Robust Estimation In Meta - Analysis

Meta analysis provides a quantitative method for combining results from separate independent studies with the same problem and has been frequently used in different areas of scientific research. By combining the results from different independent studies, the method allows the researchers to accommodate the heterogeneity of different researches and obtains more reliable results. However existing estimation methods are sensitive to the presence of outliers in the data sets. If the impact of outliers is not accommodated appropriately, such effect will cause failure or even breakdown of parameter estimation. In this thesis we explore the robust estimation for the parameters in meta-regression, including the between-study variance and regression parameters. Huber’s rho function is adopted to derive the formulae of robust maximum likelihood(ML) estimation. The asymptotic properties of proposed robust estimators are established. Corresponding iterative algorithm of robust estimation is developed which is easy to implement in the software. The performance of the proposed methodology is assessed by Monte Carlo simulation studies, and our results show that the robust estimation methods outperform the conventional ML methods when the data set is contaminated by outliers. Two real examples are used for illustrations and the results also support the use of robust estimations in practice.