to be beneficial and a simple targeted method is proposed and practically verified to perform well. We demonstrate our general result HAL-estimator of a treatment-specific mean and of the integrated square density. We also present simulations for these two examples confirming the theory.