Effectiveness of Vaccines and Antiviral Drugs in Preventing Severe and Fatal COVID-19, Hong Kong.

We compared the effectiveness and interactions of molnupiravir and nirmatrelvir/ritonavir and 2 vaccines, CoronaVac and Comirnaty, in a large population of inpatients with COVID-19 in Hong Kong. Both the oral antiviral drugs and vaccines were associated with lower risks for all-cause mortality and progression to serious/critical/fatal conditions (study outcomes). No significant interaction effects were observed between the antiviral drugs and vaccinations; their joint effects were additive. If antiviral drugs were prescribed within 5 days of confirmed COVID-19 diagnosis, usage was associated with lower risks for the target outcomes for patients >60, but not <60, years of age; no significant clinical benefit was found if prescribed beyond 5 days. Among patients >80 years of age, 3-4 doses of Comirnaty vaccine were associated with significantly lower risks for target outcomes. Policies should encourage COVID-19 vaccination, and oral antivirals should be made accessible to infected persons within 5 days of confirmed diagnosis.

Bayesian adaptive model selection design for optimal biological dose finding in phase I/II clinical trials.

Identification of the optimal dose presents a major challenge in drug development with molecularly targeted agents, immunotherapy, as well as chimeric antigen receptor T-cell treatments. By casting dose finding as a Bayesian model selection problem, we propose an adaptive design by simultaneously incorporating the toxicity and efficacy outcomes to select the optimal biological dose (OBD) in phase I/II clinical trials. Without imposing any parametric assumption or shape constraint on the underlying dose-response curves, we specify curve-free models for both the toxicity and efficacy endpoints to determine the OBD. By integrating the observed data across all dose levels, the proposed design is coherent in dose assignment and thus greatly enhances efficiency and accuracy in pinning down the right dose. Not only does our design possess a completely new yet flexible dose-finding framework, but it also has satisfactory and robust performance as demonstrated by extensive simulation studies. In addition, we show that our design enjoys desirable coherence properties, while most of existing phase I/II designs do not. We further extend the design to accommodate late-onset outcomes which are common in immunotherapy. The proposed design is exemplified with a phase I/II clinical trial in chronic lymphocytic leukemia.

The GR2D2 estimator for the precision matrices.

Biological networks are important for the analysis of human diseases, which summarize the regulatory interactions and other relationships between different molecules. Understanding and constructing networks for molecules, such as DNA, RNA and proteins, can help elucidate the mechanisms of complex biological systems. The Gaussian Graphical Models (GGMs) are popular tools for the estimation of biological networks. Nonetheless, reconstructing GGMs from high-dimensional datasets is still challenging. The current methods cannot handle the sparsity and high-dimensionality issues arising from datasets very well. Here, we developed a new GGM, called the GR2D2 (Graphical $R^2$-induced Dirichlet Decomposition) model, based on the R2D2 priors for linear models. Besides, we provided a data-augmented block Gibbs sampler algorithm. The R code is available at https://github.com/RavenGan/GR2D2. The GR2D2 estimator shows superior performance in estimating the precision matrices compared with the existing techniques in various simulation settings. When the true precision matrix is sparse and of high dimension, the GR2D2 provides the estimates with smallest information divergence from the underlying truth. We also compare the GR2D2 estimator with the graphical horseshoe estimator in five cancer RNA-seq gene expression datasets grouped by three cancer types. Our results show that GR2D2 successfully identifies common cancer pathways and cancer-specific pathways for each dataset.

Unit information Dirichlet process prior.

Prior distributions, which represent one's belief in the distributions of unknown parameters before observing the data, impact Bayesian inference in a critical and fundamental way. With the ability to incorporate external information from expert opinions or historical datasets, the priors, if specified appropriately, can improve the statistical efficiency of Bayesian inference. In survival analysis, based on the concept of unit information (UI) under parametric models, we propose the unit information Dirichlet process (UIDP) as a new class of nonparametric priors for the underlying distribution of time-to-event data. By deriving the Fisher information in terms of the differential of the cumulative hazard function, the UIDP prior is formulated to match its prior UI with the weighted average of UI in historical datasets and thus can utilize both parametric and nonparametric information provided by historical datasets. With a Markov chain Monte Carlo algorithm, simulations and real data analysis demonstrate that the UIDP prior can adaptively borrow historical information and improve statistical efficiency in survival analysis.

