Analogical proportions are statements of the form : :: : that are used to map similar relationships between two pairs of objects, , , and , . Analogies have long been a subject of research in the Natural Language Processing (NLP) community, where they have been applied to a variety of reasoning and classification tasks. Lately, machine and representation learning have shown to be useful for analogical reasoning. In this paper, we discuss the possibility of adapting the analogical framework to healthcare applications, in particular to medical decision support. We particularly hypothesize that as language representations help in analogical reasoning in NLP, patient representation learned from Electronic Health Records (EHRs) may help in healthcare. We define three diferent analogy based settings adapted to EHR data that we see as first steps to the development of analogical applications to this domain. We provide statistics on the first sets of analogies that we built from a publicly available dataset of EHRs, and report preliminary, but promising results to detect patient-stay analogies following our very first experimental setting.
An analogical proportion, or an analogy, is a relation between four objects , , , and that
is expressed as “ is to as is to ” and formally denoted as : :: : . There are
two main tasks associated with analogical proportions: analogy detection and analogy solving.
Analogy detection corresponds to the task of deciding whether a quadruple ⟨, , , ⟩ is a
valid analogy. Analogy solving corresponds to finding a fourth element so that : :: :
is a valid analogy. This can be done either by retrieving from a pool of candidates or by
generating . Analogies have been extensively studied and applied to various Natural Language
Processing (NLP) tasks [
In this paper, we explore the possibility to leverage the analogy framework to solve tasks relevant to the healthcare domain. We particularly consider using Electronic Health Records (EHRs) to learn patient representations, i.e., patient embeddings. We initiate the construction of sets of patient-based analogies using relationships existing between patient hospital stays from a publicly available set of EHRs. These health records consist of clinical and administrative data collected during patient hospital stays. Generally they are composed of structured (e.g., diagnostic codes, lab tests) and unstructured data (e.g., clinical notes, nursing reports, discharge summaries), either static (e.g., patient demographics) or temporal (e.g., vital signs).
EHRs have been secondary used to conduct epidemiological and observational studies. They
have also been used as real word data to train predictive models [
Analogies have only been sporadically applied to healthcare. Nonetheless, analogical
reasoning has been applied in clinical practice by physicians for diagnosis and prognosis, as a way
of linking visible signs and symptoms to possible causes. Indeed, medical reasoning relies on
observations of previous patients with similar signs and symptoms, who happened to have a
certain disease. Several studies have investigated analogies in healthcare by applying various
machine learning methods. For instance, Rather et al. [
In this paper, we describe an ongoing work on analogical inference in healthcare. We
introduce three analogy based settings, where each setting aims to investigate specific biomedical
tasks, namely identity, predictive, and generative tasks. In comparison with previous studies
[
This paper is organized as follows. Section 2 provides a description of the MIMIC-III dataset. Section 3 defines our analogical settings and associated biomedical tasks, and justifies our task choices. Section 4 presents preliminary statistics of the analogical proportions built from MIMIC-III. Section 5 initiates a discussion addressing some analogical postulates that could be useful when generating our analogies. Section 6 illustrates the feasibility of our approach by providing preliminary results using one of our experimental settings. Section 7 discusses perspectives for future research.
We propose to use EHRs as a source of patient medical history data and aim to consider both its
structured and unstructured data to define our analogies. In particular we experiment with a
publicly available dataset of EHRs called MIMIC-III (Medical Information Mart for Intensive
Care-III) [
The database contains a combination of structured and unstructured data and is accessible to researchers under a data use agreement, where users are required to follow a HIPAA training course demanded by the National Institutes of Health (NIH).
