On the choice of time scales in competing risks predictions

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.

Key Points for Clinicians About the SEER Oral Cancer Survival Calculator

Importance

In the setting of a new cancer diagnosis, the focus is usually on the cancer as the main threat to survival, but people may have other conditions that pose an equal or greater threat to their life than their cancer: a competing risk of death. This is especially true for patients who have cancer of the oral cavity, because prolonged exposure to alcohol and tobacco are risk factors for cancer in this location but also can result in medical conditions with the potential to shorten life expectancy, competing as a cause of death that may intervene in conjunction with or before the cancer.

Observations

A calculator designed for public use has been released that allows patients age 20 to 86 years who have a newly diagnosed oral cancer to obtain estimates of their health status-adjusted age, life expectancy in the absence of the cancer, and probability of surviving, dying of the cancer, or dying of other causes within 1 to 10 years after diagnosis. The models in the calculator showed that patients with oral cavity cancer had a higher than average risk of death from other causes than the matched US population, and this risk increases by stage.

Conclusions and Relevance

The Surveillance, Epidemiology and End Results Program Oral Cancer Survival Calculator supports a holistic approach to the life of the patient, and the risk of death of other causes is treated equally to consideration of the probability of death of the cancer. This tool may be usefully paired with the other available prognostic calculators for oral cancer and is an example of the possibilities now available with registry linkages to partially overlapping or independent data sets and statistical techniques that allow the use of 2 time scales in 1 analysis.

Fair comparisons of cause-specific and relative survival by accounting for the systematic removal of patients from risk-sets

BACKGROUND

In population-based cancer studies it is common to try to isolate the impact of cancer by estimating net survival. Net survival is defined as the probability of surviving cancer in the absence of any other-causes of death. Net survival can be estimated either in the cause-specific or relative survival framework. Cause-specific survival considers deaths from the cancer as the event of interest. Relative survival incorporates general population expected mortality rates to represent the other-cause mortality rate. Estimation approaches in both frameworks are impacted by the systematic removal of patients from the risk-set, commonly referred to as informative censoring in the cause-specific framework. In the relative survival framework, the Pohar Perme estimator combats the effect of this systematic removal of patients through weighting. When the two frameworks have been compared, informative censoring is rarely accounted for in the cause-specific framework.

METHODS

We investigate the use of weighted cause-specific Kaplan-Meier estimates to overcome the impact of informative censoring and compared approaches to defining weights. Individuals remaining in the risk-set are upweighted using their predicted other-cause survival obtained through various model-based approaches. We also compare weights derived from expected mortality rates. We applied the approaches to US cancer registry data and conducted a simulation study.

RESULTS

Using weighted cause-specific estimates provides a better estimate of marginal net survival. The unweighted Kaplan-Meier estimates have a similar bias to the Ederer II method for relative survival. Weighted Kaplan-Meier estimates are unbiased and similar to the Pohar Perme estimator. There was little variation between the several weighting approaches.

CONCLUSION

In comparisons of cause-specific and relative survival, it is important to compare "like-with-like", therefore, a weighted approach should be considered for both frameworks. If researchers are interested in obtaining net measures in a cause-specific framework, then weighting is needed to account for informative censoring.

Neural network on interval-censored data with application to the prediction of Alzheimer's disease

Alzheimer's disease (AD) is a progressive and polygenic disorder that affects millions of individuals each year. Given that there have been few effective treatments yet for AD, it is highly desirable to develop an accurate model to predict the full disease progression profile based on an individual's genetic characteristics for early prevention and clinical management. This work uses data composed of all four phases of the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, including 1740 individuals with 8 million genetic variants. We tackle several challenges in this data, characterized by large-scale genetic data, interval-censored outcome due to intermittent assessments, and left truncation in one study phase (ADNIGO). Specifically, we first develop a semiparametric transformation model on interval-censored and left-truncated data and estimate parameters through a sieve approach. Then we propose a computationally efficient generalized score test to identify variants associated with AD progression. Next, we implement a novel neural network on interval-censored data (NN-IC) to construct a prediction model using top variants identified from the genome-wide test. Comprehensive simulation studies show that the NN-IC outperforms several existing methods in terms of prediction accuracy. Finally, we apply the NN-IC to the full ADNI data and successfully identify subgroups with differential progression risk profiles. Data used in the preparation of this article were obtained from the ADNI database.

