Marginalization of Regression-Adjusted Treatment Effects in Indirect Comparisons with Limited Patient-Level Data

Population adjustment methods such as matching-adjusted indirect comparison (MAIC) are increasingly used to compare marginal treatment effects when there are cross-trial differences in effect modifiers and limited patient-level data. MAIC is sensitive to poor covariate overlap and cannot extrapolate beyond the observed covariate space. Current outcome regression-based alternatives can extrapolate but target a conditional treatment effect that is incompatible in the indirect comparison. When adjusting for covariates, one must integrate or average the conditional estimate over the population of interest to recover a compatible marginal treatment effect. We propose a marginalization method based on parametric G-computation that can be easily applied where the outcome regression is a generalized linear model or a Cox model. In addition, we introduce a novel general-purpose method based on multiple imputation, which we term multiple imputation marginalization (MIM) and is applicable to a wide range of models. Both methods can accommodate a Bayesian statistical framework, which naturally integrates the analysis into a probabilistic framework. A simulation study provides proof-of-principle for the methods and benchmarks their performance against MAIC and the conventional outcome regression. The marginalized outcome regression approaches achieve more precise and more accurate estimates than MAIC, particularly when covariate overlap is poor, and yield unbiased marginal treatment effect estimates under no failures of assumptions. Furthermore, the marginalized regression-adjusted estimates provide greater precision and accuracy than the conditional estimates produced by the conventional outcome regression, which are systematically biased because the measure of effect is non-collapsible

Nonparametric Misclassification Simulation and Extrapolation Method and Its Application

The misclassification simulation extrapolation (MC-SIMEX) method proposed by Küchenho et al. is a general method of handling categorical data with measurement error. It consists of two steps, the simulation and extrapolation steps. In the simulation step, it simulates observations with varying degrees of measurement error. Then parameter estimators for varying degrees of measurement error are obtained based on these observations. In the extrapolation step, it uses a parametric extrapolation function to obtain the parameter estimators for data with no measurement error. However, as shown in many studies, the parameter estimators are still biased as a result of the parametric extrapolation function used in the MC-SIMEX method. Therefore, we propose a nonparametric MC-SIMEX method in which we use a nonparametric extrapolation function. It uses the fractional polynomial method with cross-validation to choose the appropriate fractional polynomial terms. An example is provided based on data from the National Health and Nutrition Examination Survey

New avenue to the Parton Distribution Functions: Self-Organizing Maps

Neural network algorithms have been recently applied to construct Parton Distribution Function (PDF) parametrizations which provide an alternative to standard global fitting procedures. We propose a technique based on an interactive neural network algorithm using Self-Organizing Maps (SOMs). SOMs are a class of clustering algorithms based on competitive learning among spatially-ordered neurons. Our SOMs are trained on selections of stochastically generated PDF samples. The selection criterion for every optimization iteration is based on the features of the clustered PDFs. Our main goal is to provide a fitting procedure that, at variance with the standard neural network approaches, allows for an increased control of the systematic bias by enabling user interaction in the various stages of the process.Comment: 34 pages, 17 figures, minor revisions, 2 figures update

Parametric G-computation for Compatible Indirect Treatment Comparisons with Limited Individual Patient Data

Population adjustment methods such as matching-adjusted indirect comparison (MAIC) are increasingly used to compare marginal treatment effects when there are cross-trial differences in effect modifiers and limited patient-level data. MAIC is based on propensity score weighting, which is sensitive to poor covariate overlap and cannot extrapolate beyond the observed covariate space. Current outcome regression-based alternatives can extrapolate but target a conditional treatment effect that is incompatible in the indirect comparison. When adjusting for covariates, one must integrate or average the conditional estimate over the relevant population to recover a compatible marginal treatment effect. We propose a marginalization method based parametric G-computation that can be easily applied where the outcome regression is a generalized linear model or a Cox model. The approach views the covariate adjustment regression as a nuisance model and separates its estimation from the evaluation of the marginal treatment effect of interest. The method can accommodate a Bayesian statistical framework, which naturally integrates the analysis into a probabilistic framework. A simulation study provides proof-of-principle and benchmarks the method's performance against MAIC and the conventional outcome regression. Parametric G-computation achieves more precise and more accurate estimates than MAIC, particularly when covariate overlap is poor, and yields unbiased marginal treatment effect estimates under no failures of assumptions. Furthermore, the marginalized regression-adjusted estimates provide greater precision and accuracy than the conditional estimates produced by the conventional outcome regression, which are systematically biased because the measure of effect is non-collapsible. This article is protected by copyright. All rights reserved

