Cross-validation in survival analysis

Cross-validation approaches for penalized Cox regression

Cross-validation is the most common way of selecting tuning parameters in penalized regression, but its use in penalized Cox regression models has received relatively little attention in the literature. Due to its partial likelihood construction, carrying out cross-validation for Cox models is not straightforward, and there are several potential approaches for implementation. Here, we propose a new approach based on cross-validating the linear predictors of the Cox model and compare it to approaches that have been proposed elsewhere. We show that the proposed approach offers an attractive balance of performance and numerical stability, and illustrate these advantages using simulated data as well as analyzing a high-dimensional study of gene expression and survival in lung cancer patients.

A review on statistical and machine learning competing risks methods

When modeling competing risks (CR) survival data, several techniques have been proposed in both the statistical and machine learning literature. State-of-the-art methods have extended classical approaches with more flexible assumptions that can improve predictive performance, allow high-dimensional data and missing values, among others. Despite this, modern approaches have not been widely employed in applied settings. This article aims to aid the uptake of such methods by providing a condensed compendium of CR survival methods with a unified notation and interpretation across approaches. We highlight available software and, when possible, demonstrate their usage via reproducible R vignettes. Moreover, we discuss two major concerns that can affect benchmark studies in this context: the choice of performance metrics and reproducibility.

Baseline Mutations and ctDNA Dynamics as Prognostic and Predictive Factors in ER-Positive/HER2-Negative Metastatic Breast Cancer Patients

PURPOSE

Prognostic and predictive biomarkers to cyclin-dependent kinases 4 and 6 inhibitors are lacking. Circulating tumor DNA (ctDNA) can be used to profile these patients and dynamic changes in ctDNA could be an early predictor of treatment efficacy. Here, we conducted plasma ctDNA profiling in patients from the PEARL trial comparing palbociclib+fulvestrant versus capecitabine to investigate associations between baseline genomic landscape and on-treatment ctDNA dynamics with treatment efficacy.

EXPERIMENTAL DESIGN

Correlative blood samples were collected at baseline [cycle 1-day 1 (C1D1)] and prior to treatment [cycle 1-day 15 (C1D15)]. Plasma ctDNA was sequenced with a custom error-corrected capture panel, with both univariate and multivariate Cox models used for treatment efficacy associations. A prespecified methodology measuring ctDNA changes in clonal mutations between C1D1 and C1D15 was used for the on-treatment ctDNA dynamic model.

RESULTS

201 patients were profiled at baseline, with ctDNA detection associated with worse progression-free survival (PFS)/overall survival (OS). Detectable TP53 mutation showed worse PFS and OS in both treatment arms, even after restricting population to baseline ctDNA detection. ESR1 mutations were associated with worse OS overall, which was lost when restricting population to baseline ctDNA detection. PIK3CA mutations confer worse OS only to patients on the palbociclib+fulvestrant treatment arm. ctDNA dynamics analysis (n = 120) showed higher ctDNA suppression in the capecitabine arm. Patients without ctDNA suppression showed worse PFS in both treatment arms.

CONCLUSIONS

We show impaired survival irrespective of endocrine or chemotherapy-based treatments for patients with hormone receptor-positive/HER2-negative metastatic breast cancer harboring plasma TP53 mutations. Early ctDNA suppression may provide treatment efficacy predictions. Further validation to fully demonstrate clinical utility of ctDNA dynamics is warranted.

A cross-validation statistical framework for asymmetric data integration

The proliferation of biobanks and large public clinical data sets enables their integration with a smaller amount of locally gathered data for the purposes of parameter estimation and model prediction. However, public data sets may be subject to context-dependent confounders and the protocols behind their generation are often opaque; naively integrating all external data sets equally can bias estimates and lead to spurious conclusions. Weighted data integration is a potential solution, but current methods still require subjective specifications of weights and can become computationally intractable. Under the assumption that local data are generated from the set of unknown true parameters, we propose a novel weighted integration method based upon using the external data to minimize the local data leave-one-out cross validation (LOOCV) error. We demonstrate how the optimization of LOOCV errors for linear and Cox proportional hazards models can be rewritten as functions of external data set integration weights. Significant reductions in estimation error and prediction error are shown using simulation studies mimicking the heterogeneity of clinical data as well as a real-world example using kidney transplant patients from the Scientific Registry of Transplant Recipients.

Favoring the hierarchical constraint in penalized survival models for randomized trials in precision medicine

BACKGROUND

The research of biomarker-treatment interactions is commonly investigated in randomized clinical trials (RCT) for improving medicine precision. The hierarchical interaction constraint states that an interaction should only be in a model if its main effects are also in the model. However, this constraint is not guaranteed in the standard penalized statistical approaches. We aimed to find a compromise for high-dimensional data between the need for sparse model selection and the need for the hierarchical constraint.

RESULTS

To favor the property of the hierarchical interaction constraint, we proposed to create groups composed of the biomarker main effect and its interaction with treatment and to perform the bi-level selection on these groups. We proposed two weighting approaches (Single Wald (SW) and likelihood ratio test (LRT)) for the adaptive lasso method. The selection performance of these two approaches is compared to alternative lasso extensions (adaptive lasso with ridge-based weights, composite Minimax Concave Penalty, group exponential lasso and Sparse Group Lasso) through a simulation study. A RCT (NSABP B-31) randomizing 1574 patients (431 events) with early breast cancer aiming to evaluate the effect of adjuvant trastuzumab on distant-recurrence free survival with expression data from 462 genes measured in the tumour will serve for illustration. The simulation study illustrates that the adaptive lasso LRT and SW, and the group exponential lasso favored the hierarchical interaction constraint. Overall, in the alternative scenarios, they had the best balance of false discovery and false negative rates for the main effects of the selected interactions. For NSABP B-31, 12 gene-treatment interactions were identified more than 20% by the different methods. Among them, the adaptive lasso (SW) approach offered the best trade-off between a high number of selected gene-treatment interactions and a high proportion of selection of both the gene-treatment interaction and its main effect.

CONCLUSIONS

Adaptive lasso with Single Wald and likelihood ratio test weighting and the group exponential lasso approaches outperformed their competitors in favoring the hierarchical constraint of the biomarker-treatment interaction. However, the performance of the methods tends to decrease in the presence of prognostic biomarkers.

Impact of calcification on clinical outcomes after drug-coated balloon angioplasty for superficial femoral artery disease: Assessment using the peripheral artery calcification scoring system

PURPOSE

To investigate whether the severity of calcification assessed by the peripheral artery calcification scoring system (PACSS) was associated with clinical outcomes of drug-coated balloon (DCB) angioplasty for femoropopliteal lesions.

