Treatment switching is common in randomised controlled trials (RCTs). Participants may switch onto a variety of different treatments, all of which may have different treatment effects. Adjustment analyses that target hypothetical estimands - estimating outcomes that would have been observed in the absence of treatment switching - have focused primarily on a single type of switch. In this study, we assess the performance of applications of inverse probability of censoring weights (IPCW) and two-stage estimation (TSE) which adjust for multiple switches by either (i) adjusting for each type of switching separately ('treatments separate') or (ii) adjusting for switches combined without differentiating between switched-to treatments ('treatments combined'). We simulate 48 scenarios in which RCT participants may switch to multiple treatments. Switch proportions, treatment effects, number of switched-to treatments and censoring proportions were varied. Method performance measures included mean percentage bias in restricted mean survival time and the frequency of model convergence. Similar levels of bias were produced by treatments combined and treatments separate in both TSE and IPCW applications. In the scenarios examined, there was no demonstrable advantage associated with adjusting for each type of switch separately, compared with adjusting for all switches together.

One primary goal of precision medicine is to estimate the individualized treatment rules that optimize patients' health outcomes based on individual characteristics. Health studies with multiple treatments are commonly seen in practice. However, most existing individualized treatment rule estimation methods were developed for the studies with binary treatments. Many require that the outcomes are fully observed. In this article, we propose a matching-based machine learning method to estimate the optimal individualized treatment rules in observational studies with multiple treatments when the outcomes are fully observed or right-censored. We establish theoretical property for the proposed method. It is compared with the existing competitive methods in simulation studies and a hepatocellular carcinoma study.

In medical and health research, investigators are often interested in countable quantities such as hospital length of stay (e.g., in days) or the number of doctor visits. Poisson regression is commonly used to model such count data, but this approach can't accommodate overdispersion-when the variance exceeds the mean. To address this issue, the negative binomial (NB) distribution (NB-D) and, by extension, NB regression provide a well-documented alternative. However, real-data applications present additional challenges that must be considered. Two such challenges are (i) the presence of (mild) outliers that can influence the performance of the NB-D and (ii) the availability of covariates that can enhance inference about the mean of the count variable of interest. To jointly address these issues, we propose the contaminated NB (cNB) distribution that exhibits the necessary flexibility to accommodate mild outliers. This model is shown to be simple and intuitive in interpretation. In addition to the parameters of the NB-D, our proposed model has a parameter describing the proportion of mild outliers and one specifying the degree of contamination. To allow available covariates to improve the estimation of the mean of the cNB distribution, we propose the cNB regression model. An expectation-maximization algorithm is outlined for parameter estimation, and its performance is evaluated through a parameter recovery study. The effectiveness of our model is demonstrated via a sensitivity analysis and on two health datasets, where it outperforms well-known count models. The methodology proposed is implemented in an R package which is available at https://github.com/arnootto/cNB.

The population-wise error rate is a type I error rate for clinical trials with multiple target populations. In such trials, a treatment is tested for its efficacy in each population. The population-wise error rate is defined as the probability that a randomly selected, future patient will be exposed to an inefficient treatment based on the study results. It can be understood and computed as an average of strata-specific family wise error rates and involves the prevalences of these strata. A major issue of this concept is that the prevalences are usually unknown in practice, so that the population-wise error rate cannot be directly controlled. Instead, one could use an estimator based on the given sample, like their maximum-likelihood estimator under a multinomial distribution. In this article, we demonstrate through simulations that this does not substantially inflate the true population-wise error rate. We differentiate between the expected population-wise error rate, which is almost perfectly controlled, and study-specific values of the population-wise error rate which are conditioned on all subgroup sample sizes and vary within a narrow range. Thereby, we consider up to eight different overlapping populations and moderate to large sample sizes. In these settings, we also consider the maximum strata-wise family wise error rate, which is found to be, on average, at least bounded by twice the significance level used for population-wise error rate control.

