Abstract: Non-responses and missing data are common in observational studies. Ignoring or inadequately handling missing data may lead to biased parameter estimates, incorrect standard errors and as a consequence, incorrect statistical inference and conclusions. We present a strategy for modelling non-ignorable missing where the probability of nonresponse depends on the outcome. Using a simple case of logistic regression, we quantity the bias in regression estimates and show the observed likelihood is non-identifiable under non-ignorable missing data mechanism. We then adopt a selection model factorisation of the joint distribution as the basis for a sensitivity analysis to study changes in estimated parameters and the robustness of study conclusions against different assumptions. Using simulated data, we explore the performance of the Bayesian selection model in correcting for bias in a logistic regression. We then implement our strategy using survey data from the 45 and Up Study to investigate factors associated with dwelling type change from baseline to follow-up survey. Our findings have practical implications for the use of the 45 and Up Study data to answer important health and quality-of-life questions.