MATERIALS AND METHODS

We retrospectively analyzed 733 limbs with intermittent claudication of 626 patients, who underwent DCB angioplasty for de novo femoropopliteal lesions between January 2017 and February 2021 at seven cardiovascular centers in Japan. The patients were categorized using the PACSS classification (grades 0-4: no visible calcification of the target lesion, unilateral wall calcification < 5 cm, unilateral calcification ≥ 5 cm, bilateral wall calcification < 5 cm, and bilateral calcification ≥ 5 cm, respectively). The main outcome was primary patency at 1 year. The Cox proportional hazards analysis was used to explore whether the PACSS classification was an independent predictor of clinical outcomes.

RESULTS

The distribution of PACSS was grade 0 in 38%, grade 1 in 17%, grade 2 in 7%, grade 3 in 16%, and grade 4 in 23%. The 1-year primary patency rates in these grades, respectively, were 88.2%, 89.3%, 71.9%, 96.5%, and 82.6%, respectively (p < 0.001). Multivariate analysis disclosed that PACSS grade 4 (hazard ratio: 1.82, 95% confidence interval 1.15-2.87, p = 0.010) was associated with restenosis.

CONCLUSION

The PACSS grade 4 calcification was independently associated with poor clinical outcomes after DCB angioplasty for de novo femoropopliteal lesions.

Conformalized survival analysis

In this paper, we develop an inferential method based on conformal prediction, which can wrap around any survival prediction algorithm to produce calibrated, covariate-dependent lower predictive bounds on survival times. In the Type I right-censoring setting, when the censoring times are completely exogenous, the lower predictive bounds have guaranteed coverage in finite samples without any assumptions other than that of operating on independent and identically distributed data points. Under a more general conditionally independent censoring assumption, the bounds satisfy a doubly robust property which states the following: marginal coverage is approximately guaranteed if either the censoring mechanism or the conditional survival function is estimated well. The validity and efficiency of our procedure are demonstrated on synthetic data and real COVID-19 data from the UK Biobank.

Multiobjective semisupervised learning with a right-censored endpoint adapted to the multiple imputation framework

Semisupervised learning aims to use additional knowledge in the search for data structure. In clinical applications, including predictive information in the construction of a data-driven classification is of major importance. This work was motivated by a study that aimed to identify different patterns of immune parameters that would be associated with relapse-free survival in a cohort of breast cancer patients. Supervised and unsupervised objectives can be concomitantly optimized using multiobjective optimization. We propose such a procedure that addresses two challenges in the semisupervised approach, that is, missing data and additional knowledge based on survival time. The former was handled by using multiple imputation and consensus clustering. Survival information was incorporated in the supervised objective through the estimation of a cross-validation error of a Cox regression. A simulation study was performed to assess the performance of the proposed procedure. On complete datasets, the performances were compared to those of an existing modified multiobjective semisupervised learning method. The added value of including the survival data in the learning process was assessed by comparing the procedure to unsupervised learning. The proposed procedure showed better performance than the existing method, notably in the selection of the number of clusters. On incomplete datasets, the procedure showed little sensitivity to most of its parameters, even though a high number of imputations and partition initialization seeds improved the performance. The performance was degraded with a high proportion of missing data (40%) and with more ambiguous data structures. Simulation results and application on real data support the conclusion that our procedure enables the construction of a classification associated with a right-censored endpoint on a possibly incomplete dataset.

Dominant carnivore loss benefits native avian and invasive mammalian scavengers

Scavenging by large carnivores is integral for ecosystem functioning by limiting the build-up of carrion and facilitating widespread energy flows. However, top carnivores have declined across the world, triggering trophic shifts within ecosystems. Here, we compare findings from previous work on predator decline against areas with recent native mammalian carnivore loss. Specifically, we investigate top-down control on utilization of experimentally placed carcasses by two mesoscavengers—the invasive feral cat and native forest raven. Ravens profited most from carnivore loss, scavenging for five times longer in the absence of native mammalian carnivores. Cats scavenged on half of all carcasses in the region without dominant native carnivores. This was eight times more than in areas where other carnivores were at high densities. All carcasses persisted longer than the three-week monitoring period in the absence of native mammalian carnivores, while in areas with high carnivore abundance, all carcasses were fully consumed. Our results reveal that top-carnivore loss amplifies impacts associated with carnivore decline—increased carcass persistence and carrion access for smaller scavengers. This suggests that even at low densities, native mammalian carnivores can fulfil their ecological functions, demonstrating the significance of global carnivore conservation and supporting management approaches, such as trophic rewilding.

Image analysis reveals molecularly distinct patterns of TILs in NSCLC associated with treatment outcome

Despite known histological, biological, and clinical differences between lung adenocarcinoma (LUAD) and squamous cell carcinoma (LUSC), relatively little is known about the spatial differences in their corresponding immune contextures. Our study of over 1000 LUAD and LUSC tumors revealed that computationally derived patterns of tumor-infiltrating lymphocytes (TILs) on H&E images were different between LUAD (N = 421) and LUSC (N = 438), with TIL density being prognostic of overall survival in LUAD and spatial arrangement being more prognostically relevant in LUSC. In addition, the LUAD-specific TIL signature was associated with OS in an external validation set of 100 NSCLC treated with more than six different neoadjuvant chemotherapy regimens, and predictive of response to therapy in the clinical trial CA209-057 (n = 303). In LUAD, the prognostic TIL signature was primarily comprised of CD4+ T and CD8+ T cells, whereas in LUSC, the immune patterns were comprised of CD4+ T, CD8+ T, and CD20+ B cells. In both subtypes, prognostic TIL features were associated with transcriptomics-derived immune scores and biological pathways implicated in immune recognition, response, and evasion. Our results suggest the need for histologic subtype-specific TIL-based models for stratifying survival risk and predicting response to therapy. Our findings suggest that predictive models for response to therapy will need to account for the unique morphologic and molecular immune patterns as a function of histologic subtype of NSCLC.

