Patient care may be improved by recommending treatments based on patient characteristics when there is treatment effect heterogeneity. Recently, there has been a great deal of attention focused on the estimation of optimal treatment rules that maximize expected outcomes. However, there has been comparatively less attention given to settings where the outcome is right-censored, especially with regard to the practical use of estimators. In this study, simulations were undertaken to assess the finite-sample performance of estimators for optimal treatment rules and estimators for the expected outcome under treatment rules. The simulations were motivated by the common setting in biomedical and public health research where the data is observational, survival times may be right-censored, and there is interest in estimating baseline treatment decisions to maximize survival probability. A variety of outcome regression and direct search estimation methods were compared for optimal treatment rule estimation across a range of simulation scenarios. Methods that flexibly model the outcome performed comparatively well, including in settings where the treatment rule was non-linear. R code to reproduce this study's results are available on Github.
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The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong to the class of mixtures on which the estimator is based. In a situation where $P$ is a mixture of well enough separated but nonparametric distributions it is shown that the components of the population version of the estimator correspond to the well separated components of $P$. This provides some theoretical justification for the use of such estimators for cluster analysis in case that $P$ has well separated subpopulations even if these subpopulations differ from what the mixture model assumes.
Aspiration thrombectomy is a treatment option for ischemic stroke due to occlusions in large vessels. During the therapy a device is inserted into the vessel and suction is applied. A new one-dimensional model is introduced that is capable of simulating this procedure while accounting for the fluid-structure interactions in blood flow. To solve the coupling problem at the tip of the device a problem-suited Riemann solver is constructed based on relaxation of the hyperbolic model. Numerical experiments investigating the role of the catheter size and the suction forces are presented.
Temporal network data is often encoded as time-stamped interaction events between senders and receivers, such as co-authoring scientific articles or communication via email. A number of relational event frameworks have been proposed to address specific issues raised by complex temporal dependencies. These models attempt to quantify how individual behaviour, endogenous and exogenous factors, as well as interactions with other individuals modify the network dynamics over time. It is often of interest to determine whether changes in the network can be attributed to endogenous mechanisms reflecting natural relational tendencies, such as reciprocity or triadic effects. The propensity to form or receive ties can also, at least partially, be related to actor attributes. Nodal heterogeneity in the network is often modelled by including actor-specific or dyadic covariates. However, comprehensively capturing all personality traits is difficult in practice, if not impossible. A failure to account for heterogeneity may confound the substantive effect of key variables of interest. This work shows that failing to account for node level sender and receiver effects can induce ghost triadic effects. We propose a random-effect extension of the relational event model to deal with these problems. We show that it is often effective over more traditional approaches, such as in-degree and out-degree statistics. These results that the violation of the hierarchy principle due to insufficient information about nodal heterogeneity can be resolved by including random effects in the relational event model as a standard.
Large Language models (LLMs) have demonstrated significant potential in transforming healthcare by automating tasks such as clinical documentation, information retrieval, and decision support. In this aspect, carefully engineered prompts have emerged as a powerful tool for using LLMs for medical scenarios, e.g., patient clinical scenarios. In this paper, we propose a modified version of the MedQA-USMLE dataset, which is subjective, to mimic real-life clinical scenarios. We explore the Chain of Thought (CoT) reasoning based on subjective response generation for the modified MedQA-USMLE dataset with appropriate LM-driven forward reasoning for correct responses to the medical questions. Keeping in mind the importance of response verification in the medical setting, we utilize a reward training mechanism whereby the language model also provides an appropriate verified response for a particular response to a clinical question. In this regard, we also include human-in-the-loop for different evaluation aspects. We develop better in-contrast learning strategies by modifying the 5-shot-codex-CoT-prompt from arXiv:2207.08143 for the subjective MedQA dataset and developing our incremental-reasoning prompt. Our evaluations show that the incremental reasoning prompt performs better than the modified codex prompt in certain scenarios. We also show that greedy decoding with the incremental reasoning method performs better than other strategies, such as prompt chaining and eliminative reasoning.
We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the \emph{latent} block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal polytopes of the variants of the stochastic blockmodel, and discuss how both facilitate the development of goodness-of-fit tests and understanding of model behavior. The general testing methodology developed here extends to any finite mixture of log-linear models on discrete data, and as such is the first application of the algebraic statistics machinery for latent-variable models.
Several mixed-effects models for longitudinal data have been proposed to accommodate the non-linearity of late-life cognitive trajectories and assess the putative influence of covariates on it. No prior research provides a side-by-side examination of these models to offer guidance on their proper application and interpretation. In this work, we examined five statistical approaches previously used to answer research questions related to non-linear changes in cognitive aging: the linear mixed model (LMM) with a quadratic term, LMM with splines, the functional mixed model, the piecewise linear mixed model, and the sigmoidal mixed model. We first theoretically describe the models. Next, using data from two prospective cohorts with annual cognitive testing, we compared the interpretation of the models by investigating associations of education on cognitive change before death. Lastly, we performed a simulation study to empirically evaluate the models and provide practical recommendations. Except for the LMM-quadratic, the fit of all models was generally adequate to capture non-linearity of cognitive change and models were relatively robust. Although spline-based models have no interpretable nonlinearity parameters, their convergence was easier to achieve, and they allow graphical interpretation. In contrast, piecewise and sigmoidal models, with interpretable non-linear parameters, may require more data to achieve convergence.
