Statistical developments for network meta-analysis and methane emissions quantification

Abstract

This thesis provides statistical contributions to solve challenges in Network Meta-Analysis (NMA) and the quantification of methane emissions from the oil and gas industry.

NMA is an extension of pairwise meta-analysis which facilitates the simultaneous comparison of multiple treatments using data from randomized controlled trials. Some treatments may involve combinations of components, such as one or more drugs given in different combinations. Component NMA (CNMA) is an extension of NMA which allows the estimation of the relative effects of components. In Chapter 2, we compare the popular Bayesian and frequentist approaches to additive CNMA and show that there is an important difference in the assumptions underlying these commonly used models. We prove that the most popular Bayesian CNMA model is prone to misspecification, while the frequentist approach makes a less restrictive assumption. We develop novel Bayesian CNMA models which avoid the restrictive assumption and are robust, and demonstrate in a simulation study that the proposed Bayesian models have favourable statistical properties compared to the existing Bayesian model. The use of all CNMA approaches is demonstrated on a published network.

A commonly reported item in an NMA is a list of treatments ranked from most to least preferred, also known as a treatment hierarchy. In Chapter 3, we present the Precision Of Treatment Hierarchy (POTH), a metric which quantifies the level of certainty in a treatment hierarchy from Bayesian or frequentist NMA. POTH summarises the level of certainty into a single number between 0 and 1, making it simple to interpret regardless of the number of treatments in the network. We propose modifications of POTH which can be used to investigate the role of individual treatments or subsets of treatments in the level of certainty in the hierarchy. We calculate POTH for a database of published NMAs to investigate its distribution and relationships with network characteristics. We also provide an in-depth worked example to demonstrate the methods on a real dataset.

In the second part of the thesis, we focus on some problems in the quantification of methane emissions from the oil and gas industry. Measurement-based methane inventories, which involve surveying oil and gas facilities and compiling data to estimate methane emissions, are becoming the gold standard for quantifying emissions. However, there is a current lack of statistical guidance for the design and analysis of such surveys. In Chapter 4, we propose the novel application of multi-stage survey sampling techniques to analyse measurement-based methane survey data, providing estimators of total and stratum-level emissions and an interpretable variance decomposition. We also suggest a potentially more efficient approach involving the Hajek estimator, and outline a simple Monte Carlo approach which can be combined with the multi-stage approach to incorporate measurement error. We investigate the performance of the multi-stage estimators in a simulation study and apply the methods to aerial survey data of oil and gas facilities in British Columbia, Canada, to estimate the methane emissions in the province.

In Chapter 5, we introduce a Bayesian model for measurements from a methane quantification technology given a true emission rate. The models are fit using data collected in controlled releases (CR) of methane for six different technology types. We use a weighted bootstrap algorithm to provide the distribution of the true emission rate given a new measurement, which synthesizes the new measurement data with the CR data and external information about the possible true emission rate. We present results for the measurement uncertainty of six quantification technologies. Finally, we demonstrate the use of the weighted bootstrap algorithm with different priors and data.