Large Sample Approximation Research Articles

Nonstationary A/B Tests: Optimal Variance Reduction, Bias Correction, and Valid Inference

We develop an analytical framework to appropriately model and adequately analyze A/B tests in presence of nonparametric nonstationarities in the targeted business metrics. A/B tests, also known as online randomized controlled experiments, have been used at scale by data-driven enterprises to guide decisions and test innovative ideas to improve core business metrics. Meanwhile, nonstationarities, such as the time-of-day effect and the day-of-week effect, can often arise nonparametrically in key business metrics involving purchases, revenue, conversions, customer experiences, and so on. First, we develop a generic nonparametric stochastic model to capture nonstationarities in A/B test experiments, where each sample represents a visit or action associated with a time label. We build a practically relevant limiting regime to facilitate analyzing large-sample estimator performances under nonparametric nonstationarities. Second, we show that ignoring or inadequately addressing nonstationarities can cause standard A/B test estimators to have suboptimal variance and nonvanishing bias, therefore leading to loss of statistical efficiency and accuracy. We provide a new estimator that views time as a continuous strata and performs poststratification with a data-dependent number of stratification levels. Without making parametric assumptions, we prove a central limit theorem for the proposed estimator and show that the estimator attains the best achievable asymptotic variance and is asymptotically unbiased. Third, we propose a time-grouped randomization that is designed to balance treatment and control assignments at granular time scales. We show that when the time-grouped randomization is integrated to standard experimental designs to generate experiment data, simple A/B test estimators can achieve asymptotically optimal variance. A brief account of numerical experiments are conducted to illustrate the analysis. This paper was accepted by Baris Ata, stochastic models and simulation. Supplemental Material: The online appendices and data files are available at https://doi.org/10.1287/mnsc.2022.01205 .

Exact Inference for Common Odds Ratio in Meta-Analysis with Zero-Total-Event Studies

AbstractStemming from the high-profile publication of Nissen and Wolski (N Engl J Med 356:2457–2471, 2007) and subsequent discussions with divergent views on how to handle observed zero-total-event studies, defined to be studies that observe zero number of event in both treatment and control arms, the research topic concerning the common odds ratio model with zero-total-event studies remains to be an unresolved problem in meta-analysis. In this article, we address this problem by proposing a novel repro samples method to handle zero-total-event studies and make inference for the common odds ratio. The development explicitly accounts for the sampling scheme that generates the observed data and does not rely on any large sample approximations. It is theoretically justified with a guaranteed finite-sample performance. Simulation studies are designed to demonstrate the empirical performance of the proposed method. It shows that the proposed confidence set, although a little conservative, achieves the desired empirical coverage rate in all situations. The development also shows that the zero-total-event studies contain meaningful information and impact the inference for the common odds ratio. The proposed method is used to perform a meta-analysis of the 48 trials reported in Nissen and Wolski (N Engl J Med 356:2457–2471, 2007) as well

Shrinkage Estimation and Forecasting in Dynamic Regression Models Under Structural Instability

Abstract This paper introduces a Stein-like shrinkage method for estimating slope coefficients and forecasting in first order dynamic regression models under structural breaks. The model allows for unit root and non-stationary regressors. The proposed shrinkage estimator is a weighted average of a restricted estimator that ignores the break in the slope coefficients, and an unrestricted estimator that uses the observations within each regime. The restricted estimator is the most efficient estimator but inconsistent when there is a break. However, the unrestricted estimator is consistent but not efficient. Therefore, the proposed shrinkage estimator balances the trade-off between the bias and variance efficiency of the restricted estimator. The averaging weight is proportional to the weighted distance of the restricted estimator, and the unrestricted estimator. We derive the analytical large-sample approximation of the bias, mean squared error, and risk for the shrinkage estimator, the unrestricted estimator, and the restricted estimator. We show that the risk of the shrinkage estimator is lower than the risk of the unrestricted estimator under any break size and break points. Moreover, we extend the results for the model with a unit root and non-stationary regressors. We evaluate the finite sample performance of our proposed method via extensive simulation study, and empirically in forecasting output growth.

Optimizing population mean estimation using regression and factor type estimators in the presence of non-response

This paper addresses the problem of estimating the population mean of the study variable, Y, in the presence of non-response. To address this, we incorporated two additional variables, X and Z, as auxiliary variables. We introduced two classes of estimators that combine regression and factor type estimators, each applied under distinct circumstances, and described their properties. The biases and mean square errors (MSEs) of these proposed estimators were computed using a large sample approximation. To assess the effectiveness of our estimators compared to existing ones, we conducted an empirical study. The results from both empirical and theoretical investigations indicate promising outcomes for the proposed estimators.

