Interpretable Machine Learning Classifiers for Brain Tumour Survival Prediction

Prediction of survival in patients diagnosed with a brain tumour is challenging because of heterogeneous tumour behaviours and responses to treatment. Better estimations of prognosis would support treatment planning and patient support. Advances in machine learning have informed development of clinical predictive models, but their integration into clinical practice is almost non-existent. One reasons for this is the lack of interpretability of models. In this paper, we use a novel brain tumour dataset to compare two interpretable rule list models against popular machine learning approaches for brain tumour survival prediction. All models are quantitatively evaluated using standard performance metrics. The rule lists are also qualitatively assessed for their interpretability and clinical utility. The interpretability of the black box machine learning models is evaluated using two post-hoc explanation techniques, LIME and SHAP. Our results show that the rule lists were only slightly outperformed by the black box models. We demonstrate that rule list algorithms produced simple decision lists that align with clinical expertise. By comparison, post-hoc interpretability methods applied to black box models may produce unreliable explanations of local model predictions. Model interpretability is essential for understanding differences in predictive performance and for integration into clinical practice.


Introduction
Glioblastomas (GBM) are the most common malignant brain tumour and have the poorest outcomes. Average survival is 12-18 months and the 5-year survival rate is less than 5% [1]. Lower grade gliomas have an average survival of 7 years, but ultimately most progress to GBM and death [2]. An accurate prediction of prognosis for patients would inform treatment planning and patient support, but this is challenging. Various factors impact prognosis, but the precise contribution of each factor, and combination of factors to outcomes appears to vary between patients.
At the group level, basic statistical models are well-established in brain tumour survival analysis, but patient level survival prediction remains a challenge, possibly because of the well described biological heterogeneity of the disease and of treatment responses. Several survival studies have used the Cox proportional hazards (Cox PH) model [3], a popular survival model in statistics, to identify relevant clinical features for the construction of a brain tumour nomogram [4,5,6,7] which graphically depict a statistical model to be used to estimate individualised cancer prognosis [8]. However, simple multivariable regression techniques are ineffective at identifying novel informative patterns from data [9], so machine learning (ML) approaches are increasingly being explored in brain tumour survival analyses [10,11] (see also Kourou et al. [12] and Wang et al. [13] for general reviews). Such studies often use genetic or imaging data, with complex black box models to make prognostic predictions. In clinical practice this type of data is seldom, hence these models are of little use. Fulop et al. [14] used a large clinical and molecular brain tumour dataset to predict 400-, 900-and greater than 900-day survival after surgery using several ML methods.
The authors found that a neural network model performed the best with an accuracy of 59%. Furthermore, the authors used LIME [15] to understand the main drivers behind the wrong predictions and emphasized the importance of model interpretability for clinical decision-making. Senders et al. [16] recently used demographic, socioeconomic, clinical, and radiographic features for the creation of an online calculator for the prediction of glioblastoma survival. The authors compared 15 ML and statistical algorithms and an Accelerated Failure Time [17] algorithm was selected. However, a follow-up Letter to the Editor in the same journal [18] noted inconsistencies in the model calculations and highlighted the danger of non-healthcare professionals accessing this online resource which may provide misleading information. Although ML can be used to build predictive models with superior performance and generalisability [13,19], the implementation of such models in a clinical setting can come with safety, legal and ethical considerations. In healthcare, there is a desire for interpretable and explainable AI/ML models to give end users (e.g. clinicians) the support that will allow them to accept or reject predictions, thus enabling them to make informed judgements when it comes to high-stake medical decisions (see Ahmad et al. [20] and Holzinger et al. [21] for reviews on interpretable ML in healthcare).
There is no all-purpose definition of interpretability since this is a subjective concept that is often domain-specific [22,23]. One way to define interpretability is as the degree to which a human can understand the cause of a decision [24].
Thus a model M 1 may be considered more interpretable than a model M 2 if M 1 's decisions are easier to comprehend than those of M 2 [25]. Interpretability may be achieved by either using an intrinsically interpretable model whereby its simple structure allows end-users to understand feature relationships and final predictions, or by applying post-hoc explanation techniques to analyse and extract information from a trained model [26]. Most ML models are not originally designed to be interpretable and advancement in ML performance has led to the belief in a model's accuracy-interpretability trade-off [22]. However, interpretability may be used as a tool to improve accuracy [25] and models with interpretability constraints have already been shown to perform on par with unconstrained models across several healthcare domains [27,28,29].
In this paper we explore the use of Bayesian Rule Lists (BRL) [30] and Falling Rule Lists (FRL) [31] as two types of intrinsically interpretable ML models and apply them to the prediction of patient survival using a novel brain tumour dataset. Both models combine pre-mined frequent patterns from the dataset into a decision list using Bayesian statistics [30]. The FRL model is an extension of the BRL algorithm which produces an ordered decision list whereby the estimated probability of success decreases down the list [31]. The BRL and FRL algorithms are compared to a baseline Cox PH model and popular black box models by looking at the prediction for brain tumour survival. To represent the class of black box methods, we chose random forest (RF) [32], logistic regression (LR) [33] and support vector machine (SVM) [34], each of which have varying degrees of interpretability. Finally, in an attempt to understand the decisions made by non-transparent models, post-hoc interpretability methods LIME (Local Interpretable Model-Agnostic Explanations) [15] and SHAP (SHapley Additive exPlanations) [35] are applied to the black box models. For a given instance (e.g. patient), the explanations produced by the post-hoc methods are compared between the three ML models.
The remainder of this paper is organised as follows: In Section 2 we introduce both the raw and final dataset and the required preprocessing techniques; Section 3 outlines model construction; in Section 4 we report the model's quantitative and qualitative results; in Section 5 we analyse and discuss the results and Section 6 closes with final conclusions.

