Heterogeneity in treatment effects across diverse populations

Differences in patient characteristics, including age, sex, and race influence the safety and effectiveness of drugs, biologic products, and medical devices. Here we provide a summary of the topics discussed during the opening panel at the 2018 Johns Hopkins Center for Excellence in Regulatory Science and Innovation symposium on Assessing and Communicating Heterogeneity of Treatment Effects for Patient Subpopulations: Challenges and Opportunities. The goal of this session was to provide a brief overview of FDA-regulated therapeutics, including drugs, biologics and medical devices, and some of the major sources of heterogeneity of treatment effects (HTE) related to patient demographics, such as age, sex and race. The panel discussed the US Food and Drug Administration's role in reviewing and regulating drugs, devices, and biologic products and the challenges associated with ensuring that diverse patient populations benefit from these therapeutics. Ultimately, ensuring diverse demographic inclusion in clinical trials, and designing basic and clinical research studies to account for the intended patient population's age, sex, race, and genetic factors among other characteristics, will lead to better, safer therapies for diverse patient populations.     

On prediction with time dependent arma models

The general nonstationary ARMA model with time dependent coefficients is considered and a necessary and sufficient condition for the existence of the solution of such a model is given. A simple form of the above solution is expressed as a one-sided-moving average, in terms of one-sided Green's functions. Using these results we solve the Prediction Problem and give some expressions for the h(>0) step-ahead linear predictor of such a process. A few examples are added to illustrate the theory.     

Family Influence on Physical Health During the Middle Years: The Case of Onset of Hypertension

Using survival analysis for 367 married women and 340 married men, this article investigates (a) change in hazard rates and survival probabilities with age for the onset of hypertension and (b) the influences of stressful marital and parental relationships on the hazard rates and survival probabilities of hypertension. Hazard and survival plots show that the risk for hypertension increases during the middle years to maximum, then decreases with age for both men and women. Log‐logistic survival models demonstrate that although marital stress significantly increases the likelihood of earlier hypertension among these long‐time married men and women, parental stress increases the likelihood of earlier hypertension only for women. These models control for the effects of stressful work conditions, health behaviors, hostility, and education. Employing a longitudinal research design strengthens confidence in the findings. The findings demonstrate that stressful close relationships may be more important determinants of physical health than is generally assumed.     

Analysis of multivariate arma processes with non-stationary innovations

The paper considers vector ARMA processes with nonstationary innovations. It is suggested that this class of models provide a very efficient framework for nonstationary problems. A generalization of the Yule-Walker equations relating the underlying process is obtained. Identification procedures are discussed. The associated prediction problem is solved using the Hilbert space approach.     

Time Series Properties of the Class of Generalized First-Order Autoregressive Processes with Moving Average Errors

A new class of time series models known as Generalized Autoregressive of order one with first-order moving average errors has been introduced in order to reveal some hidden features of certain time series data. The variance and autocovariance of the process is derived in order to study the behaviour of the process. It is shown that in special cases these new results reduce to the standard ARMA results. Estimation of parameters based on the Whittle procedure is discussed. We illustrate the use of this class of model by using two examples.     

Derivation of Kurtosis and Option Pricing Formulas for Popular Volatility Models with Applications in Finance

This article discusses some topics relevant to financial modeling. The kurtosis of a distribution plays an important role in controlling tail-behavior and is used in edgeworth expansion of the call prices. We present derivations of the kurtosis for a number of popular volatility models useful in financial applications, including the class of random coefficient GARCH models. Option pricing formulas for various classes of volatility models are also derived and a simple proof of the option pricing formula under the Black–Scholes model is given.     

Generalized Autoregressive (GAR) Model: A Comparison of Maximum Likelihood and Whittle Estimation Procedures Using a Simulation Study

This article evaluates the performance of two estimators namely, the Maximum Likelihood Estimator (MLE) and Whittle's Estimator (WE), through a simulation study for the Generalised Autoregressive (GAR) model.

As expected, it is found that for the parameters α and σ², the MLE and WE have a better performance than Method of Moments (MOM) estimator. For the parameter δ, MOM sometimes appears to have a slightly better performance than MLE and WE, possibly due to truncation approximations associated with the hypergeometric functions for calculating the autocorrelation function. However, the MLE and WE can be used in practice without loss of efficiency.     

Testing the null hypothesis of zero serial correlation in short panel time series: a comparison of tail probabilities

It is known that the analysis of short panel time series data is very important in many practical problems. This paper calculates the exact moments up to order 4 under the null hypothesis of no serial correlation when there are many independent replications of size 3. We further calculate the tail probabilities under the null hypothesis using the Edgeworth approximation for $n=3, 4$ and $5,$ when the structure of the pdf (probability density function) of the test statistic is in essence different. Finally, we compare the three types of tail probabilities, namely, the Edgeworth approximation, the normal approximation and the exact probabilities through a large scale simulation study.     

Added variable plots for linear regression with censored data

In linear regression the structure of the hat matrix plays an important part in regression diagnostics. In this note we investigate the properties of the hat matrix for regression with censored responses in the presence of one or more explanatory variables observed without censoring. The censored points in the scatterplot are renovated to positions had they been observed without censoring in a renovation process based on Buckley-James censored regression estimators. This allows natural links to be established with the structure of ordinary least squares estimators. In particular, we show that the renovated hat matrix may be partitioned in a manner which assists in deciding whether further explanatory variables should be added to the linear model. The added variable plot for regression with censored data is developed as a diagnostic tool for this decision process.     

Approximate Asymptotic Variance-Covariance Matrix for the Whittle Estimators of GAR(1) Parameters

Generalized Autoregressive (GAR) processes have been considered to model some features in time series. The Whittle's estimates have been investigated for the GAR(1) process by a simulation study by Shitan and Peiris (2008 Shitan , M. , Peiris , S. ( 2008 ). Generalised autoregressive (GAR) model: a comparison of maximum likelihood and whittle estimation procedures using a simulation study . Commun. Statist. Simul. Computat. 37 ( 3 ): 560 – 570 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). This article derives approximate theoretical expressions for the enteries of the asymptotic variance-covariance matrix for those estimates of GAR(1) parameters. These results are supported by a simulation study.