arXiv subjects

Qingyuan Zhao

Publications and source records attributed to Qingyuan Zhao.

At least 37 records · Page 2Linked to original sources

arXiv2023

What is a randomization test?

The meaning of randomization tests has become obscure in statistics education and practice over the last century. This article makes a fresh attempt at rectifying this core concept of statistics. A new term -- "quasi-randomization test" -- is introduced to define significance tests based on theoretical models and distinguish these tests from the "randomization tests" based on the physical act of randomization. The practical importance of this distinction is illustrated through a real stepped-wedge cluster-randomized trial. Building on the recent literature of randomization inference, a general framework of conditional randomization tests is developed and some practical methods to construct conditioning events are given. The proposed terminology and framework are then applied to understand several widely used (quasi-)randomization tests, including Fisher's exact test, permutation tests for treatment effect, quasi-randomization tests for independence and conditional independence, adaptive randomization, and conformal prediction.

stat.ME↗

arXiv2023

Simultaneous Hypothesis Testing Using Internal Negative Controls with An Application to Proteomics

Negative control is a common technique in scientific investigations and broadly refers to the situation where a null effect (''negative result'') is expected. Motivated by a real proteomic dataset, we will present three promising and closely connected methods of using negative controls to assist simultaneous hypothesis testing. The first method uses negative controls to construct a permutation p-value for every hypothesis under investigation, and we give several sufficient conditions for such p-values to be valid and positive regression dependent on the set (PRDS) of true nulls. The second method uses negative controls to construct an estimate of the false discovery rate (FDR), and we give a sufficient condition under which the step-up procedure based on this estimate controls the FDR. The third method, derived from an existing ad hoc algorithm for proteomic analysis, uses negative controls to construct a nonparametric estimator of the local false discovery rate. We conclude with some practical suggestions and connections to some closely related methods that are propsed recently.

stat.ME↗

arXiv2022

A unified analysis of regression adjustment in randomized experiments

Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand this phenomenon, we develop a unified comparison of the asymptotic variance of a class of linear regression-adjusted estimators. Our analysis is based on the classical theory for linear regression with heteroscedastic errors and thus does not assume that the postulated linear model is correct. For a completely randomized binary treatment, we provide sufficient conditions under which some regression-adjusted estimators are guaranteed to be more asymptotically efficient than others. We explore other settings such as general treatment assignment mechanisms and generalized linear models, and find that the variance dominance phenomenon no longer occurs.

stat.ME↗

arXiv2022

A Latent Mixture Model for Heterogeneous Causal Mechanisms in Mendelian Randomization

Mendelian Randomization (MR) is a popular method in epidemiology and genetics that uses genetic variation as instrumental variables for causal inference. Existing MR methods usually assume most genetic variants are valid instrumental variables that identify a common causal effect. There is a general lack of awareness that this effect homogeneity assumption can be violated when there are multiple causal pathways involved, even if all the instrumental variables are valid. In this article, we introduce a latent mixture model MR-PATH that groups instruments that yield similar causal effect estimates together. We develop a Monte-Carlo EM algorithm to fit this mixture model, derive approximate confidence intervals for uncertainty quantification, and adopt a modified Bayesian Information Criterion (BIC) for model selection. We verify the efficacy of the Monte-Carlo EM algorithm, confidence intervals, and model selection criterion using numerical simulations. We identify potential mechanistic heterogeneity when applying our method to estimate the effect of high-density lipoprotein cholesterol on coronary heart disease and the effect of adiposity on type II diabetes.

stat.AP↗

arXiv2021

Selective inference for effect modification via the lasso

Effect modification occurs when the effect of the treatment on an outcome varies according to the level of other covariates and often has important implications in decision making. When there are tens or hundreds of covariates, it becomes necessary to use the observed data to select a simpler model for effect modification and then make valid statistical inference. We propose a two stage procedure to solve this problem. First, we use Robinson's transformation to decouple the nuisance parameters from the treatment effect of interest and use machine learning algorithms to estimate the nuisance parameters. Next, after plugging in the estimates of the nuisance parameters, we use the Lasso to choose a low-complexity model for effect modification. Compared to a full model consisting of all the covariates, the selected model is much more interpretable. Compared to the univariate subgroup analyses, the selected model greatly reduces the number of false discoveries. We show that the conditional selective inference for the selected model is asymptotically valid given the rate assumptions in classical semiparametric regression. Extensive simulation studies are conducted to verify the asymptotic results and an epidemiological application is used to demonstrate the method.