A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks

We propose a nonparametric method for estimating the pricing formula of a derivative asset using learning networks. Although not a substitute for the more traditional arbitrage-based pricing formulas, network pricing formulas may be more accurate and computationally more efficient alternatives when the underlying asset's price dynamics are unknown, or when the pricing equation associated with no-arbitrage condition cannot be solved analytically. To assess the potential value of network pricing formulas, we simulate Black-Scholes option prices and show that learning networks can recover the Black-Scholes formula from a two-year training set of daily options prices, and that the resulting network formula can be used successfully to both price and delta-hedge options out-of-sample. For comparison, we estimate models using four popular methods: ordinary least squares, radial basis function networks, multilayer perceptron networks, and projection pursuit. To illustrate the practical relevance of our network pricing approach, we apply it to the pricing and delta-hedging of S&P 500 futures options from 1987 to 1991.

The Phase Diagram of Four Flavor SU(2) Lattice Gauge Theory at Nonzero Chemical Potential and Temperature

SU(2) lattice gauge theory with four flavors of quarks is simulated at nonzero chemical potential $\mu$ and temperature $T$ and the results are compared to the predictions of Effective Lagrangians. Simulations on $16^4$ lattices indicate that at zero $T$ the theory experiences a second order phase transition to a diquark condensate state. Several methods of analysis, including equation of state fits suggested by Chiral Perturbation Theory, suggest that mean-field scaling describes this critical point. Nonzero $T$ and $\mu$ are studied on $12^3 \times 6$ lattices. For low $T$, increasing $\mu$ takes the system through a line of second order phase transitions to a diquark condensed phase. Increasing $T$ at high $\mu$, the system passes through a line of first order transitions from the diquark phase to the quark-gluon plasma phase. Metastability is found in the vicinity of the first order line. There is a tricritical point along this line of transitions whose position is consistent with theoretical predictions.Comment: 42 pages revtex, 25 figures postscrip

Marginalization of Regression-Adjusted Treatment Effects in Indirect Comparisons with Limited Patient-Level Data

Population adjustment methods such as matching-adjusted indirect comparison (MAIC) are increasingly used to compare marginal treatment effects when there are cross-trial differences in effect modifiers and limited patient-level data. MAIC is sensitive to poor covariate overlap and cannot extrapolate beyond the observed covariate space. Current outcome regression-based alternatives can extrapolate but target a conditional treatment effect that is incompatible in the indirect comparison. When adjusting for covariates, one must integrate or average the conditional estimate over the population of interest to recover a compatible marginal treatment effect. We propose a marginalization method based on parametric G-computation that can be easily applied where the outcome regression is a generalized linear model or a Cox model. In addition, we introduce a novel general-purpose method based on multiple imputation, which we term multiple imputation marginalization (MIM) and is applicable to a wide range of models. Both methods can accommodate a Bayesian statistical framework, which naturally integrates the analysis into a probabilistic framework. A simulation study provides proof-of-principle for the methods and benchmarks their performance against MAIC and the conventional outcome regression. The marginalized outcome regression approaches achieve more precise and more accurate estimates than MAIC, particularly when covariate overlap is poor, and yield unbiased marginal treatment effect estimates under no failures of assumptions. Furthermore, the marginalized covariate-adjusted estimates provide greater precision and accuracy than the conditional estimates produced by the conventional outcome regression, which are systematically biased because the measure of effect is non-collapsible.Comment: 86 pages (28 of supplementary appendices and references), 5 figures. Updated after PhD viva comments. arXiv admin note: text overlap with arXiv:2004.1480