Recurrent events data are often encountered in biomedical settings, where individuals may also experience a terminal event such as death. A useful estimand to summarize such data is the marginal mean of the cumulative number of recurrent events up to a specific time horizon, allowing also for the possible presence of a terminal event. Recently, it was found that augmented estimators can estimate this quantity efficiently, providing improved inference. Improvement in efficiency by the use of covariate adjustment is increasing in popularity as the methods get further developed, and is supported by regulatory agencies EMA (2015) and FDA (2023). Motivated by these arguments, this article presents novel efficient estimators for clinical data from randomized controlled trials, accounting  for additional information from auxiliary covariates.   Moreover, in randomized studies when both right censoring and competing risks are present, we propose a novel doubly augmented estimator of the marginal mean  , which has two optimal augmentation components due to censoring and randomization. We provide theoretical and asymptotic details for the novel estimators,   also confirmed by simulation studies. Then, we discuss how to improve efficiency, both theoretically by computing the expected amount of variance reduction, and practically by showing the performance of different working regression models that are needed in the augmentation, when they are correctly specified or misspecified. The methods are applied to the   LEADER study, a randomized controlled trial that studied cardiovascular safety of     treatments in type 2 diabetes patients.

Meta-analysis of randomized controlled trials is commonly used to evaluate treatments and inform policy decisions because it provides comprehensive summaries of all available evidence. However, meta-analyses are limited to draw population inference of treatment effects because they usually do not define target populations of interest specifically, and results of the individual randomized controlled trials in those meta-analyses may not generalize to the target populations. To leverage evidence from multiple randomized controlled trials in the generalizability context, we bridge the ideas from meta-analysis and causal inference. We integrate meta-analysis with causal inference approaches estimating target population average treatment effect. We evaluate the performance of the methods via simulation studies and apply the methods to generalize meta-analysis results from randomized controlled trials of treatments on schizophrenia to adults with schizophrenia who present to usual care settings in the United States. Our simulation results show that all methods perform comparably and well across different settings. The data analysis results show that the treatment effect in the target population is meaningful, although the effect size is smaller than the sample average treatment effect. We recommend applying multiple methods and comparing the results to ensure robustness, rather than relying on a single method.

The proportional hazards (PH) assumption is often violated in clinical trials. If the most commonly used Log-rank test is used for trial design in non-proportional hazard (NPH) cases, it will result in power loss or inflation, and the effect measures hazard ratio will become difficult to interpret. To circumvent the issue caused by the NPH for trial design and to make the effect measures easy to interpret and communicate, two simulation-free methods about restricted mean survival time group sequential (GS-RMST) design are introduced in this study: the independent increment GS-RMST (GS-RMSTi) design and the non-independent increment GS-RMST (GS-RMSTn) design. For the above two designs, the corresponding analytic expression of the variance-covariance matrix, the calculations of the stopping boundaries and sample size are given in the study. Simulation studies show that both designs can achieve the corresponding nominal type I error and nominal power. The GS-RMSTn simulation studies show that the Max-Combo test group sequential design is robust in different NPH scenarios and is suitable for discovering whether there is a treatment effect difference. However, it does not have a corresponding easy-to-interpret effect measure indicating effect difference magnitude. GS-RMST performs well in both PH and NPH scenarios, and it can obtain time-scale effect measures that are easy to understand by both physicians and patients. Examples of both GS-RMST designs are also illustrated.

The study of the predictive ability of a marker is mainly based on the accuracy measures provided by the so-called confusion matrix. Besides, the area under the receiver operating characteristic curve has become a popular index for summarizing the overall accuracy of a marker. However, the nature of the relationship between the marker and the outcome, and the role that potential confounders play in this relationship could be fundamental in order to extrapolate the observed results. Directed acyclic graphs commonly used in epidemiology and in causality, could provide good feedback for learning the possibilities and limits of this extrapolation applied to the binary classification problem. Both the covariate-specific and the covariate-adjusted receiver operating characteristic curves are valuable tools, which can help to a better understanding of the real classification abilities of a marker. Since they are strongly related with the conditional distributions of the marker on the positive (subjects with the studied characteristic) and negative (subjects without the studied characteristic) populations, the use of proportional hazard regression models arises in a very natural way. We explore the use of flexible proportional hazard Cox regression models for estimating the covariate-specific and the covariate-adjusted receiver operating characteristic curves. We study their large- and finite-sample properties and apply the proposed estimators to a real-world problem. The developed code (in R language) is provided on Supplemental Material.