This work explores the dimension reduction problem for Bayesian nonparametric regression and density estimation. More precisely, we are interested in estimating a functional parameter $f$ over the unit ball in $\mathbb{R}^d$, which depends only on a $d_0$-dimensional subspace of $\mathbb{R}^d$, with $d_0 < d$.It is well-known that rescaled Gaussian process priors over the function space achieve smoothness adaptation and posterior contraction with near minimax-optimal rates. Moreover, hierarchical extensions of this approach, equipped with subspace projection, can also adapt to the intrinsic dimension $d_0$ (\cite{Tokdar2011DimensionAdapt}).When the ambient dimension $d$ does not vary with $n$, the minimax rate remains of the order $n^{-\beta/(2\beta +d_0)}$.%When $d$ does not vary with $n$, the order of the minimax rate remains the same regardless of the ambient dimension $d$. However, this is up to multiplicative constants that can become prohibitively large when $d$ grows. The dependences between the contraction rate and the ambient dimension have not been fully explored yet and this work provides a first insight: we let the dimension $d$ grow with $n$ and, by combining the arguments of \cite{Tokdar2011DimensionAdapt} and \cite{Jiang2021VariableSelection}, we derive a growth rate for $d$ that still leads to posterior consistency with minimax rate.The optimality of this growth rate is then discussed.Additionally, we provide a set of assumptions under which consistent estimation of $f$ leads to a correct estimation of the subspace projection, assuming that $d_0$ is known.
Direct reciprocity based on the repeated prisoner's dilemma has been intensively studied. Most theoretical investigations have concentrated on memory-$1$ strategies, a class of elementary strategies just reacting to the previous-round outcomes. Though the properties of "All-or-None" strategies ($AoN_K$) have been discovered, simulations just confirmed the good performance of $AoN_K$ of very short memory lengths. It remains unclear how $AoN_K$ strategies would fare when players have access to longer rounds of history information. We construct a theoretical model to investigate the performance of the class of $AoN_K$ strategies of varying memory length $K$. We rigorously derive the payoffs and show that $AoN_K$ strategies of intermediate memory length $K$ are most prevalent, while strategies of larger memory lengths are less competent. Larger memory lengths make it hard for $AoN_K$ strategies to coordinate, and thus inhibiting their mutual reciprocity. We then propose the adaptive coordination strategy combining tolerance and $AoN_K$' coordination rule. This strategy behaves like $AoN_K$ strategy when coordination is not sufficient, and tolerates opponents' occasional deviations by still cooperating when coordination is sufficient. We found that the adaptive coordination strategy wins over other classic memory-$1$ strategies in various typical competition environments, and stabilizes the population at high levels of cooperation, suggesting the effectiveness of high level adaptability in resolving social dilemmas. Our work may offer a theoretical framework for exploring complex strategies using history information, which are different from traditional memory-$n$ strategies.
During the evolution of large models, performance evaluation is necessarily performed to assess their capabilities and ensure safety before practical application. However, current model evaluations mainly rely on specific tasks and datasets, lacking a united framework for assessing the multidimensional intelligence of large models. In this perspective, we advocate for a comprehensive framework of cognitive science-inspired artificial general intelligence (AGI) tests, aimed at fulfilling the testing needs of large models with enhanced capabilities. The cognitive science-inspired AGI tests encompass the full spectrum of intelligence facets, including crystallized intelligence, fluid intelligence, social intelligence, and embodied intelligence. To assess the multidimensional intelligence of large models, the AGI tests consist of a battery of well-designed cognitive tests adopted from human intelligence tests, and then naturally encapsulates into an immersive virtual community. We propose increasing the complexity of AGI testing tasks commensurate with advancements in large models and emphasizing the necessity for the interpretation of test results to avoid false negatives and false positives. We believe that cognitive science-inspired AGI tests will effectively guide the targeted improvement of large models in specific dimensions of intelligence and accelerate the integration of large models into human society.
Researchers in many fields endeavor to estimate treatment effects by regressing outcome data (Y) on a treatment (D) and observed confounders (X). Even absent unobserved confounding, the regression coefficient on the treatment reports a weighted average of strata-specific treatment effects (Angrist, 1998). Where heterogeneous treatment effects cannot be ruled out, the resulting coefficient is thus not generally equal to the average treatment effect (ATE), and is unlikely to be the quantity of direct scientific or policy interest. The difference between the coefficient and the ATE has led researchers to propose various interpretational, bounding, and diagnostic aids (Humphreys, 2009; Aronow and Samii, 2016; Sloczynski, 2022; Chattopadhyay and Zubizarreta, 2023). We note that the linear regression of Y on D and X can be misspecified when the treatment effect is heterogeneous in X. The "weights of regression", for which we provide a new (more general) expression, simply characterize how the OLS coefficient will depart from the ATE under the misspecification resulting from unmodeled treatment effect heterogeneity. Consequently, a natural alternative to suffering these weights is to address the misspecification that gives rise to them. For investigators committed to linear approaches, we propose relying on the slightly weaker assumption that the potential outcomes are linear in X. Numerous well-known estimators are unbiased for the ATE under this assumption, namely regression-imputation/g-computation/T-learner, regression with an interaction of the treatment and covariates (Lin, 2013), and balancing weights. Any of these approaches avoid the apparent weighting problem of the misspecified linear regression, at an efficiency cost that will be small when there are few covariates relative to sample size. We demonstrate these lessons using simulations in observational and experimental settings.
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