Utility of Continuous Disease Subtyping Systems for Improved Evaluation of Etiologic Heterogeneity

Molecular pathologic diagnosis is important in clinical (oncology) practice. Integration of molecular pathology into epidemiological methods (i.e., molecular pathological epidemiology) allows for investigating the distinct etiology of disease subtypes based on biomarker analyses, thereby contributing to precision medicine and prevention. However, existing approaches for investigating etiological heterogeneity deal with categorical subtypes. We aimed to fully leverage continuous measures available in most biomarker readouts (gene/protein expression levels, signaling pathway activation, immune cell counts, microbiome/microbial abundance in tumor microenvironment, etc.). We present a cause-specific Cox proportional hazards regression model for evaluating how the exposure-disease subtype association changes across continuous subtyping biomarker levels. Utilizing two longitudinal observational prospective cohort studies, we investigated how the association of alcohol intake (a risk factor) with colorectal cancer incidence differed across the continuous values of tumor epigenetic DNA methylation at long interspersed nucleotide element-1 (LINE-1). The heterogeneous alcohol effect was modeled using different functions of the LINE-1 marker to demonstrate the method's flexibility. This real-world proof-of-principle computational application demonstrates how the new method enables visualizing the trend of the exposure effect over continuous marker levels. The utilization of continuous biomarker data without categorization for investigating etiological heterogeneity can advance our understanding of biological and pathogenic mechanisms.

Variable Selection for Generalized Linear Models with Interval-Censored Failure Time Data

Variable selection is often needed in many fields and has been discussed by many authors in various situations. This is especially the case under linear models and when one observes complete data. Among others, one common situation where variable selection is required is to identify important risk factors from a large number of covariates. In this paper, we consider the problem when one observes interval-censored failure time data arising from generalized linear models, for which there does not seem to exist an established method. To address this, we propose a penalized least squares method with the use of an unbiased transformation and the oracle property of the method is established along with the asymptotic normality of the resulting estimators of regression parameters. Simulation studies were conducted and demonstrated that the proposed method performed well for practical situations. In addition, the method was applied to a motivating example about children’s mortality data of Nigeria.

Sparse modelling of cancer patients' survival based on genomic copy number alterations

Copy number alterations (CNA) are structural variation in the genome, in which some regions exhibit more or less than the normal two chromosomal copies. This genomic CNA profile provides critical information in tumour progression and is therefore informative for patients' survival. It is currently a statistical challenge to model patients' survival using their genomic CNA profiles while at the same time identify regions in the genome that are associated with patients' survival. Some methods have been proposed, including Cox proportional hazard (PH) model with ridge, lasso, or elastic net penalties. However, these methods do not take the general dependencies between genomic regions into account and produce results that are difficult to interpret. In this paper, we extend the elastic net penalty by introducing additional penalty that takes into account general dependencies between genomic regions. This new model produces smooth parameter estimates while simultaneously performs variable selection via sparse solution. The results indicate that the proposed method shows a better prediction performance than other models in our simulation study, while enabling us to investigate regions in the genome that are associated with the patients' survival with sensible interpretation. We illustrate the method using a real dataset from a lung cancer cohort and simulated data.

Construction of a prediction model for drug removal rate in hemodialysis based on chemical structures

Abstract

In designing drug dosing for hemodialysis patients, the removal rate (RR) of the drug by hemodialysis is important. However, acquiring the RR is difficult, and there is a need for an estimation method that can be used in clinical settings. In this study, the RR predictive model was constructed using the RR of known drugs by quantitative structure–activity relationship (QSAR) analysis. Drugs were divided into a model construction drug set (75%) and a model validation drug set (25%). The RR was collected from 143 medicines. The objective variable (RR) and chemical structural characteristics (descriptors) of the drug (explanatory variable) were used to construct a prediction model using partial least squares (PLS) regression and artificial neural network (ANN) analyses. The determination coefficients in the PLS and ANN methods were 0.586 and 0.721 for the model validation drug set, respectively. QSAR analysis successfully constructed dialysis RR prediction models that were comparable or superior to those using pharmacokinetic parameters. Considering that the RR dataset contains potential errors, we believe that this study has achieved the most reliable RR prediction accuracy currently available. These predictive RR models can be achieved using only the chemical structure of the drug. This model is expected to be applied at the time of hemodialysis.

Graphic Abstract

Supplementary Information

The online version contains supplementary material available at 10.1007/s11030-021-10348-7.

Fitting and Cross-Validating Cox Models to Censored Big Data With Missing Values Using Extensions of Partial Least Squares Regression Models

Fitting Cox models in a big data context -on a massive scale in terms of volume, intensity, and complexity exceeding the capacity of usual analytic tools-is often challenging. If some data are missing, it is even more difficult. We proposed algorithms that were able to fit Cox models in high dimensional settings using extensions of partial least squares regression to the Cox models. Some of them were able to cope with missing data. We were recently able to extend our most recent algorithms to big data, thus allowing to fit Cox model for big data with missing values. When cross-validating standard or extended Cox models, the commonly used criterion is the cross-validated partial loglikelihood using a naive or a van Houwelingen scheme -to make efficient use of the death times of the left out data in relation to the death times of all the data. Quite astonishingly, we will show, using a strong simulation study involving three different data simulation algorithms, that these two cross-validation methods fail with the extensions, either straightforward or more involved ones, of partial least squares regression to the Cox model. This is quite an interesting result for at least two reasons. Firstly, several nice features of PLS based models, including regularization, interpretability of the components, missing data support, data visualization thanks to biplots of individuals and variables -and even parsimony or group parsimony for Sparse partial least squares or sparse group SPLS based models, account for a common use of these extensions by statisticians who usually select their hyperparameters using cross-validation. Secondly, they are almost always featured in benchmarking studies to assess the performance of a new estimation technique used in a high dimensional or big data context and often show poor statistical properties. We carried out a vast simulation study to evaluate more than a dozen of potential cross-validation criteria, either AUC or prediction error based. Several of them lead to the selection of a reasonable number of components. Using these newly found cross-validation criteria to fit extensions of partial least squares regression to the Cox model, we performed a benchmark reanalysis that showed enhanced performances of these techniques. In addition, we proposed sparse group extensions of our algorithms and defined a new robust measure based on the Schmid score and the R coefficient of determination for least absolute deviation: the integrated R Schmid Score weighted. The R-package used in this article is available on the CRAN, http://cran.r-project.org/web/packages/plsRcox/index.html. The R package bigPLS will soon be available on the CRAN and, until then, is available on Github https://github.com/fbertran/bigPLS.

Choosing placental hypoxic-ischemic measures that have clinical implications in child development and diseases

PURPOSE

Placental hypoxic-ischemic pathology is one of the common causes for adverse outcomes. But there is no commonly accepted evaluation system on specific morphological and histopathological measures of the placenta.

OBJECTIVE

This study aims to systematically select several core placental hypoxic-ischemic measures that have a high prognostic relevance to child health.

METHODS

We used data from the Collaborative Perinatal Project, a multicenter prospective cohort study that recruited over 55,000 pregnant women and followed their offspring to 7 years old. Women who had information on placental pathology and child outcomes were included. 57 placental measures considered to be relevant to hypoxia-ischemia were selected. Apgar score, intelligence quotient, preeclampsia, birth weight and subclinical neurology injuries were chosen as outcomes. The least absolute shrinkage and selection operator (LASSO) procedure as well as training and testing methods were used to select a more efficient and simpler placental hypoxic-ischemic measures that may have clinical implications.