Fractional accumulative calibration-free odds (f-aCFO) design for delayed toxicity in phase I clinical trials.

The calibration-free odds (CFO) design has been demonstrated to be robust, model-free, and practically useful but faces challenges when dealing with late-onset toxicity. The emergence of the time-to-event (TITE) method and fractional method leads to the development of TITE-CFO and fractional CFO (fCFO) designs to accumulate delayed toxicity. Nevertheless, existing CFO-type designs have untapped potential because they primarily consider dose information from the current position and its two neighboring positions. To incorporate information from all doses, we propose the accumulative CFO (aCFO) design by utilizing data at all dose levels similar to a tug-of-war game where players distant from the center also contribute their strength. This approach enhances full information utilization while still preserving the model-free and calibration-free characteristics. Extensive simulation studies demonstrate performance improvement over the original CFO design, emphasizing the advantages of incorporating information from a broader range of dose levels. Furthermore, we propose to incorporate late-onset outcomes into the TITE-aCFO and f-aCFO designs, with f-aCFO displaying superior performance over existing methods in both fixed and random simulation scenarios. In conclusion, the aCFO and f-aCFO designs can be considered robust, efficient, and user-friendly approaches for conducting phase I trials without or with late-onsite toxicity.

Bayesian nonparametric analysis of restricted mean survival time.

The restricted mean survival time (RMST) evaluates the expectation of survival time truncated by a prespecified time point, because the mean survival time in the presence of censoring is typically not estimable. The frequentist inference procedure for RMST has been widely advocated for comparison of two survival curves, while research from the Bayesian perspective is rather limited. For the RMST of both right- and interval-censored data, we propose Bayesian nonparametric estimation and inference procedures. By assigning a mixture of Dirichlet processes (MDP) prior to the distribution function, we can estimate the posterior distribution of RMST. We also explore another Bayesian nonparametric approach using the Dirichlet process mixture model and make comparisons with the frequentist nonparametric method. Simulation studies demonstrate that the Bayesian nonparametric RMST under diffuse MDP priors leads to robust estimation and under informative priors it can incorporate prior knowledge into the nonparametric estimator. Analysis of real trial examples demonstrates the flexibility and interpretability of the Bayesian nonparametric RMST for both right- and interval-censored data.

Quasi-rerandomization for observational studies.

BACKGROUND: In the causal analysis of observational studies, covariates should be carefully balanced to approximate a randomized experiment. Numerous covariate balancing methods have been proposed for this purpose. However, it is often unclear what type of randomized experiments the balancing approaches aim to approximate; and this may cause ambiguity and hamper the synthesis of balancing characteristics within randomized experiments. METHODS: Randomized experiments based on rerandomization, known for significant improvement on covariate balance, have recently gained attention in the literature, but no attempt has been made to integrate this scheme into observational studies for improving covariate balance. Motivated by the above concerns, we propose quasi-rerandomization, a novel reweighting method, where observational covariates are rerandomized to be the anchor for reweighting such that the balanced covariates obtained from rerandomization can be reconstructed by the weighted data. RESULTS: Through extensive numerical studies, not only does our approach demonstrate similar covariate balance and comparable estimation precision of treatment effect to rerandomization in many situations, but it also exhibits advantages over other balancing techniques in inferring the treatment effect. CONCLUSION: Our quasi-rerandomization method can approximate the rerandomized experiments well in terms of improving the covariate balance and the precision of treatment effect estimation. Furthermore, our approach shows competitive performance compared with other weighting and matching methods. The codes for the numerical studies are available at https://github.com/BobZhangHT/QReR .

Time-to-event calibration-free odds design: A robust efficient design for phase I trials with late-onset outcomes.

