Potential for Cure by Stage across the Cancer Spectrum in the United States

Cancer can be a survivable disease, especially when detected at an early stage. Cancer survivors currently comprise approximately 5% of the entire population in several western nations (1–4), and the percentage is expected to increase substantially in the coming years due to population aging (5, 6), advances in early detection and treatment (7), reduction of competing risks such as cardiovascular mortality (8), and overdiagnosis of nonlethal cancer (9).

Cure fraction is defined statistically as the proportion of diagnosed patients with cancer in a population who survive past the early peak in cancer-specific mortality to the point of attaining virtually the same risk of death as the age- and sex-matched general population with similar competing risks (10). Statistically, cured patients are those who achieve stable long-term survival with minimal risk of mortality from their initial cancer. For cancer types for which long-term risk of cancer death does not reach zero, cure fraction can still characterize the proportion of patients with this asymptotic level of risk (11–13). When used to evaluate cancer screening, cure fraction has the advantage of avoiding lead-time bias by virtue of its basis on long-term mortality data, as opposed to survival duration. By providing a measure of the overall effectiveness of cancer detection, treatment, and follow-up, cure fraction serves as a useful real-world indicator of long-term cancer outcomes in populations. For example, studies of cure fraction by cancer site have been used to monitor public health progress in cancer care, as well as to identify cancer types for which existing control strategies have had a limited effect (14–20).

Stage at diagnosis is among the strongest predictors of cancer outcomes, including survivorship trajectory and mortality risk, which differ starkly between localized and metastatic cancers (12). Accordingly, cure fraction is expected to vary substantially by both cancer type and stage. Understanding differences in cure fraction by cancer type and stage, in turn, can shed light on the potential for reducing the population burden of cancer through earlier detection, especially using new screening interventions (in addition to optimized treatment), by shifting the population proportion of later-stage to earlier-stage disease. This information also serves as quantitative evidence to help guide the allocation of public health resources for cancer prevention, detection, treatment, and management (21). To date, most studies of cure fraction have focused on individual cancer types or have not reported stage-specific cure fractions. Therefore, to better understand the potential for long-term cure through diagnosis at earlier stages across the spectrum of cancers, we undertook an analysis of cure fraction stratified by stage for all major stageable cancer types in the US population.

We obtained cause-specific survival data for this study from the US Surveillance, Epidemiology, and End Results (SEER) population-based cancer registries for 17 geographic regions from 2006 to 2015, with follow-up for mortality through 2020 (https://seer.cancer.gov/data/). These years were selected to enable uniform classification of cancer stage according to the 6th edition of the American Joint Committee on Cancer (AJCC) staging manual (22), and to enable a balance between recentness of data and availability of long-term follow-up. We included patients diagnosed with a first primary malignancy at ages 40 to 84 years, excluding those diagnosed only by death certificate or autopsy and those with missing/unknown data on age, vital status, survival time, or cause of death (1.5% of the starting cohort). Survival time was defined as the duration of the interval from diagnosis until death from the primary cancer (coded according to SEER's cause-specific death classification; ref. 23), death from another cause, or the end of follow-up on December 31, 2020.

