Absolute risk from double nested case-control designs: cause-specific proportional hazards models with and without augmented estimating equations

We estimate relative hazards and absolute risks (or cumulative incidence or crude risk) under cause-specific proportional hazards models for competing risks from double nested case-control (DNCC) data. In the DNCC design, controls are time-matched not only to cases from the cause of primary interest, but also to cases from competing risks (the phase-two sample). Complete covariate data are available in the phase-two sample, but other cohort members only have information on survival outcomes and some covariates. Design-weighted estimators use inverse sampling probabilities computed from Samuelsen-type calculations for DNCC. To take advantage of additional information available on all cohort members, we augment the estimating equations with a term that is unbiased for zero but improves the efficiency of estimates from the cause-specific proportional hazards model. We establish the asymptotic properties of the proposed estimators, including the estimator of absolute risk, and derive consistent variance estimators. We show that augmented design-weighted estimators are more efficient than design-weighted estimators. Through simulations, we show that the proposed asymptotic methods yield nominal operating characteristics in practical sample sizes. We illustrate the methods using prostate cancer mortality data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial Study of the National Cancer Institute.

A New Personalized Oral Cancer Survival Calculator to Estimate Risk of Death From Both Oral Cancer and Other Causes

Importance

Standard cancer prognosis models typically do not include much specificity in characterizing competing illnesses or general health status when providing prognosis estimates, limiting their utility for individuals, who must consider their cancer in the context of their overall health. This is especially true for patients with oral cancer, who frequently have competing illnesses.

Objective

To describe a statistical framework and accompanying new publicly available calculator that provides personalized estimates of the probability of a patient surviving or dying from cancer or other causes, using oral cancer as the first data set.

Design, Setting, and Participants

The models used data from the Surveillance, Epidemiology, and End Results (SEER) 18 registry (2000 to 2011), SEER-Medicare linked files, and the National Health Interview Survey (NHIS) (1986 to 2009). Statistical methods developed to calculate natural life expectancy in the absence of the cancer, cancer-specific survival, and other-cause survival were applied to oral cancer data and internally validated with 10-fold cross-validation. Eligible participants were aged between 20 and 94 years with oral squamous cell carcinoma.

Exposures

Histologically confirmed oral cancer, general health status, smoking, and selected serious comorbid conditions.

Main Outcomes and Measures

Probabilities of surviving or dying from the cancer or from other causes, and life expectancy in the absence of the cancer.

Results

A total of 22 392 patients with oral squamous cell carcinoma (13 544 male [60.5%]; 1476 Asian and Pacific Islander [6.7%]; 1792 Black [8.0%], 1589 Hispanic [7.2%], 17 300 White [78.1%]) and 402 626 NHIS interviewees were included in this calculator designed for public use for patients ages 20 to 86 years with newly diagnosed oral cancer to obtain estimates of health status-adjusted age, life expectancy in the absence of the cancer, and the probability of surviving, dying from the cancer, or dying from other causes within 1 to 10 years after diagnosis. The models in the calculator estimated that patients with oral cancer have a higher risk of death from other causes than their matched US population, and that this risk increases by stage.

Conclusions and relevance

The models developed for the calculator demonstrate that survival estimates that exclude the effects of coexisting conditions can lead to underestimates or overestimates of survival. This new calculator approach will be broadly applicable for developing future prognostic models of cancer and noncancer aspects of a person's health in other cancers; as registries develop more linkages, available covariates will become broader, strengthening future tools.

Competing risks predictions with different time scales under the additive risk model

In the analysis for competing risks data, regression modeling of the cause-specific hazard functions has been usually conducted using the same time scale for all event types. However, when the true time scale is different for each event type, it would be appropriate to specify regression models for the cause-specific hazards on different time scales for different event types. Often, the proportional hazards model has been used for regression modeling of the cause-specific hazard functions. However, the proportionality assumption may not be appropriate in practice. In this article, we consider the additive risk model as an alternative to the proportional hazards model. We propose predictions of the cumulative incidence functions under the cause-specific additive risk models employing different time scales for different event types. We establish the consistency and asymptotic normality of the predicted cumulative incidence functions under the cause-specific additive risk models specified on different time scales using empirical processes and derive consistent variance estimators of the predicted cumulative incidence functions. Through simulation studies, we show that the proposed prediction methods perform well. We illustrate the methods using stage III breast cancer data obtained from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute.

Semiparametric marginal regression for clustered competing risks data with missing cause of failure

Clustered competing risks data are commonly encountered in multicenter studies. The analysis of such data is often complicated due to informative cluster size (ICS), a situation where the outcomes under study are associated with the size of the cluster. In addition, the cause of failure is frequently incompletely observed in real-world settings. To the best of our knowledge, there is no methodology for population-averaged analysis with clustered competing risks data with an ICS and missing causes of failure. To address this problem, we consider the semiparametric marginal proportional cause-specific hazards model and propose a maximum partial pseudolikelihood estimator under a missing at random assumption. To make the latter assumption more plausible in practice, we allow for auxiliary variables that may be related to the probability of missingness. The proposed method does not impose assumptions regarding the within-cluster dependence and allows for ICS. The asymptotic properties of the proposed estimators for both regression coefficients and infinite-dimensional parameters, such as the marginal cumulative incidence functions, are rigorously established. Simulation studies show that the proposed method performs well and that methods that ignore the within-cluster dependence and the ICS lead to invalid inferences. The proposed method is applied to competing risks data from a large multicenter HIV study in sub-Saharan Africa where a significant portion of causes of failure is missing.

