The paper considers the problem of estimation of the parameters in  nite mixture models.In this article, a new method is proposed for of estimation of the parameters in  nite mixture models. Traditionally, the parameter estimation in  nite mixture models is performed from a likelihood point of view by exploiting the expectation maximization (EM) method and the Least Square Principle. Ridge regression is an alternative to the ordinary least squares method when multicollinearity presents among the regressor variables in multiple linear regression analysis. Accordingly, we propose a new shrinkage ridge estimation approach. Based on this principle, we propose an iterative algorithm called RidgeIterative Weighted least Square (RIWLS) to estimate the parameters. Monte-Carlo simulation studies are conducted to appraise the performance of our method. The results show that the Proposed estimator perform better than the IWLS method.

Objective: Bipolar disorder is defined as a common and severe chronic disorder that causes several problems in a person's psychosocial functioning. This study aimed at modeling the development of bipolar disorder episodes using its determinant risk factors over time. Method: This retrospective cohort study was conducted in Hamadan province, the West of Iran, from April 2008 to September 2014. In this study, 124 patients with bipolar disorder (both Type I and Type II) participated. All patients had experienced 4 relapses. GENERALIZED ESTIMATING Equation (GEE) was used to model bipolar disorder episodes, and significance level was set at 0. 05. Results: The mean (± SD) age of the patients was 33. 2 (± 11. 55). Males were more likely to experience mania than depression compared to females (odds ratio = 2. 30, 95% CI (1. 37-3. 86)). Patients who received psychotherapy plus medicine were less likely to experience mania than depression compared to drug receivers (odds ratio = 0. 39, 95% CI (0. 18-0. 88)). In the spring, patients were more likely to experience mania than depression compared to the winter (OR = 2. 22, 95% CI (1. 18-4. 19)). Conclusion: The results of the present study revealed that among bipolar disorder patients in the West of Iran, mania was much more prevalent than depression and mixed episodes. Moreover, it was found that sex, treatment, and season can determine the episodes of bipolar disorder.

Objectives: Elderly people with knee osteoarthritis are more likely to become disabled than others. We aimed to explore the association between two treatments and pain severity in women aged 50-75 years who suffered from knee osteoarthritis.Methods & Materials: 40 women with knee osteoarthritis were randomized into two groups: to either received common treatment or common treatment accompanied by knee traction. The binary response variable was pain severity. Participants were followed up for 10 times. Because of missing data, the multiple-imputation-based GENERALIZED ESTIMATING EQUATIONS (MI-GEE) method was used to estimate the odds of a pain as a function of the treatment groups adjusted for age and body mass index. Data were analyzed by R software. Adjusted odds ratios and 95% confidence intervals were estimated.Results: In multivariate model, we found an association between pain severity and treatment (P=0.004). The pain odds ratios was 0.28 (95% CI: 0.12-0.65) for common treatment accompanied by knee traction group.Conclusion: The pain was found to be lower among patients treated with common treatment accompanied by knee traction than patients treated with only common treatment.

BACKGROUND: The celebrated GENERALIZED ESTIMATING EQUATIONS (GEE) approach is often used in longitudinal data analysis.While this method behaves robustly against misspecification of the working correlation structure, it has some limitations on efficacy of estimators, goodness-of-fit tests and model selection criteria. The quadratic inference functions (QIF) is a new statistical methodology that overcomes these limitations.METHODS: We administered the use of QIF and GEE in comparing the superior and inferior Ahmed glaucoma valve (AGV) implantation, while our focus was on the efficiency of estimation and using model selection criteria; we compared the effect of implant location on intraocular pressure (IOP) in refractory glaucoma patients. We modeled the relationship between IOP and implant location, patient's sex and age, best corrected visual acuity, history of cataract surgery, preoperative IOP and months after surgery with assuming unstructured working correlation.RESULTS: 63 eyes of 63 patients were included in this study; 28 eyes in inferior group and 35 eyes in superior group.The GEE analysis revealed that preoperative IOP has a significant effect on IOP (p=0.011). However, QIF showed that preoperative IOP, months after surgery and squared months are significantly associated with IOP after surgery (p<0.05). Overall, estimates from QIF are more efficient than GEE (RE=1.272).CONCLUSIONS: In the case of unstructured working correlation, the QIF is more efficient than GEE. There were no considerable difference between these locations; our results confirmed previously published works which mentioned it is better that glaucoma patients undergo superior AGV implantation.

Marginal model is one of the approaches that can be used in analyzing longitudinal data. In this model, to obtain valid inference, correlations between responses of the same individuals are considered as parameters to be estimated. The various marginal models for analyzing longitudinal data with binary responses such as marginal models with marginal odds ratio. conditional odds ratio, dependence ratio, multivariate probit and the method of GENERALIZED ESTIMATING EQUATIONS (GEE) are reviewed and compared. Some residuals for examining the goodness of fit of these models are presented. In an empirical example, these models are fitted to some data.

In this paper, we consider a system of GENERALIZED resolvent EQUATIONS involving GENERALIZED pseudocontractive mapping with corresponding system of variational inclusions in real Banach spaces. We establish an equivalence between the system of GENERALIZED resolvent EQUATIONS and the system of variational inclusions using the concept of H(.,.)-co-accretive mapping. Furthermore, we prove the existence of solution of system of GENERALIZED resolvent EQUATIONS and discuss the convergence of iterative sequences generated by the proposed algorithm.

Objective: Anterior cruciate ligament (ACL) tear is one of the most common knee injuries. Kinesthesia is impaired after ACL tear. In this study, using hybrid GENERALIZED estimation EQUATIONS (GEE), which is an efficient method in analyzing correlated data, we try to evaluate the effects of reconstruction surgery and functional brace, along with control of confounding factors, on improving kinesthesia in patients with ACL tear.Materials & Methods: This quasi-experimental study using convenient non-probabilistic sampling, was conducted on 60 patients with acute ACL tear. To evaluate the kinesthesia motion sense, the continuous passive motion machine was used. The test speed was 0.5 degrees per second. The response variable in this study was the kinesthesia motion sense. Surgery, brace, eyes, limbs, BMI, the dominant side, the affected side and age, were considered as the independent variables. R 2.13.0 software was used for fitting the hybrid GEE model.Results: Reconstructive surgery was effective in improving kinesthesia.(OR: 13.94, CI: 95%, 7.486-25.997, P<0.001). However, the functional brace did not improve the kinesthesia motion sense (OR: 0.73, CI: 95%, 0.52-1.033, P=0.076). The odds of getting a threshold of motion sense in patients with a left dominant side, if the affected side was right, in normal conditions, was 0.019 times the left side. (OR: 0.019, CI: 95%, 0.010-0.035, P<0.001). Lack of significant relationship between patients’ limbs and kinesthesia motion sense, indicates that affected limbs can also affect the healthy limbs’ kinesthesia motion sense (OR: 0.97, CI: 95%, 0.806-1.015, P=0.728).Conclusion: Among all other variables included in this study, the variables of reconstruction surgery, affected side, and interaction of the affected side and the dominant side showed a significant relationship.