The Raw Dataset
This paper explores an anonymised hospital-based brain tumour dataset collected from routine electronic healthcare data of patients who presented to 4 regional neuro-oncology teams in the UK with a brain tumour diagnosis. Initially, the dataset contained 1296 patient records and 225 predictor variables.
A preliminary exploratory analysis of the data led to the removal of incomplete variables (features less than 60% filled) (n=179) and variables irrelevant to predicting outcomes (e.g. location of first imaging, clinician ordering CT (open access CT), contrast agent) (n=14), as well as the grouping of duplicated predictor variables (e.g. Symptom 1 and Symptom 1 -other) (n=10). Additionally, a number of patients were removed due to incomplete records (i.e. a patient is missing more than 60% of the reduced predictor variables) (n=51) or because of a lack of symptomatology information (i.e. a patient did not present with any symptoms or signs) (n=227). The remaining 1018 patients records contained 21 predictor variables and one dependent variable, namely patient survival in days.
The raw dataset contained significant heterogeneity with more than 30 different brain tumour types, the most common being glioblastoma (n=540), followed by metastasis (n=198), glioma (n=186) and meningioma (n=174). The minimum age of diagnosis is 16 years while the oldest is 97 years, and a median age of 61 years. There are an almost equal number of male and female patients (51% and 49%, respectively). 18% of patients had a previous history of cancer and 48% of patients presented with a co-morbidity, the most common being cardiovascular (15% of all patients). The most common location for a tumour was in the frontal lobe (34%) followed by the temporal lobe (22%). More than half of the patients (68%) had some type of surgery and 23% of patients underwent chemotherapy. This is inline with current treatment protocols where surgery is often the first line of treatment, followed by chemotherapy and concurrent radiotherapy for malignant tumours [36]. Finally, 23% of patients received no treatment, reflecting either the benign nature of the tumour, or conversely its advanced state or poor clinical condition of the patient.
Patient survival was measured in days from radiological diagnosis of brain tumour and 35% of patients were still alive at the time of dataset analysis. This is known as censored data, which is common in survival analysis, whereby the 5 value of an observation, in this case survival, is only partially known [37]. In the raw dataset, the largest survival time is 3964 days, or about 10 years, however only 11 patients have a survival time greater than 2000 days. At the time of data analysis, all patients with censored survival data had been alive for more than one year following diagnosis.

Preprocessing
Next, we review various pre-processing steps that were needed to get the narrowed-down dataset of 1018 patients into a state suitable for our analyses.