A pre-operative prognostic model predicting all cause and cause specific mortality for women presenting with invasive breast cancer

PURPOSE

The aim of this study is to develop a pre-operative prognostic model based on known pre-operative factors.

METHODS

A database of ultrasound (US) lesions undergoing biopsy documented US lesion size, stiffness, and patient source prospectively. Women with invasive cancer presenting between 2010 and 2015 were the study group. Breast and axillary core results and ER, PR and HER receptor status were collected prospectively. Assessment of US skin thickening, US distal enhancement and presence of chronic kidney disease (CKD) was performed retrospectively. Patient survival and cause of death were ascertained from computer records. Predictive models for (i) all-cause mortality (ACM) and (ii) breast cancer death (BCD) were built and then validated using bootstrap k-fold cross-validation. A comparison of predictive performance was made between a full cause-specific Cox model, a sub cause-specific Cox model, and a full Fine-Gray sub-distribution hazard model.

RESULTS

1136 patients were included in the study. The median follow-up time was 6.2 years. 125 (11%) women died from breast cancer and 155 (14%) died from other causes. For the prediction of BCD, the cause-specific Cox sub-model performed the best. The time dependent AUC begins above 0.91 in year one to 3 reducing to 0.83 in year 6. The factors included in the Cox sub model were tumour size, skin thickening, source of detection, tumour grade, ER status, pre-operative nodal metastasis and CKD.

CONCLUSION

We have shown that a model based on preoperative factors can predict BCD. Such prediction if externally validated and incorporating treatment data could be useful for treatment planning and patient counselling.

Semiparametric regression and risk prediction with competing risks data under missing cause of failure

The cause of failure in cohort studies that involve competing risks is frequently incompletely observed. To address this, several methods have been proposed for the semiparametric proportional cause-specific hazards model under a missing at random assumption. However, these proposals provide inference for the regression coefficients only, and do not consider the infinite dimensional parameters, such as the covariate-specific cumulative incidence function. Nevertheless, the latter quantity is essential for risk prediction in modern medicine. In this paper we propose a unified framework for inference about both the regression coefficients of the proportional cause-specific hazards model and the covariate-specific cumulative incidence functions under missing at random cause of failure. Our approach is based on a novel computationally efficient maximum pseudo-partial-likelihood estimation method for the semiparametric proportional cause-specific hazards model. Using modern empirical process theory we derive the asymptotic properties of the proposed estimators for the regression coefficients and the covariate-specific cumulative incidence functions, and provide methodology for constructing simultaneous confidence bands for the latter. Simulation studies show that our estimators perform well even in the presence of a large fraction of missing cause of failures, and that the regression coefficient estimator can be substantially more efficient compared to the previously proposed augmented inverse probability weighting estimator. The method is applied using data from an HIV cohort study and a bladder cancer clinical trial.

Summarizing causal differences in survival curves in the presence of unmeasured confounding

Proportional hazard Cox regression models are frequently used to analyze the impact of different factors on time-to-event outcomes. Most practitioners are familiar with and interpret research results in terms of hazard ratios. Direct differences in survival curves are, however, easier to understand for the general population of users and to visualize graphically. Analyzing the difference among the survival curves for the population at risk allows easy interpretation of the impact of a therapy over the follow-up. When the available information is obtained from observational studies, the observed results are potentially subject to a plethora of measured and unmeasured confounders. Although there are procedures to adjust survival curves for measured covariates, the case of unmeasured confounders has not yet been considered in the literature. In this article we provide a semi-parametric procedure for adjusting survival curves for measured and unmeasured confounders. The method augments our novel instrumental variable estimation method for survival time data in the presence of unmeasured confounding with a procedure for mapping estimates onto the survival probability and the expected survival time scales.

Quantifying diagnostic accuracy improvement of new biomarkers for competing risk outcomes

The net reclassification improvement (NRI) and the integrated discrimination improvement (IDI) were originally proposed to characterize accuracy improvement in predicting a binary outcome, when new biomarkers are added to regression models. These two indices have been extended from binary outcomes to multi-categorical and survival outcomes. Working on an AIDS study where the onset of cognitive impairment is competing risk censored by death, we extend the NRI and the IDI to competing risk outcomes, by using cumulative incidence functions to quantify cumulative risks of competing events, and adopting the definitions of the two indices for multi-category outcomes. The "missing" category due to independent censoring is handled through inverse probability weighting. Various competing risk models are considered, such as the Fine and Gray, multistate, and multinomial logistic models. Estimation methods for the NRI and the IDI from competing risk data are presented. The inference for the NRI is constructed based on asymptotic normality of its estimator, and the bias-corrected and accelerated bootstrap procedure is used for the IDI. Simulations demonstrate that the proposed inferential procedures perform very well. The Multicenter AIDS Cohort Study is used to illustrate the practical utility of the extended NRI and IDI for competing risk outcomes.

