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Title: Prior constraints in estimation of causal effects in natural experiments Authors:  Sara Geneletti - London School of Economics (United Kingdom) [presenting]
Gianluca Baio - University College London (United Kingdom)
Jose Pina-Sanchez - Leeds University (United Kingdom)
Aidan OKeeffe - University College London (United Kingdom)
Sylvia Richardson - MRC Biostatistics - Cambridge (United Kingdom)
Federico Ricciardi - University College London (United Kingdom)
John Paul Gosling - Leeds University (United Kingdom)
Abstract: Topics are considered where constraints are placed on prior distributions in order to obtain causal effect estimates. The first topic is the estimation of the causal effect of statins (a type of cholesterol lowering drug) in the UK population using a regression discontinuity design. We considered both continuous and binary outcomes and imposed constraints on the prior distributions of some parameters in order to stabilise and obtain causal effect estimates. The second topic involves generating continuous values for the severity of non-custodial sentences. A long-standing issue in criminology is that sentence types come in two flavours -- custodial sentences measured in days and non-custodial sentences measured as factor levels -- making it difficult to compare the two types of outcomes and evaluate the effect of policy changes on sentencing. We describe a method to extend a continuous severity score based on sentence length to non-custodial outcomes. This method involves using prior constraints to impose an ordering by ensuring the severity of non-custodial outcomes cannot exceed certain thresholds. The data thus generated can be used as part of an interrupted time series design to estimate the causal effects of changing sentencing guidelines.