Sharing information across patient subgroups to draw conclusions from sparse treatment networks.

Network meta-analysis (NMA) usually provides estimates of the relative effects with the highest possible precision. However, sparse networks with few available studies and limited direct evidence can arise, threatening the robustness and reliability of NMA estimates. In these cases, the limited amount of available information can hamper the formal evaluation of the underlying NMA assumptions of transitivity and consistency. In addition, NMA estimates from sparse networks are expected to be imprecise and possibly biased as they rely on large-sample approximations that are invalid in the absence of sufficient data. We propose a Bayesian framework that allows sharing of information between two networks that pertain to different population subgroups. Specifically, we use the results from a subgroup with a lot of direct evidence (a dense network) to construct informative priors for the relative effects in the target subgroup (a sparse network). This is a two-stage approach where at the first stage, we extrapolate the results of the dense network to those expected from the sparse network. This takes place by using a modified hierarchical NMA model where we add a location parameter that shifts the distribution of the relative effects to make them applicable to the target population. At the second stage, these extrapolated results are used as prior information for the sparse network. We illustrate our approach through a motivating example of psychiatric patients. Our approach results in more precise and robust estimates of the relative effects and can adequately inform clinical practice in presence of sparse networks.

On the Use of Inverse Exponentiation to Improve the Efficiency of Calibration Estimators in Stratified Double Sampling

This study introduces the concept of inverse exponentiation in formulating calibration weights in stratified double sampling and proposes a more improved calibration estimator based on Koyuncu and Kadilar (2014) calibration estimator. The variance of the proposed logarithmic calibration estimator has been derived under large sample approximation. Calibration asymptotic optimum estimator and its approximate variance estimator are derived for the proposed logarithmic calibration estimator. Results of empirical study showed that the proposed logarithmic calibration estimator performs better than the Koyuncu and Kadilar (2014) calibration estimator with appreciable gains in efficiency. Also, simulation study for the comparison of the proposed logarithmic estimator with a Global estimator [Generalized Regression (GREG) estimator ] proved the robustness of the proposed logarithmic calibration estimator and by extension the efficacy of inverse exponentiation in calibration weightings. Analysis and evaluation are presented. International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 91-102

Adjusting Incidence Estimates with Laboratory Test Performances: A Pragmatic Maximum Likelihood Estimation-Based Approach.

Understanding the incidence of disease is often crucial for public policy decision-making, as observed during the COVID-19 pandemic. Estimating incidence is challenging, however, when the definition of incidence relies on tests that imperfectly measure disease, as in the case when assays with variable performance are used to detect the SARS-CoV-2 virus. To our knowledge, there are no pragmatic methods to address the bias introduced by the performance of labs in testing for the virus. In the setting of a longitudinal study, we developed a maximum likelihood estimation-based approach to estimate laboratory performance-adjusted incidence using the expectation-maximization algorithm. We constructed confidence intervals (CIs) using both bootstrapped-based and large-sample interval estimator approaches. We evaluated our methods through extensive simulation and applied them to a real-world study (TrackCOVID), where the primary goal was to determine the incidence of and risk factors for SARS-CoV-2 infection in the San Francisco Bay Area from July 2020 to March 2021. Our simulations demonstrated that our method converged rapidly with accurate estimates under a variety of scenarios. Bootstrapped-based CIs were comparable to the large-sample estimator CIs with a reasonable number of incident cases, shown via a simulation scenario based on the real TrackCOVID study. In more extreme simulated scenarios, the coverage of large-sample interval estimation outperformed the bootstrapped-based approach. Results from the application to the TrackCOVID study suggested that assuming perfect laboratory test performance can lead to an inaccurate inference of the incidence. Our flexible, pragmatic method can be extended to a variety of disease and study settings.

Modified Classes of Stratified Exponential Ratio Estimators of Population Mean with Equal Optimal Efficiency

This paper introduces new classes of exponential ratio estimators for population mean and derives expressions for their biases and mean square errors (MSEs) under the large sample approximation. Asymptotic optimum estimator and its approximate MSE are derived for each class of estimators. Their properties are studied and some special members of their families are identified. Analytically, the proposed classes of estimators have been shown to have equal optimal efficiency under certain prescribed conditions. It is observed that the proposed classes of estimators fare better than the regression estimator and all the modified existing estimators under review with appreciable efficiency gains.