Compared with most of the existing phase I designs, the recently proposed calibration-free odds (CFO) design has been demonstrated to be robust, model-free, and easy to use in practice. However, the original CFO design cannot handle late-onset toxicities, which have been commonly encountered in phase I oncology dose-finding trials with targeted agents or immunotherapies. To account for late-onset outcomes, we extend the CFO design to its time-to-event (TITE) version, which inherits the calibration-free and model-free properties. One salient feature of CFO-type designs is to adopt game theory by competing three doses at a time, including the current dose and the two neighboring doses, while interval-based designs only use the data at the current dose and is thus less efficient. We conduct comprehensive numerical studies for the TITE-CFO design under both fixed and randomly generated scenarios. TITE-CFO shows robust and efficient performances compared with interval-based and model-based counterparts. As a conclusion, the TITE-CFO design provides robust, efficient, and easy-to-use alternatives for phase I trials when the toxicity outcome is late-onset.

Double bias correction for high-dimensional sparse additive hazards regression with covariate measurement errors.

We propose an inferential procedure for additive hazards regression with high-dimensional survival data, where the covariates are prone to measurement errors. We develop a double bias correction method by first correcting the bias arising from measurement errors in covariates through an estimating function for the regression parameter. By adopting the convex relaxation technique, a regularized estimator for the regression parameter is obtained by elaborately designing a feasible loss based on the estimating function, which is solved via linear programming. Using the Neyman orthogonality, we propose an asymptotically unbiased estimator which further corrects the bias caused by the convex relaxation and regularization. We derive the convergence rate of the proposed estimator and establish the asymptotic normality for the low-dimensional parameter estimator and the linear combination thereof, accompanied with a consistent estimator for the variance. Numerical experiments are carried out on both simulated and real datasets to demonstrate the promising performance of the proposed double bias correction method.

Unit information prior for adaptive information borrowing from multiple historical datasets.

In clinical trials, there often exist multiple historical studies for the same or related treatment investigated in the current trial. Incorporating historical data in the analysis of the current study is of great importance, as it can help to gain more information, improve efficiency, and provide a more comprehensive evaluation of treatment. Enlightened by the unit information prior (UIP) concept in the reference Bayesian test, we propose a new informative prior called UIP from an information perspective that can adaptively borrow information from multiple historical datasets. We consider both binary and continuous data and also extend the new UIP to linear regression settings. Extensive simulation studies demonstrate that our method is comparable to other commonly used informative priors, while the interpretation of UIP is intuitive and its implementation is relatively easy. One distinctive feature of UIP is that its construction only requires summary statistics commonly reported in the literature rather than the patient-level data. By applying our UIP to phase III clinical trials for investigating the efficacy of memantine in Alzheimer's disease, we illustrate its ability to adaptively borrow information from multiple historical datasets. The Python codes for simulation studies and the real data application are available at https://github.com/JINhuaqing/UIP.

Reduction in number to treat versus number needed to treat.

BACKGROUND: We propose a new measure of treatment effect based on the expected reduction in the number of patients to treat (RNT) which is defined as the difference of the reciprocals of clinical measures of interest between two arms. Compared with the conventional number needed to treat (NNT), RNT shows superiority with both binary and time-to-event endpoints in randomized controlled trials (RCTs). METHODS: Five real RCTs, two with binary endpoints and three with survival endpoints, are used to illustrate the concept of RNT and compare the performances between RNT and NNT. For survival endpoints, we propose two versions of RNT: one is based on the survival rate and the other is based on the restricted mean survival time (RMST). Hypothetical scenarios are also constructed to explore the advantages and disadvantages of RNT and NNT. RESULTS: Because there is no baseline for computation of NNT, it fails to differentiate treatment effect in the absolute scale. In contrast, RNT conveys more information than NNT due to its reversed order of differencing and inverting. For survival endpoints, two versions of RNT calculated as the difference of the reciprocals of survival rates and RMSTs are complementary to each other. The RMST-based RNT can capture the entire follow-up profile and thus is clinically more intuitive and meaningful, as it inherits the time-to-event characteristics for survival endpoints instead of using truncated binary endpoints at a specific time point. CONCLUSIONS: The RNT can serve as an alternative measure for quantifying treatment effect in RCTs, which complements NNT to help patients and clinicians better understand the magnitude of treatment benefit.

Dynamic ordering design for dose finding in drug-combination trials.