RESULTS

Of the 57 measures, 7 were selected as candidates by LASSO. Based on the training and testing methods, we retained placental measures with a higher odds ratio of child morbidity. We further narrowed down to four measures that had the highest prognostic relevance. They were: short cord length (ΣOR = 8.51), calcification of cut surface (ΣOR = 8.31), opaque membranes (ΣOR = 5.26), Hofbauer cells in terminal villi (ΣOR = 4.69).

CONCLUSIONS

Our four-measure system is relatively simple and closely related to the child health. It may be used as a novel placental hypoxic-ischemic evaluation criterion, and function as the first line tool for future research.

Comparison of statistical methodologies used to estimate the treatment effect on time-to-event outcomes in observational studies

The use of real-world data became more and more popular in the pharmaceutical industry. The impact of real-world evidence is now well emphasized by the regulatory authorities. Indeed, the analysis of this type of data can play a key role for treatment efficacy and safety. The aim of this work is to assess various methods and give guidance on the comparisons of drugs, mostly with respect to time-to-event data, in non-randomized studies with potentially confounding variables. For that purpose, several statistical methodologies are compared based on simulation studies. These methodologies belong to family classes of methods that are widely used for this type of problem: regression, matching, weighting and subclassification methods. The evaluation criteria used to compare methods performances are the relative bias, the mean square error, the coverage probability and the width of the confidence interval. In this paper, we consider different scenarios of dataset features in order to study the effect of the sample size, the number of covariates and the magnitude of the treatment effect on the statistical methodologies performances. These statistical analyses are conducted within a proportional hazard model framework. Furthermore, we highlight the advantage of using techniques to identify relevant covariates for time-to-event outcomes by comparing two variable selection methods under a frequentist and a Bayesian inference. Based on simulation results, recommendations on each of the family of methods are provided to guide decision making.

Globaltest confidence regions and their application to ridge regression

We construct confidence regions in high dimensions by inverting the globaltest statistics, and use them to choose the tuning parameter for penalized regression. The selected model corresponds to the point in the confidence region of the parameters that minimizes the penalty, making it the least complex model that still has acceptable fit according to the test that defines the confidence region. As the globaltest is particularly powerful in the presence of many weak predictors, it connects well to ridge regression, and we thus focus on ridge penalties in this paper. The confidence region method is quick to calculate, intuitive, and gives decent predictive potential. As a tuning parameter selection method it may even outperform classical methods such as cross‐validation in terms of mean squared error of prediction, especially when the signal is weak. We illustrate the method for linear models in simulation study and for Cox models in real gene expression data of breast cancer samples.

Stratified Cox models with time-varying effects for national kidney transplant patients: A new blockwise steepest ascent method

Analyzing the national transplant database, which contains about 300,000 kidney transplant patients treated in over 290 transplant centers, may guide the disease management and inform the policy of kidney transplantation. Cox models stratified by centers provide a convenient means to account for the clustered data structure, while studying more than 160 predictors with effects that may vary over time. As fitting a time-varying effect model with such a large sample size may defy any existing software, we propose a blockwise steepest ascent procedure by leveraging the block structure of parameters inherent from the basis expansions for each coefficient function. The algorithm iteratively updates the optimal blockwise search direction, along which the increment of the partial likelihood is maximized. The proposed method can be interpreted from the perspective of the minorization-maximization algorithm and increases the partial likelihood until convergence. We further propose a Wald statistic to test whether the effects are indeed time varying. We evaluate the utility of the proposed method via simulations. Finally, we apply the method to analyze the national kidney transplant data and detect the time-varying nature of the effects of various risk factors.

A Validated Prediction Model for End-Stage Kidney Disease in Type 1 Diabetes

OBJECTIVE

End-stage kidney disease (ESKD) is a life-threatening complication of diabetes that can be prevented or delayed by intervention. Hence, early detection of people at increased risk is essential.

RESEARCH DESIGN AND METHODS

From a population-based cohort of 5,460 clinically diagnosed Danish adults with type 1 diabetes followed from 2001 to 2016, we developed a prediction model for ESKD accounting for the competing risk of death. Poisson regression analysis was used to estimate the model on the basis of information routinely collected from clinical examinations. The effect of including an extended set of predictors (lipids, alcohol intake, etc.) was further evaluated, and potential interactions identified in a survival tree analysis were tested. The final model was externally validated in 9,175 adults from Denmark and Scotland.

RESULTS

During a median follow-up of 10.4 years (interquartile limits 5.1; 14.7), 303 (5.5%) of the participants (mean [SD] age 42.3 [16.5] years) developed ESKD, and 764 (14.0%) died without having developed ESKD. The final ESKD prediction model included age, male sex, diabetes duration, estimated glomerular filtration rate, micro- and macroalbuminuria, systolic blood pressure, hemoglobin A_1c, smoking, and previous cardiovascular disease. Discrimination was excellent for 5-year risk of an ESKD event, with a C-statistic of 0.888 (95% CI 0.849; 0.927) in the derivation cohort and confirmed at 0.865 (0.811; 0.919) and 0.961 (0.940; 0.981) in the external validation cohorts from Denmark and Scotland, respectively.

CONCLUSIONS

We have derived and validated a novel, high-performing ESKD prediction model for risk stratification in the adult type 1 diabetes population. This model may improve clinical decision making and potentially guide early intervention.

A kernel regression model for panel count data with nonparametric covariate functions

The local kernel pseudo-partial likelihood is employed for estimation in a panel count model with nonparametric covariate functions. An estimator of the derivative of the nonparametric covariate function is derived first, and the nonparametric function estimator is then obtained by integrating the derivative estimator. Uniform consistency rates and pointwise asymptotic normality are obtained for the local derivative estimator under some regularity conditions. Moreover, the baseline function estimator is shown to be uniformly consistent. Demonstration of the asymptotic results strongly relies on the modern empirical theory, which generally does not require the Poisson assumption. Simulation studies also illustrate that the local derivative estimator performs well in a finite-sample regardless of whether the Poisson assumption holds. We also implement the proposed methodology to analyze a clinical study on childhood wheezing.

Survival prediction models since liver transplantation - comparisons between Cox models and machine learning techniques

BACKGROUND

Predicting survival of recipients after liver transplantation is regarded as one of the most important challenges in contemporary medicine. Hence, improving on current prediction models is of great interest.Nowadays, there is a strong discussion in the medical field about machine learning (ML) and whether it has greater potential than traditional regression models when dealing with complex data. Criticism to ML is related to unsuitable performance measures and lack of interpretability which is important for clinicians.

