The study of longitudinal data plays a significant role in medicine, epidemiology and social sciences. Typically, the interest is in the dependence of an outcome variable on the covariates. The Generalized Linear Models (GLMs) were proposed to unify the regression approach for a wide variety of discrete and continuous longitudinal data. The responses (outcomes) in longitudinal data are usually correlated. Hence, we need to use an extension of the GLMs that account for such correlation. This can be done by inclusion of random effects in the linear predictor; that is the Generalized Linear Mixed Models (GLMMs) (also called random effects models). The maximum likelihood estimates (MLE) are obtained for the regression parameters of a logit model, when the traditional assumption of normal random effects is relaxed. In this case a more convenient distribution, such as the lognormal distribution, is used. However, adding non-normal random effects to the GLMM considerably complicates the likelihood estimation. So, the direct numerical evaluation techniques (such as Newton-Raphson) become analytically and computationally tedious. To overcome such problems, we propose and develop a Monte Carlo EM (MCEM) algorithm, to obtain the maximum likelihood estimates. The proposed method is illustrated using a simulated data.
BACKGROUND: Tibial plateau fractures present an important entity in orthopaedic fractures. Arthroscopic-assisted reduction and internal fixation is a good alternative to ORIF as it has the advantage of direct visualisation of the articular surface of the plateau, direct assessment of the reduction of the articular surface, and managing any associated intra-articular pathology.
AIM: Our study aim is to determine the results of arthroscopic assisted reduction and internal fixation of tibial plateau fractures.
METHODS: This study involved 25 patients with tibial plateau fractures presenting to the emergency department of Cairo University Hospitals between the periods of November 2016 and May 2017. The patients were followed up for an average of 14 months (11-18 months). According to Schatzker’s classification, five patients had type I, eleven had type II, and nine patients had type III fractures.
RESULTS: The average time to full union in Schatzker type I was 9.1 weeks, in type II was 10.2 weeks, and in type III it was 9.4. The mean clinical Rasmussen score among the 25 patients was 26 (range, 24-30). A group of 19 patients (76%) had excellent results, (4 type I, 8 types II, and 7 types III) 6 patients (24 %) had good results (1 type I, 3 types II, 2 types III). Radiologic results were excellent in (14 cases) 56.0% and good results (11 cases) 44%.
CONCLUSION: Arthroscopic assisted reduction and fixation of tibial plateau fractures have the advantages of checking the adequacy of reduction, avoiding the need for detachment of the meniscus, and allowing for accurate diagnosis and management of associated knee injuries. Therefore, we recommend that arthroscopic assisted reduction and fixation of tibial plateau fractures should be used more often.
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