My methodological research will be split into three areas of estimation. Please see `Case for Support' for further clarification. In Methodology area 1 (G-estimation) I plan to develop: (1a) Bias-adjusted Structural Mean Models (SMMs) for Mendelian randomisation (MR) analyses using multiple instrumental variables (IVs) that use genome-wide association study (GWAS) data for IV selection; (1b) SMMs that can detect and, if necessary, adjust for pleiotropy in MR analyses; (1c) SMMs that are robust to weak instrument bias in MR analyses; (1d) Optimal time-dependent weights for the Rank Preserving Structural Failure Time Model (RPSFTM) that provide more precise G-estimates of the causal effect of treatment in clinical trials of late stage cancer patients; (1e) RPSFTMs that are valid in the presence of treatment effect heterogeneity. Objectives (1a)-(1e) will be in conjunction with Professor's Nuala Sheehan, George Davey Smith, Stijn Vansteelandt and Dr Ian White. In Methodology area 2 (Minimum variance unbiased estimation) I plan to: (2a) Extend MVUE methodology from two-stage to multi-stage Adaptive Seamless Designs (ASDs); (2b) Adapt and apply new MVUE methodology from (2a) to quantify sensitivity, specificity, ROC curve and risk prediction model parameters in multi-stage trials into diagnostic biomarkers. Objectives (2a-2b) will be in collaboration with Professor's Ekkehard Glimm and Toby Prevost. In Methodology area 3 (Shrinkage estimation) I plan to develop: (3a) Methods of shrinkage estimation for selected treatments in two-stage and multi-stage ASDs; (3b) A common Empirical Bayesian framework for bias-adjusted meta-analysis in the presence of small study effects. Objectives (3a-b) will be in conjunction with Professor's Werner Brannath, Sue Todd and Dr Gerta Rucker