Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTest of Significance for High-dimensional Thresholds with Application to Individualized Minimal Clinically Important Difference
123
0
0.0
(
0
)
Added by
Huijie Feng
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
This work is motivated by learning the individualized minimal clinically important difference, a vital concept to assess clinical importance in various biomedical studies. We formulate the scientific question into a high-dimensional statistical problem where the parameter of interest lies in an individualized linear threshold. The goal of this paper is to develop a hypothesis testing procedure for the significance of a single element in this high-dimensional parameter as well as for the significance of a linear combination of this parameter. The difficulty dues to the high-dimensionality of the nuisance component in developing such a testing procedure, and also stems from the fact that this high-dimensional threshold model is nonregular and the limiting distribution of the corresponding estimator is nonstandard. To deal with these challenges, we construct a test statistic via a new bias corrected smoothed decorrelated score approach, and establish its asymptotic distributions under both the null and local alternative hypotheses. In addition, we propose a double-smoothing approach to select the optimal bandwidth parameter in our test statistic and provide theoretical guarantees for the selected bandwidth. We conduct comprehensive simulation studies to demonstrate how our proposed procedure can be applied in empirical studies. Finally, we apply the proposed method to a clinical trial where the scientific goal is to assess the clinical importance of a surgery procedure.
rate research
Read More
In clinical trials, minimum clinically important difference (MCID) has attracted increasing interest as an important supportive clinical and statistical inference tool. Many estimation methods have been developed based on various intuitions, while little theoretical justification has been established. This paper proposes a new estimation framework of MCID using both diagnostic measurements and patient-reported outcomes (PROs). It first provides a precise definition of population-based MCID so that estimating such a MCID can be formulated as a large margin classification problem. The framework is then extended to personalized MCID to allow individualized thresholding value for patients whose clinical profiles may affect their PRO responses. More importantly, we show that the proposed estimation framework is asymptotically consistent, and a finite-sample upper bound is established for its prediction accuracy compared against the ideal MCID. The advantage of our proposed method is also demonstrated in a variety of simulated experiments as well as applications to two benchmark datasets and two phase-3 clinical trials.
We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This two-sample test based on a nontrivial extension of the one-sample central limit theorem (Chernozhukov et al., 2017) provides a practically useful procedure with rigorous theoretical guarantees on its size and power assessment. In particular, the proposed test is easy to compute and does not require the independently and identically distributed assumption, which is allowed to have different distributions and arbitrary correlation structures. Further desired features include weaker moments and tail conditions than existing methods, allowance for highly unequal sample sizes, consistent power behavior under fairly general alternative, data dimension allowed to be exponentially high under the umbrella of such general conditions. Simulated and real data examples are used to demonstrate the favorable numerical performance over existing methods.
We propose a new method for changepoint estimation in partially-observed, high-dimensional time series that undergo a simultaneous change in mean in a sparse subset of coordinates. Our first methodological contribution is to introduce a MissCUSUM transformation (a generalisation of the popular Cumulative Sum statistics), that captures the interaction between the signal strength and the level of missingness in each coordinate. In order to borrow strength across the coordinates, we propose to project these MissCUSUM statistics along a direction found as the solution to a penalised optimisation problem tailored to the specific sparsity structure. The changepoint can then be estimated as the location of the peak of the absolute value of the projected univariate series. In a model that allows different missingness probabilities in different component series, we identify that the key interaction between the missingness and the signal is a weighted sum of squares of the signal change in each coordinate, with weights given by the observation probabilities. More specifically, we prove that the angle between the estimated and oracle projection directions, as well as the changepoint location error, are controlled with high probability by the sum of two terms, both involving this weighted sum of squares, and representing the error incurred due to noise and the error due to missingness respectively. A lower bound confirms that our changepoint estimator, which we call MissInspect, is optimal up to a logarithmic factor. The striking effectiveness of the MissInspect methodology is further demonstrated both on simulated data, and on an oceanographic data set covering the Neogene period.
Consider the problem of estimating the local average treatment effect with an instrument variable, where the instrument unconfoundedness holds after adjusting for a set of measured covariates. Several unknown functions of the covariates need to be estimated through regression models, such as instrument propensity score and treatment and outcome regression models. We develop a computationally tractable method in high-dimensional settings where the numbers of regression terms are close to or larger than the sample size. Our method exploits regularized calibrated estimation, which involves Lasso penalties but carefully chosen loss functions for estimating coefficient vectors in these regression models, and then employs a doubly robust estimator for the treatment parameter through augmented inverse probability weighting. We provide rigorous theoretical analysis to show that the resulting Wald confidence intervals are valid for the treatment parameter under suitable sparsity conditions if the instrument propensity score model is correctly specified, but the treatment and outcome regression models may be misspecified. For existing high-dimensional methods, valid confidence intervals are obtained for the treatment parameter if all three models are correctly specified. We evaluate the proposed methods via extensive simulation studies and an empirical application to estimate the returns to education.
Though Gaussian graphical models have been widely used in many scientific fields, limited progress has been made to link graph structures to external covariates because of substantial challenges in theory and computation. We propose a Gaussian graphical regression model, which regresses both the mean and the precision matrix of a Gaussian graphical model on covariates. In the context of co-expression quantitative trait locus (QTL) studies, our framework facilitates estimation of both population- and subject-level gene regulatory networks, and detection of how subject-level networks vary with genetic variants and clinical conditions. Our framework accommodates high dimensional responses and covariates, and encourages covariate effects on both the mean and the precision matrix to be sparse. In particular for the precision matrix, we stipulate simultaneous sparsity, i.e., group sparsity and element-wise sparsity, on effective covariates and their effects on network edges, respectively. We establish variable selection consistency first under the case with known mean parameters and then a more challenging case with unknown means depending on external covariates, and show in both cases that the convergence rate of the estimated precision parameters is faster than that obtained by lasso or group lasso, a desirable property for the sparse group lasso estimation. The utility and efficacy of our proposed method is demonstrated through simulation studies and an application to a co-expression QTL study with brain cancer patients.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
