Combining cox regressions across a heterogeneous distributed research network facing small and zero counts

Studies of the effects of medical interventions increasingly take place in distributed research settings using data from multiple clinical data sources including electronic health records and administrative claims. In such settings, privacy concerns typically prohibit sharing of individual patient data, and instead, cross-network analyses can only utilize summary statistics from the individual databases such as hazard ratios and standard errors. In the specific but very common context of the Cox proportional hazards model, we show that combining such per site summary statistics into a single network-wide estimate using standard meta-analysis methods leads to substantial bias when outcome counts are small. This bias derives primarily from the normal approximations of the per site likelihood that the methods utilized. Here we propose and evaluate methods that eschew normal approximations in favor of three more flexible approximations: a skew-normal, a one-dimensional grid, and a custom parametric function that mimics the behavior of the Cox likelihood function. In extensive simulation studies, we demonstrate how these approximations impact bias in the context of both fixed-effects and (Bayesian) random-effects models. We then apply these approaches to three real-world studies of the comparative safety of antidepressants, each using data from four observational health care databases.

Binomial Count Information: How Do the Usual Approximations Fare?

Focus Decision-making is often aided by examining False Positive Error-risk profiles [FPEs]. In this research report, the decision-making jeopardy that one invites by eschewing the Exact factorial-binomial Probability-values used to form the FPEs in favor of: (i) Normal Approximations [NA], or (ii) Continuity-Corrected Normal Approximations [CCNA] is addressed. Results Referencing an audit context where testing sample sizes for Re-Performance & Re-Calculation protocols are, by economic necessity, in the range of 20 to 100 account items, there are indications that audit decisions would benefit by using the Exact Probability-values. Specifically, using a jeopardy-screen of ±2.5% created by benchmarking the NA & the CCNA by the Exact FPEs, it is observed that: (i) for sample sizes of 100 there is little difference between the Exact and the CCNA FPEs, (ii) almost uniformly for both sample extremes of 20 and 100, the FPEs created using the NA are lower and outside the jeopardy screen, finally (iii) for the CCNA-arm for sample sizes of n = 20, only sometimes are the CCNA FPEs interior to the jeopardy screen. These results call into question not using the Exact Factorial Binomial results. Finally, an illustrative example is offered of an A priori FPE-risk Decision-Grid that can be parametrized and used in a decision-making context.

Functional Gaussian Approximation for Dependent Structures

This book has its origin in the need for developing and analyzing mathematical models for phenomena that evolve in time and influence each another, and aims at a better understanding of the structure and asymptotic behavior of stochastic processes. This monograph has double scope. First, to present tools for dealing with dependent structures directed toward obtaining normal approximations. Second, to apply the normal approximations presented in the book to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including the functional central limit theorem (CLT) and functional moderate deviation principle (MDP). The results will point out large classes of dependent random variables which satisfy invariance principles, making possible the statistical study of data coming from stochastic processes both with short and long memory. Over the course of the book different types of dependence structures are considered, ranging from the traditional mixing structures to martingale-like structures and to weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications have been carefully selected to exhibit the importance of the theoretical results. They include random walks in random scenery and determinantal processes. In addition, due to their importance in analyzing new data in economics, linear processes with dependent innovations will also be considered and analyzed.

Heteroskedasticity- and Autocorrelation-robust F and t Tests in Stata

In this article, we consider time-series, ordinary least-squares, and instrumental-variable regressions and introduce a new pair of commands, har and hart, that implement more accurate heteroskedasticity- and autocorrelation-robust (HAR) F and t tests. These tests represent part of the recent progress on HAR inference. The F and t tests are based on the convenient F and t approximations and are more accurate than the conventional chi-squared and normal approximations. The underlying smoothing parameters are selected to target the type I and type II errors, which are the two fundamental objects in every hypothesis testing problem. The estimation command har and the postestimation test command hart allow for both kernel HAR variance estimators and orthonormal-series HAR variance estimators. In addition, we introduce another pair of new commands, gmmhar and gmmhart, that implement the recently developed F and t tests in a two-step generalized method of moments framework. For these commands, we opt for the orthonormal-series HAR variance estimator based on the Fourier bases because it allows us to develop convenient F and t approximations as in the first-step generalized method of moments framework. Finally, we present several examples to demonstrate these commands.