In epidemiological studies, evaluating the health impacts stemming from multiple exposures is one of the important goals. To analyze the effects of multiple exposures on discrete or time-to-event health outcomes, researchers often employ generalized linear models, Cox proportional hazards models, and machine learning methods. However, observational studies are prone to unmeasured confounding factors, which can introduce the potential for substantial bias in the multiple exposure effects. To address this issue, we propose a novel outcome model-based sensitivity analysis method for non-Gaussian and time-to-event outcomes with multiple exposures. All the proposed sensitivity analysis problems are formulated as linear programming problems with quadratic and linear constraints, which can be solved efficiently. Analytic solutions are provided for some optimization problems, and a numerical study is performed to examine how the proposed sensitivity analysis behaves in finite samples. We illustrate the proposed method using two real data examples.

Accelerated failure time models are appealing due to their intuitive interpretation. However, when covariates are subject to measurement errors, naive estimation becomes severely biased. To address this issue, the regression calibration (RC) approach is a widely applicable and effective method. Traditionally, the RC method requires a good predictor for the true covariate, which can be obtained through parametric distribution assumptions or validation datasets. Consequently, the performance of the estimator depends on the plausibility of these assumptions. In this work, we propose a novel method that utilizes error augmentation to duplicate covariates, facilitating nonparametric estimation. Our approach does not require a validation set or parametric distribution assumptions for the true covariate. Through simulation studies, we demonstrate that our approach is more robust and less impacted by heavy censoring rates compared to conventional analyses. Additionally, an analysis of a subset of a real dataset suggests that the conventional RC method may have a tendency to overcorrect the attenuation effect of measurement error.

Clinical decisions are often guided by clinical prediction models or diagnostic tests. Decision curve analysis (DCA) combines classical assessment of predictive performance with the consequences of using these strategies for clinical decision-making. In DCA, the best decision strategy is the one that maximizes the net benefit: the net number of true positives (or negatives) provided by a given strategy. Here, we employ Bayesian approaches to DCA, addressing four fundamental concerns when evaluating clinical decision strategies: (i) which strategies are clinically useful, (ii) what is the best available decision strategy, (iii) which of two competing strategies is better, and (iv) what is the expected net benefit loss associated with the current level of uncertainty. While often consistent with frequentist point estimates, fully Bayesian DCA allows for an intuitive probabilistic interpretation framework and the incorporation of prior evidence. We evaluate the methods using simulation and provide a comprehensive case study. Software implementation is available in the bayesDCA R package. Ultimately, the Bayesian DCA workflow may help clinicians and health policymakers adopt better-informed decisions.

Independent censoring is usually assumed in survival data analysis. However, dependent censoring, where the survival time is dependent on the censoring time, is often seen in real data applications. In this project, we model the vector of survival time and censoring time marginally through semiparametric heteroscedastic accelerated failure time models and model their association by the vector of errors in the model. We show that this semiparametric model is identified, and the generalized estimating equation approach is extended to estimate the parameters in this model. It is shown that the estimators of the model parameters are consistent and asymptotically normal. Simulation studies are conducted to compare it with the estimation method under a parametric model. A real dataset from a prostate cancer study is used for illustration of the new proposed method.

Using informative sources to enhance statistical analysis in target studies has become an increasingly popular research topic. However, cohorts with time-to-event outcomes have not received sufficient attention, and external studies often encounter issues of incomparability due to population heterogeneity and unmeasured risk factors. To improve individualized risk assessments, we propose a novel methodology that adaptively borrows information from multiple incomparable sources. By extracting aggregate statistics through transitional models applied to both the external sources and the target population, we incorporate this information efficiently using the control variate technique. This approach eliminates the need to load individual-level records from sources directly, resulting in low computational complexity and strong privacy protection. Asymptotically, our estimators of both relative and baseline risks are more efficient than traditional results, and the power of covariate effects testing is much enhanced. We demonstrate the practical performance of our method via extensive simulations and a real case study.

