Using a Competing-Risks Model to Predict the Prognosis of Meningioma Patients: Fine-Gray and Cause-Specic Hazard Analyses

Background: We aimed to identify the risk factors for meningioma using a competing-risks model. Method: Patients entered into the Surveillance, Epidemiology, and End Results (SEER) database between 1973 and 2015 were selected. Univariate analysis was performed using the cumulative incidence function (CIF) to show the probability of each event and Gray’s test to estimate the difference in the CIF between groups. Multivariate analysis using the Fine-Gray model and the cause-specic (CS) hazard model to explore factors affecting the cumulative incidence rate of meningioma patients. Result: Of the 1502 eligible patients, 419 died of meningioma and 398 died of competing events. The Fine-Gray model showed that age at diagnosis (35–64 vs 18–34 years: hazard ratio [HR]=2.490, p=0.031; >64 vs 18–34 years: HR=4.486, p<0.001), sex (male vs female: HR=1.388, p=0.002), tumor grade (II/III vs unknown: HR=1.630, p<0.001), and SEER stage (distant vs localized: HR=1.711, p<0.001) were risk factors for patients. The CS model showed that age at diagnosis (35–64 vs 18–34 years: HR=2.677, p=0.031; >64 vs 18–34 years: HR=5.982, p<0.001), marital status (divorced/separated/widowed vs married: HR=1.277, p=0.047), sex (male vs female: HR=1.486, p<0.001), tumor grade (II/III vs unknown: HR=1.775, p<0.001), and SEER stage (distant vs localized: HR=1.660, p<0.001) were risk factors for patients. Conclusion: This study is the rst to establish a competing-risks analysis model for the risk assessment of meningioma patients. These results may help clinicians to better understand meningioma patients and provide them with support. The results for the Fine-Gray model showed that age at diagnosis (35–64 vs 18–34 years: hazard ratio [HR] = 2.490, 95% condence interval [CI] = 1.089–5.691, p = 0.031; >64 vs 18–34 years: HR = 4.486, 95% CI = 1.961–10.262, p < 0.001), sex (male vs female: HR = 1.388, 95% CI = 1.130–1.705, p = 0.002), tumor grade (II/III vs unknown: HR = 1.630, 95% CI = 1.264–2.102, p < 0.001), and SEER stage (distant vs localized: HR = 1.711, 95% CI = 1.241–2.358, p < 0.001) were risk factors for patients. The results for the CS model showed that age at diagnosis (35–64 vs 18–34 years: HR = 2.677, 95% CI = 1.093–6.556, p = 0.031; >64 vs 18–34 years: HR = 5.982, 95% CI = 2.441–14.658, p < 0.001), marital status (DSW vs married: HR = 1.277, 95% CI = 1.003–1.625, p = 0.047), sex (male vs female: HR = 1.486, 95% CI = 1.208– 1.829, p < 0.001), tumor grade (II/III vs unknown: HR = 1.775, 95% CI = 1.377–2.289, p < 0.001), and SEER stage (distant vs localized: HR = 1.660, 95% CI = 1.220–2.258, p < 0.001) were risk factors for patients. We also include the results obtained using the multivariate Cox regression for comparison in Table 3.


Background
Meningioma accounts for about one-third of all intracranial brain tumors and is the most-common primary intracranial tumor in the United States, with an average annual incidence of 7.44/100,000. [1][2][3][4][5][6] Only about 5% of meningiomas are atypical or malignant meningiomas (WHO II and III); most meningiomas are WHO I. [7] Although the prognosis of benign meningioma (WHO I) is generally good, atypical meningioma (WHO II) and malignant meningioma (WHO III) are invasive tumors associated with a poor prognosis and high mortality. [8,9] One study found that WHO I meningiomas mainly affect females, while males are main affected by atypical and malignant meningiomas. [7] Most previous reports on risk factors for meningioma survival have been based on the Cox proportionalhazards regression model. A survival analysis based on the Cox model usually considers only one endpoint: the one that is of interest to the researcher. However, in clinical trials of tumors, it is not always only the endpoints that are of interest to researchers, and there are some endings that are not of interest. These endpoints represent competing events. Traditional survival analysis will treat such competing events (or "risks") by censoring, which will lead to miscalculations of the survival function. [10] This situation means that previous studies have often been adversely affected by competing-risks bias. [11,12] Page 3/20 The Surveillance, Epidemiology, and End Results (SEER) program is a coordinated system of populationbased state cancer registries collecting demographic, clinical, and outcome information on all cancers diagnosed in representative geographic regions and subpopulations. [13,14] The database is run by the National Cancer Institute, and it collects and publishes incidence and survival data from populationbased cancer registries covering approximately 30% of the United States population. [15] Since 2004, the SEER database has o cially begun to record information on nonmalignant brain tumors due to the "Bene cial Brain Tumor Registration Amendment". [16,17] Few studies have used SEER data to examine the survival of meningioma patients. The present study attempted to identify the risk factors for meningioma by utilizing a competing-risks model, with the aim of helping to reduce the risk of bias due to competing events and thereby increase the accuracy of the analysis.

