Assessing the similarity of dose response and target doses in two non-overlapping subgroups

We consider two problems that are attracting increasing attention in clinical dose finding studies. First, we assess the similarity of two non-linear regression models for two non-overlapping subgroups of patients over a restricted covariate space. To this end, we derive a confidence interval for the maximum difference between the two given models. If this confidence interval excludes the equivalence margins, similarity of dose response can be claimed. Second, we address the problem of demonstrating the similarity of two target doses for two non-overlapping subgroups, using again a confidence interval based approach. We illustrate the proposed methods with a real case study and investigate their operating characteristics (coverage probabilities, Type I error rates, power) via simulation.Comment: Keywords and Phrases: equivalence testing, multiregional trial, target dose estimation, subgroup analyse

Models for calculating confidence intervals for neural networks

This research focused on coding and analyzing existing models to calculate confidence intervals on the results of neural networks. The three techniques for determining confidence intervals determination were the non-linear regression, the bootstrapping estimation, and the maximum likelihood estimation. Confidence intervals for non-linear regression, bootstrap estimation, and maximum likelihood were coded in Visual Basic. The neural network used the backpropagation algorithm with an input layer, one hidden layer and an output layer with one unit. The hidden layer had a logistic or binary sigmoidal activation function and the output layer had a linear activation function. These techniques were tested on various data sets with and without additional noise. Out of eight cases studied, non-linear regression and bootstrapping each had the four lowest values for the average coverage probability minus the nominal probability. For the average coverage probabilities minus the nominal probabilities of all data sets, the bootstrapping estimation obtained the lowest values. The ranges and standard deviations of the coverage probabilities over 15 simulations for the three techniques were computed, and it was observed that the non-linear regression obtained consistent results with the least range and standard deviation, and bootstrapping had the largest ranges and standard deviations. The bootstrapping estimation technique gave a slightly better average coverage probability (CP) minus nominal values than the non-linear regression method, but it had considerably more variation in individual simulations. The maximum likelihood estimation had the poorest results with respect to the average CP minus nominal values

Estimation of a regression spline sample selection model

It is often the case that an outcome of interest is observed for a restricted non-randomly selected sample of the population. In such a situation, standard statistical analysis yields biased results. This issue can be addressed using sample selection models which are based on the estimation of two regressions: a binary selection equation determining whether a particular statistical unit will be available in the outcome equation. Classic sample selection models assume a priori that continuous regressors have a pre-specified linear or non-linear relationship to the outcome, which can lead to erroneous conclusions. In the case of continuous response, methods in which covariate effects are modeled flexibly have been previously proposed, the most recent being based on a Bayesian Markov chain Monte Carlo approach. A frequentist counterpart which has the advantage of being computationally fast is introduced. The proposed algorithm is based on the penalized likelihood estimation framework. The construction of confidence intervals is also discussed. The empirical properties of the existing and proposed methods are studied through a simulation study. The approaches are finally illustrated by analyzing data from the RAND Health Insurance Experiment on annual health expenditures

On sequential confidence estimation of parameters of stochastic dynamical systems with conditionally Gaussian noises

We consider the problem of non-asymptotical confidence estimation of linear parameters in multidimensional dynamical systems defined by general regression models with discrete time and conditionally Gaussian noises under the assumption that the number of unknown parameters does not exceed the dimension of the observed process. We develop a non-asymptotical sequential procedure for constructing a confidence region for the vector of unknown parameters with a given diameter and given confidence coefficient that uses a special rule for stopping the observations. A key role in the procedure is played by a novel property established for sequential least squares point estimates earlier proposed by the authors. With a numerical modeling example of a two-dimensional first order autoregression process with random parameters, we illustrate the possibilities for applying confidence estimates to construct adaptive predictions

Statistical Software for State Space Methods

In this paper we review the state space approach to time series analysis and establish the notation that is adopted in this special volume of the Journal of Statistical Software. We first provide some background on the history of state space methods for the analysis of time series. This is followed by a concise overview of linear Gaussian state space analysis including the modelling framework and appropriate estimation methods. We discuss the important class of unobserved component models which incorporate a trend, a seasonal, a cycle, and fixed explanatory and intervention variables for the univariate and multivariate analysis of time series. We continue the discussion by presenting methods for the computation of different estimates for the unobserved state vector: filtering, prediction, and smoothing. Estimation approaches for the other parameters in the model are also considered. Next, we discuss how the estimation procedures can be used for constructing confidence intervals, detecting outlier observations and structural breaks, and testing model assumptions of residual independence, homoscedasticity, and normality. We then show how ARIMA and ARIMA components models fit in the state space framework to time series analysis. We also provide a basic introduction for non-Gaussian state space models. Finally, we present an overview of the software tools currently available for the analysis of time series with state space methods as they are discussed in the other contributions to this special volume.