In studying the association between clinical measurements and time-to-event outcomes within a cure model, utilizing repeated observations rather than solely baseline values may lead to more accurate estimation. However, there are two main challenges in this context. First, longitudinal measurements are usually observed at discrete time points and second, for diseases that respond well to treatment, a high censoring proportion may occur by the end of the trial. In this article, we propose a joint modelling approach to simultaneously study the longitudinal observations and time-to-event outcome with an assumed cure fraction. We employ the functional principal components analysis (FPCA) to model the longitudinal data, offering flexibility by not assuming a specific form for the longitudinal curve. We used a Cox's proportional hazards mixture cure model to study the survival outcome. To investigate the longitudinal binary observations, we adopt a quasi-likelihood method which builds pseudo normal distribution for the binary data and use the E-M algorithm to estimate the parameters. The tuning parameters are selected using the Akaike information criterion. Our proposed method is evaluated through extensive simulation studies and applied to a clinical trial data to study the relationship between the longitudinal prostate specific antigen (PSA) measurements and overall survival in men with metastatic prostate cancer.

Missing data arise in most applied settings and are ubiquitous in electronic health records (EHR). When data are missing not at random (MNAR) with respect to measured covariates, sensitivity analyses are often considered. These solutions, however, are often unsatisfying in that they are not guaranteed to yield actionable conclusions. Motivated by an EHR-based study of long-term outcomes following bariatric surgery, we consider the use of double sampling as a means to mitigate MNAR outcome data when the statistical goals are estimation and inference regarding causal effects. We describe assumptions that are sufficient for the identification of the joint distribution of confounders, treatment, and outcome under this design. Additionally, we derive efficient and robust estimators of the average causal treatment effect under a nonparametric model and under a model assuming outcomes were, in fact, initially missing at random (MAR). We compare these in simulations to an approach that adaptively estimates based on evidence of violation of the MAR assumption. Finally, we also show that the proposed double sampling design can be extended to handle arbitrary coarsening mechanisms, and derive nonparametric efficient estimators of any smooth full data functional.

Hazard models are the most commonly used tool to analyze time-to-event data. If more than one time scale is relevant for the event under study, models are required that can incorporate the dependence of a hazard along two (or more) time scales. Such models should be flexible to capture the joint influence of several time scales, and nonparametric smoothing techniques are obvious candidates. -splines offer a flexible way to specify such hazard surfaces, and estimation is achieved by maximizing a penalized Poisson likelihood. Standard observation schemes, such as right-censoring and left-truncation, can be accommodated in a straightforward manner. Proportional hazards regression with a baseline hazard varying over two time scales is presented. Efficient computation is possible by generalized linear array model (GLAM) algorithms or by exploiting a sparse mixed model formulation. A companion R-package is provided.

With an increasing focus on precision medicine in medical research, numerous studies have been conducted in recent years to clarify the relationship between treatment effects and patient characteristics. The treatment effects for patients with different characteristics are always heterogeneous, and therefore, various heterogeneous treatment effect machine learning estimation methods have been proposed owing to their flexibility and high estimation accuracy. However, most machine learning methods rely on black-box models, preventing direct interpretation of the relationship between patient characteristics and treatment effects. Moreover, most of these studies have focused on continuous or binary outcomes, although survival outcomes are also important in medical research. To address these challenges, we propose a heterogeneous treatment effect estimation method for survival data based on RuleFit, an interpretable machine learning method. Numerical simulation results confirmed that the prediction performance of the proposed method was comparable to that of existing methods. We also applied a dataset from an HIV study, the AIDS Clinical Trials Group Protocol 175 dataset, to illustrate the interpretability of the proposed method using real data. Consequently, the proposed survival causal rule ensemble method provides an interpretable model with sufficient estimation accuracy.

