Modeling Of Bayes Instrumental Variables Analysis And Application In Observational Study Data

Background:Observational studies do not restrict the inclusion of subjects and implement extra intervention,which lead to better extrapolation of research result and better compliance. However, observationalstudies do not randomize the subjects and are susceptible to various confounding factors. Traditionalmethods including regression, stratification, and multivariate analysis can only eliminate the biasraised by measured confounder, while instrumental variables (IV) analysis is a newly presentedmethod to handle the bias caused by unmeasured confounder. Bayes statistic can inference thecausality according to the information provided by prior distribution and current sample to, whichoffer a way to connect current research with previous studies. The combination of bayes theory andIV analysis would make full use of the both methods. Studies on bayes IV are limited, exploring thefeasibility and application condition of bayes IV in observational study has both practice value andtheory significance.Aim:This thesis aims to model an alternative IV analysis method based on bayes theory, which mayreuse the result in previous studies related to current study and to be more flexible with noassumption on the distribution of parameter. The structured model will be verified in simulated studyand compare with traditional IV methods in different conditions to explore the feasibility andapplication conditions. After testifying the performance of the structured model, the method will beadopted to analysis the data in the survey of health service。Method:This thesis systematically reviews the previous studies on IV analysis theory and application andselects the most common used methods in specified data type of exposure and outcome as thetraditional IV methods. The selected methods will be combined with bayes theory to model thebayes IV analysis method. The combination is implemented by treat the traditional IV methods asfundament and inference the posterior distribution in the means of MCMC chain with specified priordistribution and initial values. The bayes IV method was compared with traditional IV methods ondifferent conditions to access the accuracy and precision and obtain the best estimation method inspecified condition. The obtained best method was adopted to analysis the data in health survey and balance possible unmeasured confounders.Result:The study generated three different kinds of exposure and outcome: continuous exposure andcontinuous outcome, binary exposure and binary outcome, and continuous exposure and binaryoutcome. Bayes and traditional IV analysis methods were compared on the conditions of differentrelation between exposure and outcome, different strength of IV, different strength of unmeasuredconfounder. The performance criterions include bias, mean square deviation, coverage, with ofconfidential interval.When there are no unmeasured confounders in the model, ordinary linear and logistic regressionmay derive unbiased result, while the result may be heavily biased when the existence ofunmeasured confounder and IV analysis could reduce the bias significantly. The performance ofdifferent IV analysis methods vary heavily in different data type of exposure and outcome. In detail,traditional2stage least square (2SLS) method is the best performance method when the exposureand outcome are both continuous, least square prediction substitution (LSPS) method and bayesLSPS derive the smallest bias when exposure and outcome are both binary, least square residualinclusion (LSRI) method and bayes LSRI is the most reliable method when exposure is continuousand outcome is binary. The difference between bayes IV and traditional IV is small based on thesame correct model. The performance of the two methods is not influenced by the relation betweenexposure and outcome, while will be influenced by the strength of IV and the strength ofunmeasured confounder, the stronger of the IV the better of the performance, the stronger of theunmeasured confounder the worse of the performance. Compared with traditional IV method, bayesIV method usually derived higher coverage and wider confidential interval and performs better onthe condition of strong IV.As for the actual application of IV analysis in health survey data, the results of univariate IVanalysis is tend to the results of multivariate linear/logistic regression, which verified the effect of IVanalysis on reducing bias caused by unmeasured confounder. The results of multivariate IV analysisconsolidate the effect of physical exercises on health improvement in elder people.Conclusion:According to different data types of exposure and outcome in epidemiology study, correct IVanalysis could reduce bias caused by unmeasured confounder significantly. Based on correct model, bayes IV analysis methods perform well in different conditions and are lightly better than traditionalIV methods when the strength of IV is strong. The performance of bayes IV analysis on theconditions of limited sample size and unperfected IV need further research.Physical exercises could improve the health of elder people in Shanghai, further studies shouldtake exercise time, exercise frequency, exercise intensity into account and adopt morecomprehensive scale of life quality to develop more scientific exercises strategies.