8, 526 4, 818 66.24 23, 345 19, 709 2.33 9.74 18.0
As we defined previously, an analogy is a 4-ary relation and is usually written as : :: : . In this paper, we define three analogy based settings and associated tasks that we are interested in investigating with EHR data. We name our three settings as follows: (i) Identity; (ii) Identity + Sequent; (iii) Identity + Directly Sequent. For these settings, we do not want to learn “full” patient representation, but patient-stay representations (i.e., learn a numeric vector representation of EHR data that belong to a single hospital stay) which we hope to be simpler. Identity In the first setting, we propose to build analogies of the form: 1 : 2 1 1 :: 3 2 : 4 2 where refers to the stay of patient . Here, pairs of the analogy quadruples are made of two random stays belonging to the same patient. Since there is no constraint on the order of stays, 1 can happen before 1 or the inverse. Note that 1 and 2 could be the same patient, and that 1 2 1 and 2, or 3 and 4, could represent the same time stamp. Furthermore, 1 and 3 or 2 and 4 could be the same when 1 = 2 (but not when 1 ̸= 2). In this setting we aim at investigating identity tasks, i.e., associating an unafected sample of data to the patient it belongs. Note that this setting fits several data cleaning and data privacy related applications Identity + Sequent For this setting, we add a temporal constraint to analogies, as we force 11 ≪ 2 1 and 23 ≪ 4 2 where ≪ denotes temporal sequentiality between stays of a same patient, i.e., after 1 and 24 takes place after 2 but not necessarily directly right after. We consider cases 1 3 where 1 = 2. In this setting, we also define a relation named diagnosis, which forces 1 and 1 23 to have the same diagnosis. This relation provides more meaning to our analogies and gives us more medical insight into the relationship between our patients. For example, based on the 12 takes place diferent stays associated with a single patient we hope to see how a certain disease develops (similarly or diferently) between two distinct patients.
Identity + Directly Sequent In this third setting, we make the temporal constraint more strict as we force the two stays of the same patient to be directly sequent (no other stay can exist in between). We note this constraint 11 ≺ 2 1 and 23 ≺ 4 2 The diagnosis relation is kept between 1 and 23 , and cases where 1 = 2 are also 1 considered. With these three settings, we aim at investigating the applicability of two tasks: analogy detection and analogy inference. For instance, given an analogy of the form : :: : , we can either propose potential values for an unknown stay (i.e., predictive task) or generate stays which would enrich our dataset with synthetic stays (i.e., generative task).
For the last two settings, we define additional settings by considering three levels of relaxation
of the diagnosis constraint. It is satisfied either if both stays are associated with the very same
primary diagnostic code (level 4) or in more relax settings, i.e., if both codes belong to the
same level-3 or level-2 branch of the hierarchy of the ICD-9-CM (International Classification of
Diseases, Ninth Revision, Clinical Modification) [
We computed some preliminary statistics on MIMIC-III dataset to check how many analogical proportions can be formed for each of the three analogical settings and based on the three level diagnosis constraint as shown in Table 3. To form the analogies, we built tuples of each of the two stays that belong to a single patient . We kept only adult patients (aged 18 and above) that have at least two hospital stays. For our first setting, we define a valid analogy as a quadruple of four stays ( 1
2 , 24 ), where each pair of two stays belong to a single patient . Since we do not restrict the order of the stays for each of the pairs, our analogies were made of all the permutations of all the stays belonging to a patient. 3
For our second and third settings, we define a valid analogy to be a quadruple made of four stays ( 1 2 have the same diagnostic code. As an order constraint is introduced for these two settings, we had to make sure that 11 takes place before 1 and 23 takes place before 24 . For the second 2 setting, the stays do not necessarily happen directly right after, where other stays can exist in between. As for the third setting, one stay immediately follows the other, i.e., there is no other stay in between them.
For the diagnosis constraint, we referred to the ICD-9-CM, which is the standard nomenclature for assigning diagnosis codes to each hospital stay. Indeed, each stay has a unique primary diagnosis code and a set of secondary codes. Diagnostic codes are organized hierarchically as follows: (1) chapter, (2) block, (3) 3-digit category, and (4) full code. As an example, the diagnosis code 767.4 and its hierarchy are presented Table 2.
1 2 3 4
760–779 764–779 767 767.4 and third analogical settings, we preprocessed our diagnosis codes in the following manner. We kept only the primary diagnostic code associated with each patient-stay. We filtered ICD-9 codes that appeared only once. For the second level and third level diagnosis settings, we performed the same preprocessing except that we had to first convert the ICD-9 codes into their corresponding category and block formats.