Analyzing discrete competing risks data with partially overlapping or independent data sources and nonstandard sampling schemes, with application to cancer registries

This paper demonstrates the flexibility of a general approach for the analysis of discrete time competing risks data that can accommodate complex data structures, different time scales for different causes, and nonstandard sampling schemes. The data may involve a single data source where all individuals contribute to analyses of both cause-specific hazard functions, overlapping datasets where some individuals contribute to the analysis of the cause-specific hazard function of only one cause while other individuals contribute to analyses of both cause-specific hazard functions, or separate data sources where each individual contributes to the analysis of the cause-specific hazard function of only a single cause. The approach is modularized into estimation and prediction. For the estimation step, the parameters and the variance-covariance matrix can be estimated using widely available software. The prediction step utilizes a generic program with plug-in estimates from the estimation step. The approach is illustrated with three prognostic models for stage IV male oral cancer using different data structures. The first model uses only men with stage IV oral cancer from population-based registry data. The second model strategically extends the cohort to improve the efficiency of the estimates. The third model improves the accuracy for those with a lower risk of other causes of death, by bringing in an independent data source collected under a complex sampling design with additional other-cause covariates. These analyses represent novel extensions of existing methodology, broadly applicable for the development of prognostic models capturing both the cancer and noncancer aspects of a patient's health.

Analysis of Generalized Semiparametric Regression Models for Cumulative Incidence Functions with Missing Covariates

The cumulative incidence function quantifies the probability of failure over time due to a specific cause for competing risks data. The generalized semiparametric regression models for the cumulative incidence functions with missing covariates are investigated. The effects of some covariates are modeled as non-parametric functions of time while others are modeled as parametric functions of time. Different link functions can be selected to add flexibility in modeling the cumulative incidence functions. The estimation procedures based on the direct binomial regression and the inverse probability weighting of complete cases are developed. This approach modifies the full data weighted least squares equations by weighting the contributions of observed members through the inverses of estimated sampling probabilities which depend on the censoring status and the event types among other subject characteristics. The asymptotic properties of the proposed estimators are established. The finite-sample performances of the proposed estimators and their relative efficiencies under different two-phase sampling designs are examined in simulations. The methods are applied to analyze data from the RV144 vaccine efficacy trial to investigate the associations of immune response biomarkers with the cumulative incidence of HIV-1 infection.

Mortality Risk Factors Among Patients With Cirrhosis and a Low Model for End-Stage Liver Disease Sodium Score (≤15): An Analysis of Liver Transplant Allocation Policy Using Aggregated Electronic Health Record Data

Although the Model for End-Stage Liver Disease sodium (MELD Na) score is now used for liver transplant allocation in the United States, mortality prediction may be underestimated by the score. Using aggregated electronic health record data from 7834 adult patients with cirrhosis, we determined whether the cause of cirrhosis or cirrhosis complications was associated with an increased risk of death among patients with a MELD Na score ≤15 and whether patients with the greatest risk of death could benefit from liver transplantation (LT). Over median follow-up of 2.3 years, 3715 patients had a maximum MELD Na score ≤15. Overall, 3.4% were waitlisted for LT. Severe hypoalbuminemia, hepatorenal syndrome, and hepatic hydrothorax conferred the greatest risk of death independent of MELD Na score with 1-year predicted mortality >14%. Approximately 10% possessed these risk factors. Of these high-risk patients, only 4% were waitlisted for LT, despite no difference in nonliver comorbidities between waitlisted patients and those not listed. In addition, risk factors for death among waitlisted patients were the same as those for patients not waitlisted, although the effect of malnutrition was significantly greater for waitlisted patients (hazard ratio 8.65 [95% CI 2.57-29.11] vs. 1.47 [95% CI 1.08-1.98]). Using the MELD Na score for allocation may continue to limit access to LT.

Statistical Methods for Cohort Studies of CKD: Survival Analysis in the Setting of Competing Risks

Survival analysis is commonly used to evaluate factors associated with time to an event of interest (e.g., ESRD, cardiovascular disease, and mortality) among CKD populations. Time to the event of interest is typically observed only for some participants. Other participants have their event time censored because of the end of the study, death, withdrawal from the study, or some other competing event. Classic survival analysis methods, such as Cox proportional hazards regression, rely on the assumption that any censoring is independent of the event of interest. However, in most clinical settings, such as in CKD populations, this assumption is unlikely to be true. For example, participants whose follow-up time is censored because of health-related death likely would have had a shorter time to ESRD, had they not died. These types of competing events that cause dependent censoring are referred to as competing risks. Here, we first describe common circumstances in clinical renal research where competing risks operate and then review statistical approaches for dealing with competing risks. We compare two of the most popular analytical methods used in settings of competing risks: cause-specific hazards models and the Fine and Gray approach (subdistribution hazards models). We also discuss practical recommendations for analysis and interpretation of survival data that incorporate competing risks. To demonstrate each of the analytical tools, we use a study of fibroblast growth factor 23 and risks of mortality and ESRD in participants with CKD from the Chronic Renal Insufficiency Cohort Study.

