Graphical representation of survival curves in the presence of time-dependent categorical covariates with application to liver transplantation

Graphical representation of survival curves is often used to illustrate associations between exposures and time-to-event outcomes. However, when exposures are time-dependent, calculation of survival probabilities is not straightforward. Our aim was to develop a method to estimate time-dependent survival probabilities and represent them graphically. Cox models with time-dependent indicators to represent state changes were fitted, and survival probabilities were plotted using pre-specified times of state changes. Time-varying hazard ratios for the state change were also explored. The method was applied to data from the Adult-to-Adult Living Donor Liver Transplantation Cohort Study (A2ALL). Survival curves showing a ‘split’ at a pre-specified time t allow for the qualitative comparison of survival probabilities between patients with similar baseline covariates who do and do not experience a state change at time t. Time since state change interactions can be visually represented to reflect changing hazard ratios over time. A2ALL study results showed differences in survival probabilities among those who did not receive a transplant, received a living donor transplant, and received a deceased donor transplant. These graphical representations of survival curves with time-dependent indicators improve upon previous methods and allow for clinically meaningful interpretation.     

Inflation projections for monetary policy decision making

Many central banks set inflation targets over the medium term and inflation projections are a key input for monetary policy decision making. In this paper, we present the procedures used by the Spanish Central Bank staff to project consumer price inflation. We also provide some illustrations of their policy uses, such as fan charts, deflation probabilities and the monitoring of inflation targets.     

Analysis of microtubule dynamics using growth curve models

Microtubules are part of the structural network within a cell's cytoplasm, providing structural support as well as taking part in many of the cellular processes. A large body of data provide evidence that dynamics of microtubules in a cell is reponsible for the performance of many critical cellular functions such as cell division. In this article, we study the effect of four different isoforms of a protein tau on microtubule dynamics using growth curve models. The results show that a linear growth curve model is sufficient to explain the data. Moreover, we find that a mutated version of a 3-repeat tau protein has a similar effect as a 4-repeat tau protein on microtubule dynamics. The latter findings conform with the biological understanding of the effect of the protein tau on microtubule dynamics.     

Approximating the risk score for disease diagnosis using MARS

In disease screening and diagnosis, often multiple markers are measured and combined to improve the accuracy of diagnosis. McIntosh and Pepe [Combining several screening tests: optimality of the risk score, Biometrics 58 (2002), pp. 657–664] showed that the risk score, defined as the probability of disease conditional on multiple markers, is the optimal function for classification based on the Neyman–Pearson lemma. They proposed a two-step procedure to approximate the risk score. However, the resulting receiver operating characteristic (ROC) curve is only defined in a subrange (L, h) of false-positive rates in (0,1) and the determination of the lower limit L needs extra prior information. In practice, most diagnostic tests are not perfect, and it is usually rare that a single marker is uniformly better than the other tests. Using simulation, I show that multivariate adaptive regression spline is a useful tool to approximate the risk score when combining multiple markers, especially when ROC curves from multiple tests cross. The resulting ROC is defined in the whole range of (0,1) and is easy to implement and has intuitive interpretation. The sample code of the application is shown in the appendix.     

Nonparametric and semiparametric estimation of the three way receiver operating characteristic surface

In many situations the diagnostic decision is not limited to a binary choice. Binary statistical tools such as receiver operating characteristic (ROC) curve and area under the ROC curve (AUC) need to be expanded to address three-category classification problem. Previous authors have suggest various ways to model the extension of AUC but not the ROC surface. Only simple parametric approaches are proposed for modeling the ROC measure under the assumption that test results all follow normal distributions. We study the estimation methods of three-dimensional ROC surfaces with nonparametric and semiparametric estimators. Asymptotical results are provided as a basis for statistical inference. Simulation studies are performed to assess the validity of our proposed methods in finite samples. We consider an Alzheimer's disease example from a clinical study in the US as an illustration. The nonparametric and semiparametric modelling approaches for the three way ROC analysis can be readily generalized to diagnostic problems with more than three classes.     