METHODS

In this paper, ML techniques such as random forests and neural networks are applied to large data of 62294 patients from the United States with 97 predictors selected on clinical/statistical grounds, over more than 600, to predict survival from transplantation. Of particular interest is also the identification of potential risk factors. A comparison is performed between 3 different Cox models (with all variables, backward selection and LASSO) and 3 machine learning techniques: a random survival forest and 2 partial logistic artificial neural networks (PLANNs). For PLANNs, novel extensions to their original specification are tested. Emphasis is given on the advantages and pitfalls of each method and on the interpretability of the ML techniques.

RESULTS

Well-established predictive measures are employed from the survival field (C-index, Brier score and Integrated Brier Score) and the strongest prognostic factors are identified for each model. Clinical endpoint is overall graft-survival defined as the time between transplantation and the date of graft-failure or death. The random survival forest shows slightly better predictive performance than Cox models based on the C-index. Neural networks show better performance than both Cox models and random survival forest based on the Integrated Brier Score at 10 years.

CONCLUSION

In this work, it is shown that machine learning techniques can be a useful tool for both prediction and interpretation in the survival context. From the ML techniques examined here, PLANN with 1 hidden layer predicts survival probabilities the most accurately, being as calibrated as the Cox model with all variables.

TRIAL REGISTRATION

Retrospective data were provided by the Scientific Registry of Transplant Recipients under Data Use Agreement number 9477 for analysis of risk factors after liver transplantation.

Simultaneous variable selection and estimation for joint models of longitudinal and failure time data with interval censoring

This paper discusses variable selection in the context of joint analysis of longitudinal data and failure time data. A large literature has been developed for either variable selection or the joint analysis but there exists only limited literature for variable selection in the context of the joint analysis when failure time data are right censored. Corresponding to this, we will consider the situation where instead of right-censored data, one observes interval-censored failure time data, a more general and commonly occurring form of failure time data. For the problem, a class of penalized likelihood-based procedures will be developed for simultaneous variable selection and estimation of relevant covariate effects for both longitudinal and failure time variables of interest. In particular, a Monte Carlo EM (MCEM) algorithm is presented for the implementation of the proposed approach. The proposed method allows for the number of covariates to be diverging with the sample size and is shown to have the oracle property. An extensive simulation study is conducted to assess the finite sample performance of the proposed approach and indicates that it works well in practical situations. An application is also provided.

A new lung donor score to predict short and long-term survival in lung transplantation

Background

Donor selection criteria are crucial for a successful lung transplant outcome. Our objective was to develop a new donor score to predict short- and long-term survival and validate it with five existing lung donor scores (Oto, Eurotransplant, Minnesota, Maryland-UNOS, Louisville-UNOS).

Methods

All 454 adult lung transplants at our center between 1992–2015 were included to develop a new score. Discriminative ability for all scores was calculated by the area under time-dependent receiver operating characteristic curves (time-dependent AUC) at 30-day, 1, 5 and 10-year survival, and their fit compared with Akaike’s information criterion. For the new score, five pre-selected donor risk factors were derived: age, diabetes mellitus, smoking history, pulmonary infection, PaO₂/FiO₂-ratio, weighed via simplification of a multiple Cox model, and shrinkage used to avoid overfitting. The score sub-weighting resulted in a total of 17 points.

Results

The existing scores showed predictive accuracy better than chance in prediction of survival of 5-year (AUC 0.58–0.60) to 10-year survival (AUC 0.58–0.64). Our new score had better discriminative ability as the existing scores with regard to 1, 5 and 10-year survival (AUC 0.59, 0.64, 0.66, respectively). Additional adjustment for recipient and surgical procedure variables improved the time-dependent AUC’s slightly. For the secondary outcomes primary graft dysfunction and bronchiolitis obliterans syndrome, the new score showed also a good predictive accuracy.

Conclusions

The proposed Zurich Donor Score is simple, well adapted for the current urge of extended donors use, and shows higher discriminative ability compared to preexisting donor scores regarding short- to long-term survival.

Variable selection for high-dimensional partly linear additive Cox model with application to Alzheimer's disease

Variable selection has been discussed under many contexts and especially, a large literature has been established for the analysis of right-censored failure time data. In this article, we discuss an interval-censored failure time situation where there exist two sets of covariates with one being low-dimensional and having possible nonlinear effects and the other being high-dimensional. For the problem, we present a penalized estimation procedure for simultaneous variable selection and estimation, and in the method, Bernstein polynomials are used to approximate the involved nonlinear functions. Furthermore, for implementation, a coordinate-wise optimization algorithm, which can accommodate most commonly used penalty functions, is developed. A numerical study is performed for the evaluation of the proposed approach and suggests that it works well in practical situations. Finally the method is applied to an Alzheimer's disease study that motivated this investigation.

Accounting for grouped predictor variables or pathways in high-dimensional penalized Cox regression models

BACKGROUND

The standard lasso penalty and its extensions are commonly used to develop a regularized regression model while selecting candidate predictor variables on a time-to-event outcome in high-dimensional data. However, these selection methods focus on a homogeneous set of variables and do not take into account the case of predictors belonging to functional groups; typically, genomic data can be grouped according to biological pathways or to different types of collected data. Another challenge is that the standard lasso penalisation is known to have a high false discovery rate.

RESULTS

We evaluated different penalizations in a Cox model to select grouped variables in order to further penalize variables that, in addition to having a low effect, belong to a group with a low overall effect; and to favor the selection of variables that, in addition to having a large effect, belong to a group with a large overall effect. We considered the case of prespecified and disjoint groups and proposed diverse weights for the adaptive lasso method. In particular we proposed the product Max Single Wald by Single Wald weighting (MSW*SW) which takes into account the information of the group to which it belongs and of this biomarker. Through simulations, we compared the selection and prediction ability of our approach with the standard lasso, the composite Minimax Concave Penalty (cMCP), the group exponential lasso (gel), the Integrative L1-Penalized Regression with Penalty Factors (IPF-Lasso), and the Sparse Group Lasso (SGL) methods. In addition, we illustrated the methods using gene expression data of 614 breast cancer patients.

CONCLUSIONS

The adaptive lasso with the MSW*SW weighting method incorporates both the information in the grouping structure and the individual variable. It outperformed the competitors by reducing the false discovery rate without severely increasing the false negative rate.

