Pathologic complete response (pCR) is a common primary endpoint for a phase II trial or even accelerated approval of neoadjuvant cancer therapy. If granted, a two-arm confirmatory trial is often required to demonstrate the efficacy with a time-to-event outcome such as overall survival. However, the design of a subsequent phase III trial based on prior information on the pCR effect is not straightforward. Aiming at designing such phase III trials with overall survival as primary endpoint using pCR information from previous trials, we consider a mixture model that incorporates both the survival and the binary endpoints. We propose to base the comparison between arms on the difference of the restricted mean survival times, and show how the effect size and sample size for overall survival rely on the probability of the binary response and the survival distribution by response status, both for each treatment arm. Moreover, we provide the sample size calculation under different scenarios and accompany them with an R package where all the computations have been implemented. We evaluate our proposal with a simulation study, and illustrate its application through a neoadjuvant breast cancer trial.
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Just-in-time adaptive interventions (JITAIs) are time-varying adaptive interventions that use frequent opportunities for the intervention to be adapted--weekly, daily, or even many times a day. The micro-randomized trial (MRT) has emerged for use in informing the construction of JITAIs. MRTs can be used to address research questions about whether and under what circumstances JITAI components are effective, with the ultimate objective of developing effective and efficient JITAI. The purpose of this article is to clarify why, when, and how to use MRTs; to highlight elements that must be considered when designing and implementing an MRT; and to review primary and secondary analyses methods for MRTs. We briefly review key elements of JITAIs and discuss a variety of considerations that go into planning and designing an MRT. We provide a definition of causal excursion effects suitable for use in primary and secondary analyses of MRT data to inform JITAI development. We review the weighted and centered least-squares (WCLS) estimator which provides consistent causal excursion effect estimators from MRT data. We describe how the WCLS estimator along with associated test statistics can be obtained using standard statistical software such as R (R Core Team, 2019). Throughout we illustrate the MRT design and analyses using the HeartSteps MRT, for developing a JITAI to increase physical activity among sedentary individuals. We supplement the HeartSteps MRT with two other MRTs, SARA and BariFit, each of which highlights different research questions that can be addressed using the MRT and experimental design considerations that might arise.
When to initiate treatment on patients is an important problem in many medical studies such as AIDS and cancer. In this article, we formulate the treatment initiation time problem for time-to-event data and propose an optimal individualized regime that determines the best treatment initiation time for individual patients based on their characteristics. Different from existing optimal treatment regimes where treatments are undertaken at a pre-specified time, here new challenges arise from the complicated missing mechanisms in treatment initiation time data and the continuous treatment rule in terms of initiation time. To tackle these challenges, we propose to use restricted mean residual lifetime as a value function to evaluate the performance of different treatment initiation regimes, and develop a nonparametric estimator for the value function, which is consistent even when treatment initiation times are not completely observable and their distribution is unknown. We also establish the asymptotic properties of the resulting estimator in the decision rule and its associated value function estimator. In particular, the asymptotic distribution of the estimated value function is nonstandard, which follows a weighted chi-squared distribution. The finite-sample performance of the proposed method is evaluated by simulation studies and is further illustrated with an application to a breast cancer data.
We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017--2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and $q$-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called "inverse-cubic power-law" still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors -- speed of the market time flow and the asset cross-correlation magnitude -- while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution.
We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is also coupled with the mechanical deformation of the matrix assuming that the fractures are open and filled by the fluids, as well as small deformations and a linear elastic constitutive law. The model is discretized using the gradient discretization method [26], which covers a large class of conforming and non conforming schemes. This framework allows for a generic convergence analysis of the coupled model using a combination of discrete functional tools. Here, we describe the model together with its numerical discretization, and we prove a convergence result assuming the non-degeneracy of the phase mobilities and that the discrete solutions remain physical in the sense that, roughly speaking, the porosity does not vanish and the fractures remain open. This is, to our knowledge, the first convergence result for this type of models taking into account two-phase flows in fractured porous media and the non-linear poromechanical coupling. Previous related works consider a linear approximation obtained for a single phase flow by freezing the fracture conductivity [36, 37]. Numerical tests employing the Two-Point Flux Approximation (TPFA) finite volume scheme for the flows and $\mathbb P_2$ finite elements for the mechanical deformation are also provided to illustrate the behavior of the solution to the model.
