Availability: Mtreemix, a software package for estimating trees mixtures models, is freely available for noncommercial users at http://mtreemix. bioinf.mpi-inf.mpg.de. The raw cancer datasets and R code for the analysis with Cox models are available upon request from the corresponding author.
The work at the Max–Planck-Institute for Informatics was performed in the context of the BioSapiens Network of Excellence (EU contact no. LSHG-CT-2003-503265).
Meningiomas are derived from the arachnoidal cap cells of the leptomeninges, the soft coverings of the brain and spinal cord. Although the matrix tissue constitutes <5% of the intracranial and intraspinal mass, meningiomas are estimated to constitute between 13 and 26% of the primary tumors. Most meningiomas are sporadic slowly growing benign tumors and correspond histologically to WHO grade I. However, certain histological subtypes and also a minority of common type meningiomas show a more aggressive biological behavior and are associated with an increased risk of recurrence and an unfavorable prognosis. Therefore, the current WHO classification of brain tumors1 distinguishes 3 grades of meningiomas: the common type [WHO grade I], the atypical or intermediate-type [WHO grade II] and the anaplastic [WHO grade III] meningioma.
For an appropriate treatment of tumor patients, prediction of time until death or time until progression after initial treatment is an important task. Because of many clinical, topographical, radiological and surgical factors, histology is not solely decisive for the prognosis,2, 3, 4 although mitotic activity, cellular pleomorphism with prominent nucleoli and micronecrosis, and focally raised cell density have been discussed as indicators of a poorer prognosis.5, 6, 7, 8 A major challenge is the identification of genetic prognostic markers that better reflect tumor biology.
The meningioma is one of the cytogenetically best-studied solid tumors. The characteristic and most frequent chromosomal aberration in meningiomas is monosomy 22,9 which, however, has been shown not to be relevant for prognosis as an isolated anomaly.10 The progression from common-type to atypical and anaplastic meningioma is characterized by 2 different cytogenetic events: First, secondary loss of up to 6 further chromosomes, with mostly a typical pattern of clonal evolution, and second, partial or complete loss of the short arm of one chromosome 1.11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21
The identification of pathogenic routes in human tumors is one of the main challenges in molecular oncology. For many tumor types, genetic events defined by somatic chromosome alterations are known to accumulate over time in the course of the disease. On the basis of these findings, genetic changes associated with chromosome instability are believed to play an important role in both tumorgenesis and tumor progression in meningiomas. There is a vast amount of literature on linking single genetic alterations to survival,22 but only few efforts have been made to construct more complex and comprehensive markers. Until now, only Zang19 has proposed a model of clonal evolution in meningiomas based on conventional cytogenetic studies. The pool of the cytogenetic findings of 394 meningiomas led to his empirical model of meningioma progression.
Cytogenetic analyses show that numerical and structural chromosome changes with pronounced hypodiploidy, or rarely hyperdiploidy, and especially deletion of the short arm of a chromosome 1, are accompanied by more aggressive biological characteristics.9, 12, 13, 14, 16, 17, 18, 20 We have established a mathematical model for estimating the most likely cytogenetic pathways in meningiomas, based on oncogenetic trees mixture models.23 In these models each tumor is represented by the genetic events that have occurred in the tumor. The most important difference of the mathematical approach compared with the hand-crafted model19 is that it allows an objective assignment of the estimated time to recurrence for a single tumor based on its genetic status.
The basis for oncogenetic trees mixtures models are single oncogenetic trees as introduced by Desper et al.24 that can be used to estimate the most likely pathogenetic routes in tumors from observed subsets of genetic events. An oncogenetic tree for modeling cancer progression is a directed tree, in which nodes represent genetic events and edges are labeled with the conditional likelihood of observing a genetic event given its precursor event has occurred. These models are of high explanatory power, but often only for a portion of the analyzed tumor samples. A subset of genetic events is only represented by this tree model if for any event in this subset all precursor events in the tree also belong to the subset. All other subsets of events are assigned likelihood zero. Von Heydebreck et al.25 propose to include additional hidden events in the tree and to model genetic events as leaves in the tree. This method trades feasibility of maximum-likelihood estimation of oncogenetic trees with reduced interpretability due to the introduction of hidden events.