Penalized full likelihood approach to variable selection for Cox's regression model under nested case-control sampling

Assuming Cox's regression model, we consider penalized full likelihood approach to conduct variable selection under nested case-control (NCC) sampling. Penalized non-parametric maximum likelihood estimates (PNPMLEs) are characterized by self-consistency equations derived from score functions. A cross-validation method based on profile likelihood is used to choose the tuning parameter within a family of penalty functions. Simulation studies indicate that the numerical performance of (P)NPMLE is better than weighted partial likelihood in estimating the log-relative risk and in identifying the covariates and the model, under NCC sampling. LASSO performs best when cohort size is small; SCAD performs best when cohort size is large and may eventually perform as well as the oracle estimator. Using the SCAD penalty, we establish the consistency, asymptotic normality, and oracle properties of the PNPMLE, as well as the sparsity property of the penalty. We also propose a consistent estimate of the asymptotic variance using observed profile likelihood. Our method is illustrated to analyze the diagnosis of liver cancer among those in a type 2 diabetic mellitus dataset who were treated with thiazolidinediones in Taiwan.

A surrogate ℓ0 sparse Cox's regression with applications to sparse high-dimensional massive sample size time-to-event data

Sparse high-dimensional massive sample size (sHDMSS) time-to-event data present multiple challenges to quantitative researchers as most current sparse survival regression methods and software will grind to a halt and become practically inoperable. This paper develops a scalable ℓ₀ -based sparse Cox regression tool for right-censored time-to-event data that easily takes advantage of existing high performance implementation of ℓ₂ -penalized regression method for sHDMSS time-to-event data. Specifically, we extend the ℓ₀ -based broken adaptive ridge (BAR) methodology to the Cox model, which involves repeatedly performing reweighted ℓ₂ -penalized regression. We rigorously show that the resulting estimator for the Cox model is selection consistent, oracle for parameter estimation, and has a grouping property for highly correlated covariates. Furthermore, we implement our BAR method in an R package for sHDMSS time-to-event data by leveraging existing efficient algorithms for massive ℓ₂ -penalized Cox regression. We evaluate the BAR Cox regression method by extensive simulations and illustrate its application on an sHDMSS time-to-event data from the National Trauma Data Bank with hundreds of thousands of observations and tens of thousands sparsely represented covariates.

Clinical practice update on heart failure 2019: pharmacotherapy, procedures, devices and patient management. An expert consensus meeting report of the Heart Failure Association of the European Society of Cardiology

The European Society of Cardiology (ESC) has published a series of guidelines on heart failure (HF) over the last 25 years, most recently in 2016. Given the amount of new information that has become available since then, the Heart Failure Association (HFA) of the ESC recognized the need to review and summarise recent developments in a consensus document. Here we report from the HFA workshop that was held in January 2019 in Frankfurt, Germany. This expert consensus report is neither a guideline update nor a position statement, but rather a summary and consensus view in the form of consensus recommendations. The report describes how these guidance statements are supported by evidence, it makes some practical comments, and it highlights new research areas and how progress might change the clinical management of HF. We have avoided re-interpretation of information already considered in the 2016 ESC/HFA guidelines. Specific new recommendations have been made based on the evidence from major trials published since 2016, including sodium-glucose co-transporter 2 inhibitors in type 2 diabetes mellitus, MitraClip for functional mitral regurgitation, atrial fibrillation ablation in HF, tafamidis in cardiac transthyretin amyloidosis, rivaroxaban in HF, implantable cardioverter-defibrillators in non-ischaemic HF, and telemedicine for HF. In addition, new trial evidence from smaller trials and updated meta-analyses have given us the chance to provide refined recommendations in selected other areas. Further, new trial evidence is due in many of these areas and others over the next 2 years, in time for the planned 2021 ESC guidelines on the diagnosis and treatment of acute and chronic heart failure.

Prognostic models for breast cancer: a systematic review

BACKGROUND

Breast cancer is the most common cancer in women worldwide, with a great diversity in outcomes among individual patients. The ability to accurately predict a breast cancer outcome is important to patients, physicians, researchers, and policy makers. Many models have been developed and tested in different settings. We systematically reviewed the prognostic models developed and/or validated for patients with breast cancer.

METHODS

We conducted a systematic search in four electronic databases and some oncology websites, and a manual search in the bibliographies of the included studies. We identified original studies that were published prior to 1st January 2017, and presented the development and/or validation of models based mainly on clinico-pathological factors to predict mortality and/or recurrence in female breast cancer patients.

RESULTS

From the 96 articles selected from 4095 citations found, we identified 58 models, which predicted mortality (n = 28), recurrence (n = 23), or both (n = 7). The most frequently used predictors were nodal status (n = 49), tumour size (n = 42), tumour grade (n = 29), age at diagnosis (n = 24), and oestrogen receptor status (n = 21). Models were developed in Europe (n = 25), Asia (n = 13), North America (n = 12), and Australia (n = 1) between 1982 and 2016. Models were validated in the development cohorts (n = 43) and/or independent populations (n = 17), by comparing the predicted outcomes with the observed outcomes (n = 55) and/or with the outcomes estimated by other models (n = 32), or the outcomes estimated by individual prognostic factors (n = 8). The most commonly used methods were: Cox proportional hazards regression for model development (n = 32); the absolute differences between the predicted and observed outcomes (n = 30) for calibration; and C-index/AUC (n = 44) for discrimination. Overall, the models performed well in the development cohorts but less accurately in some independent populations, particularly in patients with high risk and young and elderly patients. An exception is the Nottingham Prognostic Index, which retains its predicting ability in most independent populations.

CONCLUSIONS

Many prognostic models have been developed for breast cancer, but only a few have been validated widely in different settings. Importantly, their performance was suboptimal in independent populations, particularly in patients with high risk and in young and elderly patients.

Signet ring cell component, not the Lauren subtype, predicts poor survival: an analysis of 198 cases of gastric cancer

AIM

Prognostic differences between major histologic gastric cancer groups, intestinal and diffuse are uncertain, since cellular components in each of them possibly have different behaviors.

MATERIALS & METHODS

We reviewed 198 gastric cancer patients charts diagnosed from January 2003 to December 2015 in a tertiary hospital. Multivariate Cox proportional survival models were used to evaluate the impact of histologic groups on overall survival.

RESULTS

About a third had the signet-ring cell carcinoma (SRCC). In a comparison of the different histologic subtypes, SRCC had the worst prognosis of all. The median durations of survival for patients with stage III and stage IV were 19.7 and 7.7 months, respectively.

CONCLUSION

Signet-ring cell component seem to have a relevant role in defining prognosis for gastric cancer.

Risk prediction for estrogen receptor-specific breast cancers in two large prospective cohorts

BACKGROUND

Few published breast cancer (BC) risk prediction models consider the heterogeneity of predictor variables between estrogen-receptor positive (ER+) and negative (ER-) tumors. Using data from two large cohorts, we examined whether modeling this heterogeneity could improve prediction.