The main ideas behind the classical multivariate logistic regression model make sense when translated to the functional setting, where the explanatory variable $X$ is a function and the response $Y$ is binary. However, some important technical issues appear (or are aggravated with respect to those of the multivariate case) due to the functional nature of the explanatory variable. First, the mere definition of the model can be questioned: while most approaches so far proposed rely on the $L_2$-based model, we suggest an alternative (in some sense, more general) approach, based on the theory of Reproducing Kernel Hilbert Spaces (RKHS). The validity conditions of such RKHS-based model, as well as its relation with the $L_2$-based one are investigated and made explicit in two formal results. Some relevant particular cases are considered as well. Second we show that, under very general conditions, the maximum likelihood (ML) of the logistic model parameters fail to exist in the functional case. Third, on a more positive side, we suggest an RKHS-based restricted version of the ML estimator. This is a methodological paper, aimed at a better understanding of the functional logistic model, rather than focusing on numerical and practical issues.
Causal inference in longitudinal observational health data often requires the accurate estimation of treatment effects on time-to-event outcomes in the presence of time-varying covariates. To tackle this sequential treatment effect estimation problem, we have developed a causal dynamic survival (CDS) model that uses the potential outcomes framework with the recurrent sub-networks with random seed ensembles to estimate the difference in survival curves of its confidence interval. Using simulated survival datasets, the CDS model has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping. However, increasing the sample size is not effective to alleviate the adverse impact from high level of confounding. In two large clinical cohort studies, our model identified the expected conditional average treatment effect and detected individual effect heterogeneity over time and patient subgroups. CDS provides individualised absolute treatment effect estimations to improve clinical decisions.
In this article we have conducted a reanalysis of the phase III aducanumab (ADU) summary statistics announced by Biogen, in particular the result of the Clinical Dementia Rating-Sum of Boxes (CDR-SB). The results showed that the evidence on the efficacy of the drug is very low and a more clearer view of the results of clinical trials are presented in the Bayesian framework that can be useful for future development and research in the field.
We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors. A common challenge with these algorithms is the choice of the number of iterations to perform. This is critical when each iteration is expensive, as is the case when dealing with modern data sets, such as genome-wide association studies with thousands of rows and up to hundred of thousands of columns. We develop coupling techniques tailored to the setting of high-dimensional regression with shrinkage priors, which enable practical, non-asymptotic diagnostics of convergence without relying on traceplots or long-run asymptotics. By establishing geometric drift and minorization conditions for the algorithm under consideration, we prove that the proposed couplings have finite expected meeting time. Focusing on a class of shrinkage priors which includes the 'Horseshoe', we empirically demonstrate the scalability of the proposed couplings. A highlight of our findings is that less than 1000 iterations can be enough for a Gibbs sampler to reach stationarity in a regression on 100,000 covariates. The numerical results also illustrate the impact of the prior on the computational efficiency of the coupling, and suggest the use of priors where the local precisions are Half-t distributed with degree of freedom larger than one.
In medical and biological research, longitudinal data and survival data types are commonly seen. Traditional statistical models mostly consider to deal with either of the data types, such as linear mixed models for longitudinal data, and the Cox models for survival data, while they do not adjust the association between these two different data types. It is desirable to have a joint modeling approach which accomadates both data types and the dependency between them. In this paper, we extend traditional single-index models to a new joint modeling approach, by replacing the single-index component to a varying coefficient component to deal with longitudinal outcomes, and accomadate the random censoring problem in survival analysis by nonparametric synthetic data regression for the link function. Numerical experiments are conducted to evaluate the finite sample performance.
In this paper we introduce a covariance framework for the analysis of EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. We perform a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. Apart from that, we illustrate our method on real EEG and MEG data sets. The proposed covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed for accurate dipole localization, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, such as in combined EEG/fMRI experiments in which the correlation between EEG and fMRI signals is investigated.
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