Drug-combination studies have become increasingly popular in oncology. One of the critical concerns in phase I drug-combination trials is the uncertainty in toxicity evaluation. Most of the existing phase I designs aim to identify the maximum tolerated dose (MTD) by reducing the two-dimensional searching space to one dimension via a prespecified model or splitting the two-dimensional space into multiple one-dimensional subspaces based on the partially known toxicity order. Nevertheless, both strategies often lead to complicated trials which may either be sensitive to model assumptions or induce longer trial durations due to subtrial split. We develop two versions of dynamic ordering design (DOD) for dose finding in drug-combination trials, where the dose-finding problem is cast in the Bayesian model selection framework. The toxicity order of dose combinations is continuously updated via a two-dimensional pool-adjacent-violators algorithm, and then the dose assignment for each incoming cohort is selected based on the optimal model under the dynamic toxicity order. We conduct extensive simulation studies to evaluate the performance of DOD in comparison with four other commonly used designs under various scenarios. Simulation results show that the two versions of DOD possess competitive performances in terms of correct MTD selection as well as safety, and we apply both versions of DOD to two real oncology trials for illustration.

Bayesian enhancement two-stage design with error control for phase II clinical trials.

Phase II clinical trials make a critical decision of go or no-go to a subsequent phase III studies. A considerable proportion of promising drugs identified in phase II trials fail the confirmative efficacy test in phase III. Recognizing the low posterior probabilities of H1 when accepting the drug under Simon's two-stage design, the Bayesian enhancement two-stage (BET) design is proposed to strengthen the passing criterion. Under the BET design, the lengths of highest posterior density (HPD) intervals, posterior probabilities of H0 and H1 are computed to calibrate the design parameters, aiming to improve the stability of the trial characteristics and strengthen the evidence for proceeding the drug development forward. However, from a practical perspective, the HPD interval length lacks transparency and interpretability. To circumvent this problem, we propose the BET design with error control (BETEC) by replacing the HPD interval length with the posterior error rate. The BETEC design can achieve a balance between the posterior false positive rate and false negative rate and, more importantly, it has an intuitive and clear interpretation. We compare our method with the BET design and Simon's design through extensive simulation studies. As an illustration, we further apply BETEC to two recent clinical trials, and investigate its performance in comparison with other competitive designs. Being both efficient and intuitive, the BETEC design can serve as an alternative toolbox for implementing phase II single-arm trials.

Restricted mean survival time for interval-censored data.

Restricted mean survival time (RMST) evaluates the mean event-free survival time up to a prespecified time point. It has been used as an alternative measure of treatment effect owing to its model-free structure and clinically meaningful interpretation of treatment benefit for right-censored data. In clinical trials, another type of censoring called interval censoring may occur if subjects are examined at several discrete time points and the survival time falls into an interval rather than being exactly observed. The missingness of exact observations under interval-censored cases makes the nonparametric measure of treatment effect more challenging. Employing the linear smoothing technique to overcome the ambiguity, we propose a new model-free measure for the interval-censored RMST. As an alternative to the commonly used log-rank test, we further construct a hypothesis testing procedure to assess the survival difference between two groups. Simulation studies show that the bias of our proposed interval-censored RMST estimator is negligible and the testing procedure delivers promising performance in detecting between-group difference with regard to size and power under various configurations of survival curves. The proposed method is illustrated by reanalyzing two real datasets containing interval-censored observations.

START: single-to-double arm transition design for phase II clinical trials.

Phase II clinical trials designed for evaluating a drug's treatment effect can be either single-arm or double-arm. A single-arm design tests the null hypothesis that the response rate of a new drug is lower than a fixed threshold, whereas a double-arm scheme takes a more objective comparison of the response rate between the new treatment and the standard of care through randomization. Although the randomized design is the gold standard for efficacy assessment, various situations may arise where a single-arm pilot study prior to a randomized trial is necessary. To combine the single- and double-arm phases and pool the information together for better decision making, we propose a Single-To-double ARm Transition design (START) with switching hypotheses tests, where the first stage compares the new drug's response rate with a minimum required level and imposes a continuation criterion, and the second stage utilizes randomization to determine the treatment's superiority. We develop a software package in R to calibrate the frequentist error rates and perform simulation studies to assess the trial characteristics. Finally, a metastatic pancreatic cancer trial is used for illustrating the decision rules under the proposed START design.