Imputation
Given the small dataset size, missing data was managed though imputation rather than deletion. Treating all missing data the same would be a strong oversimplification as missing data can come from a variety of sources [38]. An entry for a feature may be absent, but this does not imply that the entry is 6 truly missing. For example, a patient may only present with one symptom thus leaving the remaining symptom features empty. This creates the appearance of missing data but in fact the empty entries are correctly missing. The variables to be imputed were all believed to be missing completely at random.
A number of imputation techniques were tried to determine which method was appropriate for each incomplete variable. In particular, a baseline modeand mean-fill was used for categorical and continuous variables, respectively, and were compared to a k-nearest neighbours (k-NN) [39] and regression [40] imputation technique. For k-NN, the use of normalised and non-normalised features were both explored to account for differences in numerical values. The continuous variables in the dataset are constrained thus outliers were not a concern (e.g. the feature Symptom 1 Duration must fall between 0 and 52 weeks). For each variable with missing values, the imputation techniques were evaluated on the entire dataset using 10-fold cross-validation. The imputation of categorical and continuous variables was assessed using accuracy and the standard mean square error, respectively. The optimal imputation method for each variable was then implemented on the full dataset, whereby the missing variables were replaced with the model's predicted output. More information about the imputation methods are described in a forthcoming paper based on the following thesis [41].

Discretisation
Following imputation, all continuous variables (Age, Symptom 1 Duration, and Maximum Tumour Size) were discretised in order to support the association rule mining [42] employed by the BRL and FRL algorithms (see Section 3.3).
Most rule-mining approaches make the (restrictive) assumption that all features are binary or categorical. As part of the discretisation process, we compared three methods: uniform binning, quantiles and k-means. Each feature was divided into groups ranging from size 2 to 12, increasing by increments of two.
We chose the maximum to be 12 as it was a natural divider for the feature Maximum Tumour Size, which contained the largest range in values (0 -120).
The accuracy of the discretised features was compared to the continuous feature, using the BRL model with default hyperparameters. Classification of patient survival greater than one year was evaluated on the entire dataset using 5-foldcross validation.

Dealing with Feature Collinearity
Finally, in our dataset, two sets of features were found to be highly correlated: Tumour Type and Likely Grade as well as First Treatment and Extent of Resection. Tumour type refers to the kind of tumour a patient is diagnosed with, while likely grade is an indicator of how quickly a tumour is likely to grow or spread. A grade I/II tumour is benign (slow growing and unlikely to spread within the brain) and a grade III/IV tumour is malignant (fast growing and likely to spread within the brain). However, by definition, a glioblastoma is a grade IV glioma tumour. Thus to reduce collinearity in the data, Tumour Type and Likely Grade were combined into a single feature called Diagnosis. Tumour types were separated into benign (or low-grade) and malignant (or high-grade) categories (e.g. Glioma Benign and Glioma Malignant). Metastatic tumours encompass a mix of tumour types that originate elsewhere in the body. By the fact that they migrate to the brain, metastatic tumours are all aggressive and thus classified as malignant. The second set of features, First Treatment and Extent of Resection (EOR), also suffer from multicollinearity. EOR refers to the amount of cancerous cells removed during surgery (e.g. 90-99%) and is only relevant if the first treatment a patient receives is surgery, which is not always the case. Thus we integrated EOR information into First Treatment (e.g. Surgery 100%, Surgery 90-99%) to create a more informative feature -the feature name remained First Treatment.

The Final Dataset
Our final dataset contains 1018 patient records and 19 predictor variables including patient demographics (e.g. sex, age), medical history (e.g. history of cancer, comorbidity), symptom features (e.g. symptom types and duration), 8 radiological tumour analysis (e.g. diagnosis, morphology) and treatment details (e.g. first treatment, post-op performance status). Many of these prognostic factors have been well-documented in the literature including age, Karnofsky performance (KP) score, symptoms, morphology, diagnosis (i.e. tumour type, likely grade) and treatment [43,44,45,46,47]. Table 1 provides a detailed summary of the salient variables in the final dataset, including their descriptions, value and percentage of each value present in the dataset following imputation and discretisation (see Table 4 in the Appendix for a comprehensive overview of all predictor variables in the final dataset). We briefly discuss some of the salient features below and some final processing of the features.  Table 7 in Appendix) KP Score: This is a standard way of assessing a patient's ability to perform everyday tasks [48]. The scale is a 'gold standard' in clinical oncology and is commonly used to determine a cancer patient's expected tolerance to treatments (e.g. chemotherapy). The scores ranges from 0 (dead) to 100 (normal) and is scored in deciles, although the values are ordinal (see Table 10 in the Appendix for the original definition of the KP scores). This means that a value assigned to a patient is based on a ranking but the numerical value associated with this rank is not meaningful. Thus the difference between the values 70 and 90 is not equivalent to the difference between the values 40 and 60. Furthermore, the KP scale may be subject to bias [49]. A patient's KP score is determined by clinicians, and when compiling a dataset this can result in inter-observer subjectivity [50,51]. To reduce the bias associated with the KP score, values of 70 and below were aggregated due to their negative association with survival [52] (a KP score of 70 reflects someone who can 'care for self, but who is unable to carry on normal activity or to do active work'). KP scores of 80 and above remained separate allowing for a more fine-grained analysis of the values associated with survival.

