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Supplemental material, sj-pdf-1-ctj-10.1177_17407745231174544 for Overview of modern approaches for identifying and evaluating heterogeneous treatment effects from clinical data by Ilya Lipkovich, David Svensson, Bohdana Ratitch and Alex Dmitrienko in Clinical Trials

Supplemental material, sj-pdf-1-ctj-10.1177_17407745231174544 for Overview of modern approaches for identifying and evaluating heterogeneous treatment effects from clinical data by Ilya Lipkovich, David Svensson, Bohdana Ratitch and Alex Dmitrienko in Clinical Trials

Observational cohort studies are increasingly being used for comparative effectiveness research to assess the safety of therapeutics. Recently, various doubly robust methods have been proposed for average treatment effect estimation by combining the treatment model and the outcome model via different vehicles, such as matching, weighting, and regression. The key advantage of doubly robust estimators is that they require either the treatment model or the outcome model to be correctly specified to obtain a consistent estimator of average treatment effects, and therefore lead to a more accurate and often more precise inference. However, little work has been done to understand how doubly robust estimators differ due to their unique strategies of using the treatment and outcome models and how machine learning techniques can be combined to boost their performance. Here we examine multiple popular doubly robust methods and compare their performance using different treatment and outcome modeling via extensive simulations and a real-world application. We found that incorporating machine learning with doubly robust estimators such as the targeted maximum likelihood estimator gives the best overall performance. Practical guidance on how to apply doubly robust estimators is provided.

Additional file 1 Table S1. Classification of top 20 baseline comorbidities.

Figure S1. Relationship between biomarker values and number of exacerbations in the previous year in the STRATOS 1 all-comers population (full analysis set). Figure S2. Relationship between biomarker values and region in the STRATOS 1 all-comers population (full analysis set). Figure S3. Relationship between biomarker values and age categories in the STRATOS 1 all-comers population (full analysis set). (DOCX 1067 kb)

Parameter modifications applied to the SIDES algorithm. (DOCX 17 kb)

Bayesian Model Averaging (BMA) is a new area in modern applied statistics that provides data analysts with an efficient tool for discovering promising models and obtaining esti-mates of their posterior probabilities via Markov chain Monte Carlo (MCMC). These probabilities can be further used as weights for model averaged predictions and estimates of the parameters of interest. As a result, variance components due to model selection are estimated and accounted for, contrary to the practice of conventional data analysis (such as, for example, stepwise model selection). In addition, variable activation probabilities can be obtained for each variable of interest. This dissertation is aimed at connecting BMA and various ramifications of the multivari-ate technique called Reduced-Rank Regression (RRR). In particular, we are concerned with Canonical Correspondence Analysis (CCA) in ecological applications where the data are represented by a site by species abundance matrix with site-specific covariates. Our goal is to incorporate the multivariate techniques, such as Redundancy Analysis and Ca-nonical Correspondence Analysis into the general machinery of BMA, taking into account such complicating phenomena as outliers and clustering of observations within a single data-analysis strategy. Traditional implementations of model averaging are concerned with selection of variables. We extend the methodology of BMA to selection of subgroups of observations and im-plement several approaches to cluster and outlier analysis in the context of the multivari-ate regression model. The proposed algorithm of cluster analysis can accommodate re-strictions on the resulting partition of observations when some of them form sub-clusters that have to be preserved when larger clusters are formed. Ph. D.

Few issues in modern finance have inspired the interest of both practitioners and theoreticians more than risk evaluation and management. The basic principle governing risk management in an infrastructure project finance deal is intuitive and well-articulated: allocate project-specific risks to parties best able to bear them (taking into account each party's appetite for, and aversion to, risk); control performance risk through incentives; and use market hedging instruments (derivatives) for covering marketwide risks arising from fluctuations in, for instance, interest and exchange rates, among other things. In practice, however, governments have been asked to provide guarantees for various kinds of projects, often at no charge, because of problems associated with market imperfections: a) Derivative markets (swaps, forwards) for currency and interest-rate risk hedging either do not exist or are inadequately developed in most developing countries. b) Limited contracting possibilities (because of problems with credibility of enforcement). c) Differing methods for risk measurement and evaluation. Two factors distinguish the financing of infrastructure projects from corporate and traditional limited-recourse project finance: 1) a high concentration of project risk early in the project life cycle (pre-completion), and 2) a risk profile that changes as the project comes to fruition, with a relatively stable cash flow subject to market and regulatory risk once the project is completed. The authors introduce INFRISK, a computer-based risk-management approach to infrastructure project transactions that involve the private sector. Developed in-house in the Economic Development Institute of the World Bank, INFRISK is a guide to practitioners in the field and a training tool for raising awareness and improving expertise in the application of modern risk management techniques. INFRISK can analyze a project's exposure to a variety of market, credit, and performance risks form the perspective of key contracting parties (project promoter, creditor, and government). Their model is driven by the concept of the project's economic viability. Drawing on recent developments in the literature on project evaluation under uncertainty, INFRISK generates probability distributions for key decision variables, such as a project's net present value, internal rate of return, or capacity to service its debt on time during the life of the project. Computationally, INFRISK works in conjunction with Microsoft Excel and supports both the construction and the operation phases of a capital investment project. For a particular risk variable of interest (such as the revenue stream, operations and maintenance costs, and construction costs, among others) the program first generates a stream of probability of distributions for each year of a project's life through a Monte Carlo simulation technique. One of the key contributions made by INFRISK is to enable the use of a broader set of probability distributions (uniform, normal, beta, and lognormal) in conducting Monte Carlo simulations rather than relying only on the commonly used normal distribution. A user's guide provides instruction on the use of the package.

This research is motivated by an issue frequently encountered in environmental water quality evaluation. Many times, the sample size of water monitoring data is too small to have adequate power. Here, we present a Bayesian power prior approach by incorporating the current data and historical data and/or the data collected at neighboring stations to make stronger statistical inferences on the parameters of interest. The elicitation of power prior distributions is based on the availability of historical data, and is realized by raising the likelihood function of the historical data to a fractional power. The power prior Bayesian analysis has been proven to be a useful class of informative priors in Bayesian inference. In this dissertation, we propose a modified approach to constructing the joint power prior distribution for the parameter of interest and the power parameter. The power parameter, in this modified approach, quantifies the heterogeneity between current and historical data automatically, and hence controls the influence of historical data on the current study in a sensible way. In addition, the modified power prior needs little to ensure its propriety. The properties of the modified power prior and its posterior distribution are examined for the Bernoulli and normal populations. The modified and the original power prior approaches are compared empirically in terms of the mean squared error (MSE) of parameter estimates as well as the behavior of the power parameter. Furthermore, the extension of the modified power prior to multiple historical data sets is discussed, followed by its comparison with the random effects model. Several sets of water quality data are studied in this dissertation to illustrate the implementation of the modified power prior approach with normal and Bernoulli models. Since the power prior method uses information from sources other than current data, it has advantages in terms of power and estimation precision for decisions with small sample sizes, relative to methods that ignore prior information. Ph. D.