Unblinded sample size re-estimation (SSR) is often planned in a clinical trial when there is large uncertainty about the true treatment effect. For Proof-of Concept (PoC) in a Phase II dose finding study, contrast test can be adopted to leverage information from all treatment groups. In this article, we propose two-stage SSR designs using frequentist conditional power and Bayesian posterior predictive power for both single and multiple contrast tests. The Bayesian SSR can be implemented under a wide range of prior settings to incorporate different prior knowledge. Taking the adaptivity into account, all type I errors of final analysis in this paper are rigorously protected. Simulation studies are carried out to demonstrate the advantages of unblinded SSR in multi-arm trials.
An important task in drug development is to identify patients, which respond better or worse to an experimental treatment. Identifying predictive covariates, which influence the treatment effect and can be used to define subgroups of patients, is a key aspect of this task. Analyses of treatment effect heterogeneity are however known to be challenging, since the number of possible covariates or subgroups is often large, while samples sizes in earlier phases of drug development are often small. In addition, distinguishing predictive covariates from prognostic covariates, which influence the resp…
To better understand effects of exposure to food allergens, food challenge studies are designed to slowly increase the dose of an allergen delivered to allergic individuals until an objective reaction occurs. These dose-to-failure studies are used to determine acceptable intake levels and are analyzed using parametric failure time models. Though these models can provide estimates of the survival curve, their parametric form may misrepresent the survival function for doses of interest, and different models that describe the data similarly may produce different dose-to-failure estimates. Motivat…
Purpose: We propose a general framework for quantifying predictive uncertainties of dose-related quantities and leveraging this information in a dose mimicking problem in the context of automated radiation therapy treatment planning. Methods: A three-step pipeline, comprising feature extraction, dose statistic prediction and dose mimicking, is employed. In particular, the features are produced by a convolutional variational autoencoder and used as inputs in a previously developed nonparametric Bayesian statistical method, estimating the multivariate predictive distribution of a collection of p…
There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health outcome. A main focus in these studies is inference on dose levels associated with a given increase in risk relative to a baseline. Popular methods either dichotomize the continuous response or focus on modeling changes with the dose in the expectation of the outcome. Such choices may lead to information loss and provide inaccurate inference on dose-response relati…
Aims: Combinations of treatments can offer additional benefit over the treatments individually. However, trials of these combinations are lower priority than the development of novel therapies, which can restrict funding, timelines and patient availability. This paper develops a novel trial design to facilitate the evaluation of novel combination therapies that combines elements of phase II and phase III trials. Methods: This trial uses response adaptive randomisation to increase the information collected about successful novel drug combinations and Bayesian dose-response modelling to undertak…
A major practical impediment when implementing adaptive dose-finding designs is that the toxicity outcome used by the decision rules may not be observed shortly after the initiation of the treatment. To address this issue, we propose the data augmentation continual reassessment method (DA-CRM) for dose finding. By naturally treating the unobserved toxicities as missing data, we show that such missing data are nonignorable in the sense that the missingness depends on the unobserved outcomes. The Bayesian data augmentation approach is used to sample both the missing data and model parameters fro…
We reveal the relations between the conditional normalized maximum likelihood (CNML) distributions and Bayesian predictive densities based on the latent information priors (LIPs). In particular, CNML3, which is one type of CNML distributions, is investigated. The Bayes projection of a predictive density, which is an information projection of the predictive density on a set of Bayesian predictive densities, is considered. We prove that the sum of the Bayes projection divergence of CNML3 and the conditional mutual information is asymptotically constant. This result implies that the Bayes project…
Personalized cancer treatments based on the molecular profile of a patient's tumor are an emerging and exciting class of treatments in oncology. As genomic tumor profiling is becoming more common, targeted treatments to specific molecular alterations are gaining traction. To discover new potential therapeutics that may apply to broad classes of tumors matching some molecular pattern, experimentalists and pharmacologists rely on high-throughput, in-vitro screens of many compounds against many different cell lines. We propose a hierarchical Bayesian model of how cancer cell lines respond to drug…
Today there are approximately 85,000 chemicals regulated under the Toxic Substances Control Act, with around 2,000 new chemicals introduced each year. It is impossible to screen all of these chemicals for potential toxic effects either via full organism in vivo studies or in vitro high-throughput screening (HTS) programs. Toxicologists face the challenge of choosing which chemicals to screen, and predicting the toxicity of as-yet-unscreened chemicals. Our goal is to describe how variation in chemical structure relates to variation in toxicological response to enable in silico toxicity characte…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of statistical uncertainty, with the parameter of interest being known precisely given the entire population. We argue that the foundation of Bayesian inference is to assign a distribution on missing observations conditional on what has been observed. In the conditionally i.i.d. setting with an observed sample of size $n$, the Bayesian would thus assign a predict…
Construction methods for prior densities are investigated from a predictive viewpoint. Predictive densities for future observables are constructed by using observed data. The simultaneous distribution of future observables and observed data is assumed to belong to a parametric submodel of a multinomial model. Future observables and data are possibly dependent. The discrepancy of a predictive density to the true conditional density of future observables given observed data is evaluated by the Kullback-Leibler divergence. It is proved that limits of Bayesian predictive densities form an essentia…