Symptom 1: A symptom is observed by the patient themselves (subjective)
and is often what drives a patient to consult a physician. Symptom 1 refers to the first symptom a patient presents with. The symptom data in the raw dataset had a high cardinality of 37 different symptom types, with many of these types pertaining to a small number of patients. Thus we decided to group symptom types into six overarching categories -e.g. Headache, Fits/Faints/Falls and Behavioural/Cognitive -based on work by Ozama et al. [53] to create a more homogeneous set of symptom types. An outline of the symptom groupings are summarised in Table 5 of the Appendix.
Sign 1: A sign is observed by a physician (objective). Sign 1 refers to the first sign a patient presents with. The sign data in the raw dataset also had a high cardinality (26 different types), thus the data was additionally grouped into six larger domains -e.g. neurological and cognitive-based on the advice of the consulting clinical experts (see Table 6 in the Appendix). Although all patients in the final reduced dataset presented with at least one symptom, 43% of patients did not present with any signs.
Diagnosis (Tumour Type): Brain tumours are broadly named based on the type of normal cell that they most resemble, and their location in the brain [54]. In the raw dataset the tumour types had a high cardinality with many entries referring to the same general tumour type (e.g. meningioma suprasellar and meningioma at cerebellopontine (CP) angle). Tumour types that appeared in less than 10 patients were grouped into a "Rare Tumour" category. Additionally, the tumour type may be benign (i.e. grade I/II), or malignant (i.e. grade III/IV). In the final dataset, the brain tumour types were reorganised based on type and malignancy (e.g. Glioma Benign, Glioma Malignant), and reduced to a cardinality of 9.
Morphology: Each tumour type can have a different sub-classification, which is represented as morphology. A tumour with heterogenous morphology contains diverse cell types with distinct molecular structure that may have different levels of sensitivity to treatment [55]. In comparison, a homogenous tumor contains the same or similar genetic or epigenetic characteristics [56].
Hence tumour morphology may be indicative of treatment response.
First Treatment: The first type of cancer treatment a patient receives is based on the presumed type based on imaging, location of the tumour, and the patient's overall health (e.g. KP score ≤ 70). Surgery, for example, may be the only treatment necessary depending on the grade of the tumour and extent of resection. Information on extent of resection was included in the first treatment types (e.g. Surgery 100%, Surgery 90-99%, Biopsy, etc.). Other treatment types include radiotherapy and chemotherapy.

Modelling Techniques
As the black box ML models (RF, LR and SVM) cannot directly handle categorical variables, one-hot encoding was used for all 19 features, which resulted in 94 different feature types. For ease in model feature comparison, one-hot encoded features were also used by the Cox PH model. Due to the small dataset size, nested cross validation [57] was implemented for hyperparameter tuning and model assessment. The inner loop, which is responsible for the model selection, used 3-fold cross-validation, and the outer loop, which is responsible for estimating model performance, used 5-fold cross-validation. Nested cross validation was repeated for three different random seeds resulting in a 3 × 5 × 3 setup. For each model, the average accuracy [58], macro-F1 [59], and area under the receiver operating characteristic curve (AUROC) [60] were reported. All models performed binary classification and one year survival labels were created from the survival data. This resulted in a relatively even split of the dataset: 443 patients (44%) survived less than a year and 575 patients (56%) survived more than a year.