Associations between persistent organic pollutants, type 2 diabetes, diabetic nephropathy and mortality

OBJECTIVE

Relationships were examined between persistent organic pollutants (POPs) and incident type 2 diabetes, end-stage renal disease (ESRD) and mortality.

METHODS

In a nested case-control study, 300 persons without diabetes had baseline examinations between 1969 and 1974; 149 developed diabetes (cases) and 151 remained non-diabetic (controls) during 8.0 and 23.1 years of follow-up, respectively. POPs were measured at baseline. ORs for diabetes were computed by logistic regression analysis. The cases were followed from diabetes onset to ESRD, death or 2013. HRs for ESRD and mortality were computed by cause-specific hazard models. Patterns of association were explored using principal components analysis.

RESULTS

PCB151 increased the odds for incident diabetes, whereas hexachlorobenzene (HCB) was protective after adjusting for age, sex, body mass index, sample storage characteristics, glucose and lipid levels. Associations between incident diabetes and polychlorinatedbiphenyl (PCB) or persistent pesticide (PST) components were mostly positive but non-significant. Among the cases, 29 developed ESRD and 48 died without ESRD. PCB28, PCB49 and PCB44 increased the risk of ESRD after adjusting for baseline demographic and clinical characteristics. Several PCBs and PSTs increased the risk of death without ESRD. The principal components analysis identified PCBs with low-chlorine load positively associated with ESRD and death without ESRD, and several PSTs associated with death without ESRD.

CONCLUSIONS

Most POPs were positively but not significantly associated with incident diabetes. PCB151 was significantly predictive and HCB was significantly protective for diabetes. Among participants with diabetes, low-chlorine PCBs increase the risk of ESRD and death without ESRD, whereas several PSTs predict death without ESRD.

Elevated Blood Neutrophil-to-Lymphocyte Ratio: A Readily Available Biomarker Associated with Death due to Disease in High Risk Nonmetastatic Melanoma

BACKGROUND

Elevated peripheral blood neutrophil-to-lymphocyte ratio (NLR) is associated with poor oncologic outcomes in patients with stage IV melanoma and other solid tumors, but its impact has not been characterized for patients with high-risk, nonmetastatic melanoma.

METHODS

Retrospective review of a melanoma database identified patients with high-risk melanoma who underwent operation with curative intent at a single institution. NLR was calculated from blood samples obtained within 2 weeks before operation. Multiple primary melanomas and concurrent hematologic or other metastatic malignancies were excluded. Cumulative incidence of death due to disease was estimated, and Gray's test was used to examine the effect of NLR on melanoma disease-specific death (DOD). Multivariable competing risks regression models assessed associated factors.

RESULTS

Data on 1431 patients with high-risk, nonmetastatic melanoma were analyzed. Median follow-up for survivors was 4 years. High NLR (≥3 or as continuous variable) was associated with older age, male sex, thicker primaries, higher mitotic index, and more advanced nodal status. On multivariate analysis, high NLR (≥3 or as a continuous variable), older age, male sex, ulcerated primary, lymphovascular invasion, and positive nodal status were all independently associated with worse DOD.

CONCLUSIONS

NLR is a readily available blood test that was independently associated with DOD in patients with high-risk, nonmetastatic melanoma. It is unclear whether high NLR is a passive indicator of poor prognosis or a potential therapeutic target. Further studies to evaluate the prognostic role of NLR to potentially identify those more likely to benefit from adjuvant immunotherapy may prove informative.

Instrumental variable with competing risk model

In this paper, we discuss causal inference on the efficacy of a treatment or medication on a time-to-event outcome with competing risks. Although the treatment group can be randomized, there can be confoundings between the compliance and the outcome. Unmeasured confoundings may exist even after adjustment for measured covariates. Instrumental variable methods are commonly used to yield consistent estimations of causal parameters in the presence of unmeasured confoundings. On the basis of a semiparametric additive hazard model for the subdistribution hazard, we propose an instrumental variable estimator to yield consistent estimation of efficacy in the presence of unmeasured confoundings for competing risk settings. We derived the asymptotic properties for the proposed estimator. The estimator is shown to be well performed under finite sample size according to simulation results. We applied our method to a real transplant data example and showed that the unmeasured confoundings lead to significant bias in the estimation of the effect (about 50% attenuated). Copyright © 2017 John Wiley & Sons, Ltd.