In clinical trials, subjects are usually recruited sequentially. According to the outcomes amassed thus far in a trial, the response-adaptive randomization (RAR) design has been shown to be an advantageous treatment assignment procedure that skews the treatment allocation proportion to pre-specified objectives, such as sending more patients to a more promising treatment. Unfortunately, there are circumstances under which very few data of the primary endpoints are collected in the recruitment period, such as circumstances relating to public health emergencies and chronic diseases, and RAR is thus difficult to apply in allocating treatments using available outcomes. To overcome this problem, if an informative surrogate endpoint can be acquired much earlier than the primary endpoint, the surrogate endpoint can be used as a substitute for the primary endpoint in the RAR procedure. In this paper, we propose an RAR procedure that relies only on surrogate endpoints. The validity of the statistical inference on the primary endpoint and the patient benefit of this approach are justified by both theory and simulation. Furthermore, different types of surrogate endpoint and primary endpoint are considered. The results reassure that RAR with surrogate endpoints can be a viable option in some cases for clinical trials when primary endpoints are unavailable for adaptation.

To assess the preliminary therapeutic impact of a novel treatment, futility monitoring is commonly employed in Phase II clinical trials to facilitate informed decisions regarding the early termination of trials. Given the rapid evolution in cancer treatment development, particularly with new agents like immunotherapeutic agents, the focus has often shifted from objective response to time-to-event endpoints. In trials involving multiple time-to-event endpoints, existing monitoring designs typically select one as the primary endpoint or employ a composite endpoint as the time to the first occurrence of any event. However, relying on a single efficacy endpoint may not adequately evaluate an experimental treatment. Additionally, the time-to-first-event endpoint treats all events equally, ignoring their differences in clinical priorities. To tackle these issues, we propose a Bayesian futility monitoring design for a two-arm randomized Phase II trial, which incorporates the win ratio approach to account for the clinical priority of multiple time-to-event endpoints. A joint lognormal distribution was assumed to model the time-to-event variables for the estimation. We conducted simulation studies to assess the operating characteristics of the proposed monitoring design and compared them to those of conventional methods. The proposed design allows for early termination for futility if the endpoint with higher clinical priority (e.g., death) deteriorates in the treatment arm, compared to the time-to-first-event approach. Meanwhile, it prevents an aggressive early termination if the endpoint with lower clinical priority (e.g., cancer recurrence) shows deterioration in the treatment arm, offering a more tailored approach to decision-making in clinical trials with multiple time-to-event endpoints.

Measurement burst designs typically administer brief cognitive tests four times per day for 1 week, resulting in a maximum of 28 data points per week per test for every 6 months. In Alzheimer's disease clinical trials, utilizing measurement burst designs holds great promise for boosting statistical power by collecting huge amount of data. However, appropriate methods for analyzing these complex datasets are not well investigated. Furthermore, the large amount of burst design data also poses tremendous challenges for traditional computational procedures such as SAS mixed or Nlmixed. We propose to analyze burst design data using novel hierarchical linear mixed effects models or hierarchical mixed models for repeated measures. Through simulations and real-world data applications using the novel SAS procedure Hpmixed, we demonstrate these hierarchical models' efficiency over traditional models. Our sample simulation and analysis code can serve as a catalyst to facilitate the methodology development for burst design data.

The instrumental variable method is widely used in causal inference research to improve the accuracy of estimating causal effects. However, the weak correlation between instruments and exposure, as well as the direct impact of instruments on the outcome, can lead to biased estimates. To mitigate the bias introduced by such instruments in nonlinear causal inference, we propose a two-stage nonlinear causal effect estimation based on model averaging. The model uses different subsets of instruments in the first stage to predict exposure after a nonlinear transformation with the help of sliced inverse regression. In the second stage, adaptive Lasso penalty is applied to instruments to obtain the estimation of causal effect. We prove that the proposed estimator exhibits favorable asymptotic properties and evaluate its performance through a series of numerical studies, demonstrating its effectiveness in identifying nonlinear causal effects and its capability to handle scenarios with weak and invalid instruments. We apply the proposed method to the Atherosclerosis Risk in Communities dataset to investigate the relationship between BMI and hypertension.

