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The etiology, pathogenesis, and prognosis for a newly emerging disease are generally unknown to clinicians. Effective interventions and treatments at the earliest possible times are warranted to suppress the fatality of the disease to a minimum, and inappropriate treatments should be abolished. In this situation, the ability to extract most information out of the data available is critical so that important decisions can be made. Ineffectiveness of the treatment can be reflected by a constant fatality over time while effective treatment normally leads to a decreasing fatality rate. A statistical test for constant fatality over time is proposed in this article. The proposed statistic is shown to converge to a Brownian motion asymptotically under the null hypothesis. With the special features of the Brownian motion, we are able to analyze the first passage time distribution based on a sequential tests approach. This allows the null hypothesis of constant fatality rate to be rejected at the earliest possible time when adequate statistical evidence accumulates. Simulation studies show that the performance of the proposed test is good and it is extremely sensitive in picking up decreasing fatality rate. The proposed test is applied to the severe acute respiratory syndrome data in Hong Kong and Beijing.

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We model the load sharing phenomenon in a -out-of-system through the accelerated failure time model. This model leads to multivariate families of distributions for ordered random variables, which are particular cases of the sequential order statistics. For illustrative purpose, we discuss the model, and the estimation problem for a two component parallel system under the setting of a linear failure rate distribution. In this set up, we discuss a test for the hypothesis that the failure times of components are statistically independent against the alternative that they show the load sharing phenomenon. We report simulation studies showing the performance of the estimators, and the test procedure. The test is also applied to two data sets for illustrative purpose.Index Terms-Accelerated failure time model, conditional distribution, Cox proportional hazard model, EM algorithm, linear failure rate distribution, sequential order statistics.