Populations of specific components are often heterogeneous and consist of a small number of different sub-populations. For example there are often two groups: defective components with shorter lifetimes and standard components with longer lifetimes. Another heterogeneous population results when components produced by two different manufacturing lines are combined. In either case a mixture results. The resulting population can be described using the statistical concept of a mixture. It is a well-known result that a mixture of distributions with decreasing failure rates has a decreasing failure rate. However, little is known about the monotonicity of a mixture when the various subpopulations have failure rates which are not necessarily decreasing. In this paper we study and attempt to determine the shape as well as the overall behavior of the failure rate of a mixture from two subpopulations each of which has increasing linear failure rate.

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Populations of specific components are often heterogeneous and consist of a small number of different sub-populations. For example there are often two groups: defective components with shorter lifetimes and standard components with longer lifetimes. Another heterogeneous population results when components produced by two different manufacturing lines are combined. In either case a mixture results. The resulting population can be described using the statistical concept of a mixture. It is a well-known result that a mixture of distributions with decreasing failure rates has a decreasing failure rate. However, little is known about the monotonicity of a mixture when the various subpopulations have failure rates which are not necessarily decreasing. In this paper we study and attempt to determine the shape as well as the overall behavior of the failure rate of a mixture from two subpopulations each of which has increasing linear failure rate.

Ten phase 1 studies of LY2140023 monohydrate (LY2140023), an mGlu2/3 receptor agonist, in healthy male and female subjects were pooled to evaluate the adverse event profile. These studies included both single-dose (5-200 mg) and multiple-dose (20-160 mg 2 times a day) treatment groups. The percentage of subjects reporting treatment-emergent adverse events (TEAEs) were assessed in placebo and LY2140023 dose groups: 5 to 20, 40, 60 to 80, and more than 80 mg (120-200 mg). The severity and duration of TEAEs were also determined. Electroencephalograms were performed in 1 study to detect if there were any prodromal signs of convulsions or seizures. Subjects who received either placebo or LY2140023 and participated in the single-dose (n = 159) and multiple-dose (n = 102) treatment groups were included in these analyses. No clear trends for increased TEAE incidence occurred with higher doses of LY2140023 in both the single-dose and multiple-dose treatment groups. The TEAEs with the highest incidence were gastrointestinal and nervous system events. No serious adverse events occurred in any of the 10 studies, and most TEAEs were mild in severity and transient in nature. There were no clinically significant changes in electroencephalograms in subjects receiving LY2140023 (n = 26). LY2140023 was generally well tolerated in healthy subjects.

Abstract:Populations of many types of component are heterogeneous and often consist of a small number of different subpopulations. This is called a mixture and it arises in a number of situations. For example, a majority of products in industrial populations are mixtures of defective items with shorter lifetimes and standard items with longer lifetimes. It is a well-known result that distributions with decreasing failure rates are closed under mixture. However, mixtures of distributions with increasing failure rates are not easily classifiable. If the subpopulations involved in the mixture have increasing failure rates, there might be some upward movement in the mixture and later a general downward pull towards the strongest component. Little work has been done in describing the shape of mixture failure rates when all subpopulations do not have decreasing failure rate. In this paper, we present general results that describe the shape and behavior of a failure rate of a mixture obtained from two Weibull subpopulations with strictly increasing failure rates.