Low-Dose Enzalutamide in Metastatic Prostate Cancer-Longevity Over Conventional Survival Analysis

BACKGROUND

Enzalutamide is an important drug in the treatment of prostate cancer. Standard dosing often requires dose reduction because of side effects. There is no information on survival outcomes with lower doses. We investigated the impact of starting enzalutamide at ≤ 50% dose on metastatic prostate cancer outcomes including patients' longevity.

PATIENTS AND METHODS

Records of metastatic prostate cancer patients treated with enzalutamide at one center were retrospectively reviewed. Low-dose enzalutamide (≤80 mg/day) was compared with standard-dose (160 mg/day). The primary objective was to compute the restricted mean survival time (RMST - time scale) and restricted mean attained age (RMAA - age scale) using the Irwin method. Secondary objectives included overall survival (OS), progression-free survival (PFS), and PSA progression per PCWG3 criteria (PSA PFS). We used the logrank test and the ∆ difference between RMSTs for comparison.

RESULTS

Of 111 patients treated, 32 received a low-dose and 79 the standard-dose. Low-dose patients had less prior abiraterone or chemotherapy (28.1% vs. 65.8%, P < .001); more testosterone assessment (65.6% vs. 40.5%, P = .016); poorer ECOG performance status (48.3% score ≥2 vs. 26.6%; P = .040), more comorbidities (75.9% vs. 46.3%; P = .010)) including increased cardiovascular disease (51.7% vs. 21.4%, P = .004). Baseline PSA value and doubling time at start of enzalutamide and distribution of metastases were similar between the groups. OS and PFS did not differ between low-dose and standard-dose. Patients on low-dose had a better longevity with significantly longer RMAA, 89.1 years, versus standard-dose RMAA of 83.8 years (∆ = 5.3 years, P = .003, logrank P = .025). In a subgroup analysis by age at start of enzalutamide, <75 versus ≥75 years old, longevity was also better with low-dose in younger patients (∆ = 2.9 years, P = .034, and older, ∆ = 3.3 years, P = .011).

CONCLUSION

The longevity advantage and reduced adverse events seen in patients with prostate cancer treated with low-dose enzalutamide warrants further investigation.

On the choice of timescale for other cause mortality in a competing risk setting using flexible parametric survival models