Table 3 provides the number of valid analogies that can be formed with the defined settings. As shown, the number of analogies is the highest for the Identity setting, which could be explained as a result of the absence of constraint on both the order of stays and diagnosis. The more strict the order constraint is, the less the amount of valid analogies that could be formed. The diagnosis constraint also influences the number of analogies that could be generated. The number of analogies is the lowest for full code (level 4) settings, where less patients share the very same primary diagnosis code. In comparison, more patients can share a single diagnosis code in the category (level 3) and block (level 2) settings, where we observe the highest number of analogies in the block setting for both the second and third analogical settings.
As we are interested in exploring diferent deep learning models, we would need large amounts
of data to train them. To enlarge the training datasets, one may use analogy properties to
generate more analogies in a process called data augmentation. Training our model on diferent
equivalent forms of the same analogy could help reduce overfitting. Previous works [
However, not all these postulates hold for all our settings. Based on the current definitions of our analogical settings, we can apply reflexivity for all the three settings. Inner reflexivity can only be applied for the Identity setting. Adding this postulate for the second and third settings would require to loose our order constraint, which is inconsistent with the temporal aspect of predictive modeling. Determinism holds for all the settings. We include this postulate even if it produces trivial analogies. Central permutation can be applied on our analogies for the first setting only and in the very particular case when 1 = 2. When 1 ̸= 2, central permutation cannot be applied to increase our dataset as it would enable to associate stays of distinct patients, which is inconsistent with the aim of the Identity setting. Concerning the second and third analogy settings, central permutation cannot be applied as it violates the order constraint in most cases. Note that central permutation can be applied for these two settings for cases when 1 = 2, 2 ≤ 1, 3 ≤ 4, and the same diagnosis is associated to 1 and 23 . Inner symmetry 1 can be applied for the Identity setting, but it violates the order constraints for the other two settings. For all the three analogical settings, by applying symmetry to one valid analogy, we can increase the number of valid analogies as it does not violate any of the three constraints. In addition to valid forms, we can also consider invalid forms (i.e., that contradict some of the setting constraints or that cannot be inferred from the base cases using the allowed postulates) for classification purposes.
We set up a preliminary experiment on the analogy detection task, addressing our Identity
setting. Inspired by [
) constitutes a valid analogy. For the embedding model, we consider
the Fusion CNN model developed by [
We considered hospital stays of 200 patients extracted randomly from MIMIC-III. We define a valid analogy as a quadruple of four stays ( 1 2 , 24 ), where each pair of two stays belong to a single patient . We do not define any order constraint for our stays; therefore, 1 can happen before 12 . Quadruples where 1 = 2 are also included in the dataset. To 1 generate other valid analogies, we make use of all postulates in Section 5, except for central permutation that is only applied in the case when 1 = 2. As reflexivity forces 1 = 2, it cannot be applied in the cases where 1 ̸= 2. Accordingly, given a valid analogy : :: : , we generate 8 additional valid analogies, namely, : :: : , : :: : , : :: : , : :: : , : :: : , : :: : , : :: : , : :: : , and 2 invalid, namely,
: :: : and : :: : . When 1 = 2, we generate one more valid analogy of the form : :: :
and we consider invalid analogies as valid.
For training and evaluation, we split our dataset into 70% training set and 30% testing set, representing 939,638 analogies for training and 402,703 for testing. We randomly draw 50,000 analogies of each set (i.e., training and testing) when loading the data. Following the data augmentation procedure introduced before, given a valid analogy, we generate 9 valid analogies (i.e., positive examples) and 2 invalid analogies (i.e., negative examples) for cases when 1 ̸= 2. In contrast, we generate 12 valid analogies and no invalid analogies for cases when 1 = 2. Based on this setting, we tend to generate more valid analogies than invalid ones. We trained our model on 10 epochs, with 3 random intializations to observe how the model behaves and how much it is able to learn. We only computed the accuracy and obtained 96.85 ± 1.75 for valid analogies and 70.31 ± 1.94 for invalid analogies. Our model performs the best for positive examples which can be explained as a result of the imbalance between valid and invalid examples in the training data. Nonetheless, these preliminary results seem to show that the model learns, to some extent, patient-stay identity relationships.
To gain a deeper insight on how our classification model works, we present four examples: one true positive, one false negative, one true negative, and one false positive. Patient ids in the examples below have been changed and dates have been shifted. We provide elements of interpretation to explain why our model correctly classifies some analogies and why in other cases it does not.