Beerenwinkel et al.23 introduced mixture models of the single oncogenetic trees as used in Desper et al.24 In these mixture models, one tree component is restricted to have a star-like topology, representing independence between genetic events. Owing to the starlike component, every combination of genetic events is represented in the model. The oncogenetic trees mixture models combine interpretability of the trees of Desper et al.24 with an appropriate probabilistic framework.
The present investigation on 661 meningiomas had 2 objectives: First, we propose using oncogenetic trees mixture models for estimating the state of tumors characterized by subsets of observed genetic events obtained by metaphase cytogenetics. Second, we introduce a genetic progression score (GPS) for meningiomas and its application in cancer prognosis. The relevance of the GPS as a prognostic marker is demonstrated with Cox proportional hazards regression models.26
Material and methods
We performed a retrospective study on 661 patients [482 women and 179 men] with meningiomas operated on at the Department of Neurosurgery, University of the Saarland, between January 1973 and April 2005. The average age of the overall patient population was 57.3 years [SD ± 12.8 years]. The average age of the female patients was 57.6 years [SD ± 12.3 years]; average age of the male patients was 56.7 years [SD ± 14.1 years]. Written informed consent was obtained from each patient participating in the study.
The clinical variables investigated comprise patient gender and age, tumor location and histology, and the completeness of tumor extirpation.
We formed the following 9 groups depending on meningioma location: convexity, parasagittal region, tuberculum sellae, olfactory groove, sphenoid wing ridge, posterior cranial fossa, tentorium, ventricular and spinal channel. The classification was carried out on the basis of the preoperative CT and MRI.
Complete surgical extirpation of the tumor was defined as Simpson grades I and II27 corresponding to a macroscopically complete tumor resection with bipolar coagulation of the dura insertion.
The 661 cases investigated comprised 465 common type [WHO grade I], 156 intermediate-type [WHO atypical meningioma, grade II], and 14 anaplastic meningiomas [WHO grade III]. Meningioma grade was assessed by a combined histological and morphometric approach on routinely HE and Ki-67/Feulgen stained formalin-fixed, paraffin-embedded tissue sections.14 Table I contains a breakdown of age, sex, location, time to recurrence and time of follow-up for each grade of meningioma.
Table I. Correlation between Clinical Variables and WHO Tumor Grade in Meningiomas
No. of patients (%)
Age in years (mean ± SD)
56.8 ± 12.4
59.8 ± 12.4
60.7 ± 14.1
Time of follow-up (mean)
Cell culture and cytogenetic preparation
Cell cultures from 661 meningioma biopsies and chromosome preparations with Giemsa banding were carried out according to standard procedures.28 Many tumors were characterized by multiple patterns of cytogenetic aberrations. In total, 1,068 clonal patterns were observed in the 661 tumors.
The patients were investigated in the neurosurgical outpatient department of the University of the Saarland, either within routine follow-up or because of the appearance of neurological symptoms. A recurrence was evaluated as new evidence of tumor in CT or NMR after previous complete extirpation [Simpson grades 1 and 2]. The Simpson grade 2 was established on the basis of the operation report and the postoperative CT or NMR investigation. Average follow-up time was 40.3 months (41.5 months for female patients and 37.2 months for male patients).
Oncogenetic trees models
Mixtures of oncogenetic trees were used to describe the ordered accumulation of genetic aberrations during tumor progression. In a single oncogenetic tree, vertices represent genetic events and edges between vertices represent transitions between the events. Each edge is associated with the probability that the successor event will occur, given the predecessor event has already occurred. In the model, genetic events are assumed to be nonreversible, thus the disease process can be fully described by the accumulation of genetic aberrations. In the mixture model, more than one tree component is estimated. Every model component describes the disease process for a subset of observations (tumors). The first component is restricted to be a starlike tree that models independence of events, reflecting de novo occurrence of aberrations. This so-called noise component guarantees that all possible patterns of aberrations are represented with positive likelihood in the mixture model. Every tumor is assigned to a specific tree according to the relative likelihood that its genetic pattern was generated by this tree. The mixture weights associated with the single trees then represent the sum over all tumors. The weight of the starlike tree thus indicates the proportion of tumors whose progression is not described by the other estimated components. Oncogenetic trees mixture models can be estimated from data consisting of genetic patterns with an Expectation-Maximization algorithm introduced by Beerenwinkel et al.23, 29
The reliability of edges in the tree models is estimated from B = 1,000 bootstrap samples of the data. Bootstrap resamples the original data with replacement, generating B bootstrap samples of the same size n as the original data. The bootstrap value of an edge in the tree model then is the number of times (out of B = 1,000) that this edge is present in the set of trees models that are estimated from the new data sets. In trees mixtures models, single tree components are treated separately in the Bootstrap analysis. First, each bootstrap sample is assigned to the tree model components according to relative likelihoods under the original estimated model. Then, for all model components separately, tree structure and parameters are reestimated. In addition, for all parameters, 95% confidence intervals are estimated based on the corresponding estimates in the bootstrapped tree models.
