We use logistic model to get point and interval estimates of the marginal risk difference in observational studies and randomized trials with dichotomous outcome. We prove that the maximum likelihood estimate of the marginal risk difference is unbiased for finite sample and highly robust to the effects of dispersing covariates. We use approximate normal distribution of the maximum likelihood estimates of the logistic model parameters to get approximate distribution of the maximum likelihood estimate of the marginal risk difference and then the interval estimate of the marginal risk difference. We illustrate application of the method by a real medical example.
Masked data are the system failure data when the exact cause of the failures might be unknown. That is, the cause of the system failures may be any one of the components. Additionally, to incorporate more information and provide more accurate analysis, modeling software fault detection and correction processes have attracted widespread research attention recently. However, stochastic fault correction time and masked data brings more difficulties in parameter estimation. In this paper, a framework of open source software growth reliability model with masked data considering both fault detection and correction processes is proposed. Furthermore, a novel Expectation Least Squares (ELS) method, an EM-like (Expectation Maximization) algorithm, is used to solve the problem of parameter estimation, because of its mathematical convenience and computational efficiency. It is note that the ELS procedure is easy to use and useful for practical applications, and it just needs more relaxed hidden assumptions. Finally, three data sets from real open source software project are applied to the proposed framework, and the results show that the proposed reliability model is useful and powerful.
When estimating treatment effect on count outcome of given population, one uses different models in different studies, resulting in non-comparable measures of treatment effect. Here we show that the marginal rate differences in these studies are comparable measures of treatment effect. We estimate the marginal rate differences by log-linear models and show that their finite-sample maximum-likelihood estimates are unbiased and highly robust with respect to effects of dispersing covariates on outcome. We get approximate finite-sample distributions of these estimates by using the asymptotic normal distribution of estimates of the log-linear model parameters. This method can be easily applied to practice.
The traditional reliability models cannot well reflect the effect of performance dependence of subsystems on the reliability of system, and neglect the problems of initial reliability and standby redundancy. In this paper, the reliability of a parallel system with active multicomponents and a single cold-standby unit has been investigated. The simultaneously working components are dependent and the dependence is expressed by a copula function. Based on the theories of conditional probability, the explicit expressions for the reliability and the MTTF of the system, in terms of the copula function and marginal lifetime distributions, are obtained. Let the copula function be the FGM copula and the marginal lifetime distribution be exponential distribution, a system with two parallel dependent units and a single cold-standby unit is taken as an example. The effect of different degrees of dependence among components on system reliability is analyzed, and the system reliability can be expressed as the linear combination of exponential reliability functions with different failure rates. For investigating how the degree of dependence affects the mean lifetime, furthermore, the parallel system with a single cold standby, comprising different number of active components, is also presented. The effectiveness of the modeling method is verified, and the method presented provides a theoretical basis for reliability design of engineering systems and physics of failure.