Cases were grouped by primary cancer site using codes from the International Classification of Diseases for Oncology, 3rd edition (ICD-O-3), and by AJCC stage (I, II, III, IV, or missing/unknown). Pre-invasive/non-invasive tumors, such as in situ neoplasms, were excluded. Primary cancer types included in this analysis, defined by anatomic site, were anus, bladder, breast, cervix, colon/rectum, esophagus, gallbladder, head/neck, kidney, liver/intrahepatic bile duct, lung, lymphoma, melanoma, ovary, pancreas, prostate, sarcoma, stomach, thyroid, urothelial tract, and uterus. Brain/other nervous system cancers, leukemia, and myeloma lack AJCC 6th edition staging criteria, and therefore were excluded. Certain benign, rare, or hematopoietic histologies (ICD-O-3 histology codes 8710–8931, 9040–9055, 9120–9342, 9580–9992) were excluded from primary solid tumor sites. Breast cancers were further subclassified using SEER Extent of Disease codes as hormone receptor (HR)-positive (i.e., positive for estrogen receptor and/or progesterone receptor), HR-negative (i.e., negative for estrogen receptor and progesterone receptor), or unknown/unclassifiable HR status (i.e., neither HR-positive nor HR-negative). Lung cancers were further subclassified histologically as squamous cell carcinoma (ICD-O-3 histology codes 8050–8052, 8070–8076, 8078, 8083–8084, 8090, 8094, 8123), adenocarcinoma (ICD-O-3 histology codes 8140–8141, 8143–8145, 8147, 8190, 8201, 8211, 8250–8255, 8260, 8290, 8310, 8320, 8323, 8333, 8401, 8440, 8470–8471, 8480–8481, 8490, 8503, 8507, 8550, 8570–8572, 8574, 8576), small-cell carcinoma (ICD-O-3 histology codes 8002, 8041–8045), neuroendocrine (ICD-O-3 histology codes 8013, 8240–8243, 8246, 8249, with or without including small-cell carcinoma), and other histologic subtypes. We also subclassified esophageal and cervical cancers as squamous cell carcinoma (ICD-O-3 histology codes 8050–8123) or adenocarcinoma (ICD-O-3 histology codes 8140–8576), kidney cancers as renal parenchyma (ICD-O-3 site code C64.9) or renal pelvis (ICD-O-3 site code C65.9), and lymphomas as non-Hodgkin or Hodgkin (based on SEER Site Recode).

Life tables were generated for 5-year age bands from 40 to 84 years at diagnosis. The primary analysis was performed on individuals ages 40 to 79 years at diagnosis, covering the range where most population screening strategies occur. We performed secondary analyses aggregated by age bands at diagnosis (40–54, 55–64, 65–74, and 75–84 years) to examine age-related changes in the ability to reach long-term survival. To evaluate the potential role of surgery in attaining statistical cure, we used SEER Therapy coding for “cancer-directed surgery” to perform a secondary analysis among patients who received primary surgical treatment with curative intent.

This study was not subject to institutional review board approval or informed consent due to its secondary use of de-identified data.

Using SEER*Stat software (https://seer.cancer.gov/seerstat/), we obtained standard life tables with cause-specific survival calculated using the actuarial method for monthly intervals up to 179 months of follow-up.

We used a mixture cure model (10, 24, 25), which divides cancer patients into two populations of “cured” and “uncured,” to estimate cure fraction by cancer type and stage, with no additional model covariates. “Uncured” patients were modeled using a two-parameter Weibull survival distribution, whereas “cured” patients were modeled as having a small exponential hazard (“residual excess risk”), thereby accounting for the possibility that complete cure (zero excess cancer-specific mortality risk) may not be possible or resolvable from the data for some cancers (11–13, 26). Given the residual excess risk, it may be more accurate to refer to “cured” patients as “long-term survivors” and “uncured” patients as “long-term nonsurvivors.”

We used the fact that cancer is a progressive disease to develop constraints on model parameters to stabilize fitting across all stages simultaneously, excluding unknown/missing stage. Specifically, the Weibull distribution for uncured patients in each stage was constrained so that long-term mortality was greater with later stage at diagnosis; the exponential hazard for cured patients in each stage was constrained so that later stages had higher potential for recurrence; and the cure fraction was constrained to decrease with later stage. These plausible constraints were implemented to enable the estimation of biologically realistic confidence intervals (CI) and median estimates that lay within feasible ranges, as compared with extremely wide CIs for early-stage cancers based on unconstrained models. We constrained the risk of recurrence to be relatively low per year, but did not require it to be zero (i.e., full statistical cure), thereby accommodating a continuing risk of recurrence for some cancers, such as lung.

