Least-false and local misspecification methods for longitudinal data with dropout

Abstract

In any longitudinal study, a dropout before the nal timepoint can rarely be avoided. The chosen dropout model is commonly one of these types: Missing Completely at Ran- dom (MCAR), Missing at Random (MAR), Missing Not at Random (MNAR) and Shared Parameter (SP). In this thesis, we present methods to estimate the longitudinal model parameters under a variety of di erent dropout models. These methods are Complete Case analysis (CC), Observed data analysis (Obs), Inverse Probability Weighted estimat- ing equations (IPW), Linear Mixed E ect models (LME), Linear Increment models (LI) and Last Observation Carried Forward (LOCF). We estimate the parameters of the longi- tudinal model under MCAR, MAR, MNAR and SP for both simulated data and real data assuming two and three timepoint examples. We show that all methods work under the MCAR model as expected. Also, the LI method give consistent estimate under the SP model. The IPW and LME give consistent estimate under MAR, while no method work under MNAR. We investigate the consequences of misspecifying the missingness mechanism by deriv- ing the so called least false values. These are the values the parameter estimates converge to, when the assumptions may be wrong. This constitutes the central part of the thesis. In order to calculate the least false values, we use the approximation to the extended skew normal distribution (ESN) as produced in Ho et al. [2012]. We give closed form expressions to calculate the least false values 3 and 4 for LI, CC and LME methods. For the IPW, we provide a closed form for 3 under SP, MAR and MNAR while for 4 we failed to nd closed form under MNAR and we use a numerical calculation instead. The knowledge of the least false values allows us to conduct sensitivity analysis which will be illustrated. This method provides an alternative to a local misspeci cation sensitivity procedure which has been developed for likelihood-based analysis. The LME method is a likelihood based method, and this idea can be also adapted for the IPW estimating equation ap- proach. We compare the results obtained by our method with the results found by using the local misspeci cation method. We show that Copas and Eguchi [2005] method and LME least false match very well. Both gave very close results. This suggests that our least false method can provide a credible alternative to Copas and Eguchi in sensitivity anal- ysis. In fact it might be preferred since there is no assumption of local misspeci cation. Moreover, we apply the local misspeci cation and least false methods to estimate the bias and sensitivity for two real data examples with two timepoint and three timepoint data. We show how the IPW method is much more sensitive to misspeci cation than the LME method.