In competing risks settings where the events are death due to cancer and death due to other causes, it is common practice to use time since diagnosis as the timescale for all competing events. However, attained age has been proposed as a more natural choice of timescale for modeling other cause mortality. We examine the choice of using time since diagnosis versus attained age as the timescale when modeling other cause mortality, assuming that the hazard rate is a function of attained age, and how this choice can influence the cumulative incidence functions ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>C</mml:mi> <mml:mi>I</mml:mi> <mml:mi>F</mml:mi></mml:mrow> <mml:annotation>$CIF$</mml:annotation></mml:semantics> </mml:math> s) derived using flexible parametric survival models. An initial analysis on the colon cancer data from the population-based Swedish Cancer Register indicates such an influence. A simulation study is conducted in order to assess the impact of the choice of timescale for other cause mortality on the bias of the estimated <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>C</mml:mi> <mml:mi>I</mml:mi> <mml:mi>F</mml:mi> <mml:mi>s</mml:mi></mml:mrow> <mml:annotation>$CIFs$</mml:annotation></mml:semantics> </mml:math> and how different factors may influence the bias. We also use regression standardization methods in order to obtain marginal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>C</mml:mi> <mml:mi>I</mml:mi> <mml:mi>F</mml:mi></mml:mrow> <mml:annotation>$CIF$</mml:annotation></mml:semantics> </mml:math> estimates. Using time since diagnosis as the timescale for all competing events leads to a low degree of bias in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>C</mml:mi> <mml:mi>I</mml:mi> <mml:mi>F</mml:mi></mml:mrow> <mml:annotation>$CIF$</mml:annotation></mml:semantics> </mml:math> for cancer mortality ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>C</mml:mi> <mml:mi>I</mml:mi> <mml:msub><mml:mi>F</mml:mi> <mml:mn>1</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$CIF_{1}$</mml:annotation></mml:semantics> </mml:math> ) under all approaches. It also leads to a low degree of bias in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>C</mml:mi> <mml:mi>I</mml:mi> <mml:mi>F</mml:mi></mml:mrow> <mml:annotation>$CIF$</mml:annotation></mml:semantics> </mml:math> for other cause mortality ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>C</mml:mi> <mml:mi>I</mml:mi> <mml:msub><mml:mi>F</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$CIF_{2}$</mml:annotation></mml:semantics> </mml:math> ), provided that the effect of age at diagnosis is included in the model with sufficient flexibility, with higher bias under scenarios where a covariate has a time-varying effect on the hazard rate for other cause mortality on the attained age scale.

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.

Nonsmooth backfitting for the excess risk additive regression model with two survival time scales

We consider an extension of Aalen’s additive regression model that allows covariates to have effects that vary on two different time scales. The two time scales considered are equal up to a constant for each individual and vary across individuals, such as follow-up time and age in medical studies or calendar time and age in longitudinal studies. The model was introduced in Scheike (2001), where it was solved using smoothing techniques. We present a new backfitting algorithm for estimating the structured model without having to use smoothing. Estimators of the cumulative regression functions on the two time scales are suggested by solving local estimating equations jointly on the two time scales. We provide large-sample properties and simultaneous confidence bands. The model is applied to data on myocardial infarction, providing a separation of the two effects stemming from time since diagnosis and age.

A multistate model incorporating estimation of excess hazards and multiple time scales

As cancer patient survival improves, late effects from treatment are becoming the next clinical challenge. Chemotherapy and radiotherapy, for example, potentially increase the risk of both morbidity and mortality from second malignancies and cardiovascular disease. To provide clinically relevant population-level measures of late effects, it is of importance to (1) simultaneously estimate the risks of both morbidity and mortality, (2) partition these risks into the component expected in the absence of cancer and the component due to the cancer and its treatment, and (3) incorporate the multiple time scales of attained age, calendar time, and time since diagnosis. Multistate models provide a framework for simultaneously studying morbidity and mortality, but do not solve the problem of partitioning the risks. However, this partitioning can be achieved by applying a relative survival framework, allowing us to directly quantify the excess risk. This article proposes a combination of these two frameworks, providing one approach to address (1) to (3). Using recently developed methods in multistate modeling, we incorporate estimation of excess hazards into a multistate model. Both intermediate and absorbing state risks can be partitioned and different transitions are allowed to have different and/or multiple time scales. We illustrate our approach using data on Hodgkin lymphoma patients and excess risk of diseases of the circulatory system, and provide user-friendly Stata software with accompanying example code.

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.

Excess risk estimation for matched cohort survival data

We present an excess risk regression model for matched cohort data, where the occurrence of some events for individuals with a disease is compared to that of healthy controls that are matched at the onset-of-disease by various factors. By using the matched structure, we show how to estimate the excess risk and its dependence on covariates on both proportional and additive form. We remove the individual effects on background mortality related to matching factors by considering differences. The model handles two different time scales, namely attained age and follow-up time. First, we solve estimating equations for the non-parametric and parametric components of the excess risk model, providing large sample properties for the suggested estimators. Next, we report results from a simulation study. Lastly, we describe an application of the method on childhood cancer data, to study the excess risk of cardiovascular events in adults' life among childhood cancer survivors.