Cox PH Model
The Cox PH model is a popular regression model for survival analysis [3].
This semi-parametric model predicts the risk of an event occurring (e.g. death) as a function of time. The hazard function λ(t) estimates the effect of observed variables x k on a baseline hazard function λ 0 (t). The model can be expressed 13 as: and served as an alternative statistical baseline for the ML models. Due to the one-hot encoding of the categorical variables, the resulting dataset incurred problems with high collinearity. That is, some of the independent variables were highly correlated which tends to inflate the estimated regression coefficients.
Thus the first category per feature was dropped -i.e. for a variable with k categories, k-1 dummies remained. A penalizer was also added to the model which reduces the size of the coefficients during regression, thus controlling for high correlation and improving the stability of the estimates [62]. A search for the optimal penalty parameter between the set of values {10 −3 , 10 −2 , ..., 10 1 } was performed and a value of 10 −2 was selected.
The purpose of the Cox PH model is to predict survival time. Thus the model was trained using the continuous survival data and the predicted survival time was converted to binary one year survival labels that were then used to calculate the model's performance.

Rule Lists
Rule lists are a type of intrinsically interpretable model that produces a series of if-then rules, also known as decision (or production) rules, which are used to generate predictions. Each rule is composed of two different sets of items, a and b, also known as itemsets. A decision rule is an implication of the form a → b (or if...then...), where a is an antecedent that is followed by a consequent b. As an example, for the rule: is satisfied, the model outputs a certain classification. Although the concept of decision rules is well known in AI, more recently, rule-based models have been constructed directly from data with the help of ML [63].
Instead of being crafted using domain knowledge, rules can be learned using frequent itemset mining [64,65], which looks for common patterns in the data. Itemsets, consisting of these frequent patterns, are used to construct the association rules that are normally subject to constraints on minimum support and confidence [64], although other measures such as lift [66] are possible. In particular, refers to how frequently the itemsets appear in the data, where f req(a, b) is the frequency of the itemsets containing items a and b, and N is the number of observations in the dataset. If the support threshold it is too large the algorithm may fail at finding the true patterns in the dataset, whereas a small minimum support may generate an excess amount of association rules that is not fit for effective use. Confidence, for its part, is defined as: and is the frequency of itemsets that contain a which also contain b, or how often a rule is found to be true [67]. Consequently, the performance of these rule mining algorithms is dependent on user-specified thresholds. For both the BRL and FRL models, rules were mined using the default minimum support threshold of 10% and confidence threshold of 80% that is commonly used in the literature. Different thresholds on minimum support and confidence were explored but model performance did not improve thus the default parameters were retained.
Finally, the BRL and FRL algorithms contain additional hyperparameters to specify the maximum rule cardinality and expected rule list length. The maximum rule cardinality refers to the length of the rule (or itemset). This value is typically set to 2 or 3 as it may be harder to reconcile a combination of features as being clinically logical when interpreting high cardinality rules.
The prior expected list length denotes the expected number of rules in the list (excluding the null rule).

Bayesian Rule Lists
BRLs [30] are used for classification problems where the goal is to learn

Falling Rule Lists
A FRL is an ordered decision list whereby the estimated probability of success, or P (Y = 1 | X), monotonically decreases down the list [31]. Analogous to BRL, pre-mined rules are first extracted from the data, then Bayesian modelling is used to produce a decision list (see Wang and Rudin [31] for mathematical details). To approximate the FRL, Monte Carlo sampling from the posterior distribution is required to generate an initial decision list. To enforce FRL monotonicity constrains, a combination of Gibbs and Metropolis-Hastings sampling [69] is used. Unlike BRL, following the production of an initial decision list, instead of yielding many sample lists, a point estimate is found using simulated annealing [70].

ML Algorithms
Three ML classifiers were exploited to predict the 1-year survival of pa- tients. An RF classifier [32], which uses a multitude of decision trees [71] for classification, was implemented. The number of trees were selected using grid search with 3-fold cross validation. A LR classifier [33] with L2 regularisation [72] was also employed. The regularisation parameter C LR was selected from Finally, an SVM classifier [34] with a radial basis function kernel [73] was used. The regularisation parameter C SV M was selected from {2 −4 , 2 −3 , 2 −2 , ..., 2 4 }. Both LR and SVM penalty parameterrs were chosen using a similar range of values to the original BRL paper [30]. All models were implemented using the scikit-learn package [74] and represent a group of relatively uninterpretable ML models.

Model Evaluation
The mean classification performance of the six modelling approaches on the brain tumour dataset are summarised in

Model Interpretability
Although the algorithms do not provide the same level of interpretability, the weighting of features at a global model level and local prediction level can be reasonably compared. Sequential feature selection was first performed on the dataset to assess feature significance. The final models interpretability was evaluated using feature importance (Cox PH, RF), post-hoc methods LIME and SHAP (RF, LR, SVM) and qualitative assessment (BRL, FRL). These aspects are discussed next.