Bayesian fractional polynomials

This paper sets out to implement the Bayesian paradigm for fractional polynomial models under the assumption of normally distributed error terms. Fractional polynomials widen the class of ordinary polynomials and offer an additive and transportable modelling approach. The methodology is based on a Bayesian linear model with a quasi-default hyper-g prior and combines variable selection with parametric modelling of additive effects. AMarkov chain Monte Carlo algorithm for the exploration of the model space is presented. This theoretically well-founded stochastic search constitutes a substantial improvement to ad hoc stepwise procedures for the fitting of fractional polynomial models. The method is applied to a data set on the relationship between ozone levels and meteorological parameters, previously analysed in the literatur

Population-Adjusted Indirect Treatment Comparisons with Limited Access to Patient-Level Data

Health technology assessment systems base their decision-making on health-economic evaluations. These require accurate relative treatment effect estimates for specific patient populations. In an ideal scenario, a head-to-head randomized controlled trial, directly comparing the interventions of interest, would be available. Indirect treatment comparisons are necessary to contrast treatments which have not been analyzed in the same trial. Population-adjusted indirect comparisons estimate treatment effects where there are: no head-to-head trials between the interventions of interest, limited access to patient-level data, and cross-trial differences in effect measure modifiers. Health technology assessment agencies are increasingly accepting evaluations that use these methods across a diverse range of therapeutic areas. Popular approaches include matching-adjusted indirect comparison (MAIC), based on propensity score weighting, and simulated treatment comparison (STC), based on outcome regression. There is limited formal evaluation of these methods and whether they can be used to accurately compare treatments. Thus, I undertake a review and a simulation study that compares the standard unadjusted indirect comparisons, MAIC and STC across 162 scenarios. This simulation study assumes that the trials are investigating survival outcomes and measure continuous covariates, with the log hazard ratio as the measure of effect — one of the most widely used setups in health technology assessment applications. MAIC yields unbiased treatment effect estimates under no failures of assumptions. The typical usage of STC produces bias because it targets a conditional treatment effect where the target estimand should be a marginal treatment effect. The incompatibility of estimates in the indirect comparison leads to bias as the measure of effect is non-collapsible. When adjusting for covariates, one must integrate or average the conditional model over the population of interest to recover a compatible marginal treatment effect. I propose a marginalization method based on parametric G-computation that can be easily applied where the outcome regression is a generalized linear model or a Cox model. In addition, I introduce a novel general-purpose method based on the ideas underlying multiple imputation, which is termed multiple imputation marginalization (MIM) and is applicable to a wide range of models, including parametric survival models. The approaches view the covariate adjustment regression as a nuisance model and separate its estimation from the evaluation of the marginal treatment effect of interest. Both methods can accommodate a Bayesian statistical framework, which naturally integrates the analysis into a probabilistic framework, typically required for health technology assessment. Another simulation study provides proof-of-principle for the methods and benchmarks their performance against MAIC and the conventional STC. The simulations are based on scenarios with binary outcomes and continuous covariates, with the log-odds ratio as the measure of effect. The marginalized outcome regression approaches achieve more precise and more accurate estimates than MAIC, particularly when covariate overlap is poor, and yield unbiased marginal treatment effect estimates under no failures of assumptions. Furthermore, regressionadjusted estimates of the marginal effect provide greater precision and accuracy than the conditional estimates produced by the conventional STC, which are systematically biased because the log-odds ratio is a non-collapsible measure of effect. The marginalization methods outlined in this thesis are necessary and important for health technology assessment more generally, because marginal treatment effects should be the preferred inferential target for reimbursement decisions at the population level. Treatment effectiveness inputs in health economic models are often informed by the treatment coefficient of a multivariable regression. An often overlooked issue is that this has a conditional interpretation, and that the coefficients of the regression must be marginalized over the target population of interest to produce a relevant estimate for reimbursement decisions at the population level