Clustering is basically one of the major sources of primary data mining tools. It makes
researchers understand the natural grouping of attributes in datasets. Clustering is an
unsupervised classification method with the major aim of partitioning, where objects in the
same cluster are similar, and objects which belong to different clusters vary significantly,
with respect to their attributes. However, the classical Standardized Euclidean distance,
which uses standard deviation to down weight maximum points of the ith features on the
distance clusters, has been criticized by many scholars that the method produces outliers,
lack robustness, and has 0% breakdown points. It also has low efficiency in normal
distribution. Therefore, to remedy the problem, we suggest two statistical estimators
which have 50% breakdown points namely the Sn and Qn estimators, with 58% and 82%
efficiency, respectively. The proposed methods evidently outperformed the existing methods
in down weighting the maximum points of the ith features in distance-based clustering
analysis.
Outliers in the X-direction or high leverage points are the latest known source of multicollinearity. Multicollinearity is a nonorthogonality of two or more explanatory variables in multiple regression models, which may have important influential impacts on interpreting a fitted regression model. In this paper, we performed Monte Carlo simulation studies to achieve two main objectives. The first objective was to study the effect of certain magnitude and percentage of high leverage points, which are two important issues in tending the high leverage points to be collinearity-enhancing observations, on the multicollinarity pattern of the data. The second objective was to investigate in which situations these points do make different degrees of multicollinearity, such as moderate or severe. According to the simulation results, high leverage points should be in large magnitude for at least two explanatory variables to guarantee that they are the cause of multicollinearity problems. We also proposed some practical Lower Bound (LB) and Upper Bound (UB) for High Leverage Collinearity Influential Measure (HLCIM) which is an essential measure in detecting the degree of multicollinearity. A well-known example is used to confirm the simulation results.
There are numerous parametric models for analyzing survival data such as exponential, Weibull, log-normal and gamma. One of such models is the Gompertz model which is widely used in biology and demography. Most of these models are extended to new forms for accommodating different types of censoring mechanisms and different types of covariates. In this paper the performance of the Gompertz model with time-dependent covariate in the presence of right censored data was studied. Moreover, the performance of the model was compared at different censoring proportions (CP) and sample sizes. Also, the model was compared with fixed covariate model. In addition, the effect of fitting a fixed covariate model wrongly to a data with time-dependent covariate was studied. Finally, two confidence interval estimation techniques, Wald and jackknife, were applied to the parameters of this model and the performance of the methods was compared.
High Leverage Points (HLPs) are outlying observations in the X -directions. It is very imperative to detect HLPs because the computed values of various estimates are affected by their presence. It is now evident that Diagnostic Robust Generalized Potential which is based on the Minimum Volume Ellipsoid (DRGP(MVE)) is capable of detecting multiple HLPs. However, it takes very long computational running times. Another diagnostic measure which is based on Index Set Equality denoted as DRGP(ISE) is put forward with the main aim of reducing its running time. Nonetheless, it is computationally not stable and still suffers from masking and swamping effects. Hence, in this paper, we propose another version of diagnostic measure which is based on Reweighted Fast Consistent and High Breakdown (RFCH) estimators. We call this measure Diagnostic Robust Generalized Potential based on RFCH and it is denoted by DRGP(RFCH). The results of simulation study and real data indicate that our proposed method outperformed the other two methods in term of having the least computing time, highest percentage of correct detection of HLPs and smallest percentage of swamping and masking effects compared to the DRGP(MVE) and DRGP (ISE).
Left-truncated and censored survival data are commonly encountered in medical studies. However, traditional inferential methods that heavily rely on normality assumptions often fail when lifetimes of observations in a study are both truncated and censored. Thus, it is important to develop alternative inferential procedures that ease the assumptions of normality and unconventionally relies on the distribution of data in hand. In this research, a three parameter log-normal parametric survival model was extended to incorporate left-truncated and right censored medical data with covariates. Following that, bootstrap inferential procedures using non-parametric and parametric bootstrap samples were applied to the parameters of this model. The performance of the parameter estimates was assessed at various combinations of truncation and censoring levels via a simulation study. The recommended bootstrap intervals were applied to a lung cancer survival data.
Microbial keratitis is one of the most challenging complications of contact lens (CL) wear. Proper CL practice plays an important role to reduce the risk for contact lens related microbial keratitis (CLRMK). Methods: This multi-centre case-control study was conducted from January 2008 until June 2009 to determine the risk factors associated with CLRMK. Cases were defined as respondents who were treated for CLRMK, whilst controls were respondents who were contact lens wearers without microbial keratitis. Ninety four cases were compared to 94 controls to determine the risk factors for
CLRMK. Results: The predictors for CLRMK were: Not washing hands with soap before handling CL (aOR 2.979, CI 1.020, 8.701 p=0.046), not performing rubbing technique whilst cleaning the CL (aOR 3.006, CI 1.198, 7.538 p=0.019) and, not cleaning the lens case with multipurpose solution daily (aOR 3.242 CI 1.463, 7.186 p=0.004). Sleeping overnight with the CL in the eye (aOR 2.864, CI 0.978, 8.386 p=0.049) and overall non-compliance with lens care procedures (aOR 2.590, CI 1.003, 6.689 p=0.049) contributed significantly to CLRMK. Conclusion: Health education and promotion in contact lens care are important and should be conducted by eye care practitioners to reduce the occurrence of CLRMK.
Introduction: A hospital based case control study was
conducted in government hospitals on contact lens patients
diagnosed with microbial keratitis. Methods: The objective of
this study is to determine the visual outcomes of contact lens
related microbial keratitis. The visual outcomes which
comprised of visual acuity, keratometry readings, corneal
topography findings and contrast sensitivity examinations was
determined after three months from the first presentation at the
hospitals. Results: The mean LogMAR visual acuity during
presentation was 0.96 ± 0.73 or a Snellen equivalent 6/60 (n=76)
and mean LogMAR visual acuity after three months was 0.10 ±
0.48 or a Snellen equivalent 6/7.5 (n=76) with a significant
difference (t=11.22, df=78, p=0.001). Best fit curve for the cases
had a regression coefficient, r=0.350 ± 0.063 (95% CI = 0.224,
0.447, df=78, p=0.001. The visual acuity in cases and controls
was 0.10 ± 0.48 and -0.10 ± 0.14 respectively (t= -3.61, df=154
p=0.001) after three months which showed improvement. There
was a reduction in the corneal uniformity index and corneal
asphericity in the cases. The Corneal Uniformity Index (CU
index) in cases was 63.03 ± 26.38 (n=76) and in controls, 80.13
± 11.30 (n=77), (t= -5.22, df=151, p=0.001). There was also a
reduction in the contrast sensitivity function at all spatial
frequencies in the cases which was significantly different.
Conclusion: Microbial keratitis reduced the vision, corneal
uniformity index, asphericity and contrast sensitivity after three
months in eyes of patients diagnosed with the condition.