On Efficient Ratio Estimation of Population Mean by Multivariate Calibration Weightings in Double Sampling for Stratification

This study proposed a new ratio estimator for estimating population mean in stratified double sampling using the principle of multivariate calibration weightings. The bias and Mean Square Error (MSE) expressions for the proposed estimator are obtained under large sample approximation. Analytical results showed that under certain prescribed conditions, the new estimator is more efficient than all related existing estimators under review. The relative performances of the new estimator with a corresponding Global Estimator were evaluated through a simulation study. Numerical and simulation results proved the dominance of the new estimator.

A simulation based optimization of factor-type exponential estimators in sample surveys with coefficients of variation and kurtosis

In the context of sample surveys, this article presents factor-type exponential ratio estimators as a technique for estimating population means. These estimators use supplementary information for an auxiliary variable, such as coefficients of variation and coefficients of kurtosis. The research includes a range of alpha values from −1 to +1 to improve estimate.Following that, the study rigorously develops formulas for both bias and mean square error for the suggested estimators. Up to the first degree of large sample approximation, these formulas are produced. The empirical findings we present are renowned in that they show that the suggested estimators consistently beat existing exponential estimators with significantly lower mean squared errors.We calculate the suggested estimator’s percent relative efficiency in comparison to the traditional mean estimator to put a number on how effective it is. We show persuasive proof of the significant improvement offered by our estimators over existing exponential estimators by a complete numerical illustration and a rigorously conducted simulations exercise. Summary:We present factor-type exponential ratio estimators for estimating population means in sample surveys. Key points:We take into account auxiliary information, different alpha values, and various correlation circumstances. Objective:We want to improve population mean estimation precision. Method:To assess our estimators, we use numerical examples and simulations. Results:Our estimators typically outperform competitors, with smaller mean squared errors. Advantage:We demonstrate their robustness and efficiency in improving population mean estimate through rigorous simulations.

Robust variance estimation in small meta-analysis with the standardized mean difference.

Conventional random-effects models in meta-analysis rely on large sample approximations instead of exact small sample results. While random-effects methods produce efficient estimates and confidence intervals for the summary effect have correct coverage when the number of studies is sufficiently large, we demonstrate that conventional methods result in confidence intervals that are not wide enough when the number of studies is small, depending on the configuration of sample sizes across studies, the degree of true heterogeneity and number of studies. We introduce two alternative variance estimators with better small sample properties, investigate degrees of freedom adjustments for computing confidence intervals, and study their effectiveness via simulation studies.

Adroit family of estimators of population mean using known auxiliary parameters

This article introduces an upgraded family of dual estimators for the population mean of main variable using some known supplementary information. To construct the family of estimators, a suitable transformation on the study variable as well as auxiliary variable has been used. The sampling features of the proposed class of estimators have been studied up to first order under large sample approximation. Several existing estimators have been observed and found as particular members of the proposed family of estimators. The optimum values of the characterizing scalars of the suggested family of estimators are obtained through the method of maxima–minima. The least value of the Mean Squared Error (MSE) of the proposed class of estimators is also obtained for these optimal values of the characterizing constants. The proposed family of estimators is compared theoretically with the other competing estimators of population mean. To judge the performance of the suggested family of estimators over others, numerical illustration has also been given. The estimator with minimum MSE is recommended for practical utility in different areas of applications. The results show the suggested estimator performs better than the competing estimators, therefore it may be used in different applications.

Exact inference for fixed effects meta-analysis of tables.

Meta-analysis of associations between rare outcomes and binary exposures are particularly important in studies of a drug's potential side-effects. But meta-analysis of the resulting contingency tables presents substantial practical difficulties, as analysts are currently forced to pick between "exact" inference-that eliminates concern over using large-sample approximations with small cell counts-and explicitly allowing for heterogeneity of the underlying effects. A controversial example is given by the Avandia meta-analysis (Nissen and Wolski. N Engl J Med. 2007;356(24):2457-2471) of rosiglitazone's effects on myocardial infarction and death. While the initial Avandia analysis-using simple methods-found a significant effect, its results conflict with subsequent re-analyses that use either exact methods, or that explicitly acknowledge the plausible heterogeneity. In this article, we aim to resolve these difficulties, by providing an exact (albeit conservative) method that is valid under heterogeneity. We also provide a measure of the degree of conservatism, that indicates the approximate extent of the excess coverage. Applied to the Avandia data, we find support for Nissen and Wolski 2007's original results. Given that our method does not require strong assumptions or large cell counts, and provides intervals around the well-known conditional maximum likelihood estimate, we anticipate that it could be an attractive default method for meta-analysis of tables featuring rare events.

