Functional proportional hazards mixture cure model with applications in cancer mortality in NHANES and post ICU recovery

We develop a functional proportional hazards mixture cure model with scalar and functional covariates measured at the baseline. The mixture cure model, useful in studying populations with a cure fraction of a particular event of interest is extended to functional data. We employ the expectation-maximization algorithm and develop a semiparametric penalized spline-based approach to estimate the dynamic functional coefficients of the incidence and the latency part. The proposed method is computationally efficient and simultaneously incorporates smoothness in the estimated functional coefficients via roughness penalty. Simulation studies illustrate a satisfactory performance of the proposed method in accurately estimating the model parameters and the baseline survival function. Finally, the clinical potential of the model is demonstrated in two real data examples that incorporate rich high-dimensional biomedical signals as functional covariates measured at the baseline and constitute novel domains to apply cure survival models in contemporary medical situations. In particular, we analyze (i) minute-by-minute physical activity data from the National Health And Nutrition Examination Survey 2003-2006 to study the association between diurnal patterns of physical activity at baseline and all cancer mortality through 2019 while adjusting for other biological factors; (ii) the impact of daily functional measures of disease severity collected in the intensive care unit on post intensive care unit recovery and mortality event. Our findings provide novel epidemiological insights into the association between daily patterns of physical activity and cancer mortality. Software implementation and illustration of the proposed estimation method are provided in R.

Recurrent Events Analysis With Data Collected at Informative Clinical Visits in Electronic Health Records

Although increasingly used as a data resource for assembling cohorts, electronic health records (EHRs) pose many analytic challenges. In particular, a patient's health status influences when and what data are recorded, generating sampling bias in the collected data. In this paper, we consider recurrent event analysis using EHR data. Conventional regression methods for event risk analysis usually require the values of covariates to be observed throughout the follow-up period. In EHR databases, time-dependent covariates are intermittently measured during clinical visits, and the timing of these visits is informative in the sense that it depends on the disease course. Simple methods, such as the last-observation-carried-forward approach, can lead to biased estimation. On the other hand, complex joint models require additional assumptions on the covariate process and cannot be easily extended to handle multiple longitudinal predictors. By incorporating sampling weights derived from estimating the observation time process, we develop a novel estimation procedure based on inverse-rate-weighting and kernel-smoothing for the semiparametric proportional rate model of recurrent events. The proposed methods do not require model specifications for the covariate processes and can easily handle multiple time-dependent covariates. Our methods are applied to a kidney transplant study for illustration.

Combining biomarker trajectories to improve diagnostic accuracy in prospective cohort studies with verification bias

In this paper, we develop methods to combine multiple biomarker trajectories into a composite diagnostic marker using functional data analysis (FDA) to achieve better diagnostic accuracy in monitoring disease recurrence in the setting of a prospective cohort study. In such studies, the disease status is usually verified only for patients with a positive test result in any biomarker and is missing in patients with negative test results in all biomarkers. Thus, the test result will affect disease verification, which leads to verification bias if the analysis is restricted only to the verified cases. We treat verification bias as a missing data problem. Under both missing at random (MAR) and missing not at random (MNAR) assumptions, we derive the optimal classification rules using the Neyman-Pearson lemma based on the composite diagnostic marker. We estimate thresholds adjusted for verification bias to dichotomize patients as test positive or test negative, and we evaluate the diagnostic accuracy using the verification bias corrected area under the ROC curves (AUCs). We evaluate the performance and robustness of the FDA combination approach and assess the consistency of the approach through simulation studies. In addition, we perform a sensitivity analysis of the dependency between the verification process and disease status for the approach under the MNAR assumption. We apply the proposed method on data from the Religious Orders Study and from a non-small cell lung cancer trial.

Affinity-based measures of biomarker performance evaluation

We propose new summary measures of biomarker accuracy which can be used as companions to existing diagnostic accuracy measures. Conceptually, our summary measures are tantamount to the so-called Hellinger affinity and we show that they can be regarded as measures of agreement constructed from similar geometrical principles as Pearson correlation. We develop a covariate-specific version of our summary index, which practitioners can use to assess the discrimination performance of a biomarker, conditionally on the value of a predictor. We devise nonparametric Bayes estimators for the proposed indexes, derive theoretical properties of the corresponding priors, and assess the performance of our methods through a simulation study. The proposed methods are illustrated using data from a prostate cancer diagnosis study.

Discrimination surfaces with application to region-specific brain asymmetry analysis

Discrimination surfaces are here introduced as a diagnostic tool for localizing brain regions where discrimination between diseased and nondiseased participants is higher. To estimate discrimination surfaces, we introduce a Mann-Whitney type of statistic for random fields and present large-sample results characterizing its asymptotic behavior. Simulation results demonstrate that our estimator accurately recovers the true surface and corresponding interval of maximal discrimination. The empirical analysis suggests that in the anterior region of the brain, schizophrenic patients tend to present lower local asymmetry scores in comparison with participants in the control group.

Bootstrap-based procedures for inference in nonparametric receiver-operating characteristic curve regression analysis

Prior to using a diagnostic test in a routine clinical setting, the rigorous evaluation of its diagnostic accuracy is essential. The receiver-operating characteristic curve is the measure of accuracy most widely used for continuous diagnostic tests. However, the possible impact of extra information about the patient (or even the environment) on diagnostic accuracy also needs to be assessed. In this paper, we focus on an estimator for the covariate-specific receiver-operating characteristic curve based on direct regression modelling and nonparametric smoothing techniques. This approach defines the class of generalised additive models for the receiver-operating characteristic curve. The main aim of the paper is to offer new inferential procedures for testing the effect of covariates on the conditional receiver-operating characteristic curve within the above-mentioned class. Specifically, two different bootstrap-based tests are suggested to check (a) the possible effect of continuous covariates on the receiver-operating characteristic curve and (b) the presence of factor-by-curve interaction terms. The validity of the proposed bootstrap-based procedures is supported by simulations. To facilitate the application of these new procedures in practice, an R-package, known as npROCRegression, is provided and briefly described. Finally, data derived from a computer-aided diagnostic system for the automatic detection of tumour masses in breast cancer is analysed.