Feature Selection
Typically, the purpose of feature selection is to remove irrelevant features or noise from the data and improve computational efficiency. We used feature selection to assess which features were most pertinent to the data and to compare these results to the feature importance of the individual models.
Sequential feature selection from mlxtend 1 allows for a range of k -features to be specified and the feature combination that scores the best during cross validation is returned. Although SVM was the best performing model, the algorithm cannot be run in conjunction with the feature selector as a result of the kernel transformation, thus RF, the second best model, was run with the feature selector to provide a baseline for feature comparison. The RF default parameters were used and features were assessed using AUROC with 5-fold cross validation. Due to one-hot encoding, a total of 94 feature types were evaluated and the selector returned the 10 best features (see Table 3).
The selected features included diagnosis, age at diagnosis, SIMD score, KP score, morphology, post-op status and urgency of referral. Notably, many of these features have been previously mentioned in the literature as important prognostic variables [46,47,75,76,77], however SIMD, a social measure of deprivation in Scotland, is often associated with survival in a population study setting rather than a hospital-based setting. Nonetheless, an association be-tween socio-economic status and cancer survival has long been demonstrated in research [78]. Despite the UK's universal healthcare, several cancer studies have linked deprivation with poorer survival outcome [79,80,81]. In our dataset, 62% of patients with a SIMD score of 4 or 5 (least deprived) survived greater than a year compared to 53% of patients with a SIMD score of 1 or 2 (most deprived).
Additionally, post-op performance status (scale 0 -5) accounts for two of the top ten feature values returned suggesting it is valuable predictor (see Table   7 in   RF feature importance is given in Figure 6. This was obtained using permutation importance, which measures the decrease in a model's performance when a feature value is randomly shuffled [32] but does not indicate whether the feature is positively or negatively correlated with the predicted outcome. Given our dataset, which contain features with cardinalities ranging from 2 (e.g. Sex) to 9 (e.g. Diagnosis), permutation importance was preferred over the frequently-used mean decrease in impurity (MDI) [83] because the latter is often biased towards features with high cardinality [84]. As can be seen, the three most influential features for the RF model were a younger age at diagnosis, a post-op status of 0 and heterogeneous tumour morphology. All three features were also used by the rule lists and sequential feature selector. Note the three feature values were not used to train the Cox PH model (due to collinearity problems as discussed previously), however the Cox PH model found the inverse feature values (i.e. an older age at diagnosis, a post-op status of 4/5 and homogeneous tumour morphology) to be informative.
Notably, the Cox PH model is seldomly used to determine feature impor-tance, rather it is a modelling technique to help adjust for confounders while assessing the effect side of a variable of interest.

Local Surrogate Model
Compared to feature importance, LIME and SHAP can assess interpretability at the local level for individual predictions, rather than at the global modular level. Local explanations may be more accurate than global explanations [26] and are beneficial for understanding why instances are classified incorrectly.
For example, Figure 7 illustrates LIME's explanation of an observation that was classified incorrectly by LR and SVM (i.e. wrongly predicted survival > 1 year) and correctly by RF (i.e. rightly predicted survival < 1 year). The top 10 influential features for the given test instance are shown. Figure 8 shows an explanation by SHAP of the same observation classified by RF. Both surrogate models were applied to all three ML models, and the same prediction instance was compared across the three models (see Figures 11 and 12 (Figure 8), features such as lobe, midline shift, SIMD and symptom type were in the top 10 most influential features.
The discrepancy between LIME and SHAP for the same model highlights the unreliability of post-hoc interpretability methods [22].