Early CMV-replication after allogeneic stem cell transplantation is associated with a reduced relapse risk in lymphoma

A preventive effect of early human cytomegalovirus (HCMV) replication was evaluated in 136 non-Hodgkin lymphoma (NHL) patients with mature B-cell NHLs (n = 94), and mature T- and NK-cell NHLs (n = 42) after allogeneic stem cell transplantation (alloSCT). Most study-patients (85%) had received at least 2 cycles of chemotherapy and 60% had also received an autograft prior to alloSCT. First detection of CMV-replication by HCMV antigenemia/viremia was found at a median of day +33 after alloSCT. The cumulative incidence of relapse at 5 years after alloSCT was 38% (95% confidence interval [95%CI]: 26-49) in 82 patients without compared to 22% (95%CI: 8-37) in 54 patients with HCMV antigenemia/viremia (p = .013). A decreased relapse risk of HCMV replication was confirmed by multivariate analysis for HCMV antigenemia/viremia (Hazard ratio [HR]: 0.29, 95%CI: 0.11-0.76, p < .014). This report demonstrated a possible improvement of relapse incidence after replicative HCMV infection in patients with NHL after alloSCT.

On the choice of time scales in competing risks predictions

In the standard analysis of competing risks data, proportional hazards models are fit to the cause-specific hazard functions for all causes on the same time scale. These regression analyses are the foundation for predictions of cause-specific cumulative incidence functions based on combining the estimated cause-specific hazard functions. However, in predictions arising from disease registries, where only subjects with disease enter the database, disease-related mortality may be more naturally modeled on the time since diagnosis time scale while death from other causes may be more naturally modeled on the age time scale. The single time scale methodology may be biased if an incorrect time scale is employed for one of the causes and an alternative methodology is not available. We propose inferences for the cumulative incidence function in which regression models for the cause-specific hazard functions may be specified on different time scales. Using the disease registry data, the analysis of other cause mortality on the age scale requires left truncating the event time at the age of disease diagnosis, complicating the analysis. In addition, standard Martingale theory is not applicable when combining regression models on different time scales. We establish that the covariate conditional predictions are consistent and asymptotically normal using empirical process techniques and propose consistent variance estimators for constructing confidence intervals. Simulation studies show that the proposed two time scales method performs well, outperforming the single time-scale predictions when the time scale is misspecified. The methods are illustrated with stage III colon cancer data obtained from the Surveillance, Epidemiology, and End Results program of National Cancer Institute.

miR-1207-3p Is a Novel Prognostic Biomarker of Prostate Cancer

MicroRNAs (miRNAs) have been found to be dysregulated in prostate cancer (PCa). In this study, we investigated if miR-1207-3p is capable of distinguishing between indolent and aggressive PCa and if it contributes to explaining the disproportionate aggressiveness of PCa in men of African ancestry (moAA). A total of 404 patients with primary adenocarcinoma of the prostate were recruited between 1988 and 2003 at the Moffitt Cancer Center, Tampa, FL, USA. Patient clinicopathological features and demographic characteristics such as race were identified. RNA samples from 404 postprostatectomy prostate tumor tissue samples were analyzed by real-time quantitative reverse transcription polymerase chain reaction for the mRNA expression of miR-1207-3p. miR-1207-3p expression in PCa that resulted in overall death or PCa-specific death is significantly higher than in PCa cases that did not. The same positive correlation holds true for other clinical characteristics such as biochemical recurrence, Gleason score, clinical stage, and prostate-specific antigen level. Furthermore, miR-1207-3p expression was significantly less in moAA in comparison to Caucasian men. We also evaluated whether miR-1207-3p is associated with clinical outcomes adjusted for age at diagnosis and tumor stage in the modeling. Using competing risk regression, the PCa patients with a high miR-1207-3p expression (≥6 vs 3) had a high risk to develop PCa recurrence (hazard rate = 2.5, P < .001) adjusting for age at diagnosis and tumor stage. In conclusion, miR-1207-3p is a promising novel prognostic biomarker for PCa. Furthermore, miR-1207-3p may also be important in explaining the disproportionate aggressiveness of PCa in moAA.

Developing points-based risk-scoring systems in the presence of competing risks

Predicting the occurrence of an adverse event over time is an important issue in clinical medicine. Clinical prediction models and associated points‐based risk‐scoring systems are popular statistical methods for summarizing the relationship between a multivariable set of patient risk factors and the risk of the occurrence of an adverse event. Points‐based risk‐scoring systems are popular amongst physicians as they permit a rapid assessment of patient risk without the use of computers or other electronic devices. The use of such points‐based risk‐scoring systems facilitates evidence‐based clinical decision making. There is a growing interest in cause‐specific mortality and in non‐fatal outcomes. However, when considering these types of outcomes, one must account for competing risks whose occurrence precludes the occurrence of the event of interest. We describe how points‐based risk‐scoring systems can be developed in the presence of competing events. We illustrate the application of these methods by developing risk‐scoring systems for predicting cardiovascular mortality in patients hospitalized with acute myocardial infarction. Code in the R statistical programming language is provided for the implementation of the described methods. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Functional distance between recipient and donor HLA-DPB1 determines nonpermissive mismatches in unrelated HCT

