Methods for estimating relative risk in studies of common binary outcomes

Studying the effect of exposure or intervention on a dichotomous outcome is very common in medical research. Logistic regression (LR) is often used to determine such association which provides odds ratio (OR). OR often overestimates the effect size for prevalent outcome data. In such situations, use of relative risk (RR) has been suggested. We propose modifications in Zhang and Yu and Diaz-Quijano methods. These methods were compared with stratified Mantel Haenszel method, LR, log binomial regression (LBR), Zhang and Yu method, Poisson/Cox regression, modified Poisson/Cox regression, marginal probability method, COPY method, inverse probability of treatment weighted LBR, and Diaz-Quijano method. Our proposed modified Diaz-Quijano (MDQ) method provides RR and its confidence interval similar to those estimated by modified Poisson/Cox and LBRs. The proposed modifications in Zhang and Yu method provides better estimate of RR and its standard error as compared to Zhang and Yu method in a variety of situations with prevalent outcome. The MDQ method can be used easily to estimate the RR and its confidence interval in the studies which require reporting of RRs. Regression models which directly provide the estimate of RR without convergence problems such as the MDQ method and modified Poisson/Cox regression should be preferred.     

Some Multiple Decision Procedures for Comparing Several Population Proportions

In this article, comparison of several population proportions using multiple decision approach is studied. The probability of the order of the sample proportions matching with the order of the population proportions is being controlled. A related multiple comparison procedure with a control is also discussed. For ranking the proportions in multinomial distribution, the simultaneous confidence interval is constructed and used for the ranking. Some examples are used to illustrate the multiple decision procedures discussed in this paper.     

A Comparison of Spatiotemporal Surveillance Methods for Nonhomogeneous Change Size

Spatiotemporal surveillance, especially in detection of emerging outbreaks is of particular importance. When an outbreak spreads across some areas, the incidence rate at the center of the outbreak area might be expected to be much higher than the rate at its edge. However, to the best of our knowledge, all existing methods assume a uniformly increasing rate across the entire area of the outbreak. The purpose of this study is to compare the performance of the spatiotemporal surveillance methods such as multivariate cumulative sum (MCUSUM) or multivariate exponentially weighted moving average (MEWMA) when the changes in size are nonhomogeneous. Monte Carlo simulations were conducted to examine the properties of these spatiotemporal surveillance methods and compared them in terms of the detection speed and the identification rate under various scenarios. The results showed that when nonhomogeneous change sizes are involved, the MCUSUM method taking into account spatial nonhomogeneity of increase rates yields a better identification than the method ignoring such change size pattern although the detection speeds are similar. Further, a case study for the detection of male thyroid cancer data in New Mexico in the United States was performed to demonstrate the applicability of these methods.     

Multidimensional scaling models with inequality and equality constraints

Recently, a lot of attention has been brought to constrained estimation theory in multidimensional scaling models. So far, only equality constraints have been thoroughly studied. In this paper, the optimization theory is extended to general multidi-mensional scaling models with both inequality and equality constraints. A Newton-Raphson based algorithm is developed to produce the constrained least squares estimate. To illustrate the theory, some classical color data are reanalyzed in the context of the linear Euclidean distance model.     

Ridge estimation in logistic regression

The variance of the Maximum Likelihood Estimator (MLE) of the slope parameter in a logistic regression model becomes large as the degree of collinearity among the explanatory variables increases. In a Monte Carlo study, we observed that a ridge type estimator is at least as good as, and often much better than, the MLE in terms of Total and Prediction Mean Squared Error criteria. Using a set of medical data it is illustrated that the ridge trace of the estimator considered here is a useful diagnostic tool in logistic regression analysis.     

Expectations of the maximum of sums and the sum of maxima for correlated normal variables

This paper compares expectations of the maximum of sums and the sum of maxima for correlated normal variables. General formulas are given for the expected differences and relative expected differences. Numerical values are computed for the special case of a correlated structure with common variance and covariance to illustrate the general magnitude of the differences which may occur. It is numerically shown that an approximation to the relative differences based on the extreme value distribution is very good. General correlated models with location-scale parameters are also considered. This result should be useful in application. Examples are discussed.     

A Spatiotemporal Model for Pollutant Concentrations

ABSTRACT

Contamination of underground water tables can be characterized by measurements that are mixtures of short-term spiking, long-term decline, and steady-state variations in contaminant levels. Classical statistical models often fail to capture the changes in contaminant flow because they rely on fitting smooth spatial and temporal functions across the region, smooth functions that might not comprehensively characterize contaminant change. In this article, a more comprehensive approach is presented for modeling such processes. This approach uses a new class of spatiotemporal models that can characterize a broad range of environmental processes. It also effectively uses Bayesian hierarchical model fitting and a novel use of near neighbors to model contamination in an underground water table.     

Calibration for Randomized Response Estimators

In the present article, we consider the calibration procedure for the Warner's and Mangat–Singh's (:M–S) randomized response survey estimators using auxiliary information associated with the variable of interest. In the calibration procedure, we can use auxiliary information such as age, gender, and income for the respondents of RR questions from an external source, and then the classical RR estimators can be improved with respect to the problems of noncoverage or nonresponse. From the efficiency comparison study, we show that the calibration estimators are more efficient than those of Warner's and Mangat-Singh's when the known population cell and marginal counts of auxiliary information are used for the calibration procedure.     

How Do Nonlinear Unit Root Tests Perform with Non Normal Errors?

This article examines how popular nonlinear unit root tests perform in the presence of non normal errors. Non normal errors normally do not pose a problem in the usual linear unit root tests since the least squares estimator will still be the most efficient under certain ideal conditions regardless of normal or non normal errors. Whether similar results will carry over to nonlinear unit root tests with non normal errors is a question that merits examination. We find that in contrast to the linear tests, the presence of non normal errors in nonlinear unit root tests will lead to a significant loss of power.     

A residual-based test for autocorrelation in quantile regression models

Quantile regression (QR) models have been increasingly employed in many applied areas in economics. At the early stage, applications in the QR literature have usually used cross-sectional data, but the recent development has seen an increase in the use of QR in both time-series and panel data sets. However, testing for possible autocorrelation, especially in the context of time-series models, has received little attention. As a rule of thumb, one might attempt to apply the usual Breusch–Godfrey LM test to the residuals of a baseline QR. In this paper, we demonstrate analytically and by Monte Carlo simulations that such an application of the LM test can result in potentially large size distortions, especially in either low or high quantiles. We then propose a correct test (named the QF test) for autocorrelation in QR models, which does not suffer from size distortion. Monte Carlo simulations demonstrate that the proposed test performs fairly well in finite samples, across either different quantiles or different underlying error distributions.