Partitioned and Non-Partitioned Regularized Additive Hazard Models with and Without Spatial Dependence

Spatial effects are often simultaneously investigated with non-linear effects of continuous covariates and the usual linear effect. In this work the performance of models with and without spatial dependence in partitioned (PM) and non-partitioned models (NPM) for four (4) censoring percentages, three(3) levels of Weibull baseline variances (WBV), and sample sizes 100, 500 & 1000 were investigated. Hazard models were adapted to the generalized additive predictors and analyses were carried out via MCMC simulation technique. The performances of the models were again assessed when fitted to the diabetic data set. Results suggest that; partition models outperformed the non-partition ones. Models with spatial dependence perform better than models without spatial dependence in denser event times and when WBVs are low. The partition models perform better with spatial dependence than the Non-partitioned models. For the diabetic data set, it is seen that covariates Age and Blood Sugar level (BSL) violates the proportionality assumptions upon test. Further assessment from the graph of coefficient against time; suggest that Age be put to cut-points while BSL was estimated for models with and without Penalized splines for the sake of comparison, since the graph shows just a slight deviation from proportionality. Hazard rates for the time varying Age; indicate that as the time of study rolls by, the hazard of experiencing the event death from the disease increases steadily between intervals but constant within each time interval. A unit change in hazard rate for BSL indicates a decrease for PM implemented for with and without penalized splines. The model without penalized splines was however, seen to be better with smaller DIC (Deviance Information Criteria) value. Marriage is seen to be significant in the management of the disease in comparison to single patients. In addition patients are advised to visit their physicians on a regular basis to run a routine check to keep their BSL in good range. The study provides a means of moving out of non-linear ruts in survival data analysis. Intervals increase sample sizes (pseudoobservations), which in turn improves the modified Partitioned model when they are with or without spatial dependence.

Primary Gross Tumor Volume is Prognostic and Suggests Treatment in Upper Esophageal Cancer

Background: To aid clinicians strategizing treatment for upper esophageal squamous cell carcinoma (ESCC), this retrospective study investigated associations between primary gross tumor volume (GTVp) and prognosis in patients given surgical resection, radiotherapy, or both resection and radiotherapy. Methods: The population comprised 568 patients with upper ESCC given definitive treatment, including 238, 216, and 114 who underwent surgery, radiotherapy, or combined radiotherapy and surgery. GTVp as a continuous variable was entered into the multivariate Cox model using penalized splines (P-splines) to determine the optimal cutoff value. Propensity score matching (PSM) was used to adjust imbalanced characteristics among the treatment groups. Results: P-spline regression revealed a dependence of patient outcomes on GTVp, with 30 cm3 being an optimal cut-off for differences in overall and progression-free survival (OS, PFS). GTVp ≥ 30 cm3 was a negative independent prognostic factor for OS and PFS. PSM analyses confirmed the prognostic value of GTVp. For GTVp < 30 cm3, no significant survival differences were observed among the 3 treatments. For GTVp ≥ 30 cm3, the worst 5-year OS rate was experienced by those given surgery. The 5-year PFS rate of patients given combined radiotherapy and surgery was significantly better than that of patients given radiotherapy. The surgical complications of patients given the combined treatment were comparable to those who received surgery, but radiation side effects were significantly lower. Conclusion: GTVp is prognostic for OS and PFS in upper ESCC. For patients with GTVp ≥ 30 cm3, radiotherapy plus surgery was more effective than either treatment alone.

Cross-Validation, Information Theory, or Maximum Likelihood? A Comparison of Tuning Methods for Penalized Splines

Functional data analysis techniques, such as penalized splines, have become common tools used in a variety of applied research settings. Penalized spline estimators are frequently used in applied research to estimate unknown functions from noisy data. The success of these estimators depends on choosing a tuning parameter that provides the correct balance between fitting and smoothing the data. Several different smoothing parameter selection methods have been proposed for choosing a reasonable tuning parameter. The proposed methods generally fall into one of three categories: cross-validation methods, information theoretic methods, or maximum likelihood methods. Despite the well-known importance of selecting an ideal smoothing parameter, there is little agreement in the literature regarding which method(s) should be considered when analyzing real data. In this paper, we address this issue by exploring the practical performance of six popular tuning methods under a variety of simulated and real data situations. Our results reveal that maximum likelihood methods outperform the popular cross-validation methods in most situations—especially in the presence of correlated errors. Furthermore, our results reveal that the maximum likelihood methods perform well even when the errors are non-Gaussian and/or heteroscedastic. For real data applications, we recommend comparing results using cross-validation and maximum likelihood tuning methods, given that these methods tend to perform similarly (differently) when the model is correctly (incorrectly) specified.