In disease mapping, the relative risk of a disease is commonly estimated across different areas within a region of interest. The number of cases in an area is often assumed to follow a Poisson distribution whose mean is decomposed as the product between an offset and the logarithm of the disease's relative risk. The log risk may be written as the sum of fixed effects and latent random effects. A modified Besag-York-Mollié (BYM2) model decomposes each latent effect into a weighted sum of independent and spatial effects. We build on the BYM2 model to allow for heavy-tailed latent effects and accommodate potentially outlying risks, after accounting for the fixed effects. We assume a scale mixture structure wherein the variance of the latent process changes across areas and allows for outlier identification. We propose two prior specifications for this scale mixture parameter. These are compared through various simulation studies and in the analysis of Zika cases from the first (2015-2016) epidemic in Rio de Janeiro city, Brazil. The simulation studies show that the proposed model always performs at least as well as an alternative available in the literature, and often better, both in terms of widely applicable information criterion, mean squared error and of outlier identification. In particular, the proposed parametrisations are more efficient, in terms of outlier detection, when outliers are neighbours. Our analysis of Zika cases finds 23 out of 160 districts of Rio as potential outliers, after accounting for the socio-development index. Our proposed model may help prioritise interventions and identify potential issues in the recording of cases.

Deviation from the treatment strategy under investigation occurs in many clinical trials. We term this intervention deviation. Per-protocol analyses are widely adopted to estimate a hypothetical estimand without the occurrence of intervention deviation. Per-protocol by censoring is prone to selection bias when intervention deviation is associated with time-varying confounders that also influence counterfactual outcomes. This can be corrected by inverse probability of censoring weighting, which gives extra weight to uncensored individuals who had similar prognostic characteristics to censored individuals. Such weights are computed by modelling selected covariates. Inverse probability of censoring weighting relies on the no unmeasured confounding assumption whose plausibility is not statistically testable. Suboptimal implementation of inverse probability of censoring weighting which violates the assumption will lead to bias. In a simulation study, we evaluated the performance of per-protocol and inverse probability of censoring weighting with different implementations to explore whether inverse probability of censoring weighting is a safe alternative to per-protocol. Scenarios were designed to vary intervention deviation in one or both arms with different prevalences, correlation between two confounders, effect of each confounder, and sample size. Results show that inverse probability of censoring weighting with different combinations of covariates outperforms per-protocol in most scenarios, except for an unusual case where selection bias caused by two confounders is in two directions, and 'cancels' out.

Kernel machine regression is a nonparametric regression method widely applied in biomedical and environmental health research. It employs a kernel function to measure the similarities between sample pairs, effectively identifying significant exposures and assessing their nonlinear impacts on outcomes. This article introduces an enhanced framework, the generalized Bayesian kernel machine regression. In comparison to traditional kernel machine regression, generalized Bayesian kernel machine regression provides substantial flexibility to accommodate a broader array of outcome variables, ranging from continuous to binary and count data. Simulations show generalized Bayesian kernel machine regression can successfully identify the nonlinear relationships between independent variables and outcomes of various types. In the real data analysis, we applied generalized Bayesian kernel machine regression to uncover cytosine phosphate guanine sites linked to health-related conditions such as asthma and smoking. The results identify crucial cytosine phosphate guanine sites and provide insights into their complex, nonlinear relationships with outcome variables.

Bayesian methods are becoming increasingly in demand in clinical and public health comparative effectiveness research. Limited literature has explored parametric Bayesian causal approaches to handle time-dependent treatment and time-dependent covariates. In this article, building on to the work on Bayesian g-computation, we propose a fully Bayesian causal approach, implemented using latent confounder classes which represent the patient's disease and health status. Our setting is suitable when the latent class represents a true disease state that the physician is able to infer without misclassification based on manifest variables. We consider a causal effect that is confounded by the visit-specific latent class in a longitudinal setting and formulate the joint likelihood of the treatment, outcome and latent class models conditionally on the class indicators. The proposed causal structure with latent classes features dimension reduction of time-dependent confounders. We examine the performance of the proposed method using simulation studies and compare the proposed method to other causal methods for longitudinal data with time-dependent treatment and time-dependent confounding. Our approach is illustrated through a study of the effectiveness of intravenous immunoglobulin in treating newly diagnosed juvenile dermatomyositis.