We fit the model using a Markov chain Monte Carlo (MCMC) technique to optimize the likelihood of data given a parameter set, and to recover uncertainty in parameters given the data, while respecting the constraints by stage. We estimated 95% CIs using the sampled parameters of the MCMC fit. All analyses were conducted using R (https://www.r-project.org/) and Stan software (27) with the R package feather (28). Code and data are available at https://github.com/grailbio-publications/Hubbell_Cure_Fraction. Due to privacy concerns related to providing data with small numbers of events in some cells, we provide the specifications for the original SEER data draw, along with synthetic data generated to match the large-scale statistics to demonstrate the code. Figures and tables reported in this paper are from the original data only. Interested individuals can retrieve the original SEER data from the draw specifications.

Table 1 summarizes characteristics of the 2,391,278 cancer cases included in this analysis, stratified by stage at diagnosis. At the end of follow-up (maximum = 14 years and 11 months), 787,476 cases (32.9%) had died from their cancer, 347,794 (14.5%) had died from another cause, and 1,256,008 (52.5%) were still alive. Observed (not extrapolated) cumulative cause-specific mortality risk for the entire cohort at the end of follow-up was 12.0% for stage I cancers of all types combined, 14.5% for stage II, 45.8% for stage III, and 77.5% for stage IV.

Table 2 provides the fitted long-term cure fraction for each cancer type by stage. Adding a small residual excess risk of death (≤4%) for long-term survivors considered to be cured noticeably improved the likelihood of the model fit, consistent with prior studies of long-term cancer recurrence and relapse. Cure fractions for nine illustrative cancer types are shown in Fig. 1, and those for all 21 cancer types, as well as major subtypes, are provided in Supplementary Fig. S1. These results show that cure fractions vary among cancer types and stages at diagnosis, with most cancers following one of two stage-specific behavior patterns. The first pattern, exemplified by colorectal cancer, shows high cure fraction at all stages before metastasis, followed by a precipitous decline from stage III (58% cure; 95% CI, 57%–59%) to stage IV (7% cure; 95% CI, 7%–7%). The second pattern, illustrated by gallbladder cancer as an example, shows a steady decrease in cure fraction at each stage, from 50% at stage I (95% CI, 46%–54%) to 24% (95% CI, 22%–27%) at stage II, 22% (95% CI, 19%–25%) at stage III, and 2% (95% CI, 2%–3%) at stage IV. For most cancers, cure fraction was appreciably higher at stages I and II than at stages III and IV (usually by >50% for stage I versus IV).

The mixture cure model allocates individuals to one of two populations: those not cured, who are at acute risk of cancer mortality; and those cured, who are at the asymptotic risk of cancer recurrence and mortality. In scenarios where few deaths occur, these populations are difficult to distinguish by observed events. In such instances, a relatively low cure fraction may not reflect the number of long-term survivors, as even the not-cured fraction experiences a low cancer mortality rate.

Figure 2 illustrates the correlation between the difference in 5-year cause-specific survival between stage I, II, or III and stage IV for each cancer type, and the difference in cure fraction for the same between-stage comparisons by type. The close correlation between these two metrics (ρ = 0.968) indicates that 5-year survival difference by stage is a strong predictor of stage-specific long-term cure fraction for each cancer type. Thus, for example, if 5-year cause-specific survival for a given cancer type is 60% at stage I and 20% at stage IV, then there will be approximately 40% more patients considered cured at stage I than stage IV. Continuing with this example, under the common scenario of essentially no long-term survivors at stage IV (i.e., cure fraction = 0%), then stage I would be predicted to yield approximately 40% patients cured.

Further explication of the mixture cure model is provided using gallbladder cancer as an example. In Fig. 3A, the inset panels show the two survival curves for the two populations of patients with stage I cancer, namely, the 50% of individuals in the uncured category who follow a Weibull survival curve, and the 50% of individuals in the cured category who follow a progressively declining long-term cancer-specific survival curve with a low hazard of cause-specific death. A fit of the cancer-specific survival data is accomplished by combining the two curves on each population fraction, yielding the median fitted survival curve (solid line in main panel of Fig. 3A), which closely matches the observed cancer-specific survival data obtained directly from SEER (dots in main panel of Fig. 3A, plotted every 6 months). Fig. 3B shows the fitted two-population model simultaneously for all four stages of gallbladder cancer as an illustrative example.