Nonparametric overdose control with late-onset toxicity in phase I clinical trials.

Under the framework of Bayesian model selection, we propose a nonparametric overdose control (NOC) design for dose finding in phase I clinical trials. Each dose assignment is guided via a feasibility bound, which thereby can control the number of patients allocated to excessively toxic dose levels. Several aspects of the NOC design are explored, including the coherence property in dose assignment, calibration of design parameters, and selection of the maximum tolerated dose (MTD). We further propose a fractional NOC (fNOC) design in conjunction with a so-called fractional imputation approach, to account for late-onset toxicity outcomes. Extensive simulation studies have been conducted to show that both the NOC and fNOC designs have robust and satisfactory finite-sample performance compared with the existing dose-finding designs. The proposed methods also possess several desirable properties: treating patients more safely and also neutralizing the aggressive escalation to overly toxic doses when the toxicity outcomes are late-onset. The fNOC design is exemplified with a real cancer phase I trial.

Bayesian enhancement two-stage design for single-arm phase II clinical trials with binary and time-to-event endpoints.

Simon's two-stage design is one of the most commonly used methods in phase II clinical trials with binary endpoints. The design tests the null hypothesis that the response rate is less than an uninteresting level, versus the alternative hypothesis that the response rate is greater than a desirable target level. From a Bayesian perspective, we compute the posterior probabilities of the null and alternative hypotheses given that a promising result is declared in Simon's design. Our study reveals that because the frequentist hypothesis testing framework places its focus on the null hypothesis, a potentially efficacious treatment identified by rejecting the null under Simon's design could have only less than 10% posterior probability of attaining the desirable target level. Due to the indifference region between the null and alternative, rejecting the null does not necessarily mean that the drug achieves the desirable response level. To clarify such ambiguity, we propose a Bayesian enhancement two-stage (BET) design, which guarantees a high posterior probability of the response rate reaching the target level, while allowing for early termination and sample size saving in case that the drug's response rate is smaller than the clinically uninteresting level. Moreover, the BET design can be naturally adapted to accommodate survival endpoints. We conduct extensive simulation studies to examine the empirical performance of our design and present two trial examples as applications.

Uniformly most powerful Bayesian interval design for phase I dose-finding trials.

Interval designs have recently attracted much attention in phase I clinical trials because of their simplicity and desirable finite-sample performance. However, existing interval designs typically cannot converge to the optimal dose level since their intervals do not shrink to the target toxicity probability as the sample size increases. The uniformly most powerful Bayesian test (UMPBT) is an objective Bayesian hypothesis testing procedure, which results in the largest probability that the Bayes factor against null hypothesis exceeds the evidence threshold for all possible values of the data generating parameter. On the basis of the rejection region of UMPBT, we develop the uniformly most powerful Bayesian interval (UMPBI) design for phase I dose-finding trials. The proposed UMPBI design enjoys convergence properties because the induced interval indeed shrinks to the toxicity target and the recommended dose converges to the true maximum tolerated dose as the sample size increases. Moreover, it possesses an optimality property that the probability of incorrect decisions is minimized. We conduct simulation studies to demonstrate the competitive finite-sample operating characteristics of the UMPBI in comparison with other existing interval designs. As an illustration, we apply the UMPBI design to a panitumumab and standard gemcitabine-based chemoradiation combination trial.

Censored cumulative residual independent screening for ultrahigh-dimensional survival data.

For complete ultrahigh-dimensional data, sure independent screening methods can effectively reduce the dimensionality while retaining all the active variables with high probability. However, limited screening methods have been developed for ultrahigh-dimensional survival data subject to censoring. We propose a censored cumulative residual independent screening method that is model-free and enjoys the sure independent screening property. Active variables tend to be ranked above the inactive ones in terms of their association with the survival times. Compared with several existing methods, our model-free screening method works well with general survival models, and it is invariant to the monotone transformation of the responses, as well as requiring substantially weaker moment conditions. Numerical studies demonstrate the usefulness of the censored cumulative residual independent screening method, and the new approach is illustrated with a gene expression data set.