The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As the non-parametric model,... Show moreThe additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As the non-parametric model, additive hazards offer a very flexible way of modeling time-varying covariate effects. It is most commonly estimated by ordinary least squares. In this paper, we consider the case where covariates are bounded, and derive the maximum likelihood estimator under the constraint that the hazard is non-negative for all covariate values in their domain. We show that the maximum likelihood estimator may be obtained by separately maximizing the log-likelihood contribution of each event time point, and we show that the maximizing problem is equivalent to fitting a series of Poisson regression models with an identity link under non-negativity constraints. We derive an analytic solution to the maximum likelihood estimator. We contrast the maximum likelihood estimator with the ordinary least-squares estimator in a simulation study and show that the maximum likelihood estimator has smaller mean squared error than the ordinary least-squares estimator. An illustration with data on patients with carcinoma of the oropharynx is provided. Show less
The Globaltest is a powerful test for the global null hypothesis that there is no association between a group of features and a response of interest, which is popular in pathway testing in... Show moreThe Globaltest is a powerful test for the global null hypothesis that there is no association between a group of features and a response of interest, which is popular in pathway testing in metabolomics. Evaluating multiple feature sets, however, requires multiple testing correction. In this paper, we propose a multiple testing method, based on closed testing, specifically designed for the Globaltest. The proposed method controls the familywise error rate simultaneously over all possible feature sets, and therefore allows post hoc inference, that is, the researcher may choose feature sets of interest after seeing the data without jeopardizing error control. To circumvent the exponential computation time of closed testing, we derive a novel shortcut that allows exact closed testing to be performed on the scale of metabolomics data. An R package ctgt is available on comprehensive R archive network for the implementation of the shortcut procedure, with applications on several real metabolomics data examples. Show less
When a ranking of institutions such as medical centers or universities is based on a numerical measure of performance provided with a standard error, confidence intervals (CIs) should be calculated... Show moreWhen a ranking of institutions such as medical centers or universities is based on a numerical measure of performance provided with a standard error, confidence intervals (CIs) should be calculated to assess the uncertainty of these ranks. We present a novel method based on Tukey's honest significant difference test to construct simultaneous CIs for the true ranks. When all the true performances are equal, the probability of coverage of our method attains the nominal level. In case the true performance measures have no exact ties, our method is conservative. For this situation, we propose a rescaling method to the nominal level that results in shorter CIs while keeping control of the simultaneous coverage. We also show that a similar rescaling can be applied to correct a recently proposed Monte-Carlo based method, which is anticonservative. After rescaling, the two methods perform very similarly. However, the rescaling of the Monte-Carlo based method is computationally much more demanding and becomes infeasible when the number of institutions is larger than 30-50. We discuss another recently proposed method similar to ours based on simultaneous CIs for the true performance. We show that our method provides uniformly shorter CIs for the same confidence level. We illustrate the superiority of our new methods with a data analysis for travel time to work in the United States and on rankings of 64 hospitals in the Netherlands. Show less