Confidence interval estimation of the difference between paired AUCs based on combined biomarkers

In many diagnostic studies, multiple diagnostic tests are performed on each subject or multiple disease markers are available. Commonly, the information should be combined to improve the diagnostic accuracy. We consider the problem of comparing the discriminatory abilities between two groups of biomarkers. Specifically, this article focuses on confidence interval estimation of the difference between paired AUCs based on optimally combined markers under the assumption of multivariate normality. Simulation studies demonstrate that the proposed generalized variable approach provides confidence intervals with satisfying coverage probabilities at finite sample sizes. The proposed method can also easily provide P-values for hypothesis testing. Application to analysis of a subset of data from a study on coronary heart disease illustrates the utility of the method in practice.     

Three-group ROC predictive analysis for ordinal outcomes

Measuring the accuracy of diagnostic tests is crucial in many application areas including medicine, machine learning, and credit scoring. The receiver operating characteristic (ROC) surface is a useful tool to assess the ability of a diagnostic test to discriminate among three-ordered classes or groups. In this article, nonparametric predictive inference (NPI) for three-group ROC analysis for ordinal outcomes is presented. NPI is a frequentist statistical method that is explicitly aimed at using few modeling assumptions, enabled through the use of lower and upper probabilities to quantify uncertainty. This article also includes results on the volumes under the ROC surfaces and consideration of the choice of decision thresholds for the diagnosis. Two examples are provided to illustrate our method.     

Evaluating Probabilistic Forecasts with Bayesian Signal Detection Models

We propose the use of signal detection theory (SDT) to evaluate the performance of both probabilistic forecasting systems and individual forecasters. The main advantage of SDT is that it provides a principled way to distinguish the response from system diagnosticity, which is defined as the ability to distinguish events that occur from those that do not. There are two challenges in applying SDT to probabilistic forecasts. First, the SDT model must handle judged probabilities rather than the conventional binary decisions. Second, the model must be able to operate in the presence of sparse data generated within the context of human forecasting systems. Our approach is to specify a model of how individual forecasts are generated from underlying representations and use Bayesian inference to estimate the underlying latent parameters. Given our estimate of the underlying representations, features of the classic SDT model, such as the receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC), follow immediately. We show how our approach allows ROC curves and AUCs to be applied to individuals within a group of forecasters, estimated as a function of time, and extended to measure differences in forecastability across different domains. Among the advantages of this method is that it depends only on the ordinal properties of the probabilistic forecasts. We conclude with a brief discussion of how this approach might facilitate decision making.     

An alternative method for global and partial comparison of two diagnostic systems based on ROC curves

In this paper, an alternative method for the comparison of two diagnostic systems based on receiver operating characteristic (ROC) curves is presented. ROC curve analysis is often used as a statistical tool for the evaluation of diagnostic systems. However, in general, the comparison of ROC curves is not straightforward, in particular, when they cross each other. A similar difficulty is also observed in the multi-objective optimization field where sets of solutions defining fronts must be compared with a multi-dimensional space. Thus, the proposed methodology is based on a procedure used to compare the performance of distinct multi-objective optimization algorithms. In general, methods based on the area under the ROC curves are not sensitive to the existence of crossing points between the curves. The new approach can deal with this situation and also allows the comparison of partial portions of ROC curves according to particular values of sensitivity and specificity of practical interest. Simulations results are presented. For illustration purposes, considering real data from newborns with very low birthweight, the new method was applied in order to discriminate the better index for evaluating the risk of death.     

ROC Curves in Non‐Parametric Location‐Scale Regression Models

Abstract. The receiver operating characteristic (ROC) curve is a tool of extensive use to analyse the discrimination capability of a diagnostic variable in medical studies. In certain situations, the presence of a covariate related to the diagnostic variable can increase the discriminating power of the ROC curve. In this article, we model the effect of the covariate over the diagnostic variable by means of non‐parametric location‐scale regression models. We propose a new non‐parametric estimator of the conditional ROC curve and study its asymptotic properties. We also present some simulations and an illustration to a data set concerning diagnosis of diabetes.