Interactions between genes and environmental factors may play a key role in the etiology of many common disorders. Several regularized generalized linear models have been proposed for hierarchical selection of gene by environment interaction effects, where a gene-environment interaction effect is selected only if the corresponding genetic main effect is also selected in the model. However, none of these methods allow to include random effects to account for population structure, subject relatedness and shared environmental exposure. In this article, we develop a unified approach based on regularized penalized quasi-likelihood estimation to perform hierarchical selection of gene-environment interaction effects in sparse regularized mixed models. We compare the selection and prediction accuracy of our proposed model with existing methods through simulations under the presence of population structure and shared environmental exposure. We show that for all simulation scenarios, including and additional random effect to account for the shared environmental exposure reduces the false positive rate and false discovery rate of our proposed method for selection of both gene-environment interaction and main effects. Using the score as a balanced measure of the false discovery rate and true positive rate, we further show that in the hierarchical simulation scenarios, our method outperforms other methods for retrieving important gene-environment interaction effects. Finally, we apply our method to a real data application using the Orofacial Pain: Prospective Evaluation and Risk Assessment (OPPERA) study, and found that our method retrieves previously reported significant loci.

Instrumental variables (IVs) methods have recently gained popularity since, under certain assumptions, they may yield consistent causal effect estimators in the presence of unmeasured confounding. Existing simulation studies that evaluate the performance of IV approaches for time-to-event outcomes tend to consider either an additive or a multiplicative data-generating mechanism (DGM) and have been limited to an exponential constant baseline hazard model. In particular, the relative merits of additive versus multiplicative IV models have not been fully explored. All IV methods produce less biased estimators than naïve estimators that ignore unmeasured confounding, unless the IV is very weak and there is very little unmeasured confounding. However, the mean squared error of IV estimators may be higher than that of the naïve, biased but more stable estimators, especially when the IV is weak, the sample size is small to moderate, and the unmeasured confounding is strong. In addition, the sensitivity of IV methods to departures from their assumed DGMs differ substantially. Additive IV methods yield clearly biased effect estimators under a multiplicative DGM whereas multiplicative approaches appear less sensitive. All can be extremely variable. We would recommend that survival probabilities should always be reported alongside the relevant hazard contrasts as these can be more reliable and circumvent some of the known issues with causal interpretation of hazard contrasts. In summary, both additive IV and Cox IV methods can perform well in some circumstances but an awareness of their limitations is required in analyses of real data where the true underlying DGM is unknown.

The semiparametric accelerated failure time mixture cure model is an appealing alternative to the proportional hazards mixture cure model in analyzing failure time data with long-term survivors. However, this model was only proposed for independent survival data and it has not been extended to clustered or correlated survival data, partly due to the complexity of the estimation method for the model. In this paper, we consider a marginal semiparametric accelerated failure time mixture cure model for clustered right-censored failure time data with a potential cure fraction. We overcome the complexity of the existing semiparametric method by proposing a generalized estimating equations approach based on the expectation-maximization algorithm to estimate the regression parameters in the model. The correlation structures within clusters are modeled by working correlation matrices in the proposed generalized estimating equations. The large sample properties of the regression estimators are established. Numerical studies demonstrate that the proposed estimation method is easy to use and robust to the misspecification of working matrices and that higher efficiency is achieved when the working correlation structure is closer to the true correlation structure. We apply the proposed model and estimation method to a contralateral breast cancer study and reveal new insights when the potential correlation between patients is taken into account.

Longitudinal data are frequently encountered in medical research, where participants are followed throughout time. Additional structure and hence complexity occurs when there is pairing between the participants (e.g. matched case-control studies) or within the participants (e.g. analysis of participants' both eyes). Various modelling approaches, identified through a systematic review, are discussed, including (un)paired -tests, multivariate analysis of variance, difference scores, linear mixed models (LMMs), and new or more recent statistical methods. Next, highlighting the importance of selecting appropriate models based on the data's characteristics, the methods are applied to both a real-life case study in ophthalmology and a simulated case-control study. Key findings include the superiority of the conditional LMM and multilevel models in handling paired longitudinal data in terms of precision. Moreover, the article underscores the impact of accounting for intra-pair correlations and missing data mechanisms. Focus will be on discussing the advantages and disadvantages of the approaches, rather than on the mathematical or computational details.

