The study recognized the worth of understanding the how’s of handling censoring and censored data in survival analysis and the potential biases it might cause if researchers fail to identify and handle the concepts with utmost care. We systematically reviewed the concepts of censoring and how researchers have handled censored data and brought all the ideas under one umbrella. The review was done on articles written in the English language spanning from the late fifties to the present time. We googled through NCBI, PubMed, Google scholar and other websites and identified theories and publications on the research topic. Revelation was that censoring has the potential of biasing results and reducing the statistical power of analyses if not handled with the appropriate techniques it requires. We also found that, besides the four main approaches (complete-data analysis method; imputation approach; dichotomizing the data; the likelihood-based approach) to handling censored data, there were several other innovative approaches to handling censored data. These methods include censored network estimation; conditional mean imputation method; inverse probability of censoring weighting; maximum likelihood estimation; Buckley-Janes least squares algorithm; simple multiple imputation strategy; filter algorithm; Bayesian framework; β -substitution method; search-and-score-hill-climbing algorithm and constraint-based conditional independence algorithm; frequentist; Markov chain Monte Carlo for imputed data; quantile regression; random effects hierarchical Cox proportional hazards; Lin’s Concordance Correlation Coefficient; classical maximum likelihood estimate. We infer that the presence of incomplete information about subjects does not necessarily mean that such information must be discarded, rather they must be incorporated into the study for they might carry certain relevant information that holds the key to the understanding of the research. We anticipate that through this review, researchers will develop a deeper understanding of this concept in survival analysis and select the appropriate statistical procedures for such studies devoid of biases.

The drift towards face-based recognition systems can be attributed to recent advances in supportive technology and emerging areas of application including voting systems, access control, human-computer interactions, entertainments, and crime control. Despite the obvious advantages of such systems being less intrusive and requiring minimal cooperation of subjects, the performances of their underlying recognition algorithms are challenged by the quality of face images, usually acquired from uncontrolled environments with poor illuminations, varying head poses, ageing, facial expressions, and occlusions. Although several researchers have leveraged on the property of bilateral symmetry to reconstruct half-occluded face images, their approach becomes deficient in the presence of random occlusions. In this paper, we harnessed the benefits of the multiple imputation by the chained equation technique and image denoising using Discrete Wavelet Transforms (DWTs) to reconstruct degraded face images with random missing pixels. Numerical evaluation of the study algorithm gave a perfect (100%) average recognition rate each for recognition of occluded and augmented face images. The study also revealed that the average recognition rate for the augmented face images (75.5811) was significantly lower than the average recognition rate (430.7153) of the occluded face images. MICE augmentation is recommended as a suitable data enhancement mechanism for imputing missing data/pixel of occluded face images.

In spite of the differences in visual stimulus of human beings such as ageing, changing conditions of a person, and occlusion, recognition can even be done at a glance by the human eye many years after the previous encounter. It has been established that facial differences like the hairstyle changes, growing of one’s beard, wearing of glasses, and other forms of occlusions can hardly hinder the power of the human brain from making a face recognition. However, the same cannot easily be said about automated intelligent systems which have been developed to mimic the skill of the human brain to aid in recognition. There have been growing interests in developing a resilient and efficient recognition system mainly because of its numerous application areas (access control, entertainment/leisure, security system based on biometric data, and user-friendly human-machine interfaces). Although there have been numerous researches on face recognition under varying pose, illumination, expression, and image degradations, problems caused by occlusions are mostly ignored. This study thus focuses on facial occlusions and proposes an enhancement mechanism through face image augmentation to improve the recognition of occluded face images. This study assessed the performance of Principal Component Analysis with Singular Value Decomposition using Fast Fourier Transform (FFT-PCA/SVD) for preprocessing face recognition algorithm on face images with missingness and augmented face image database. It was found that the average recognition rates for the FFT-PCA/SVD algorithm were the same ( 90 % ) when face images with missingness and augmented face images were used as test images, respectively. The statistical evaluation revealed that there exists a significant difference in the average recognition distances for the face images with missingness and augmented face images when FFT-PCA/SVD is used for recognition. Augmented face images tend to have a relatively lower average recognition distance when used as test images. This finding is contrary to the equal performance assessment by the adopted numerical technique. The MICE algorithm is therefore recommended as a suitable imputation mechanism for enhancing/improving the performance of the face recognition system.

This study has provided a starting point for defining and working with Cox models in respect of multivariate modeling. In medical researches, there may be situations, where several risk factors potentially affect patient prognosis, howbeit, only one or two might predict patient's predicament. In seeking to find out which of the risk factors contribute the most to the survival times of

Extreme events in earthquakes, wind speed, among others are rare but may lead to catastrophic effects on humans and the environment. The primary parameter in the estimation of such rare events is the tail index which measures the tail heaviness of an underlying distribution. Since extreme events are rare, the presence of missing observations may further lead to flawed. In view of this, there is a growing effort by researchers to address this problem. However, the existing methods of estimating the tail index use only the available nonmissing data. Thus, if the missing observations are influential values, ignoring them could introduce more bias and higher mean square error (MSE) in the tail index estimation and subsequently other extreme event--estimators such as high quantiles and small exceedance probabilities. In this study, we propose imputation of the missing observations before applying some standard estimators (Hill and geometric-type) to estimate the tail index. Through a simulation study, we assess the performance of the standard estimators under the proposed data enhancement method and the existing modified estimators of the tail index. The results show that the enhanced estimators have relatively lower bias and MSE. The estimation method was illustrated with a practical dataset on wind speed with missing values. Therefore, we recommend imputation mechanism as viable for enhancing the performance of tail index estimators in the case where there is missingness.