Genetic progression score
In oncogenetic trees models consecutive genetic aberrations are associated with corresponding conditional transition probabilities. These probabilities can be converted to average waiting times by assuming Poisson processes for the occurrence of aberrations, see Ref.30 for details. Formally, the waiting time associated to an edge of the tree with corresponding conditional probability p is given by (1 − p)/p multiplied with a scaling factor that is typically set to 1. The GPS of a tumor then is defined as the average waiting time of its pattern of genetic aberrations, given the underlying tree mixture model. Tumors with few aberrations that appear early in the model receive low GPS values; tumors with many late aberrations in the model are associated with high GPS values. For 221 out of the 661 patients, more than one cytogenetic pattern was detected. In these cases, the GPS of the tumor was defined as the highest GPS of all clones found in the tumor.
Cell cultures from 661 meningioma biopsies were established. As is generally known for meningiomas, aberrant karyotypes from the individual cases showed little variation. However, varying percentages of metaphases with hypodiploid stemline and metaphases with a normal karyotype were analyzed.
In 280 cases [42.4%], we found a normal chromosome set. The question whether the normal metaphases stem from stromal or vascular cells or from meningioma cells with normal karyotype cannot be answered without doubt. However, submicroscopic deletion/inactivation of meningioma specific genes appears to be more probable.11 Monosomy 22 was diagnosed as the sole chromosome change in 241 cases [36.5%]. The deletion 1p could be ascertained in 60 [9.1%] of the investigated tumor tissue samples, which in most cases occurred within a markedly hypodiploid karyotype.
Strong correlations were found between histological measurements and the GPS (Table II). Tumors were classified into 3 distinct groups according to GPS (GPS group 0: 0 ≤ GPS < 1.88, GPS group 1: 1.88 ≤ GPS < 6.39, GPS group 2: 6.39 ≤ GPS). The values 1.88 and 6.39 correspond to the critical first 2 steps in the nontrivial component of the estimated oncogenetic tree mixture model shown in Figure 4. Higher GPS (tumors in group 2) correlated highly significant with higher histological grades (WHO Grades III) (p < 10−10, Fisher's exact test). Interestingly, the histological grades alone are not informative. There was no significant difference between the WHO grade I and WHO grade II tumors with respect to recurrences (Fig. 1). Figure 2 shows the clinical relevance of the calculated GPS classification broken down to the WHO classification. This demonstrates that the genetic aberrations, especially the deletion of 1p, are independent markers for the clinical courses of the meningioma.
Table II. Correlation between Clinical Variables and Cytogenetic Groups Defined by GPS Groups
No. of patients (%)
Histological type: No. of tumors (%)
Common type (WHO Grade I)
Atypical (WHO Grade II)
Anaplastic (WHO Grade III)
Age in years (mean ± SD)
56.8 ± 14.2
55.6 ± 14.2
61.1 ± 13.0
56.9 ± 12.0
57.5 ± 12.1
63.0 ± 14.7
Females predominated over males with a sex ratio of 2.67:1. The sex ratio was shifted when the tumors were broken down according to their chromosome sets. In GPS groups 0 and 1 which are regarded as not associated with progression, a sex ratio of 2.76:1 was found, whereas a ratio of 1.81:1 was observed in meningiomas of the highly hypodiploid karyotype with deletion 1p [GPS group 2]. On average, the female patients were slightly older than the male patients. However, patient age neither differed significantly between the groups nor between men and women (Table II).