Patients
We used SEER*Stat software (version 8.3.5, https://seer.cancer.gov/) to search for relevant meningioma patients using histological type code 9530 of ICD-O-3 (the third edition of the International Classi cation of Diseases for Oncology). Patients were selected from 1973 to 2015. We excluded patients younger than 18 years, cases that were not con rmed by microscopy, and cases for which not all of the following analyzed variables were available: age at diagnosis, race, marital status, sex, tumor grade, SEER stage, surgery, radiation, chemotherapy, receiving the rst indication of a malignant primary tumor, education level (proportion of residents with at least a bachelor's degree), employment status (proportion of residents who are unemployed), median household income, and smoking (proportion of residents who are current smokers).

Statistical analysis
We regarded other causes of death as competing events in our competing-risks analysis. Categorical data are presented as frequency and proportion values. When there is a competing risk, the outcome is not only survival, death. The cumulative incidence function (CIF) should be used to estimate the crude incidence rate because it can estimate the total incident rate of A, B, and AB, whereas the Kaplan-Meier curve cannot. The difference test for the CIF corresponds to Gray's test. Therefore, univariate analysis was performed using the CIF to show the probability of each event, while Gray's test was used to estimate the difference in the CIF between groups.
The Fine-Gray model, also known as the subdistribution hazard function or CIF regression model, is designed to t the cumulative incidence of events of interest. [18] The Fine-Gray model is suitable for research into predicting risk on an individualized basis, estimating the risk and prognosis of disease, and establishing clinical prediction models and risk scores. [11,19] Another model called the cause-speci c (CS) hazard model should be applied when competing risks are present. This model is more suitable for etiology studies. [11,19] The present study used multivariate analysis with the Fine-Gray and CS models to explore factors affecting the cumulative incidence rate of meningioma patients. The effects of competing risks tend to be stronger in the CS model than in the Fine-Gray model. We also obtained results using a Cox model for comparison with the results obtained using the other two models.
All statistical analyses were performed using SAS (version 9.2), and R software (version 3.5.0; https://www.r-project.org/). The R package 'cmprsk' was used to construct the model. All statistical tests were two-sided, with P < 0.05 considered to be indicative of statistical signi cance. Given that cancer is a reportable disease in every state of the USA, informed patient consent is not required. When a data use agreement was signed, data on cancer research become available to the public free of charge.

Patient characteristics
Of the 1502 eligible patients, 419 died of meningioma (39.83% of the total) while 398 died of competing events such as suicide, accidents, and cardiovascular diseases (37.83% of the total). Most of the patients were aged 35-64 years, white, married, female, with an unknown tumor grade, localized SEER stage, had received surgery, had not received radiation, had not received chemotherapy, had received their rst indication of a malignant primary tumor, lived where 20-50% of residents have at least a bachelor's degree, < 10% are unemployed, and < 20% are current smokers, and a median household income of USD 50,001-100,000. The baseline demographics are presented in Table 1.   Table 3.