The study of precision medicine involves dynamic treatment regimes (DTRs), which are sequences of treatment decision rules recommended based on patient-level information. The primary goal of the DTR study is to identify an optimal DTR, a sequence of treatment decision rules that optimizes the clinical outcome across multiple decision points. Statistical methods have been developed in recent years to estimate an optimal DTR, including Q-learning, a regression-based method in the DTR literature. Although there are many studies concerning Q-learning, little attention has been paid in the presence of noisy data, such as misclassified outcomes. In this article, we investigate the effect of outcome misclassification on identifying optimal DTRs using Q-learning and propose a correction method to accommodate the misclassification effect on DTR. Simulation studies are conducted to demonstrate the satisfactory performance of the proposed method. We illustrate the proposed method using two examples from the National Health and Nutrition Examination Survey Data I Epidemiologic Follow-up Study and the Population Assessment of Tobacco and Health Study.

The positive predictive value (PPV) and negative predictive value (NPV) can be expressed as functions of disease prevalence ( ) and the ratios of two binomial proportions ( ), where and . In prospective studies, where the proportion of subjects with the disease in the study cohort is an unbiased estimate of the disease prevalence, the confidence intervals (CIs) of PPV and NPV can be estimated using established methods for single proportion. However, in enrichment studies, such as case-control studies, where the proportion of diseased subjects significantly differs from disease prevalence, estimating CIs for PPV and NPV remains a challenge in terms of skewness and overall coverage, especially under extreme conditions (e.g., ). In this article, we extend the method adopted by Li, where CIs for PPV and NPV were derived from those of . We explored additional CI methods for , including those by Gart & Nam (GN), MoverJ, and Walter and convert their corresponding CIs for PPV and NPV. Through simulations, we compared these methods with established CI methods, Fieller, Pepe, and Delta in terms of skewness and overall coverage. While no method proves universally optimal, GN and MoverJ methods generally emerge as recommended choices.

We propose a novel regression tree method named "TreeFuL," an abbreviation for 'Tree with Fused Leaves.' TreeFuL innovatively combines recursive partitioning with fused regularization, offering a distinct approach to the conventional pruning method. One of TreeFuL's noteworthy advantages is its capacity for cross-validated amalgamation of non-neighboring terminal nodes. This is facilitated by a leaf coloring scheme that supports tree shearing and node amalgamation. As a result, TreeFuL facilitates the development of more parsimonious tree models without compromising predictive accuracy. The refined model offers enhanced interpretability, making it particularly well-suited for biomedical applications of decision trees, such as disease diagnosis and prognosis. We demonstrate the practical advantages of our proposed method through simulation studies and an analysis of data collected in an obesity study.

Identifying interventions that are optimally tailored to each individual is of significant interest in various fields, in particular precision medicine. Dynamic treatment regimes (DTRs) employ sequences of decision rules that utilize individual patient information to recommend treatments. However, the assumption that an individual's treatment does not impact the outcomes of others, known as the no interference assumption, is often challenged in practical settings. For example, in infectious disease studies, the vaccine status of individuals in close proximity can influence the likelihood of infection. Imposing this assumption when it, in fact, does not hold, may lead to biased results and impact the validity of the resulting DTR optimization. We extend the estimation method of dynamic weighted ordinary least squares (dWOLS), a doubly robust and easily implemented approach for estimating optimal DTRs, to incorporate the presence of interference within dyads (i.e., pairs of individuals). We formalize an appropriate outcome model and describe the estimation of an optimal decision rule in the dyadic-network context. Through comprehensive simulations and analysis of the Population Assessment of Tobacco and Health (PATH) data, we demonstrate the improved performance of the proposed joint optimization strategy compared to the current state-of-the-art conditional optimization methods in estimating the optimal treatment assignments when within-dyad interference exists.

Proportional rate models are among the most popular methods for analyzing recurrent event data. Although providing a straightforward rate-ratio interpretation of covariate effects, the proportional rate assumption implies that covariates do not modify the shape of the rate function. When the proportionality assumption fails to hold, we propose to characterize covariate effects on the rate function through two types of parameters: the shape parameters and the size parameters. The former allows the covariates to flexibly affect the shape of the rate function, and the latter retains the interpretability of covariate effects on the magnitude of the rate function. To overcome the challenges in simultaneously estimating the two sets of parameters, we propose a conditional pseudolikelihood approach to eliminate the size parameters in shape estimation, followed by an event count projection approach for size estimation. The proposed estimators are asymptotically normal with a root- convergence rate. Simulation studies and an analysis of recurrent hospitalizations using SEER-Medicare data are conducted to illustrate the proposed methods.

