Methodology (stat.ME)

Abstract: In this paper, we propose two new algorithms for maximum-likelihood estimation (MLE) of high dimensional sparse covariance matrices. Unlike most of the state of-the-art methods, which either use regularization techniques or penalize the likelihood to impose sparsity, we solve the MLE problem based on an estimated covariance graph. More specifically, we propose a two-stage procedure: in the first stage, we determine the sparsity pattern of the target covariance matrix (in other words the marginal independence in the covariance graph under a Gaussian graphical model) using the multiple hypothesis testing method of false discovery rate (FDR), and in the second stage we use either a block coordinate descent approach to estimate the non-zero values or a proximal distance approach that penalizes the distance between the estimated covariance graph and the target covariance matrix. Doing so gives rise to two different methods, each with its own advantage: the coordinate descent approach does not require tuning of any hyper-parameters, whereas the proximal distance approach is computationally fast but requires a careful tuning of the penalty parameter. Both methods are effective even in cases where the number of observed samples is less than the dimension of the data. For performance evaluation, we test the proposed methods on both simulated and real-world data and show that they provide more accurate estimates of the sparse covariance matrix than two state-of-the-art methods.

Abstract: There are limited options to estimate the treatment effects of variables which are continuous and measured at multiple time points, particularly if the true dose-response curve should be estimated as closely as possible. However, these situations may be of relevance: in pharmacology, one may be interested in how outcomes of people living with -- and treated for -- HIV, such as viral failure, would vary for time-varying interventions such as different drug concentration trajectories. A challenge for doing causal inference with continuous interventions is that the positivity assumption is typically violated. To address positivity violations, we develop projection functions, which reweigh and redefine the estimand of interest based on functions of the conditional support for the respective interventions. With these functions, we obtain the desired dose-response curve in areas of enough support, and otherwise a meaningful estimand that does not require the positivity assumption. We develop $g$-computation type plug-in estimators for this case. Those are contrasted with g-computation estimators which are applied to continuous interventions without specifically addressing positivity violations, which we propose to be presented with diagnostics. The ideas are illustrated with longitudinal data from HIV positive children treated with an efavirenz-based regimen as part of the CHAPAS-3 trial, which enrolled children $<13$ years in Zambia/Uganda. Simulations show in which situations a standard $g$-computation approach is appropriate, and in which it leads to bias and how the proposed weighted estimation approach then recovers the alternative estimand of interest.

Abstract: Recurrent events, including cardiovascular events, are commonly observed in biomedical studies. Researchers must understand the effects of various treatments on recurrent events and investigate the underlying mediation mechanisms by which treatments may reduce the frequency of recurrent events are crucial. Although causal inference methods for recurrent event data have been proposed, they cannot be used to assess mediation. This study proposed a novel methodology of causal mediation analysis that accommodates recurrent outcomes of interest in a given individual. A formal definition of causal estimands (direct and indirect effects) within a counterfactual framework is given, empirical expressions for these effects are identified. To estimate these effects, a semiparametric estimator with triple robustness against model misspecification was developed. The proposed methodology was demonstrated in a real-world application. The method was applied to measure the effects of two diabetes drugs on the recurrence of cardiovascular disease and to examine the mediating role of kidney function in this process.

Abstract: Increasing emphasis on the use of real-world evidence (RWE) to support clinical policy and regulatory decision-making has led to a proliferation of guidance, advice, and frameworks from regulatory agencies, academia, professional societies, and industry. A broad spectrum of studies use real-world data (RWD) to produce RWE, ranging from randomized controlled trials with outcomes assessed using RWD to fully observational studies. Yet many RWE study proposals lack sufficient detail to evaluate adequacy, and many analyses of RWD suffer from implausible assumptions, other methodological flaws, or inappropriate interpretations. The Causal Roadmap is an explicit, itemized, iterative process that guides investigators to pre-specify analytic study designs; it addresses a wide range of guidance within a single framework. By requiring transparent evaluation of causal assumptions and facilitating objective comparisons of design and analysis choices based on pre-specified criteria, the Roadmap can help investigators to evaluate the quality of evidence that a given study is likely to produce, specify a study to generate high-quality RWE, and communicate effectively with regulatory agencies and other stakeholders. This paper aims to disseminate and extend the Causal Roadmap framework for use by clinical and translational researchers, with companion papers demonstrating application of the Causal Roadmap for specific use cases.