A correlation between the individual cytogenetic changes and the meningioma location was highly significant [p < 10−8] (Table III). The 49 spinal tumors except for one case belonged to the groups not associated with progression [GPS groups 0 and 1]. To assess the varying distribution of the localization in dependence of cytogenetic grouping, we decided to distinguish 3 locations: the spine, the skull base and the convexity including parasagital region. Thirty of 251 meningiomas of the convexity belonged to the progression-associated groups [GPS group 2], whereas only 11 of 278 meningiomas of the skull base have a GPS higher than 6.39.
Table III. Tumor Location in Patients WHO Underwent Surgery for Meningiomas, Split by Cytogenetically Defined Groups
In brackets, percentages of locations with respect to GPS groups are given.
Tumor location (% of all cases)
Lat. and medial sphenoid
Table IV and Figure 3 show the distribution of the rate of recurrence in relation to the GPS groups. Recurrences were observed in 53 of the cases. This corresponds to a total rate of recurrence of 8.0% after complete tumor extirpation. Considering the cytogenetic findings, there is a highly significant correlation [p < 10−6] between the rate of recurrence and the GPS groups. Tumors in GPS group 2 (GPS ≥ 6.39) showed a rate of recurrence of 33.3%, tumors belonging to the other groups only showed a rate of recurrence of 6.2% (7.9% in GPS group 0 and 4.0% in GPS group 1).
Table IV. Recurrence in 661 Patients WHO Underwent Surgery for Meningiomas, Split by Cytogenetically Defined Subgroups
No. of patients (%)
We estimated oncogenetic trees mixture models23 consisting of a star component and a nontrivial tree component to obtain a concise description of the genetic development of meningiomas (Fig. 4). A total of 80% of the tumors can be explained by the nontrivial tree component. The most frequent event found by conventional cytogenetic analysis is loss of one chromosome 22, followed first by the deletion of the short arm of one chromosome 1 and subsequently by loss of chromosomes 14 and 6. This is in agreement with previously published studies.18, 19, 20, 22 Monosomies of chromosomes 10, 18 and 19 are late events as successors of monosomy of chromosome 14.
Figure 5 shows the estimated trees mixture models for the meningiomas broken down by gender. For the females (Fig. 5a) a total of 87% of the tumors can be explained by the nontrivial tree component. The most frequent events, related to cytogenetics, are in agreement with the model plotted in Figure 4, except for the monosomy of chromosomes 19 and X in female patients. For the males, the subset of the estimated tree mixture model (Fig. 5b) can explain a total of 79% of the tumors. Interestingly, a reversal concerning chromosomes 14 and 1p- is observed. For the males, monosomy 14 is estimated to be an earlier event followed by the deletion of one arm of one chromosome 1. This pathway continues with monosomies of chromosomes 6, 18 and 19. The statistical evidence for the different pathways for males and females is strong, as the high bootstrap values for the edge labels indicate stability of the models for both patient subgroups. For the females the edge between loss of chromosome 14 and loss of chromosome 1p appeared in 998 out of 1,000 bootstrapped trees, for the males in 987 out of 1,000 trees.
To assess the information gain due to the introduction of the GPS in the clinical practice, discriminatory power of the GPS with respect to tumor recurrence was compared with competing models based on single chromosomal aberrations (Table V). In univariate models, loss of chromosome 1p and loss of chromosomes 14, 18 and 10 were significantly correlated with earlier tumor recurrence. In a multivariate model built with these aberrations, only loss of 1p was significant (p = 0.02). The complex marker GPS was highly significant both as a qualitative marker (GPS ≥ 6.39) and as a quantitative marker.
Table V. Clinical Relevance of Genetic Markers for Recurrence in Meningiomas, Measured with Cox Regression Models
The first block contains p-values for a significant difference in times to tumor recurrence based on single genetic aberrations. The first column gives raw p-values, the second p-values adjusted for multiple testing, according to Holm's method. The second block lists p-values of the four individually significant aberrations in a multivariate linear model. The last block contains p-values for the genetic progression score (GPS), first as a binary marker with cutoff GPS ≥ 6.39, then as a quantitative marker.
