Semi-Parametric Non-Proportional Hazard Model With Time Varying Covariate

The application of survival analysis has extended the importance of statistical methods for time to event data that incorporate time dependent covariates. The Cox proportional hazards model is one such method that is widely used. An extension of the Cox model with time-dependent covariates was adopted when proportionality assumption are violated. The purpose of this study is to validate the model assumption when hazard rate varies with time. This approach is applied to model data on duration of infertility subject to time varying covariate. Validity is assessed by a set of simulation experiments and results indicate that a non proportional hazard model performs well in the phase of violated assumptions of the Cox proportional hazards

Extended Cox Modelling of Survival Data with Guarantee Time

Proportional Hazard regression model for censored survival data often specifies that covariates have a proportional fixed effect on the hazard function of the lifetime distribution of a subject. A modification of the proportional hazards model of Cox (1972) to accommodate the non-proportional effect on hazard with a time-varying covariate and the introduction of guarantee time into the Weibull distributed baseline hazard function. Simulations were conducted to investigate properties of the models. Our approach had shown to have the best asymptotic properties in a simulation study with mean, Absolute Bias (AB) and Mean Square Error (MSE) of the parameter estimates for the models (under different levels of censoring and sample sizes) using simulated data

Empirical Performance of Weibull Self-Similar Tele-traffic Model

The stringent memoryless assumption in general traffic modeling is often violated due to concurrent or batch arrivals. Batch arrivals often leads to self-similarity or long range dependency problems in Internet traffic. Modeling tele-traffic data in this condition requires the use of heavy tailed distribution. In this paper, we propose a general form of Weibull tele-traffic model for self-similar Internet traffic data. The model empirical performance was observed via Monte-Carlo simulation with the aid of discrete event simulation. Performance analysis for the proposed model alongside standard Poisson/ Exponential model was also achieved. The results from the analysis established the strength of Weibull model over the existing model

Construction of Asymmetric Fractional Factorial Designs

In this paper, a method of constructing Asymmetric Fractional Factorial Designs, (AFFD) is presented. This method is based on the extension of a similar concept for symmetric fractional factorial designs (SFFD). A factorial design consisting of n factors is said to be symmetric if, and only if, each factor has the same number of levels, otherwise it is called and asymmetric factorial design. The confounded interactions, and the corresponding confounded degrees of freedom, were determined. The aliases structures and the class of resolution achieved by the constructed designs were determined. Each design obtained and listed achieved a minimum of Resolution III or higher level

The Influence of Autocorrelated Errors on the Bias of Multilevel Time Series Parameter Estimates

The validity of inferences drawn from statistical test results depends on how well data meet associated assumptions. In a two-level multilevel time series model, the standard assumption that the within-individual (level-1) residuals are uncorrelated are rarely checked ornbsp little information tends to be reported on whether the data satisfy the assumption underlying the statistical techniques used. Using a simulation approach, the consequences of violating the level-1 independence of observations assumption on the parameter estimates of fixed effects and the associate errors due to bias was investigated. It was found that bias which is generally high, increases with increase autocorrelated errors, and Full maximum likelihood (FML) estimates are more biased than Restricted maximum likelihood (REML) estimates

Analysis of Optimal Connected Designs Using Minimal Replicates

Minimizing type I and type II errors with appropriate sample sizes in order to have convincing conclusions often pose a great challenge to experimenter. REML and ML criteria are popular for estimating variance-covariance matrix. Which one to use might pose another challenge to an experimenter.nbsp Huge error has effect on experiment. How to get the best information on Incomplete Block Design experiment is the focus of this paper

Multiple randomizations

Multitiered experiments are characterized by involving multiple randomizations, in a sense that we make explicit. We compare and contrast six types of multiple randomizations, using a wide range of examples, and discuss their use in designing experiments. We outline a system of describing the randomizations in terms of sets of objects, their associated tiers and the factor nesting, using randomization diagrams, which give a convenient and readily assimilated summary of an experiment's randomization. We also indicate how to formulate a randomization-based mixed model for the analysis of data from such experiments