Discussion
In medical research it is common to observe multiple endpoints that compete with each other. For example, the risk of competition for death from heart disease and cerebrovascular disease in patients with non-small-cell lung cancer increases with age. [20] Traditional survival analysis will treat the competing risks by censoring, and the incidence of the true outcome will be overestimated, leading to competing-risks bias. A study of competing-risks bias found that up to 46% of studies reported on in the literature were affected by competing-risks bias, including in advanced medical journals. [12] Meningioma accounts for 34% of all primary intracranial tumors, and approximately 7,000 new cases are diagnosed each year in the United States. [7] Meningioma arises from arachnoid cells of the leptomeninges and may occur throughout the coverings of the central nervous system. [21] Since most meningiomas follow a benign course, the State Central Cancer Registry did not collect nonmalignant cases with a diagnosis before 2004. However, studies have shown that up to 10% of meningiomas can show more-aggressive behavior and a higher tendency to relapse. [22] The Benign Tumor Registration Amendment provides for the collection of data related to benign and borderline malignant brain tumors from 2004, which represents useful information about this common but underresearched tumor.
To the best of our knowledge, the present study is the rst to use the SEER database to conduct a competing-risks analysis (including Fine-Gray model and CS model) of meningioma patients with the goal of identifying more-accurate prognostic factors. Approximately one-third (n = 398) of the meningioma patients analyzed in this study died of competing events. Using a competing-risks model, we found that age at diagnosis, sex, tumor grade, and SEER stage were risk factors for meningioma patients.
Meningioma can occur at any age, but the incidence of meningioma in people younger than 18 years is only 0.06/100,000. [23] The incidence of meningioma increases with age, and is most common among elderly people older than 65 years.
[24] A previous study of atypical and anaplastic meningiomas found that for every additional year of age, the risk increased by 1.03, which is consistent with our results. [2] In our study the Cox regression, Fine-Gray, and CS models all showed that being aged 35-64 and > 64 years were risk factors compared with an age of 18-34 years (p < 0.05). The prognosis is poor and the risk is Cox regression revealed that race other than white or black was a risk factor compared with being white (HR = 1.283, p = 0.042). However, we did not observe this result in the two competing-risks models, which indicates that the results of Cox regression are not accurate because it does not consider competing risks. Garzon-Muvdi et al. also demonstrated that race other than white or black and unknown race are not risk factors for atypical and anaplastic meningiomas compared with whites in an analysis using the Fine-Gray model (HR = 0.37, p = 0.320). [2] All three models in the present study showed that being male is a risk factor for meningioma, which is consistent with previous ndings.
[ [25][26][27] Compared with married patients, DSW was a risk factor in both the Cox model (HR = 1.398, p < 0.001) and the CS model (HR = 1.277, p < 0.05), but not in the Fine-Gray model (HR = 1.215, p > 0.05). We also found this difference for chemotherapy and the median household income. Although both the Fine-Gray and CS models are competing-risks models, they produced different results, which is due to the effects being stronger in the CS model than in the Fine-Gray model. Although the directions of the correlations were essentially the same in the two models, and their HRs were similar, they can still produce different results.
This has also happened in previous studies, [27] and it explains why two competing-risks models need to be employed. The CS model is more suitable for answering etiology studies, while the Fine-Gray model is increasingly being used for clinical predictive models and risk determination. [11,19] All three models showed that grade I is a protective factor compared to unknown grade, and that grade II/III is a risk factor. The WHO staging system classi es meningiomas into grades I, II, and III. A meningioma of grade I has a low recurrence and low invasive growth, while meningiomas of grades II and III exhibit high recurrence, high invasive growth, poor prognosis, and high mortality.
[28] We also found that all three models showed distant SEER stage to be a risk factor compared to an unknown SEER The Cox regression performed in the present study revealed that receiving the rst indication of a malignant primary tumor, having at least a bachelor's degree, and the median household income affected the survival of meningioma patients, whereas these results were not found in the competing-risks model.
This may also be due to the presence of competing-risks bias.

Limitations
The large sample is one of the main strengths of this study. However, our research was also subject to limitations. First, it had inherent limitations due to its retrospective design. Second, important information is missing from the SEER database, such as the Simpson rating. Third, the records in the SEER database are not complete, and patients may be misclassi ed. Finally, because this study is the rst to use two competing-risks models for the risk assessment of meningioma patients, further research is needed to verify the present results.

Conclusions
This study has established a competing-risks analysis model based on the SEER database for the risk assessment of meningioma patients for the rst time. The age at diagnosis, sex, tumor grade, and SEER stage were found to be signi cant risk factors. These results may help clinicians to better understand meningioma patients and provide them with appropriate support.