In secondary analyses, we found that older age at diagnosis had a limited detrimental impact on cure fraction for many cancers, although some exceptions, such as liver/intrahepatic bile duct cancer, exhibited a striking decrease in long-term survival with advancing age (Supplementary Fig. S2; Supplementary Table S1). We also found that the fraction of long-term survivors was greater in the subset of patients who underwent surgery with curative intent (Supplementary Fig. S3; Supplementary Table S2).

Using the concept of statistical cure as a real-world measure of the population burden of cancer, we illustrate that a considerable long-term cure fraction was evident at early stages for each of 21 stageable cancer types and additional subtypes examined in this study, and that these cure fractions were substantially reduced for metastatic cancers. While prior studies of cure fraction have characterized cancer types by survivorship trajectory, for example, as “relatively high survival and cure fraction, relatively short time to cure” or “very low survival and cure fraction, uncertain time to cure” (20), such patterns do not incorporate the influence of stage on cure fraction. Based on our stage-specific cure fraction estimates, even for cancers with poor survival for all stages combined, at least one third of patients (e.g., for pancreatic and liver/intrahepatic bile duct cancers) or more than half (e.g., for esophageal and lung cancers) achieved long-term survival at stage I. Conversely, for some cancers with good survival for all stages combined, fewer than one quarter of stage IV cases were considered statistically cured (e.g., for melanoma and bladder cancer).

We showed that the discrepancies in cure fraction between stage IV and stages I to II were especially pronounced for malignancies with currently recommended and broadly adopted screening strategies in the United States (i.e., breast and colorectal; refs. 29–31). In contrast, we estimated relatively high cure fractions even at stage IV for malignancies for which development of effective screening methods has been problematic (e.g., thyroid and prostate). Several other cancer types that currently lack recommended screening strategies, and would require new screening interventions, also exhibited large gaps between early- and late-stage cure fraction, illustrating the potential for general population screening to enable early detection and cure across multiple cancer types. Such unscreened cancer types collectively account for approximately 70% of cancer deaths annually (7).

No precursor lesions have been convincingly identified for the majority of human malignancies, with few exceptions such as cervix and large bowel. Hence, novel screening tools must currently aim for early detection rather than preventive screening (32). Any screening test needs to accommodate two fundamental prerequisites. First, cancer mortality reduction can be achieved only if the dwell time encompasses a period during which a substantial proportion of cancers progress to a less curable stage. Second, the survival benefit should outweigh harms due to false-positive tests, complications during diagnostic work-up, and overdiagnosis of nonlethal disease. In general, population-based screening programs with broad eligibility criteria, as opposed to personalized screening, will realize the greatest impact on the overall cancer burden. Given that age is by far the strongest determinant of absolute overall cancer risk (33), aged-based eligibility criteria can help to balance the benefits and risks of cancer screening.

We also showed that differences by stage in 5-year cancer-specific survival are highly predictive of differences by stage in long-term cure fraction across cancer types. Therefore, although 5-year cancer-specific survival is relatively short-term, it can serve as a close proxy of long-term survival. The observed stage-related differences in long-term cure fraction suggest that parallel differences between early- and late-stage cancer-specific survival curves are not explained entirely by lead-time bias (i.e., apparently longer survival, without delayed mortality, due to earlier diagnosis). Instead, persistent differences in long-term mortality outcomes—the gold standard for measuring the impact of cancer control strategies—can be presaged by contrasts in shorter-term survival.

Several statistical methods exist for estimating cure fraction (e.g., 10, 24, 25, 34–36). The mixture cure model applied in this study, one of the most commonly used, is supported by long-term follow-up data: most deaths from cancer occur shortly after diagnosis, with a generally decreasing probability of death from cancer thereafter, although mortality dynamics differ by age and cancer type (26). Flexible parametric cure models that do not assume a Weibull distribution for the uncured fraction may better accommodate older age groups, for instance, that have a high excess hazard within a few months after diagnosis (34); however, we excluded the oldest adults from our study because of their poorer-quality data (37), and because they typically are not considered eligible for general population cancer screening.