Cancer incidence and mortality trends in France over 1990–2018 for solid tumors: the sex gap is narrowing

Objective To analyze trends in cancer incidence and mortality (France, 1990–2018), with a focus on men-women disparities. Methods Incidence data stemmed from cancer registries (FRANCIM) and mortality data from national statistics (CépiDc). Incidence and mortality rates were modelled using bidimensional penalized splines of age and year (at diagnosis and at death, respectively). Trends in age-standardized rates were summarized by the average annual percent changes (AAPC) for all-cancers combined, 19 solid tumors, and 8 subsites. Sex gaps were indicated using male-to-female rate ratios (relative difference) and male-to-female rate differences (absolute difference) in 1990 and 2018, for incidence and mortality, respectively. Results For all-cancers, the sex gap narrowed over 1990–2018 in incidence (1.6 to 1.2) and mortality (2.3 to 1.7). The largest decreases of the male-to-female incidence rate ratio were for cancers of the lung (9.5 to 2.2), lip - oral cavity - pharynx (10.9 to 3.1), esophagus (12.6 to 4.5) and larynx (17.1 to 7.1). Mixed trends emerged in lung and oesophageal cancers, probably explained by differing risk factors for the two main histological subtypes. Sex incidence gaps narrowed due to increasing trends in men and women for skin melanoma (0.7 to 1, due to initially higher rates in women), cancers of the liver (7.4 to 4.4) and pancreas (2.0 to 1.4). Sex incidence gaps narrowed for colon-rectum (1.7 to 1.4), urinary bladder (6.9 to 6.1) and stomach (2.7 to 2.4) driven by decreasing trends among men. Other cancers showed similar increasing incidence trends in both sexes leading to stable sex gaps: thyroid gland (0.3 to 0.3), kidney (2.2 to 2.4) and central nervous system (1.4 to 1.5). Conclusion In France in 2018, while men still had higher risks of developing or dying from most cancers, the sex gap was narrowing. Efforts should focus on avoiding risk factors (e.g., smoking) and developing etiological studies to understand currently unexplained increasing trends.

Recurrent Events Analysis with Piece-wise exponential Additive Mixed Models

Background: Recurrent events analysis plays an important role in many applications, including the study of chronic diseases or recurrence of infections. Historically, most models for the analysis of time-to-event data, including recurrent events, have been based on Cox proportional hazards regression. Recently, however, the Piece-wise exponential Additive Mixed Model (PAMM) has gained popularity as a flexible framework for survival analysis. While many papers and tutorials have been presented in the literature on the application of Cox based models, few papers have provided detailed instructions for the application of PAMMs and to our knowledge, none exist for recurrent events analysis. Methods: The PAMM is introduced as a framework for recurrent events analysis. We describe the application of the model to unstratified and stratified shared frailty models for recurrent events. We illustrate how penalized splines can be used to estimate non-linear and time-varying covariate effects without a priori assumptions about their functional shape. The model is motivated for both, analysis on the gap timescale ("clock-reset") and calendar timescale ("clock-forward"). The data augmentation necessary for the application to recurrent events is described and explained in detail. Results: Simulations confirmed that the model provides unbiased estimates of covariate effects and the frailty variance, as well as equivalence to the Cox model when proportional hazards are assumed. Applications to recurrence of staphylococcus aureus and malaria in children illustrates the estimation of seasonality, bivariate non-linear effects, multiple timescales and relaxation of the proportional hazards assumption via time-varying effects. The R package pammtools has been extended to facilitate estimation, visualization and interpretation of PAMMs for recurrent events analysis. Conclusion: PAMMs provide a flexible framework for the analysis of time-to-event and recurrent events data. The estimation of PAMMs is based on Generalized Additive Mixed Models and thus extends the researcher’s toolbox for recurrent events analysis.

Sex Differences in Functional Topography of Association Networks

Prior work has shown that there is substantial interindividual variation in the spatial distribution of functional networks across the cerebral cortex, or functional topography. However, it remains unknown whether there are sex differences in the topography of individualized networks in youth. Here we leveraged an advanced machine learning method (sparsity-regularized non-negative matrix factorization) to define individualized functional networks in 693 youth (ages 8-23 years) who underwent functional magnetic resonance imaging as part of the Philadelphia Neurodevelopmental Cohort. Multivariate pattern analysis using support vector machines classified participant sex based on functional topography with 83% accuracy (p<0.0001). Brain regions most effective in classifying participant sex belonged to association networks, including the ventral attention and default mode networks. Mass-univariate analyses using generalized additive models with penalized splines provided convergent results. Comparative analysis using transcriptomic data from the Allen Human Brain Atlas revealed that sex differences in multivariate patterns of functional topography correlated with the expression of genes on the X-chromosome. These results identify normative developmental sex differences in the functional topography of association networks and highlight the role of sex as a biological variable in shaping brain development in youth.