The role of HLA amino acid (AA) polymorphism for the outcome of hematopoietic cell transplantation (HCT) is controversial, in particular for HLA class II. Here, we investigated this question in nonpermissive HLA-DPB1 T-cell epitope (TCE) mismatches reflected by numerical functional distance (FD) scores, assignable to all HLA-DPB1 alleles based on the combined impact of 12 polymorphic AAs. We calculated the difference in FD scores (ΔFD) of mismatched HLA-DPB1 alleles in patients and their 10/10 HLA-matched unrelated donors of 379 HCTs performed at our center for acute leukemia or myelodysplastic syndrome. Receiver-operator curve-based stratification into 2 ΔFD subgroups showed a significantly higher percentage of nonpermissive TCE mismatches for ΔFD >2.665, compared with ΔFD ≤2.665 (88% vs 25%, P < .0001). In multivariate analysis, ΔFD >2.665 was significantly associated with overall survival (hazard ratio [HR], 1.40; 95% confidence interval [CI], 1.05-1.87; P < .021) and event-free survival (HR, 1.39; 95% CI, 1.05-1.82; P < .021), compared with ΔFD ≤2.665. These associations were stronger than those observed for TCE mismatches. There was a marked but not statistically significant increase in the hazards of relapse and nonrelapse mortality in the high ΔFD subgroup, whereas no differences were observed for acute and chronic graft-versus-host disease. Seven nonconservative AA substitutions in peptide-binding positions had a significantly stronger impact on ΔFD compared with 5 others (P = .0025), demonstrating qualitative differences in the relative impact of AA polymorphism in HLA-DPB1. The novel concept of ΔFD sheds new light onto nonpermissive HLA-DPB1 mismatches in unrelated HCT.

On estimation of covariate-specific residual time quantiles under the proportional hazards model

Estimation and inference in time-to-event analysis typically focus on hazard functions and their ratios under the Cox proportional hazards model. These hazard functions, while popular in the statistical literature, are not always easily or intuitively communicated in clinical practice, such as in the settings of patient counseling or resource planning. Expressing and comparing quantiles of event times may allow for easier understanding. In this article we focus on residual time, i.e., the remaining time-to-event at an arbitrary time t given that the event has yet to occur by t. In particular, we develop estimation and inference procedures for covariate-specific quantiles of the residual time under the Cox model. Our methods and theory are assessed by simulations, and demonstrated in analysis of two real data sets.

Hierarchical likelihood inference on clustered competing risks data

The frailty model, an extension of the proportional hazards model, is often used to model clustered survival data. However, some extension of the ordinary frailty model is required when there exist competing risks within a cluster. Under competing risks, the underlying processes affecting the events of interest and competing events could be different but correlated. In this paper, the hierarchical likelihood method is proposed to infer the cause-specific hazard frailty model for clustered competing risks data. The hierarchical likelihood incorporates fixed effects as well as random effects into an extended likelihood function, so that the method does not require intensive numerical methods to find the marginal distribution. Simulation studies are performed to assess the behavior of the estimators for the regression coefficients and the correlation structure among the bivariate frailty distribution for competing events. The proposed method is illustrated with a breast cancer dataset.

Comparing center-specific cumulative incidence functions

The competing risks data structure arises frequently in clinical and epidemiologic studies. In such settings, the cumulative incidence function is often used to describe the ultimate occurrence of a particular cause of interest. If the objective of the analysis is to compare subgroups of patients with respect to cumulative incidence, imbalance with respect to group-specific covariate distributions must generally be factored out, particularly in observational studies. This report proposes a measure to contrast center- (or, more generally group-) specific cumulative incidence functions (CIF). One such application involves evaluating organ procurement organizations with respect to the cumulative incidence of kidney transplantation. In this case, the competing risks include (i) death on the wait-list and (ii) removal from the wait-list. The proposed method assumes proportional cause-specific hazards, which are estimated through Cox models stratified by center. The proposed center effect measure compares the average CIF for a given center to the average CIF that would have resulted if that particular center had covariate pattern-specific cumulative incidence equal to that of the national average. We apply the proposed methods to data obtained from a national organ transplant registry.

Competing Risk Analysis of Neurologic versus Nonneurologic Death in Patients Undergoing Radiosurgical Salvage After Whole-Brain Radiation Therapy Failure: Who Actually Dies of Their Brain Metastases?

PURPOSE

To estimate the hazard for neurologic (central nervous system, CNS) and nonneurologic (non-CNS) death associated with patient, treatment, and systemic disease status in patients receiving stereotactic radiosurgery after whole-brain radiation therapy (WBRT) failure, using a competing risk model.

PATIENTS AND METHODS

Of 757 patients, 293 experienced recurrence or new metastasis following WBRT. Univariate Cox proportional hazards regression identified covariates for consideration in the multivariate model. Competing risks multivariable regression was performed to estimate the adjusted hazard ratio (aHR) and 95% confidence interval (CI) for both CNS and non-CNS death after adjusting for patient, disease, and treatment factors. The resultant model was converted into an online calculator for ease of clinical use.

RESULTS

The cumulative incidence of CNS and non-CNS death at 6 and 12 months was 20.6% and 21.6%, and 34.4% and 35%, respectively. Patients with melanoma histology (relative to breast) (aHR 2.7, 95% CI 1.5-5.0), brainstem location (aHR 2.1, 95% CI 1.3-3.5), and number of metastases (aHR 1.09, 95% CI 1.04-1.2) had increased aHR for CNS death. Progressive systemic disease (aHR 0.55, 95% CI 0.4-0.8) and increasing lowest margin dose (aHR 0.97, 95% CI 0.9-0.99) were protective against CNS death. Patients with lung histology (aHR 1.3, 95% CI 1.1-1.9) and progressive systemic disease (aHR 2.14, 95% CI 1.5-3.0) had increased aHR for non-CNS death.