Qualitative Analysis
In medicine, where human decision making governs the process of patient treatment, a survey over domain experts is a valuable measure of interpretability [23]. The interpretability of our rule lists was assessed based on the clinical expertise of two of the current authors (M.P. and P.B.), who were provided with multiple point-estimates from both BRL and FRL models (see Figure 3, Similar features were found influential across multiple rule lists including age at diagnosis, KP score, tumour morphology, and first cancer treatment. As expected, the diagnosis (tumour type) is also an important factor for survival.
For example, benign gliomas and benign meningiomas indicted greater survival,

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(a) Random Forest (RF) feature importance for a given test instance determined by LIME.
The observation was correctly classified.
(b) Logistic Regression (LR) feature importance for a given test instance determined by LIME.
The observation was incorrectly classified.
(c) Support Vector Machine (SVM) feature importance for a given test instance determined by LIME. The observation was incorrectly classified.  both of which are highly treatable, with a 76% [2] and 70% [85] five-year survival rate, respectively. Comparatively, brain metastases indicated poor survival and only have a 1-year survival rate of 17% [86]. The impact of these feature combinations have been well-established in the literature [46,47,75,76] and were re-produced by the rule-lists. An agreement between model predictions and clinical knowledge is essential for establishing trust in the models decision making process, as well as trust that the model will make accurate predictions when applied to new data.

Model Comparison
The features found important by the three model types (Cox PH, rule lists, ML) for survival prediction are summarised visually by a Venn diagram in Figure   9. For ease of evaluation, the general feature types are used for comparison between models (e.g. sex) instead of the individual feature values (e.g. female or male). Additionally, the features used by the ML models are for a single test instance thus only general comparisons can be made.
All of the features returned by the sequential feature selector (see Table 3), except Urgency of Referral, were used by at least one of the three model types.
All features used by the baseline Cox PH model were also found important by the rule lists and ML models. We only investigated the top 10 most influential features used by the Cox PH model hence there is likely more overlap in feature significance between the three models. The features identified as influential by all models included age, diagnosis, morphology, first treatment and postop status. The rule lists and ML models had multiple overlapping features including comorbidity, KP Score, symptom 1, symptom 2 and midline shift.
Only the rule lists found sex and history of cancer to be significant, while only the ML models found SIMD, symptom 1 duration and lobe to be important. The importance of symptomatology data is interesting, as symptoms are often talked of in regards to time to diagnosis, but less often with regards to prognosis. When looking at the RF global top 10 important features (see Figure 6), symptom and sign features were not found relevant, but when using SHAP to look at a specific test instance from the RF model (see Figure 8), as well as LR and SVM (see Figure 11 and 12 in Appendix), symptom information was relevant.
As mentioned above, sex was only found relevant for the rule lists which was surprising. Majority of research into sex differences and brain tumour survival have focused on glioblastomas, which find that men are more likely to develop, and die of, glioblastomas than women [87,88,89]. In comparison, women are twice as likely to develop meningiomas compared to men but no significant difference in outcome have been reported [89,90]. Although sex may play an important role in individual tumour types, across all tumour types sex may be less influential. Finally, four features were not used by any model: Urgency of Referral, Sign 1, Side and Max Size. Note Urgency of Referral was found to be important by the sequential feature selector (see Table 3) but not by the algorithms. Given the importance of symptom 1 and symptom 2, the irrelevance of sign 1 (the first onset objective clinical abnormality) is perhaps the most surprising. Although in our dataset 42% of patients presented with no signs, as symptoms dominate, hence this feature may be less informative for classification.

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Features which are not ranked as important by models should arguably be given less attention in clinical evaluation and the use of such features should be reviewed if they currently play a decision role in the assessment. It is beneficial to simplify models, and decision making, by reducing some of the noise over features, as there is often extraneous data in healthcare that can impair decision making rather than support it.