stat.ME↗

arXiv2021

Sample-constrained partial identification with application to selection bias

Many partial identification problems can be characterized by the optimal value of a function over a set where both the function and set need to be estimated by empirical data. Despite some progress for convex problems, statistical inference in this general setting remains to be developed. To address this, we derive an asymptotically valid confidence interval for the optimal value through an appropriate relaxation of the estimated set. We then apply this general result to the problem of selection bias in population-based cohort studies. We show that existing sensitivity analyses, which are often conservative and difficult to implement, can be formulated in our framework and made significantly more informative via auxiliary information on the population. We conduct a simulation study to evaluate the finite sample performance of our inference procedure and conclude with a substantive motivating example on the causal effect of education on income in the highly-selected UK Biobank cohort. We demonstrate that our method can produce informative bounds using plausible population-level auxiliary constraints. We implement this method in the R package selectioninterval.

stat.ME↗

arXiv2021

Toward Better Practice of Covariate Adjustment in Analyzing Randomized Clinical Trials

In randomized clinical trials, adjustments for baseline covariates at both design and analysis stages are highly encouraged by regulatory agencies. A recent trend is to use a model-assisted approach for covariate adjustment to gain credibility and efficiency while producing asymptotically valid inference even when the model is incorrect. In this article we present three considerations for better practice when model-assisted inference is applied to adjust for covariates under simple or covariate-adaptive randomized trials: (1) guaranteed efficiency gain: a model-assisted method should often gain but never hurt efficiency; (2) wide applicability: a valid procedure should be applicable, and preferably universally applicable, to all commonly used randomization schemes; (3) robust standard error: variance estimation should be robust to model misspecification and heteroscedasticity. To achieve these, we recommend a model-assisted estimator under an analysis of heterogeneous covariance working model including all covariates utilized in randomization. Our conclusions are based on an asymptotic theory that provides a clear picture of how covariate-adaptive randomization and regression adjustment alter statistical efficiency. Our theory is more general than the existing ones in terms of studying arbitrary functions of response means (including linear contrasts, ratios, and odds ratios), multiple arms, guaranteed efficiency gain, optimality, and universal applicability.

stat.ME↗

arXiv2021

A note on post-treatment selection in studying racial discrimination in policing

We discuss some causal estimands used to study racial discrimination in policing. A central challenge is that not all police-civilian encounters are recorded in administrative datasets and available to researchers. One possible solution is to consider the average causal effect of race conditional on the civilian already being detained by the police. We find that such an estimand can be quite different from the more familiar ones in causal inference and needs to be interpreted with caution. We propose using an estimand new for this context -- the causal risk ratio, which has more transparent interpretation and requires weaker identification assumptions. We demonstrate this through a reanalysis of the NYPD Stop-and-Frisk dataset. Our reanalysis shows that the naive estimator that ignores the post-treatment selection in administrative records may severely underestimate the disparity in police violence between minorities and whites in these and similar data.

stat.AP↗

arXiv2021

Self-Heating Hotspots in Superconducting Nanowires Cooled by Phonon Black-Body Radiation

Controlling thermal transport is important for a range of devices and technologies, from phase change memories to next-generation electronics. This is especially true in nano-scale devices where thermal transport is altered by the influence of surfaces and changes in dimensionality. In superconducting nanowire single-photon detectors, the thermal boundary conductance (TBC) between the nanowire and the substrate it is fabricated on influences most of the performance metrics that make these detectors attractive for applications. This includes the maximum count rate, latency, jitter, and quantum efficiency. Despite its importance, the study of TBC in superconducting nanowire devices has not been done systematically, primarily due to the lack of a straightforward characterization method. Here, we show that simple electrical measurements can be used to estimate the TBC between nanowires and substrates and that these measurements match acoustic mismatch theory across a variety of substrates. Numerical simulations allow us to refine our understanding, however, open questions remain. This work should enable thermal engineering in superconducting nanowire electronics and cryogenic detectors for improved device performance.

