Statistical Methods in Medical Research

Randomized controlled trials (RCTs) have been widely recognized as the gold standard to infer the treatment effect in clinical research. Recently, there has been growing interest in enhancing and complementing the result in an RCT by integrating real-world evidence from observational studies. The unit information prior (UIP) is a newly proposed technique that can effectively borrow information from multiple historical datasets. We extend this generic approach to synthesize the non-randomized evidence into a current RCT. Not only does the UIP only require summary statistics published from observational studies for ease of implementation, but it also has clear interpretations and can alleviate the potential bias in the real-world evidence via weighting schemes. Extensive numerical experiments show that the UIP can improve the statistical efficiency in estimating the treatment effect for various types of outcome variables. The practical potential of our UIP approach is further illustrated with a real trial of hydroxychloroquine for treating COVID-19 patients.

Results from multiple diagnostic tests are combined in many ways to improve the overall diagnostic accuracy. For binary classification, maximization of the empirical estimate of the area under the receiver operating characteristic curve has widely been used to produce an optimal linear combination of multiple biomarkers. However, in the presence of a large number of biomarkers, this method proves to be computationally expensive and difficult to implement since it involves maximization of a discontinuous, non-smooth function for which gradient-based methods cannot be used directly. The complexity of this problem further increases when the classification problem becomes multi-category. In this article, we develop a linear combination method that maximizes a smooth approximation of the empirical Hyper-volume Under Manifolds for the multi-category outcome. We approximate HUM by replacing the indicator function with the sigmoid function and normal cumulative distribution function. With such smooth approximations, efficient gradient-based algorithms are employed to obtain better solutions with less computing time. We show that under some regularity conditions, the proposed method yields consistent estimates of the coefficient parameters. We derive the asymptotic normality of the coefficient estimates. A simulation study is performed to study the effectiveness of our proposed method as compared to other existing methods. The method is illustrated using two real medical data sets.

Recently, treatment interruptions such as a clinical hold in randomized clinical trials have been investigated by using a multistate model approach. The phase III clinical trial START (Stimulating Targeted Antigenic Response To non-small-cell cancer) with primary endpoint overall survival was temporarily placed on hold for enrollment and treatment by the US Food and Drug Administration (FDA). Multistate models provide a flexible framework to account for treatment interruptions induced by a time-dependent external covariate. Extending previous work, we propose a censoring and a filtering approach both aimed at estimating the initial treatment effect on overall survival in the hypothetical situation of no clinical hold. A special focus is on creating a link to causal inference. We show that calculating the matrix of transition probabilities in the multistate model after application of censoring (or filtering) yields the desired causal interpretation. Assumptions in support of the identification of a causal effect by censoring (or filtering) are discussed. Thus, we provide the basis to apply causal censoring (or filtering) in more general settings such as the COVID-19 pandemic. A simulation study demonstrates that both causal censoring and filtering perform favorably compared to a naïve method ignoring the external impact.

Repeated testing in a group sequential trial can result in bias in the maximum likelihood estimate of the unknown parameter of interest. Many authors have therefore proposed adjusted point estimation procedures, which attempt to reduce such bias. Here, we describe nine possible point estimators within a common general framework for a two-stage group sequential trial. We then contrast their performance in five example trial settings, examining their conditional and marginal biases and residual mean square error. By focusing on the case of a trial with a single interim analysis, additional new results aiding the determination of the estimators are given. Our findings demonstrate that the uniform minimum variance unbiased estimator, whilst being marginally unbiased, often has large conditional bias and residual mean square error. If one is concerned solely about inference on progression to the second trial stage, the conditional uniform minimum variance unbiased estimator may be preferred. Two estimators, termed mean adjusted estimators, which attempt to reduce the marginal bias, arguably perform best in terms of the marginal residual mean square error. In all, one should choose an estimator accounting for its conditional and marginal biases and residual mean square error; the most suitable estimator will depend on relative desires to minimise each of these factors. If one cares solely about the conditional and marginal biases, the conditional maximum likelihood estimate may be preferred provided lower and upper stopping boundaries are included. If the conditional and marginal residual mean square error are also of concern, two mean adjusted estimators perform well.

Simulation studies play an important role in evaluating the performance of statistical models developed for analyzing complex survival data such as those with competing risks and clustering. This article aims to provide researchers with a basic understanding of competing risks data generation, techniques for inducing cluster-level correlation, and ways to combine them together in simulation studies, in the context of randomized clinical trials with a binary exposure or treatment. We review data generation with competing and semi-competing risks and three approaches of inducing cluster-level correlation for time-to-event data: the frailty model framework, the probability transform, and Moran’s algorithm. Using exponentially distributed event times as an example, we discuss how to introduce cluster-level correlation into generating complex survival outcomes, and illustrate multiple ways of combining these methods to simulate clustered, competing and semi-competing risks data with pre-specified correlation values or degree of clustering.