CONCLUSION

Our nomogram provides individual estimates of neurologic death after salvage stereotactic radiosurgery for patients who have failed prior WBRT, based on histology, neuroanatomical location, age, lowest margin dose, and number of metastases after adjusting for their competing risk of death from other causes.

A Proportional Hazards Regression Model for the Sub-distribution with Covariates Adjusted Censoring Weight for Competing Risks Data

With competing risks data, one often needs to assess the treatment and covariate effects on the cumulative incidence function. Fine and Gray proposed a proportional hazards regression model for the subdistribution of a competing risk with the assumption that the censoring distribution and the covariates are independent. Covariate-dependent censoring sometimes occurs in medical studies. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with proper adjustments for covariate-dependent censoring. We consider a covariate-adjusted weight function by fitting the Cox model for the censoring distribution and using the predictive probability for each individual. Our simulation study shows that the covariate-adjusted weight estimator is basically unbiased when the censoring time depends on the covariates, and the covariate-adjusted weight approach works well for the variance estimator as well. We illustrate our methods with bone marrow transplant data from the Center for International Blood and Marrow Transplant Research (CIBMTR). Here cancer relapse and death in complete remission are two competing risks.

Evaluating hospital performance based on excess cause-specific incidence

Formal evaluation of hospital performance in specific types of care is becoming an indispensable tool for quality assurance in the health care system. When the prime concern lies in reducing the risk of a cause-specific event, we propose to evaluate performance in terms of an average excess cumulative incidence, referring to the center's observed patient mix. Its intuitive interpretation helps give meaning to the evaluation results and facilitates the determination of important benchmarks for hospital performance. We apply it to the evaluation of cerebrovascular deaths after stroke in Swedish stroke centers, using data from Riksstroke, the Swedish stroke registry. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Prediction of cardiovascular risk using Framingham, ASSIGN and QRISK2: how well do they predict individual rather than population risk?

BACKGROUND

The objective of this study was to evaluate the performance of risk scores (Framingham, Assign and QRISK2) in predicting high cardiovascular disease (CVD) risk in individuals rather than populations.

METHODS AND FINDINGS

This study included 1.8 million persons without CVD and prior statin prescribing using the Clinical Practice Research Datalink. This contains electronic medical records of the general population registered with a UK general practice. Individual CVD risks were estimated using competing risk regression models. Individual differences in the 10-year CVD risks as predicted by risk scores and competing risk models were estimated; the population was divided into 20 subgroups based on predicted risk. CVD outcomes occurred in 69,870 persons. In the subgroup with lowest risks, risk predictions by QRISK2 were similar to individual risks predicted using our competing risk model (99.9% of people had differences of less than 2%); in the subgroup with highest risks, risk predictions varied greatly (only 13.3% of people had differences of less than 2%). Larger deviations between QRISK2 and our individual predicted risks occurred with calendar year, different ethnicities, diabetes mellitus and number of records for medical events in the electronic health records in the year before the index date. A QRISK2 estimate of low 10-year CVD risk (<15%) was confirmed by Framingham, ASSIGN and our individual predicted risks in 89.8% while an estimate of high 10-year CVD risk (≥ 20%) was confirmed in only 48.6% of people. The majority of cases occurred in people who had predicted 10-year CVD risk of less than 20%.

CONCLUSIONS

Application of existing CVD risk scores may result in considerable misclassification of high risk status. Current practice to use a constant threshold level for intervention for all patients, together with the use of different scoring methods, may inadvertently create an arbitrary classification of high CVD risk.

Weighted comparison of two cumulative incidence functions with R-CIFsmry package

In this paper we propose a class of flexible weight functions for use in comparison of two cumulative incidence functions. The proposed weights allow the users to focus their comparison on an early or a late time period post treatment or to treat all time points with equal emphasis. These weight functions can be used to compare two cumulative incidence functions via their risk difference, their relative risk, or their odds ratio. The proposed method has been implemented in the R-CIFsmry package which is readily available for download and is easy to use as illustrated in the example.

Concordance for prognostic models with competing risks

The concordance probability is a widely used measure to assess discrimination of prognostic models with binary and survival endpoints. We formally define the concordance probability for a prognostic model of the absolute risk of an event of interest in the presence of competing risks and relate it to recently proposed time-dependent area under the receiver operating characteristic curve measures. For right-censored data, we investigate inverse probability of censoring weighted (IPCW) estimates of a truncated concordance index based on a working model for the censoring distribution. We demonstrate consistency and asymptotic normality of the IPCW estimate if the working model is correctly specified and derive an explicit formula for the asymptotic variance under independent censoring. The small sample properties of the estimator are assessed in a simulation study also against misspecification of the working model. We further illustrate the methods by computing the concordance probability for a prognostic model of coronary heart disease (CHD) events in the presence of the competing risk of non-CHD death.