The Bayesian measure of sample information about the parameter, known as Lindley's measure, is widely used in various problems such as developing prior distributions, models for the likelihood functions and optimal designs. The predictive information is defined similarly and used for model selection and optimal designs, though to a lesser extent. The parameter and predictive information measures are proper utility functions and have been also used in combination. Yet the relationship between the two measures and the effects of conditional dependence between the observable quantities on the Bay…
An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully acknowledged through the posterior predictive distribution. Several such rules have been recently considered and their asymptotic behavior has been characterized under the assumption that the observed features or variables used for building a classifier are conditionally independent given a simultaneous labeling of both the training samples and those from an unkn…
We consider a Bayesian framework based on "probability of decision" for dose-finding trial designs. The proposed PoD-BIN design evaluates the posterior predictive probabilities of up-and-down decisions. In PoD-BIN, multiple grades of toxicity, categorized as the mild toxicity (MT) and dose-limiting toxicity (DLT), are modeled simultaneously, and the primary outcome of interests is time-to-toxicity for both MT and DLT. This allows the possibility of enrolling new patients when previously enrolled patients are still being followed for toxicity, thus potentially shortening trial length. The Bayes…
In learning-phase clinical trials in drug development, adaptive designs can be efficient and highly informative when used appropriately. In this article, we extend the multiple comparison procedures with modeling techniques (MCP-Mod) procedure with generalized multiple contrast tests (GMCTs) to two-stage adaptive designs for establishing proof-of-concept. The results of an interim analysis of first-stage data are used to adapt the candidate dose-response models and the dosages studied in the second stage. GMCTs are used in both stages to obtain stage-wise p-values, which are then combined to d…
Phase I-II cancer clinical trial designs are intended to accelerate drug development. In cases where efficacy cannot be ascertained in a short period of time, it is common to divide the study in two stages: i) a first stage in which dose is escalated based only on toxicity data and we look for the maximum tolerated dose (MTD) set and ii) a second stage in which we search for the most efficacious dose within the MTD set. Current available approaches in the area of continuous dose levels involve fixing the MTD after stage I and discarding all collected stage I efficacy data. However, this method…
Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art workflows suffer from the need for heuristic or subjective manual choices, high computational complexity, or strong parametric assumptions. We address these problems by establishing a theoretical link between multivariate/conditional independence testing, and model comparison in the multivariate predictive modelling aka supervised learning task. This link all…
Adaptive Weighting for Time-to-Event Continual Reassessment Method: Improving Safety in Phase I Dose-Finding Through Data-Driven Delay Distribution Estimation
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Columbia University（哥伦比亚大学）
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from an estimated generative model. It is efficient and compatible with either explicit or implicit conditional generative models. Theoretically, we show that PCP guarantees correct marginal coverage with finite samples. Empirically, we study PCP on a variety of simulated and real datasets. Compared to existing methods for conformal inference, PCP provides sharper…
Loss functions are widely used to compare several competing forecasts. However, forecast comparisons are often based on mismeasured proxy variables for the true target. We introduce the concept of exact robustness to measurement error for loss functions and fully characterize this class of loss functions as the Bregman class. For such exactly robust loss functions, forecast loss differences are on average unaffected by the use of proxy variables and, thus, inference on conditional predictive ability can be carried out as usual. Moreover, we show that more precise proxies give predictive abilit…
Conformal methods create prediction bands that control average coverage under no assumptions besides i.i.d. data. Besides average coverage, one might also desire to control conditional coverage, that is, coverage for every new testing point. However, without strong assumptions, conditional coverage is unachievable. Given this limitation, the literature has focused on methods with asymptotical conditional coverage. In order to obtain this property, these methods require strong conditions on the dependence between the target variable and the features. We introduce two conformal methods based on …
Neural Conditional Simulation for Complex Spatial Processes
North Carolina State University（北卡罗来纳州立大学）；University of New South Wales Sydney（新南威尔士大学悉尼分校）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Carnegie Mellon University（卡内基梅隆大学）
The reproducibility crisis has led to an increasing number of replication studies being conducted. Sample sizes for replication studies are often calculated using conditional power based on the effect estimate from the original study. However, this approach is not well suited as it ignores the uncertainty of the original result. Bayesian methods are used in clinical trials to incorporate prior information into power calculations. We propose to adapt this methodology to the replication framework and promote the use of predictive instead of conditional power in the design of replication studies.…
We identify the average dose-response function (ADRF) for a continuously valued error-contaminated treatment by a weighted conditional expectation. We then estimate the weights nonparametrically by maximising a local generalised empirical likelihood subject to an expanding set of conditional moment equations incorporated into the deconvolution kernels. Thereafter, we construct a deconvolution kernel estimator of ADRF. We derive the asymptotic bias and variance of our ADRF estimator and provide its asymptotic linear expansion, which helps conduct statistical inference. To select our smoothing p…
We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace stochastic volatility. In contrast to other, similar stochastic volatility formalisms, this process has analytic expressions for its conditional probabilistic structure that enable straightforward estimation of dynamically changing extreme event probabilities. The process and volatility are conditionally Pareto-tailed, with tail exponent given by the reciprocal of th…