cond-mat.supr-con↗

arXiv2021

On testing mean proportionality of multivariate normal variables

This short note considers the problem of testing the null hypothesis that the mean values of two multivariate normal variables are proportional. We show that the usual likelihood ratio $χ^2$-test is valid non-asymptotically. Our proof relies on expressing the test statistic as the minimum eigenvalue of a Wishart variable and using a representation of its distribution using Legendre polynomials.

math.ST↗

arXiv2020

Mid-infrared single photon detector with superconductor Mo$_{80}$Si$_{20}$ nanowire

A mid-infrared single photon detector (MIR-SNSPD) was reported based on 30 nm-wide superconductor molybdenum silicide nanowires in this work. Saturated quantum efficiencies (QEs) were achieved at the wavelength ranging from 1.55 to 5.07 micrometer in experiments. At the same time, the intrinsic dark count rate (DCR) was below 100 cps. Thus, this device produced a noise equivalent power (NEP) of 4.5 * 10-19 W/sqrt(Hz). The results provide the foundation of developing 10 micrometer-SNSPD for the applications of infrared astronomy observation.

physics.app-ph↗

arXiv2020

BETS: The dangers of selection bias in early analyses of the coronavirus disease (COVID-19) pandemic

The coronavirus disease 2019 (COVID-19) has quickly grown from a regional outbreak in Wuhan, China to a global pandemic. Early estimates of the epidemic growth and incubation period of COVID-19 may have been biased due to sample selection. Using detailed case reports from 14 locations in and outside mainland China, we obtained 378 Wuhan-exported cases who left Wuhan before an abrupt travel quarantine. We developed a generative model we call BETS for four key epidemiological events---Beginning of exposure, End of exposure, time of Transmission, and time of Symptom onset (BETS)---and derived explicit formulas to correct for the sample selection. We gave a detailed illustration of why some early and highly influential analyses of the COVID-19 pandemic were severely biased. All our analyses, regardless of which subsample and model were being used, point to an epidemic doubling time of 2 to 2.5 days during the early outbreak in Wuhan. A Bayesian nonparametric analysis further suggests that about 5% of the symptomatic cases may not develop symptoms within 14 days of infection and that men may be much more likely than women to develop symptoms within 2 days of infection.

stat.AP↗

arXiv2020

ivmodel: An R Package for Inference and Sensitivity Analysis of Instrumental Variables Models with One Endogenous Variable

We present a comprehensive R software ivmodel for analyzing instrumental variables with one endogenous variable. The package implements a general class of estimators called k- class estimators and two confidence intervals that are fully robust to weak instruments. The package also provides power formulas for various test statistics in instrumental variables. Finally, the package contains methods for sensitivity analysis to examine the sensitivity of the inference to instrumental variables assumptions. We demonstrate the software on the data set from Card (1995), looking at the causal effect of levels of education on log earnings where the instrument is proximity to a four-year college.

stat.AP↗

arXiv2020

Selecting and ranking individualized treatment rules with unmeasured confounding

It is common to compare individualized treatment rules based on the value function, which is the expected potential outcome under the treatment rule. Although the value function is not point-identified when there is unmeasured confounding, it still defines a partial order among the treatment rules under Rosenbaum's sensitivity analysis model. We first consider how to compare two treatment rules with unmeasured confounding in the single-decision setting and then use this pairwise test to rank multiple treatment rules. We consider how to, among many treatment rules, select the best rules and select the rules that are better than a control rule. The proposed methods are illustrated using two real examples, one about the benefit of malaria prevention programs to different age groups and another about the effect of late retirement on senior health in different gender and occupation groups.

stat.ME↗

arXiv2019

Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score

Mendelian randomization (MR) is a method of exploiting genetic variation to unbiasedly estimate a causal effect in presence of unmeasured confounding. MR is being widely used in epidemiology and other related areas of population science. In this paper, we study statistical inference in the increasingly popular two-sample summary-data MR design. We show a linear model for the observed associations approximately holds in a wide variety of settings when all the genetic variants satisfy the exclusion restriction assumption, or in genetic terms, when there is no pleiotropy. In this scenario, we derive a maximum profile likelihood estimator with provable consistency and asymptotic normality. However, through analyzing real datasets, we find strong evidence of both systematic and idiosyncratic pleiotropy in MR, echoing the omnigenic model of complex traits that is recently proposed in genetics. We model the systematic pleiotropy by a random effects model, where no genetic variant satisfies the exclusion restriction condition exactly. In this case we propose a consistent and asymptotically normal estimator by adjusting the profile score. We then tackle the idiosyncratic pleiotropy by robustifying the adjusted profile score. We demonstrate the robustness and efficiency of the proposed methods using several simulated and real datasets.