Univariate models Single genetic aberrations
2.2 × 10−6
1.9 × 10−5
1.6 × 10−5
1.3 × 10−4
1.2 × 10−3
8.5 × 10−3
5.5 × 10−3
3.3 × 10−2
Multivariate model Genetic aberrations 1p-, 14-, 18-, 10-
Univariate models Multivariate GPS
(GPS group) = 2
2.1 × 10−8
4.5 × 10−5
Clinical factors of meningioma prognosis
Grading of meningiomas has always been controversial. Obviously, the biological behavior of meningiomas cannot be accounted by histological parameters alone.18, 19, 20, 31 In 1979, Zülch stated that it is not the histological grading, which is most crucial for the rate of recurrence of meningiomas, but primarily the completeness of extirpation.32 There is agreement in the literature that radical surgical extirpation is correlated with a good prognosis.27, 32, 33, 34, 35 We therefore included only patients in our study whose tumor had been macroscopically completely removed, corresponding to Simpson grades I and II.29
It is well known that females are affected far more frequently by meningiomas than males.3, 10, 31, 32, 33 This observation was confirmed in our patients with a ratio of 2.67:1. In particular, in the 49 spinal tumors investigated, the female sex was overrepresented [87% of cases]. This sex ratio was shifted when the tumors were broken down by karyotype. In the GPS group 2 (GPS ≥ 6.39), i.e. in the tumors with a pronounced aberration of the karyotype with deletion 1p, we found a sex distribution of 1.81:1. This shift confirms earlier reports.10, 14, 18
Cytogenetic aspects of meningiomas
Frequency and behavior of meningiomas at different intracranial locations were first discussed in 1922.36 In our current study, cytogenetic aberrations of meningiomas are significantly associated with the tumor location [p < 10−5, Fisher's exact test]. All but one of the 49 spinal tumors belonged to the GPS groups not associated with progression, whereas remarkable 12% of the meningiomas of the cranial vault belonged to the progression-associated groups. These findings are in agreement with previous publications. In 1980, it was shown that tumors located at the base of the skull typically contain cells with 46 chromosomes, whereas meningiomas located at the convexity show significant numbers of chromosome aberrations.10 In spinal tumors, almost exclusively a 22-monosomic karyotype was detected. It was already striking at that time that meningiomas, which recurred showed significantly more chromosome aberrations and a preference of the convexity.10 These findings are also in line with the results on a large series of meningioma patients (N > 9,000 cases37), where benign meningiomas were more frequently located at the skull than malignant meningiomas (p < 0.02).
In our study, we classified 661 meningiomas according to their GPSs (GPS values). We found a high correlation between the cytogenetic findings and the histomorphology: Higher GPSs correlated highly significantly with higher histological grades [p < 10−10, Fisher's exact test]. This result is important, since in the literature no clear correlation between the histological grading and the rate of recurrence in meningiomas has been reported.11, 35, 38, 39, 40 In our study, also no clear distinction between the histological grades I and II with respect to tumor recurrence could be shown (Fig. 1). However, WHO grade III meningiomas show a statistically significant correlation with earlier tumor recurrence.
Relevance of the gender for genetic progression models
Breaking down the oncogenetic tree by gender there is a reversal concerning chromosomes 14 and 1p- in the male population. For the males, monosomy 14 is estimated to be an earlier event followed by the deletion of one arm of one chromosome 1. Monosomy 14 has been found to be associated with aggressive behavior of meningiomas.18, 39, 40, 41, 42, 43 However, in the literature the deletion of chromosome 14 has never been correlated with the gender. It is well known, that females predominate over males with a ratio of 2.67:1. Breaking down the genetic findings by gender there is a shift of the sex distribution to 1.81:1 in favor of females. It could be shown, that the deletion of the short arm of one chromosome 1 is to be regarded as more valuable cytogenetic parameter than monosomy 14 for the prediction of tumor recurrence, particularly because all anaplastic meningiomas in our series displayed a deletion of chromosome 1p (Fig. 2).