METHODS

We built two models, for ER+ (ModelER+) and ER- tumors (ModelER-), respectively, in 281,330 women (51% postmenopausal at recruitment) from the European Prospective Investigation into Cancer and Nutrition cohort. Discrimination (C-statistic) and calibration (the agreement between predicted and observed tumor risks) were assessed both internally and externally in 82,319 postmenopausal women from the Women's Health Initiative study. We performed decision curve analysis to compare ModelER+ and the Gail model (ModelGail) regarding their applicability in risk assessment for chemoprevention.

RESULTS

Parity, number of full-term pregnancies, age at first full-term pregnancy and body height were only associated with ER+ tumors. Menopausal status, age at menarche and at menopause, hormone replacement therapy, postmenopausal body mass index, and alcohol intake were homogeneously associated with ER+ and ER- tumors. Internal validation yielded a C-statistic of 0.64 for ModelER+ and 0.59 for ModelER-. External validation reduced the C-statistic of ModelER+ (0.59) and ModelGail (0.57). In external evaluation of calibration, ModelER+ outperformed the ModelGail: the former led to a 9% overestimation of the risk of ER+ tumors, while the latter yielded a 22% underestimation of the overall BC risk. Compared with the treat-all strategy, ModelER+ produced equal or higher net benefits irrespective of the benefit-to-harm ratio of chemoprevention, while ModelGail did not produce higher net benefits unless the benefit-to-harm ratio was below 50. The clinical applicability, i.e. the area defined by the net benefit curve and the treat-all and treat-none strategies, was 12.7 × 10- 6 for ModelER+ and 3.0 × 10- 6 for ModelGail.

CONCLUSIONS

Modeling heterogeneous epidemiological risk factors might yield little improvement in BC risk prediction. Nevertheless, a model specifically predictive of ER+ tumor risk could be more applicable than an omnibus model in risk assessment for chemoprevention.

Flexible Modelling in Survival Analysis. Structuring Biological Complexity from the Information Provided by Tumor Markers

The aim of the present article is to introduce and discuss the problem of optimal modelling of the prognostic information provided by putative prognostic variables, possibly measured on a quantitative scale. A number of methodological aspects will be treated, with particular reference to the role of spline functions and artificial neural networks, which will be discussed in the context of the analysis of survival data. The problem of the evaluation and the choice of the optimal statistical models will be examined, with particular attention to the critical aspects related to the definition of prognostic indexes on the basis of the results of the selected models. Clinical examples in breast cancer on the evaluation of the prognostic impact of several tumor markers are provided. This paper is addressed to all researchers who are interested in the evaluation of the prognostic role of tumor markers, therefore we will stress the necessity of integrating the methodologies of biological, clinical and statistical research in the assessment of prognosis.

Usefulness of the CRT-SCORE for Shared Decision Making in Cardiac Resynchronization Therapy in Patients With a Left Ventricular Ejection Fraction of ≤35

Individualized estimation of prognosis after cardiac resynchronization therapy (CRT) remains challenging. Our aim was to develop a multiparametric prognostic risk score (CRT-SCORE) that could be used for patient-specific clinical shared decision making about CRT implantation. The CRT-SCORE was derived from an ongoing CRT registry, including 1,053 consecutive patients (age 67 ± 10 years, 76% male). Using preimplantation variables, 100 multiple imputed datasets were generated for model calibration. Based on multivariate Cox regression models, cross-validated linear prognostic scores were calculated, as well as survival fractions at 1 and 5 years. Specifically, the CRT-SCORE was calculated using atrioventricular junction ablation, age, gender, etiology, New York Heart Association class, diabetes, hemoglobin level, renal function, left bundle branch block, QRS duration, atrial fibrillation, left ventricular systolic and diastolic functions, and mitral regurgitation, and showed a good discriminative ability (areas under the curve 0.773 at 1 year and 0.748 at 5 years). During the long-term follow-up (median 60 months, interquartile range 31 to 85), all-cause mortality was observed in 494 (47%) patients. Based on the distribution of the CRT-SCORE, lower- and higher-risk patient groups were identified. Estimated mean survival rates of 98% at 1 year and 92% at 5 years were observed in the lowest 5% risk group (L5 CRT-SCORE: -4.42 to -1.60), whereas the highest 5% risk group (H5 CRT-SCORE: 1.44 to 2.89) showed poor survival rates: 78% at 1 year and 22% at 5 years. In conclusion, the CRT-SCORE allows accurate prediction of 1- and 5-year survival rates after CRT using readily available and CRT-specific clinical, electrocardiographic, and echocardiographic parameters. The model may assist clinicians in counseling patients and in decision making.

Comparison of variable selection methods for high-dimensional survival data with competing events

BACKGROUND

In the era of personalized medicine, it's primordial to identify gene signatures for each event type in the context of competing risks in order to improve risk stratification and treatment strategy. Until recently, little attention was paid to the performance of high-dimensional selection in deriving molecular signatures in this context. In this paper, we investigate the performance of two selection methods developed in the framework of high-dimensional data and competing risks: Random survival forest and a boosting approach for fitting proportional subdistribution hazards models.

METHODS

Using data from bladder cancer patients (GSE5479) and simulated datasets, stability and prognosis performance of the two methods were evaluated using a resampling strategy. For each sample, the data set was split into 100 training and validation sets. Molecular signatures were developed in the training sets by the two selection methods and then applied on the corresponding validation sets.

RESULTS

Random survival forest and boosting approach have comparable performance for the prediction of survival data, with few selected genes in common. Nevertheless, many different sets of genes are identified by the resampling approach, with a very small frequency of genes occurrence among the signatures. Also, the smaller the training sample size, the lower is the stability of the signatures.

CONCLUSION

Random survival forest and boosting approach give good predictive performance but gene signatures are very unstable. Further works are needed to propose adequate strategies for the analysis of high-dimensional data in the context of competing risks.

Human TERT promoter mutation enables survival advantage from MGMT promoter methylation in IDH1 wild-type primary glioblastoma treated by standard chemoradiotherapy

Background

Promoter mutation in the human telomerase reverse transcriptase gene (hTERT) occurs in ~75% of primary glioblastoma (GBM). Although the mutation appears to upregulate telomerase expression and contributes to the maintenance of telomere length, its clinical significance remains unclear.

Methods

We performed hTERT promoter genotyping on 303 isocitrate dehydrogenase 1 wild-type GBM tumors treated with standard chemoradiotherapy. We also stratified 190 GBM patients from the database of The Cancer Genome Atlas (TCGA) by hTERT gene expression. We analyzed overall and progression-free survival by Kaplan-Meier and Cox regression.

