Restricted tests for testing independence of time to failure and cause of failure in a competing-risks model

We consider the competing-risks problem without making any assumption concerning the independence of the risks. Maximum-likelihood estimates of the cause-specific hazard rates are obtained under the condition that their ratio is monotone. We also consider the likelihood-ratio test for testing the proportionality of two cause-specific hazard rates against the alternative that the ratio of these two hazard rates is monotonic. This testing problem is equivalent to testing independence against likelihood-ratio dependence of the time to failure and the cause of failure in the competing-risks setup. We allow for random censoring on the right. The asymptotic null distribution of the test statistic is obtained and is found to be of the chi-bar-square type. The problem is extended to the case of more than two risks. A numerical example is given to illustrate the procedure.     

The tail behavior of the convolutions of Gamma random variables

Two sufficient conditions for comparing convolutions of heterogeneous gamma random variables in terms of star order are established. It is further shown that if the scale parameters of heterogeneous gamma random variables are more dispersed in the sense of majorization, then the convolutions are more dispersed according to the right spread order, which generalizes and strengthens the results in Diaconis and Perlman (1987), Kochar and Xu (2010) and Zhao and Balakrishnan (2009).     

Marshall–Olkin q-Weibull distribution and max–min processes

In this paper, we introduce a new probability model known as Marshall–Olkin q-Weibull distribution. Various properties of the distribution and hazard rate functions are considered. The distribution is applied to model a biostatistical data. The corresponding time series models are developed to illustrate its application in times series modeling. We also develop different types of autoregressive processes with minification structure and max–min structure which can be applied to a rich variety of contexts in real life. Sample path properties are examined and generalization to higher orders are also made. The model is applied to a time series data on daily discharge of Neyyar river in Kerala, India.     

THE EFFECTS OF CORRELATION AMONG OBSERVATIONS ON THE ACCURACY OF APPROXIMATING THE DISTRIBUTION OF SAMPLE MEAN BY ITS ASYMPTOTIC DISTRIBUTION1

In this paper, we investigate the effects of correlation among observations on the accuracy of approximating the distribution of sample mean by its asymptotic distribution. The accuracy is investigated by the Berry-Esseen bound (BEB), which gives an upper bound on the error of approximation of the distribution function of the sample mean from its asymptotic distribution for independent observations. For a given sample size (n₀) the BEB is obtained when the observations are independent. Let this be BEB. We then find the sample size (n_*) required to have BEB below BEB₀, when the observations are dependent. Comparison of n_* with n₀ reveals the effects of correlation among observations on the accuracy of the asymptotic distribution as an approximation. It is shown that the effects of correlation among observations are not appreciable if the correlation is moderate to small but it can be severe for extreme correlations.     

Estimation and Classification of BOLD Responses Over Multiple Trials

In this article, we model functional magnetic resonance imaging (fMRI) data for event-related experiment data using a fourth degree spline to fit voxel specific blood oxygenation level-dependent (BOLD) responses. The data are preprocessed for removing long term temporal components such as drifts using wavelet approximations. The spatial dependence is incorporated in the data by the application of 3D Gaussian spatial filter. The methodology assigns an activation score to each trial based on the voxel specific characteristics of the response curve. The proposed procedure has a capability of being fully automated and it produces activation images based on overall scores assigned to each voxel. The methodology is illustrated on real data from an event-related design experiment of visually guided saccades (VGS).     

Hypothesis testing, power and sample size determination for between group comparisons in fMRI experiments

Modern methods for imaging the human brain, such as functional magnetic resonance imaging (fMRI) present a range of challenging statistical problems. In this paper, we first develop a large sample based test for between group comparisons and use it to determine the necessary sample size in order to obtain a target power via simulation under various alternatives for a given pre-specified significance level. Both testing and sample size calculations are particularly critical for neuroscientists who use these new techniques, since each subject is expensive to image.     

Assessing capacity in the setting of self-neglect: development of a novel screening tool for decision-making capacity

Compared with older adults with disabilities and those who autonomously choose to live in squalor, self-neglect syndrome arises from a predicate state of vulnerability in frail older adults. This state of vulnerability is characteristically associated with a decline in decision-making capacity regarding the ability to care for and protect oneself. We developed the COMP Screen to evaluate vulnerable older adults to identify potential gaps in decision-making capacity using a screening tool. A total of 182 older adults were evaluated and consistent declines in cognitive ability and decision-making processes were present in this population. However, there were no significant differences between elders referred for self-neglect and matched older adults. These findings suggest that declines in decision-making processes are not uncommon in vulnerable older adults but traditional conceptualizations of decision-making capacity may be inadequate for differentiating the capacity for self-care and protection in elders who self-neglect.     

Detection of outliers in the multivariate linear regression model

In this article we suggest multivariate kurtosis as a statistic for detection of outliers in a multivariate linear regression model. The statistic has some local optimality properties.     

Equal Processing Time Bicriteria Scheduling on Parallel Machines

We consider the problem of scheduling jobs on parallel, identical machines so as to minimize a primary and a secondary criteria. All the jobs are assumed to have identical processing times. Polynomial time algorithms, that generate optimal solutions, are presented for various combinations of primary and secondary criteria.     

Comparing Sub-Survival Functions in a Competing Risks Model

In the competing risks literature, one usually compares whether two risks are equal or whether one is more serious. In this paper, we propose tests for the equality of two competing risks against an ordered alternative specified by their sub-survival functions. These tests are naturally developed as extensions of those based on hazard rates and cumulative incidence functions. We note that the interpretation of the new test results is more direct compared to the situation when the hypotheses are framed in terms of their cumulative incidence functions. The proposed tests are of the Kolmogrov–Smirnov type, based on maximum differences between sub-survival functions. Our simulation studies indicate that they are excellent competitors of the existing tests, that are based mainly on differences between cumulative incidence functions. A numerical example will demonstrate the advantages of the proposed tests.