We investigate the optimal allocation design for response adaptive clinical trials, under the average reward criterion. The treatment randomization process is formatted as a Markov decision process and the Bayesian method is used to summarize the information on treatment effects. A span-contraction operator is introduced and the average reward generated by the policy identified by the operator is shown to converge to the optimal value. We propose an algorithm to approximate the optimal treatment allocation using the Thompson sampling and the contraction operator. For the scenario of two treatments with binary responses and a sample size of 200 patients, simulation results demonstrate efficient learning features of the proposed method. It allocates a high proportion of patients to the better treatment while retaining a good statistical power and having a small probability for a trial going in the undesired direction. When the difference in success probability to detect is 0.2, the probability for a trial going in the unfavorable direction is < 1.5%, which decreases further to < 0.9% when the difference to detect is 0.3. For normally distribution responses, with a sample size of 100 patients, the proposed method assigns 13% more patients to the better treatment than the traditional complete randomization in detecting an effect size of difference 0.8, with a good statistical power and a < 0.7% probability for the trial to go in the undesired direction.

Youden index, a linear function of sensitivity and specificity, provides a direct measurement of the highest diagnostic accuracy achievable by a biomarker. It is maximized at the cut-off point that optimizes the biomarker's overall classification rate while assigning equal weight to sensitivity and specificity. In this paper, we consider the problem of estimating the Youden index when only group-tested data are available. The unavailability of individual disease statuses poses a challenge, especially when there is differential false positives and negatives in disease screening. We propose both parametric and nonparametric procedures for estimation of the Youden index, and exemplify our methods by utilizing data from the National Health and Nutrition Examination Survey (NHANES) to evaluate the diagnostic ability of monocyte for predicting chlamydia.

When using the propensity score method to estimate the treatment effects, it is important to select the covariates to be included in the propensity score model. The inclusion of covariates unrelated to the outcome in the propensity score model led to bias and large variance in the estimator of treatment effects. Many data-driven covariate selection methods have been proposed for selecting covariates related to outcomes. However, most of them assume an average treatment effect estimation and may not be designed to estimate quantile treatment effects (QTEs), which are the effects of treatment on the quantiles of outcome distribution. In QTE estimation, we consider two relation types with the outcome as the expected value and quantile point. To achieve this, we propose a data-driven covariate selection method for propensity score models that allows for the selection of covariates related to the expected value and quantile of the outcome for QTE estimation. Assuming the quantile regression model as an outcome regression model, covariate selection was performed using a regularization method with the partial regression coefficients of the quantile regression model as weights. The proposed method was applied to artificial data and a dataset of mothers and children born in King County, Washington, to compare the performance of existing methods and QTE estimators. As a result, the proposed method performs well in the presence of covariates related to both the expected value and quantile of the outcome.

In clinical trials, we often encounter observations from patients' paired organs. In paired correlated data, there exist various measures to evaluate the therapeutic responses, such as risk difference, relative risk ratio, and odds ratio. These measures are essentially some forms of response rate functions. Based on this point, this article aims to test the equality of response rate functions such that the homogeneity tests of the above measures are special cases. Under an interclass correlation model, the global and constrained maximum likelihood estimations are obtained through algorithms. Furthermore, we construct likelihood ratio, score, and Wald-type statistics and provide the explicit expressions of the corresponding tests based on the risk difference, relative risk ratio, and odds ratio. Monte Carlo simulations are conducted to compare the performance of the proposed methods in terms of the empirical type I error rates and powers. The results show that the score tests perform satisfactorily as their type I error rates are close to the specified nominal level, followed by the likelihood ratio test. The Wald-type tests exhibit poor performance, especially for small sample sizes. A real example is given to illustrate the three proposed test statistics.

This study introduces a novel joint modeling framework integrating quantile regression for longitudinal continuous proportions data with Cox regression for time-to-event analysis, employing integrated nested Laplace approximation for Bayesian inference. Our approach facilitates an examination across the entire distribution of patient health metrics over time, including the occurrence of key health events and their impact on patient outcomes, particularly in the context of medication adherence and persistence. Integrated nested Laplace approximation's fast computational speed significantly enhances the efficiency of this process, making the model particularly suitable for applications requiring rapid data analysis and updates. Applying this model to a dataset of patients who underwent treatment with atorvastatin, we demonstrate the significant impact of targeted interventions on improving medication adherence and persistence across various patient subgroups. Furthermore, we have developed a dynamic prediction method within this framework that rapidly estimates persistence probabilities based on the latest medication adherence data, demonstrating integrated nested Laplace approximation's quick updates and prediction capability. The simulation study validates the reliability of our modeling approach, evidenced by minimal bias and appropriate credible interval coverage probabilities across different quantile levels.