Modeling cumulative incidence function for competing risks data

A frequent occurrence in medical research is that a patient is subject to different causes of failure, where each cause is known as a competing risk. The cumulative incidence curve is a proper summary curve, showing the cumulative failure rates over time due to a particular cause. A common question in medical research is to assess the covariate effects on a cumulative incidence function. The standard approach is to construct regression models for all cause-specific hazard rate functions and then model a covariate-adjusted cumulative incidence curve as a function of all cause-specific hazards for a given set of covariates. New methods have been proposed in recent years, emphasizing direct assessment of covariate effects on cumulative incidence function. Fine and Gray proposed modeling the effects of covariates on a subdistribution hazard function. A different approach is to directly model a covariate-adjusted cumulative incidence function, including a pseudovalue approach by Andersen and Klein and a direct binomial regression by Scheike, Zhang and Gerds. In this paper, we review the standard and new regression methods for modeling a cumulative incidence function, and give the sources of computer packages/programs that implement these regression models. A real bone marrow transplant data set is analyzed to illustrate various regression methods.

Life tables adjusted for comorbidity more accurately estimate noncancer survival for recently diagnosed cancer patients

OBJECTIVES

To provide cancer patients and clinicians with more accurate estimates of a patient's life expectancy with respect to noncancer mortality, we estimated comorbidity-adjusted life tables and health-adjusted age.

STUDY DESIGN AND SETTING

Using data from the Surveillance Epidemiology and End Results-Medicare database, we estimated comorbidity scores that reflect the health status of people who are 66 years of age and older in the year before cancer diagnosis. Noncancer survival by comorbidity score was estimated for each age, race, and sex. Health-adjusted age was estimated by systematically comparing the noncancer survival models with US life tables.

RESULTS

Comorbidity, cancer status, sex, and race are all important predictors of noncancer survival; however, their relative impact on noncancer survival decreases as age increases. Survival models by comorbidity better predicted noncancer survival than the US life tables. The health-adjusted age and national life tables can be consulted to provide an approximate estimate of a person's life expectancy, for example, the health-adjusted age of a black man aged 75 years with no comorbidities is 67 years, giving him a life expectancy of 13 years.

CONCLUSION

The health-adjusted age and the life tables adjusted by age, race, sex, and comorbidity can provide important information to facilitate decision making about treatment for cancer and other conditions.

The prognostic role of preoperative and (early) postoperatively change in CA15.3 serum levels in a single hospital cohort of primary operable breast cancers

Measuring CA15.3 serum levels in the early breast cancer setting is not recommended by current ASCO guidelines. In this large single center study, we assess the prognostic value of preoperative (n = 3746), postoperative (n = 4049) and change in (n = 3252) CA15.3, also across different breast cancer phenotypes. Preoperative, postoperative and change in CA15.3 were all significant (p = 0.0348, p < 0.0001, p < 0.0001 respectively in multivariate analysis) predictors of distant metastasis free survival. For breast cancer specific survival, only postoperative and change in CA15.3 were significant predictors (p < 0.0001 both). Multivariate prognostic models did not improve by incorporating information on preoperative CA15.3, but did improve when introducing information on postoperative CA15.3 for distant metastasis (p = 0.0365) and on change in CA15.3 for breast cancer specific survival (p = 0.0291). Change in CA15.3 impacts on prognosis (distant metastasis) differently in different breast cancer phenotypes. A decrease in CA15.3 may be informative of improved prognosis in basal like and HER2 like breast cancer.

Risk stratification of pT1-3N0 patients after radical cystectomy for adjuvant chemotherapy counselling

BACKGROUND

In pT1-T3N0 urothelial carcinoma of the bladder (UCB) patients, multi-modal therapy is inconsistently recommended. The aim of the study was to develop a prognostic tool to help decision-making regarding adjuvant therapy.

METHODS

We included 2145 patients with pT1-3N0 UCB after radical cystectomy (RC), naive of neoadjuvant or adjuvant therapy. The cohort was randomly split into development cohort based on the US patients (n=1067) and validation cohort based on the Europe patients (n=1078). Predictive accuracy was quantified using the concordance index.

RESULTS

With a median follow-up of 45 months, 5-year recurrence-free and cancer-specific survival estimates were 68% and 73%, respectively. pT-stage, ge, lymphovascular invasion, and positive margin were significantly associated with both disease recurrence and cancer-specific mortality (P-values ≤ 0.005). The accuracies of the multivariable models at 2, 5, and 7 years for predicting disease recurrence were 67.4%, 65%, and 64.4%, respectively. Accuracies at 2, 5, and 7 years for predicting cancer-specific mortality were 69.3%, 66.4%, and 65.5%, respectively. We developed competing-risk, conditional probability nomograms. External validation revealed minor overestimation.

CONCLUSION

Despite RC, a significant number of patients with pT1-3N0 UCB experience disease recurrence and ultimately die of UCB. We developed and externally validated competing-risk, conditional probability post-RC nomograms for prediction of disease recurrence and cancer-specific mortality.