stat.AP↗

arXiv2018

Powerful genome-wide design and robust statistical inference in two-sample summary-data Mendelian randomization

Two-sample summary-data Mendelian randomization (MR) has become a popular research design to estimate the causal effect of risk exposures. With the sample size of GWAS continuing to increase, it is now possible to utilize genetic instruments that are only weakly associated with the exposure. To maximize the statistical power of MR, we propose a genome-wide design where more than a thousand genetic instruments are used. For the statistical analysis, we use an empirical partially Bayes approach where instruments are weighted according to their strength, thus weak instruments bring less variation to the estimator. The estimator is highly efficient with many weak genetic instruments and is robust to balanced and/or sparse pleiotropy. We apply our method to estimate the causal effect of body mass index (BMI) and major blood lipids on cardiovascular disease outcomes and obtain substantially shorter confidence intervals. Some new and statistically significant findings are: the estimated causal odds ratio of BMI on ischemic stroke is 1.19 (95% CI: 1.07--1.32, p-value < 0.001); the estimated causal odds ratio of high-density lipoprotein cholesterol (HDL-C) on coronary artery disease (CAD) is 0.78 (95% CI 0.73--0.84, p-value < 0.001). However, the estimated effect of HDL-C becomes substantially smaller and statistically non-significant when we only use the strong instruments. By employing a genome-wide design and robust statistical methods, the statistical power of MR studies can be greatly improved. Our empirical results suggest that, even though the relationship between HDL-C and CAD appears to be highly heterogeneous, it may be too soon to completely dismiss the HDL hypothesis.

stat.AP↗

arXiv2018

Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap

To identify the estimand in missing data problems and observational studies, it is common to base the statistical estimation on the "missing at random" and "no unmeasured confounder" assumptions. However, these assumptions are unverifiable using empirical data and pose serious threats to the validity of the qualitative conclusions of the statistical inference. A sensitivity analysis asks how the conclusions may change if the unverifiable assumptions are violated to a certain degree. In this paper we consider a marginal sensitivity model which is a natural extension of Rosenbaum's sensitivity model that is widely used for matched observational studies. We aim to construct confidence intervals based on inverse probability weighting estimators, such that asymptotically the intervals have at least nominal coverage of the estimand whenever the data generating distribution is in the collection of marginal sensitivity models. We use a percentile bootstrap and a generalized minimax/maximin inequality to transform this intractable problem to a linear fractional programming problem, which can be solved very efficiently. We illustrate our method using a real dataset to estimate the causal effect of fish consumption on blood mercury level.

stat.ME↗

arXiv2018

Two-sample instrumental variable analyses using heterogeneous samples

Instrumental variable analysis is a widely used method to estimate causal effects in the presence of unmeasured confounding. When the instruments, exposure and outcome are not measured in the same sample, Angrist and Krueger (1992) suggested to use two-sample instrumental variable (TSIV) estimators that use sample moments from an instrument-exposure sample and an instrument-outcome sample. However, this method is biased if the two samples are from heterogeneous populations so that the distributions of the instruments are different. In linear structural equation models, we derive a new class of TSIV estimators that are robust to heterogeneous samples under the key assumption that the structural relations in the two samples are the same. The widely used two-sample two-stage least squares estimator belongs to this class. It is generally not asymptotically efficient, although we find that it performs similarly to the optimal TSIV estimator in most practical situations. We then attempt to relax the linearity assumption. We find that, unlike one-sample analyses, the TSIV estimator is not robust to misspecified exposure model. Additionally, to nonparametrically identify the magnitude of the causal effect, the noise in the exposure must have the same distributions in the two samples. However, this assumption is in general untestable because the exposure is not observed in one sample. Nonetheless, we may still identify the sign of the causal effect in the absence of homogeneity of the noise.

math.ST↗