Discussion
The results summarized in Table 2 demonstrate that the BRL and FRL algorithms were outperformed slightly by popular ML models. However, the innate interpretability of rule lists may mitigate potential performance loss, especially in health-care where model transparency is essential for its integration into-and influence on decision making [22]. The original BRL paper derived a stroke prediction model and found that the BRL-point estimate performed on par with SVM and only ∼2% worse than RF (their best performing model). Comparatively, the average BRL performance for brain tumour survival prediction was ∼5% worse than SVM (our best performing model). Notably the dataset used by the original authors was more than 12× the size of ours, hence the additional training data may have helped BRL performance. The minimal decrease in BRL performance for both stroke and brain tumour survival classification highlights the potential of innately interpretable algorithms for high-stake predictions.
Our results are also similar to that of Wang and Rudin [31], who found that FRL performance was slightly worse, but comparable to RF, LR and SVM on four public datasets. FRL performance on our dataset is within one standard deviation of the ML algorithms mean performance. The minimal loss in FRL performance is not surprising as the model's strong monotonicity constraints may sacrifice performance [31].
More generally, the slight loss in rule list performance compared to the ML models may be due to our dense heterogeneous dataset and limited sample size.
Rule list algorithms optimise over pre-mined rules, rather than the entire feature space, hence the algorithm's computational effort scales with the number of antecedents rather than the number of features [30]. Rule-lists are a promising interpretable model but are currently limited to categorical features and binary classification (see [91] for a recent proposal of a multi-class rule list algorithm). Similar to decision trees, rule lists cannot deal with linear relationships and due to their categorical input requirement, rules can only produce step-like predictions [26]. Additionally, a caveat to rule list interpretability is that such models are generally not stable. There may be multiple equally good rule lists and it is not clear which will be returned by the algorithm [30]. FRLs, whereby rules that favour survival less than and greater than a year are used. In comparison, FRLs have the added benefit of automatically stratifying patients by risk thus a clinician only needs to look at the top few rules to classify the most high risk patients. Similar to Senders et al. [16], an interactive graphical representation of the rule list model could be created, whereby a clinician inputs a patient's features and a prediction is returned along with the decision rules used to make that prediction. Finally, the integration of additional clinical information such as blood tests or genetic data may improve the clinical validity of rule list models. Blood tests are now being investigated as a means for brain tumour diagnosis [92,93] and genetic alterations have shown to be effective predictors for tumour prognosis [14,94].
Although the innate interpretability of rule-lists cannot be directly compared to the post-hoc interpretability of ML algorithms, general conclusions can be made. Traditional variable importance algorithms are limited to group-level analysis but LIME and SHAP enable the explanation of individual predictions to understand the contribution of each predictor. Our results showed that similar features were used by the three ML models for making predictions. However, the weighting of each feature varied between models and across interpretability techniques. The different feature weightings between models may explain the variability in model performance, but the difference within interpretability techniques highlights the inconsistency between post-hoc methods. Because post-hoc methods assess interpretability after model construction, explanations can prove misleading and unreliable [22], and there is a growing body of literature that has questioned the credibility of LIME and SHAP [22,95,96,97,98].
There is a large toolbox of post-hoc methods [26] available to assess model interpretability, however, the absence of a cohesive definition for interpretability makes it difficult to assess the quality of different interpretability techniques.
By agreeing on clear quantitative metrics for interpretability, the development of robust trusted interpretability techniques can follow [99].

Strengths and Limitations
This was the first study to apply classification algorithms to a novel brain tumour dataset for 1-year survival prediction. Brain tumours are a rare but deadly disease, and compounded by their heterogeneity, an accurate progno-sis by clinicians is a challenging task. Also, to our knowledge, this is the first study to compare intrinsic and post-hoc interpretability methods for the assessment of predictive brain tumour survival models. As ML continues to advance, the development of tools to assist clinicians with these high-stake medical decisions by providing trustworthy data-driven support will become essential for ployed. In addition, the data used in this study was heterogeneous and a second validation dataset is required for confirmation of our results. With the addition of new data, this study could also be extended to explore the application of post-hoc interpretability methods to neural networks. As discussed above, rule-lists currently require categorical features and are limited to binary classification (see [91] for multi-class rule list algorithm proposal). Extension of the rule list algorithm for multi-class classification or regression is an important next step for improving rule-list performance and constructing a competitive interpretable rule list classifier.
Finally, although not directly related to the ML models, our dataset required imputation and discretisation. There is the potential for imputation to introduce bias into the data [38,103] and the chosen imputation method can influence the final results [104]. Additionally, although discretisation can be used to improve the clarity of classification models by extracting useful feature intervals, the split of the feature will also effect a model's performance. Both pre-processing techniques have the potential to reduce model performance which we sought to mitigate during dataset preprocessing through the exploration of multiple imputation and discretisation algorithms.

Conclusion
This study investigated the performance and interpretability of multiple al-

Conflict of interest statement
The authors declare no conflict of interest.
Appendix A

42
Grade Description 0 Fully active, able to carry on all pre-disease performance without restriction.
1 Restricted in physically strenuous activity but ambulatory and able to carry out work of a light or sedentary nature, e.g., light house work, office work.
2 Ambulatory and capable of all self-care but unable to carry out any work activities; up and about more than 50% of waking hours.

3
Capable of only limited self-care; confined to bed or chair more than 50% of waking hours.

4
Completely disabled; cannot carry on any self-care; totally confined to bed or chair.