We introduce a new multiple type I error criterion for clinical trials with multiple, overlapping populations. Such trials are of interest in precision medicine where the goal is to develop treatments that are targeted to specific sub-populations defined by genetic and/or clinical biomarkers. The new criterion is based on the observation that not all type I errors are relevant to all patients in the overall population. If disjoint sub-populations are considered, no multiplicity adjustment appears necessary, since a claim in one sub-population does not affect patients in the other ones. For intersecting sub-populations we suggest to control the average multiple type I error rate, i.e. the probability that a randomly selected patient will be exposed to an inefficient treatment. We call this the population-wise error rate, exemplify it by a number of examples and illustrate how to control it with an adjustment of critical boundaries or adjusted p -values. We furthermore define corresponding simultaneous confidence intervals. We finally illustrate the power gain achieved by passing from family-wise to population-wise error rate control with two simple examples and a recently suggested multiple-testing approach for umbrella trials.

Conventional hazard regression analyses frequently assume constant regression coefficients and scalar covariates. However, some covariate effects may vary with time. Moreover, medical imaging has become an increasingly important tool in screening, diagnosis, and prognosis of various diseases, given its information visualization and quantitative assessment. This study considers an additive hazards model with time-varying coefficients and imaging predictors to examine the dynamic effects of potential scalar and imaging risk factors for the failure of interest. We develop a two-stage approach that comprises the high-dimensional functional principal component analysis technique in the first stage and the counting process-based estimating equation approach in the second stage. In addition, we construct the pointwise confidence intervals for the proposed estimators and provide a significance test for the effects of scalar and imaging covariates. Simulation studies demonstrate the satisfactory performance of the proposed method. An application to the Alzheimer’s disease neuroimaging initiative study further illustrates the utility of the methodology.

We consider the setting of an aggregate data meta-analysis of a continuous outcome of interest. When the distribution of the outcome is skewed, it is often the case that some primary studies report the sample mean and standard deviation of the outcome and other studies report the sample median along with the first and third quartiles and/or minimum and maximum values. To perform meta-analysis in this context, a number of approaches have recently been developed to impute the sample mean and standard deviation from studies reporting medians. Then, standard meta-analytic approaches with inverse-variance weighting are applied based on the (imputed) study-specific sample means and standard deviations. In this article, we illustrate how this common practice can severely underestimate the within-study standard errors, which results in poor coverage for the pooled mean in common effect meta-analyses and overestimation of between-study heterogeneity in random effects meta-analyses. We propose a straightforward bootstrap approach to estimate the standard errors of the imputed sample means. Our simulation study illustrates how the proposed approach can improve the estimation of the within-study standard errors and consequently improve coverage for the pooled mean in common effect meta-analyses and estimation of between-study heterogeneity in random effects meta-analyses. Moreover, we apply the proposed approach in a meta-analysis to identify risk factors of a severe course of COVID-19.

Common causal estimands include the average treatment effect, the average treatment effect of the treated, and the average treatment effect on the controls. Using augmented inverse probability weighting methods, parametric models are judiciously leveraged to yield doubly robust estimators, that is, estimators that are consistent when at least one the parametric models is correctly specified. Three sources of uncertainty are associated when we evaluate these estimators and their variances, that is, when we estimate the treatment and outcome regression models as well as the desired treatment effect. In this article, we propose methods to calculate the variance of the normalized, doubly robust average treatment effect of the treated and average treatment effect on the controls estimators and investigate their finite sample properties. We consider both the asymptotic sandwich variance estimation, the standard bootstrap as well as two wild bootstrap methods. For the asymptotic approximations, we incorporate the aforementioned uncertainties via estimating equations. Moreover, unlike the standard bootstrap procedures, the proposed wild bootstrap methods use perturbations of the influence functions of the estimators through independently distributed random variables. We conduct an extensive simulation study where we vary the heterogeneity of the treatment effect as well as the proportion of participants assigned to the active treatment group. We illustrate the methods using an observational study of critical ill patients on the use of right heart catherization.

Assigning optimal treatments to individual patients based on their characteristics is the ultimate goal of precision medicine. Deriving evidence-based recommendations from observational data while considering the causal treatment effects and patient heterogeneity is a challenging task, especially in situations of multiple treatment options. Herein, we propose a reference-free R-learner based on a simplex algorithm for treatment recommendation. We showed through extensive simulation that the proposed method produced accurate recommendations that corresponded to optimal treatment outcomes, regardless of the reference group. We used the method to analyze data from the Systolic Blood Pressure Intervention Trial (SPRINT) and achieved recommendations consistent with the current clinical guidelines.

A range of regularization approaches have been proposed in the data sciences to overcome overfitting, to exploit sparsity or to improve prediction. Using a broad definition of regularization, namely controlling model complexity by adding information in order to solve ill-posed problems or to prevent overfitting, we review a range of approaches within this framework including penalization, early stopping, ensembling and model averaging. Aspects of their practical implementation are discussed including available R-packages and examples are provided. To assess the extent to which these approaches are used in medicine, we conducted a review of three general medical journals. It revealed that regularization approaches are rarely applied in practical clinical applications, with the exception of random effects models. Hence, we suggest a more frequent use of regularization approaches in medical research. In situations where also other approaches work well, the only downside of the regularization approaches is increased complexity in the conduct of the analyses which can pose challenges in terms of computational resources and expertise on the side of the data analyst. In our view, both can and should be overcome by investments in appropriate computing facilities and educational resources.