Treatment effect quantiles in stratified randomized experiments and matched observational studies

Summary Evaluating the treatment effect has become an important topic for many applications. However, most existing literature focuses mainly on average treatment effects. When the individual effects are heavy tailed or have outlier values, not only may the average effect not be appropriate for summarizing treatment effects, but also the conventional inference for it can be sensitive and possibly invalid due to poor large-sample approximations. In this paper we focus on quantiles of individual treatment effects, which can be more robust in the presence of extreme individual effects. Moreover, our inference for them is purely randomization based, avoiding any distributional assumptions on the units. We first consider inference in stratified randomized experiments, extending the recent work by Caughey et al. (2021). We show that the computation of valid p-values for testing null hypotheses on quantiles of individual effects can be transformed into instances of the multiple-choice knapsack problem, which can be efficiently solved exactly or slightly conservatively. We then extend our approach to matched observational studies and propose a sensitivity analysis to investigate to what extent our inference on quantiles of individual effects is robust to unmeasured confounding. The proposed randomization inference and sensitivity analysis are simul- taneously valid for all quantiles of individual effects, noting that the analysis for the maximum or minimum individual effect coincides with the conventional analysis assuming constant treatment effects.

Process capability analysis of Taguchi index Cpm based on generalized p‐value

AbstractProduct quality is an essential issue to promote product sale, and process capability analysis plays an important role to assess and guarantee the process quality of products. Taguchi index is widely adopted to measure the process capability, because it essentially quantifies the quality loss from the actual process quality to the customer need. Large sample approximation and the bootstrap method are often used to test the hypothesis of index , but they do not have satisfactory performance under small or medium sample size. To address this issue, we propose a novel hypothesis testing method of index based on generalized p‐value theory. For application, its mathematical expression is derived in detail for the normal, gamma, and Weibull distributions, since these distributions are commonly used in engineering practice. Simulation results show that the supremum of type I error probability of the proposed testing method is closer to the significance level than the existing methods, and its type II error probability is lower as well. Based on the proposed hypothesis testing method, a new procedure of process capability analysis is designed for applications. Finally, two real cases are carried out to show the effectiveness of the newly designed procedure.

MP22-14 LAG3 EXPRESSION ASSOCIATED WITH SURVIVAL IN PATIENTS WITH BLADDER CANCER

You have accessJournal of UrologyCME1 Apr 2023MP22-14 LAG3 EXPRESSION ASSOCIATED WITH SURVIVAL IN PATIENTS WITH BLADDER CANCER Tamir Sholklapper, Laura Bukavina, Andres Correa, Alexander Kutikov, and Philip Abbosh Tamir SholklapperTamir Sholklapper More articles by this author , Laura BukavinaLaura Bukavina More articles by this author , Andres CorreaAndres Correa More articles by this author , Alexander KutikovAlexander Kutikov More articles by this author , and Philip AbboshPhilip Abbosh More articles by this author View All Author Informationhttps://doi.org/10.1097/JU.0000000000003247.14AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookLinked InTwitterEmail Abstract INTRODUCTION AND OBJECTIVE: Expression of lymphocyte activation gene-3 (LAG3), an immune cell transmembrane protein with a regulatory impact on tumor microenvironments, has been identified as a promising checkpoint for emerging immunotherapies. We sought to evaluate the impact of LAG3 expression on bladder cancer survival and the immune regulatory environment. (Figure 1A) METHODS: RNA seq data for bladder cancer was obtained in TCGA from TCGA Data Portal (https://tcga-data.nci.nih.gov/docs/publications/tcga/). Wilcoxon rank-sum test was used for all pairwise comparisons. Spearman Rho was used for all correlations, and P-values were calculated using either the exact permutation distributions (for small sample sizes) or large-sample approximations. All P-values are from two-sided tests, and P < .05 was used as the threshold for statistical significance. The Kaplan-Meier method and log-rank test were used to evaluate overall survival and compare inter-group survival, respectively. Sub-analyses were performed to compare gene enrichment values (GEV) among various immunologic cell types and immune markers with known associations with oncologic outcomes. RESULTS: We identified 424 patients with LAG3 expression and survival data in the TCGA BLCA cohort. Patients with low LAG3 expression had a statistically significant higher OS compared to patients with MIBC and lower expression (p=0.0006). When stratified by gender and age, receipt of chemotherapy, high LAG3 expression remainder significant prognostic factors for OS (p=0.023) (Figure 8B). As LAG-3 expression across immune cells, we compared LAG-3 expression across immune cell subtypes. High LAG-3 expression in muscle invasive bladder cancer (MIBC) decreased infiltration of CD8+/M2b macrophages/Th17/Tregs and B cells (p<0.001). Likewise, comparison of high and low LAG-3 expression demonstrated increased Treg expression, increased CD8+ T cell with enhanced PD1 expression, reflecting marked immunoevasive environment with CD8+ T cell dysfunction. CONCLUSIONS: Our study reported LAG-3+ cells abundance was an independent predictor for poor OS in MIBC patients within TCGA cohort. Blockade with LAG-3 inhibitors in bladder cancer is critical to explore as potential novel adjunctive therapy. Source of Funding: NA © 2023 by American Urological Association Education and Research, Inc.FiguresReferencesRelatedDetails Volume 209Issue Supplement 4April 2023Page: e302 Advertisement Copyright & Permissions© 2023 by American Urological Association Education and Research, Inc.MetricsAuthor Information Tamir Sholklapper More articles by this author Laura Bukavina More articles by this author Andres Correa More articles by this author Alexander Kutikov More articles by this author Philip Abbosh More articles by this author Expand All Advertisement PDF downloadLoading ...