Strengths of this study include the use of high-quality, population-based, broadly generalizable SEER data; uniform classification of all cases according to the AJCC 6th edition staging criteria; and long-term follow-up of a large cohort for up to 14+ years after diagnosis. Our use of modern statistical methods to fit constrained functions allowed estimation of uncertainty while producing interpretable and statistically stable results, especially in scenarios where few patients died from early-stage cancer. In particular, we recovered and quantified the difference between the acute phase of mortality (when the hazard is changing rapidly) and the late phase, when it is close to constant (and possibly zero). Our model constraints affected the range of the confidence intervals, but generally did not appreciably affect the point estimates of cure fraction.

Our study has some necessary limitations. Cohort or period effects may interfere in this analysis by up-migration of staging, despite the use of a uniform staging system during our chosen years. Secular trends in cancer risk factors (e.g., smoking) may also affect the distribution of cancer subtypes, which can vary in aggressiveness; we accounted for some subtypes of lung and breast cancers, but not other cancer types. Further, for some cancer types, changes in therapy over this time period may render earlier data obsolete. Our study is limited in part by the reliance on death-certificate-based classification of cancer-specific cause of death, which is susceptible to error. Bias may, however, have been mitigated by making comparisons mainly across stages within the same cancer type. Our analysis is also limited by the lack of detailed SEER data on treatment, which could have enabled evaluation of potential long-term effects of different therapeutic regimens by cancer type and stage; and the absence of data on morbidity and quality-of-life endpoints, such as hospitalizations, patient-reported outcomes, employment status, and costs. Early-stage cure fraction estimates may be inflated for certain cancer types (e.g., thyroid, melanoma, uterus, breast, prostate, and kidney) that are prone to overdiagnosis—that is, detection of cancer that would otherwise remain clinically silent. Some of these malignancies can be managed by active surveillance or less aggressive therapeutic regimens. In this analysis, we did not evaluate potential heterogeneity in cure fraction by race/ethnicity or other sociodemographic characteristics, but these factors may be explored in future studies. Finally, additional years of follow-up in the future will enable more robust estimates, especially within subgroups.

In summary, this study uses a mixture cure model for all major cancer types and stages to estimate the maximal potential for early-stage cancer detection to minimize long-term cancer-specific mortality for many clinically diverse cancer types, most of which have no currently recommended screening modalities. By incorporating stage data, our findings augment prior cure fraction studies, which have generally discussed the implications of their results in terms of survivorship care, treatment evaluation, and allocation of healthcare resources. Instead, by calculating early- versus late-stage differences in cure fraction across the spectrum of cancer types, we focus on the theoretical public health impact of cancer screening to substantially increase the proportion of patients cured of cancer through early detection and effective treatment.

E. Hubbell reports personal fees from GRAIL, LLC during the conduct of the study; other support from GRAIL, LLC and Illumina, Inc. outside the submitted work; also has a patent for cancer detection and analysis (multiple patents) pending, a patent for sequencing (multiple patents) issued, and a patent for microarrays (mutiple patents) issued. C.A. Clarke reports personal fees from GRAIL, LLC during the conduct of the study; personal fees from GRAIL LLC outside the submitted work. E.T. Chang reports personal fees from GRAIL, LLC and other support from GRAIL, LLC during the conduct of the study. No disclosures were reported by the other authors.

E. Hubbell: Conceptualization, software, formal analysis, visualization, methodology, writing–review and editing. C.A. Clarke: Conceptualization, supervision, writing–review and editing. K.E. Smedby: Writing–review and editing. H.-O. Adami: Writing–review and editing. E.T. Chang: Conceptualization, data curation, supervision, visualization, writing–original draft.

This work was funded by GRAIL, LLC.

The publication costs of this article were defrayed in part by the payment of publication fees. Therefore, and solely to indicate this fact, this article is hereby marked “advertisement” in accordance with 18 USC section 1734.