One goal of precision medicine is to develop effective treatments for patients by tailoring to their individual demographic, clinical, and/or genetic characteristics. To achieve this goal, statistical models must be developed that can identify and evaluate potentially heterogeneous treatment effects in a robust manner. The oft-cited existing methods for assessing treatment effect heterogeneity are based upon parametric models with interactions or conditioning on covariate values, the performance of which is sensitive to the omission of important covariates and/or the choice of their values. We propose a new Bayesian nonparametric (BNP) method for estimating heterogeneous causal effects in studies with zero-inflated outcome data, which arise commonly in health-related studies. We employ the enriched Dirichlet process (EDP) mixture in our BNP approach, establishing a connection between an outcome DP mixture and a covariate DP mixture. This enables us to estimate posterior distributions concurrently, facilitating flexible inference regarding individual causal effects. We show in a set of simulation studies that the proposed method outperforms two other BNP methods in terms of bias and mean squared error (MSE) of the conditional average treatment effect estimates. In particular, the proposed model has the advantage of appropriately reflecting uncertainty in regions where the overlap condition is violated compared to other competing models. We apply the proposed method to a study of the relationship between heart radiation dose parameters and the blood level of high-sensitivity cardiac troponin T (hs-cTnT) to examine if the effect of a high mean heart radiation dose on hs-cTnT varies by baseline characteristics.

Probability surveys are challenged by increasing nonresponse rates, resulting in biased statistical inference. Auxiliary information about populations can be used to reduce bias in estimation. Often continuous auxiliary variables in administrative records are first discretized before releasing to the public to avoid confidentiality breaches. This may weaken the utility of the administrative records in improving survey estimates, particularly when there is a strong relationship between continuous auxiliary information and the survey outcome. In this paper, we propose a two-step strategy, where the confidential continuous auxiliary data in the population are first utilized to estimate the response propensity score of the survey sample by statistical agencies, which is then included in a modified population data for data users. In the second step, data users who do not have access to confidential continuous auxiliary data conduct predictive survey inference by including discretized continuous variables and the propensity score as predictors using splines in a Bayesian model. We show by simulation that the proposed method performs well, yielding more efficient estimates of population means with 95% credible intervals providing better coverage than alternative approaches. We illustrate the proposed method using the Ohio Army National Guard Mental Health Initiative (OHARNG-MHI). The methods developed in this work are readily available in the R package AuxSurvey.

Multicancer detection (MCD) tests use blood specimens to detect preclinical cancers. A major concern is overdiagnosis, the detection of preclinical cancer on screening that would not have developed into symptomatic cancer in the absence of screening. Because overdiagnosis can lead to unnecessary and harmful treatments, its quantification is important. A key metric is the screen overdiagnosis fraction (SOF), the probability of overdiagnosis at screen detection. Estimating SOF is notoriously difficult because overdiagnosis is not observed. This estimation is more challenging with MCD tests because short-term results are needed as the technology is rapidly changing. To estimate average SOF for a program of yearly MCD tests, I introduce a novel method that requires at least two yearly MCD tests given to persons having a wide range of ages and applies only to cancers for which there is no conventional screening. The method assumes an exponential distribution for the sojourn time in an operational screen-detectable preclinical cancer (OPC) state, defined as once screen-detectable (positive screen and work-up), always screen-detectable. Because this assumption appears in only one term in the SOF formula, the results are robust to violations of the assumption. An SOF plot graphs average SOF versus mean sojourn time. With lung cancer screening data and synthetic data, SOF plots distinguished small from moderate levels of SOF. With its unique set of assumptions, the SOF plot would complement other modeling approaches for estimating SOF once sufficient short-term observational data on MCD tests become available.