Predictive value of genetic progression scores for tumor recurrence
We introduce the GPS of a tumor as the estimated average waiting time of its observed genetic pattern in the timed oncogenetic tree. Using Cox regression analysis we demonstrate that for meningiomas the GPS has prognostic value with respect to clinical outcome and recurrence. Previously it was shown that the information gain due to GPS holds true also for tumor samples from 2 other cancer types with notably different genetic backgrounds, namely glioblastoma and prostate cancer.30
Unlike in the previous graph of histology alone (Fig. 1) it turns out that classification of a tumor sample to GPS group 2 (GPS > 6.39) can be used to identify a subgroup with different prognosis with respect to time to recurrence after surgery (Fig. 3). Thus the GPS classification allows a prognostically significant distinction between low-risk and high-risk meningiomas at the time of primary surgery. It can be expected that a combination of both histopathological and cytogenetical description of meningiomas could result in an improved prognostic accuracy.14, 16, 31, 38, 39
A comparison of the new complex marker GPS with single chromosomal aberrations is crucial to validate the additional prognostic value inferred by the oncogenetic trees models. The results presented in Table V show that particularly loss of chromosomes 1p, 14, 18 and 10 are progression-associated in univariate models. However, to assess the relevance of single aberrations, the correlation structure has to be taken into account, since many tumors have a large number of simultaneous losses. In a multivariate model, only loss of chromosome 1p receives a significant p-value. This is in agreement with our oncogenetic tree model that estimates loss of chromosome 14 to be a successor of loss of chromosome 1p-. Thus loss of chromosome 14 is associated with progression towards recurrence as a consequence of the earlier relevant loss of chromosome 1p. It has to be pointed out, however, that rare but potentially significantly progression associated chromosome aberrations like the loss of one chromosome 9p are underestimated by our probabilistic approach.11, 20
The total rate of recurrence in our 661 patients after complete tumor extirpation was 8.0%. In the GPS group 0 we found a recurrence rate of 7.8% and in the GPS group 1 a rate of 4.0%. The highest recurrence rate was found in the GPS group 2 with 33.3%. These results are in agreement with the literature (7% recurrences in34 and 2% recurrences in38). In contrast to these results, in a large study containing 8,891 patients with benign meningiomas [WHO I] 20.5% recurrences were observed in the first 5 years.37 This high rate of recurrence may not be due to the longer follow-up alone but more likely because a recurrence could not always exactly be distinguished from a regrowing tumor, which had been only partially removed. In the same study, for 771 patients with malignant meningioma [WHO III] a larger rate of recurrence (32.4%) was observed, similar to the results of the present study.
In our study, the double rate of recurrences of the GPS group 0 compared with the GPS group 1 in our study indicates that false negatives (classification as normal tissue) may arise when mitoses from non-neoplastic or low-grade part of the biopsy overgrowing the tumor cells in vitro were evaluated. In this case, the geneticist has rare chance to check the histology of the tumor particle determined for tissue culture. Accordingly, the deletion of the short arm of a chromosome 1 is an independent prognostic factor, which correlates significantly with a raised risk of recurrence. Because of the limited follow-up period, we have to expect that the recurrence rate may further increase.
Our results are in agreement with former cytogenetic investigations, which indicated that the deletion of the distal part of the short arm of a chromosome 1 [1p-] is associated with progression in meningiomas.12, 13, 14, 15, 16, 17, 18 After initial speculation on the role of deletion 1p for tumor recurrence,12 the importance of this aberration besides monosomy 22, 14 and 10 for the development of atypical and anaplastic meningiomas17 and for progression from typical to atypical meningioma20 was pointed out.
According to the above-mentioned findings, the estimated trees models are in line with the literature. Especially the deletion of chromosome 1p was ascertained to be an early and crucial event in the progression in meningiomas. To verify the information gain due to GPS, it is of particular interest to demonstrate improved performance over established histopathological parameters, see also the discussion above for single genetic aberrations. By fitting multivariate Cox regression models we also found that for meningiomas the GPS is prognostic also after adjustment for age. The GPS can thus be used to further identify subgroups. We define low-risk patients as those with histological WHO Grade I tumours that belong to GPS group 0 or 1, and high-risk patients as those who harbor tumors that are Grade II or III and/or belong to GPS group 2. High-risk patients should undergo an intensified regimen of postoperative surveillance including MRR follow-up every 6 months and glucose-PET studies to assess the biological activity of early recurrent tumor growth. Consequently, a multimodal approach to meningioma grading is most promising for identifying meningiomas with an increased tendency to recur and for planning their follow-ups.