Results

We detected hTERT promoter mutation in 75% of the patients. When included as the only biomarker, hTERT mutation was not prognostic in our patient cohort by Cox regression analysis. However, when hTERT and O6-DNA methylguanine-methyltransferase (MGMT) were included together, we observed an interaction between these 2 factors. To further investigate this interaction, we performed pairwise comparison of the 4 patient subcohorts grouped by hTERT-MGMT status (MUT-M, WT-M, MUT-U, and WT-U). MGMT methylated patients showed improved survival only in the presence of hTERT promoter mutation: MUT-M versus MUT-U (overall survival of 28.3 vs 15.9 mos, log-rank P < .0001 and progression-free survival of 15.4 vs 7.86 mo, log-rank P < .0001). These results were confirmed by Cox analyses. Analogously, the cohort from TCGA demonstrated survival benefit of MGMT promoter methylation only in patients with high hTERT expression. In addition, hTERT mutation was negatively prognostic in our MGMT unmethylated patients, while the analogous association with high expression was not observed in the cohort from TCGA.

Conclusion

The prognostic influence of MGMT promoter methylation depends on hTERT promoter mutation. This interaction warrants further mechanistic investigation.

Development and validation of a screening instrument to identify cardiometabolic predictors of mortality in older individuals with cancer: Secondary analysis of the Australian Longitudinal Study of Ageing (ALSA)

OBJECTIVE

The objective of this study was to identify significant cardiometabolic predictors of mortality among older cancer survivors and develop and validate a screening instrument to assess individual risk of mortality.

MATERIALS AND METHODS

Retrospective cohort study used collected data from the ALSA. Cox proportional hazards model was used to derive the risk equation for mortality that could be evaluated at 10years. Measures of discrimination and calibration were calculated in the validation cohort.

RESULTS

The equation was developed using 294 cancer survivors and validated in 127 different cancer survivors. Significant cardiometabolic predictors of mortality included in the final model are age, sex, history of cerebrovascular disease, non-adherence to exercise guidelines (150min moderate activity per week), and smoking. Discrimination and calibration were acceptable with minimal differences in C statistics (0.0442, 95% CI: -0.0149 to 0.103) and adjusted R2 values (0.0407, 95% CI: -0.181 to 0.0998) between the development and validation cohorts, respectively.

CONCLUSION

We have developed and validated the first screening tool to predict cardiometabolic risk of mortality in older cancer survivors and defined centile values for risk classification. Further validation and research on the usability and usefulness of the tool in clinical practice are recommended in order to target cancer survivors for interventions. Cost effectiveness of such an approach should also be examined.

Robust estimation of the expected survival probabilities from high-dimensional Cox models with biomarker-by-treatment interactions in randomized clinical trials

Background

Thanks to the advances in genomics and targeted treatments, more and more prediction models based on biomarkers are being developed to predict potential benefit from treatments in a randomized clinical trial. Despite the methodological framework for the development and validation of prediction models in a high-dimensional setting is getting more and more established, no clear guidance exists yet on how to estimate expected survival probabilities in a penalized model with biomarker-by-treatment interactions.

Methods

Based on a parsimonious biomarker selection in a penalized high-dimensional Cox model (lasso or adaptive lasso), we propose a unified framework to: estimate internally the predictive accuracy metrics of the developed model (using double cross-validation); estimate the individual survival probabilities at a given timepoint; construct confidence intervals thereof (analytical or bootstrap); and visualize them graphically (pointwise or smoothed with spline). We compared these strategies through a simulation study covering scenarios with or without biomarker effects. We applied the strategies to a large randomized phase III clinical trial that evaluated the effect of adding trastuzumab to chemotherapy in 1574 early breast cancer patients, for which the expression of 462 genes was measured.

Results

In our simulations, penalized regression models using the adaptive lasso estimated the survival probability of new patients with low bias and standard error; bootstrapped confidence intervals had empirical coverage probability close to the nominal level across very different scenarios. The double cross-validation performed on the training data set closely mimicked the predictive accuracy of the selected models in external validation data. We also propose a useful visual representation of the expected survival probabilities using splines. In the breast cancer trial, the adaptive lasso penalty selected a prediction model with 4 clinical covariates, the main effects of 98 biomarkers and 24 biomarker-by-treatment interactions, but there was high variability of the expected survival probabilities, with very large confidence intervals.

Conclusion

Based on our simulations, we propose a unified framework for: developing a prediction model with biomarker-by-treatment interactions in a high-dimensional setting and validating it in absence of external data; accurately estimating the expected survival probability of future patients with associated confidence intervals; and graphically visualizing the developed prediction model. All the methods are implemented in the R package biospear, publicly available on the CRAN.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-017-0354-0) contains supplementary material, which is available to authorized users.

Asp73-dependent and -independent regulation of the affinity of ligands for human histamine H1 receptors by Na. Biochem Pharmacol 2016;128:46-54. [PMID: 28040476 DOI: 10.1016/j.bcp.2016.12.021]

The affinity of ligands for G-protein-coupled receptors (GPCRs) is allosterically regulated by Na⁺ via a highly conserved aspartate residue (Asp^2.50) in the second transmembrane domain of GPCRs. In the present study, we examined the Na⁺-mediated regulation of the affinity of ligands for G_q/11-protein-coupled human histamine H₁ receptors in Chinese hamster ovary cells. The affinities of 3 agonists and 20 antihistamines were evaluated by their displacement curves against the binding of [³H]-mepyramine to membrane preparations in the presence or absence of 100mM NaCl. The affinities of most drugs including histamine, an agonist, and d-chlorpheniramine, a first-generation antihistamine, were reduced by NaCl, with the extent of NaCl-mediated changes varying widely between drugs. In contrast, the affinities of some second-generation antihistamines such as fexofenadine were increased by NaCl. These changes were retained in intact cells. The mutation of Asp^2.50 (Asp73) to asparagine abrogated NaCl-induced reductions in affinities for histamine and d-chlorpheniramine, but not NaCl-induced increases in the affinity for fexofenadine. Quantitative structure-activity relationship (QSAR) analyses showed that these Na⁺-mediated changes were explained and predicted by a combination of the molecular energies and implicit solvation energies of the compounds. These results suggest that Na⁺ diversely regulates the affinity of ligands for H₁ receptors from the extracellular sites of receptors via Asp73-dependent and -independent mechanisms in a manner that depends on the physicochemical properties of ligands. These results may contribute to a deeper understanding of the fundamental mechanisms by which the affinity of ligands for their receptors is allosterically regulated by Na⁺.