The Power of the Mantel-Haenszel Test when Adjustment is by the True or Estimated Propensity Score

The power of the Mantel-Haenszel test for no treatment effect in the case of binary exposure and response variates was examined through simulation studies when subclasses were formed on the basis of the true and estimated propensity scores and by direct stratification on two continuous covariates. The power of these tests was also compared to the score test in a misspecified logistic regression model. In general adjustment by the true propensity score was most likely to reject a false null hypothesis, the score test was more likely to reject a false null hypothesis than the Mantel-Haenszel test when adjustment is by the estimated propensity score or subclassification on the covariates. There was litte difference in the observed powers of the Mantel-Haenszel tests between adjustment by the estimated propensity score and subclassification on the covariates.     

Asymptotic Distribution of Score Statistics for Spatial Cluster Detection with Censored Data

Summary Cook, Gold, and Li (2007, Biometrics 63, 540–549) extended the Kulldorff (1997, Communications in Statistics 26, 1481–1496) scan statistic for spatial cluster detection to survival‐type observations. Their approach was based on the score statistic and they proposed a permutation distribution for the maximum of score tests. The score statistic makes it possible to apply the scan statistic idea to models including explanatory variables. However, we show that the permutation distribution requires strong assumptions of independence between potential cluster and both censoring and explanatory variables. In contrast, we present an approach using the asymptotic distribution of the maximum of score statistics in a manner not requiring these assumptions.     

Multiple contrast tests in the presence of heteroscedasticity

This paper proposes a general approach for handling multiple contrast tests for normally distributed data in the presence of heteroscedasticity. Three candidate procedures are described and compared by simulations. Only the procedure with both comparison-specific degrees of freedom and a correlation matrix depending on sample variances maintains the alpha-level over all situations. Other approaches may fail notably as the variances differ more. Furthermore, related approximate simultaneous confidence intervals are given. The approach will be applied to a toxicological experiment.     

Detection of Cyclic Trends in Incidence Data Using the Efficiency Score Method

In studies involving a cyclic regularity, researchers usually have a good working knowledge regarding the peak time in the cycle. Capitalizing on this information, we derive the asymptotically uniformly most powerful unbiased test for detecting a cyclic trend using the likelihood score, and present the asymptotic power function of the test and the approximate formula for sample size. Numerical studies demonstrate great advantages of the proposed test over the standard test in terms of power and sample size. Asymptotic power of the score test is satisfactorily close to actual power. We also generalize this method so that it is applicable for incidence data from unequally spaced intervals or risk populations of unequal size.     

Sensitivity of test for overdispersion in Poisson regression

Overdispersion or extra-Poisson variation is very common for count data. This phenomenon arises when the variability of the counts greatly exceeds the mean under the Poisson assumption, resulting in substantial bias for the parameter estimates. To detect whether count data are overdispersed in the Poisson regression setting, various tests have been proposed and among them, the score tests derived by Dean (1992) are popular and easy to implement. However, such tests can be sensitive to anomalous or extreme observations. In this paper, diagnostic measures are proposed for assessing the sensitivity of Dean's score test for overdispersion in Poisson regression. Applications to the well-known fabric faults and Ames salmonella assay data sets illustrate the usefulness of the diagnostics in analyzing overdispersed count data.     

A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives

Count data often show a higher incidence of zero counts than would be expected if the data were Poisson distributed. Zero-inflated Poisson regression models are a useful class of models for such data, but parameter estimates may be seriously biased if the nonzero counts are overdispersed in relation to the Poisson distribution. We therefore provide a score test for testing zero-inflated Poisson regression models against zero-inflated negative binomial alternatives.     

Score Tests for Exploring Complex Models: Application to HIV Dynamics Models

In biostatistics, more and more complex models are being developed. This is particularly the case in system biology. Fitting complex models can be very time‐consuming, since many models often have to be explored. Among the possibilities are the introduction of explanatory variables and the determination of random effects. The particularity of this use of the score test is that the null hypothesis is not itself very simple; typically, some random effects may be present under the null hypothesis. Moreover, the information matrix cannot be computed, but only an approximation based on the score. This article examines this situation with the specific example of HIV dynamics models. We examine the score test statistics for testing the effect of explanatory variables and the variance of random effect in this complex situation. We study type I errors and the statistical powers of this score test statistics and we apply the score test approach to a real data set of HIV‐infected patients.