Bayesian Conditional Transformation Models

Recent developments in statistical regression methodology shift away from pure mean regression towards distributional regression models. One important strand thereof is that of conditional transformation models (CTMs). CTMs infer the entire conditional distribution directly by applying a transformation function to the response conditionally on a set of covariates towards a simple log-concave reference distribution. Thereby, CTMs allow not only variance, kurtosis or skewness but the complete conditional distribution to depend on the explanatory variables. We propose a Bayesian notion of conditional transformation models (BCTMs) focusing on exactly observed continuous responses, but also incorporating extensions to randomly censored and discrete responses. Rather than relying on Bernstein polynomials that have been considered in likelihood-based CTMs, we implement a spline-based parametrization for monotonic effects that are supplemented with smoothness priors. Furthermore, we are able to benefit from the Bayesian paradigm via easily obtainable credible intervals and other quantities without relying on large sample approximations. A simulation study demonstrates the competitiveness of our approach against its likelihood-based counterpart but also Bayesian additive models of location, scale and shape and Bayesian quantile regression. Two applications illustrate the versatility of BCTMs in problems involving real world data, again including the comparison with various types of competitors.

Optimized inferences of finite population mean using robust parameters in systematic sampling.

In this article, we have proposed a generalized estimator for mean estimation by combining the ratio and regression methods of estimation in the presence of auxiliary information using systematic sampling. We incorporated some robust parameters of the auxiliary variable to obtain precise estimates of the proposed estimator. The mathematical expressions for bias and mean square error of proposed the estimator are derived under large sample approximation. Many other generalized ratio and product-type estimators are obtained from the proposed estimator using different choices of scalar constants. Some special cases are also discussed in which the proposed generalized estimator reduces to the usual mean, classical ratio, product, and regression type estimators. Mathematical conditions are obtained for which the proposed estimator will perform more precisely than the challenging estimators mentioned in this article. The efficiency of the proposed estimator is evaluated using four populations. Results showed that the proposed estimator is efficient and useful for survey sampling in comparison to the other existing estimators.

Robust Inference for Partially Observed Functional Response Data.

Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in quantitative ultrasound signal analysis, this paper investigates a class of robust M-estimators for partially observed functional data including functional location and quantile estimators. Consistency of the estimators is established under general conditions on the partial observation process. Under smoothness conditions on the class of M-estimators, asymptotic Gaussian process approximations are established and used for large sample inference. The large sample approximations justify a bootstrap approximation for robust inferences about the functional response process. The performance is demonstrated in simulations and in the analysis of irregular functional data from quantitative ultrasound analysis.

An analytical study of the critical values of response rate in single-arm phase II clinical trial designs

A single-arm phase II clinical trial is usually conducted for finding an appropriate dose-level and testing toxicity for an experimental cancer therapy in comparison to some historical controls, and is usually the most doable trial type due to the feasibility under limited budget, patient pool and medical conditions that can be met. We considered the standard setting of a single-arm two-stage phase II clinical trial, and investigated the patterns of critical values and sample sizes at both two stages of minimax and optimal designs under different design parameters, i.e., under different response rates of control and treatment, significant level of the test, and statistical power. We provided analytic derivations to the patterns we are interested under large sample approximation, and investigated them under finite ans small sample via a numerical study by considering extensively possible design parameters over a fine grid. We finally concluded that the critical values at different stages of the test are related to the sample sizes at different stages in a similar way for both optimal and minimax designs, but they also reveal some differences and reflected the nature of these two types of design.