Handling missing data in large healthcare dataset: a case study of   unknown trauma outcomes
  Handling of missed data is one of the main tasks in data preprocessing especially in large public service datasets. We have analysed data from the Trauma Audit and Research Network (TARN) database, the largest trauma database in Europe. For the analysis we used 165,559 trauma cases. Among them, there are 19,289 cases (13.19\%) with unknown outcome. We have demonstrated that these outcomes are not missed `completely at random' and, hence, it is impossible just to exclude these cases from analysis despite the large amount of available data. We have developed a system of non-stationary Markov models for the handling of missed outcomes and validated these models on the data of 15,437 patients which arrived into TARN hospitals later than 24 hours but within 30 days from injury. We used these Markov models for the analysis of mortality. In particular, we corrected the observed fraction of death. Two na\"ive approaches give 7.20\% (available case study) or 6.36\% (if we assume that all unknown outcomes are `alive'). The corrected value is 6.78\%. Following the seminal paper of Trunkey (1983) the multimodality of mortality curves has become a much discussed idea. For the whole analysed TARN dataset the coefficient of mortality monotonically decreases in time but the stratified analysis of the mortality gives a different result: for lower severities the coefficient of mortality is a non-monotonic function of the time after injury and may have maxima at the second and third weeks. The approach developed here can be applied to various healthcare datasets which experience the problem of lost patients and missed outcomes. 
E.M. Mirkes, T.J. Coats, J. Levesley, A.N. Gorban
stat.AP