Analysis of a true positive example. We consider the stay 11 of patient 1249, who is a female, with 83yo, sufers from Measles keratitis, admitted twice before, and with 12 Radiology reports documenting this stay. The second stay 1 of the same patient 1249, but with 81yo, 2 sufers from Pancreat cyst/pseudocyst, only admitted once before, and with 5 Radiology reports and 7 Nursing/Other reports. The stay 2 belongs to patient 4695, who is a female, 21yo, with 3 Acute venous embolism and thrombosis of superficial veins of upper extremity, admitted 5 times before, and with 5 Radiology reports and 2 Nursing/Other reports. The stay 2 of the 4 same patient 4695, but with 22yo, sufers from Hypertensive chronic kidney disease, admitted 8 times before, and with 5 Physician reports and 7 Nursing reports documenting this stay.
This example has been correctly classified as valid for all the 9 valid forms. As we do not introduce any order constraint for this setting, we can notice that for some forms like : :: : and : :: : , 12 would take place before 11 in time. The model correctly classifies these analogy forms as valid.
Analysis of a false negative example. We consider the stays in this example to belong to the same patient 1109, who is a female. The stay 1 of patient 1109, with 25yo, sufers from 1 Malignant essential hypertension, admitted 7 times before, and with 1 Radiology report and 2 Nursing/Other reports documenting this stay. The second stay 1 of patient 1109, but with 2 26yo, with Hypertensive chronic kidney disease, admitted 4 times before, and with 8 Physician reports and 4 Nursing reports. The third stay 2 of patient 1109, but with 26yo, admitted once 3 again for Hypertensive chronic kidney disease, admitted 3 times before, and with 3 Physician reports and 8 Nursing reports. The fourth stay 2 of patient 1109, with 27yo, sufers from 4 Vascular complications of medical care, admitted 5 times before, and with 3 Physician reports and 9 Nursing reports.
As we mentioned above, for cases where 1 = 2, applying central permutation would also give us valid analogies. In this example, our model incorrectly classified the form of : :: : as invalid. As there were less analogies made of four stays that belong to the same patient included in our dataset, we noticed that our model is more likely to incorrectly classify these analogies, particularly for invalid forms.
Analysis of a true negative example. with 23yo, sufers from Hypertensive chronic kidney disease, admitted 4 times before, and with 4 Physician reports and 8 Nursing reports documenting this stay. The stay 1 belongs to the same patient 553, but with 24yo, admitted once again for Hypertensive chronic kidney disease, 9 times before, and with 8 Radiology reports and 4 Nursing/Other reports. 2 belongs to patient 2387, who is a male, with 52yo, with Unspecified disease of pericardium, admitted 7 times before, and with 2 Radiology reports and 2 Nursing/Other reports. The stay 2 belongs to the same patient 2387, but with 53yo, with Unspecified pleural efusion, admitted This analogy has been correctly classified as invalid for both invalid forms, : :: :
We consider the stay 11 of patient 553, who is a male, and : :: : .
Analysis of a false positive example.
1 We consider the stay 1 of patient 2771, who is a 2 4 male, with 71yo, sufers from Subendocardial infarction, admitted 16 times before, and with 9 Nursing/Other reports. The second stay 1 belongs to the same patient 2771, but with 70yo, sufers from Other pulmonary embolism and infarction, admitted 5 before, and with 1 Radiology report and 3 Nursing/Other reports. The stay 2 of patient 2222, who is a female, with 69yo, with Diverticulosis of colon with hemorrhage, admitted 9 times before, and with 2 Physician reports and 10 Nursing reports. The stay 2 belongs to the same patient 2222, but with 67yo, with Arterial embolism and thrombosis of lower extremity, admitted 5 times before, and with 3 3 Nursing/Other reports.
This analogy has been incorrectly classified as valid for the invalid form, : :: : . We noticed that when the category of the clinical notes is similar between two hospital stays and when our hospital stays do not include a lot of clinical notes, our model seems to struggle to distinguish between the two hospital stays. 1 and 2 have the same number of Nursing/Other reports. Thus these reports may not contain enough information to help our model diferentiate
In this paper we discussed an exploratory approach to investigate analogical inference in healthcare. We started by briefly surveying some related work that address diferent applications of analogical reasoning in diferent domains. We defined three analogical settings for diferent healthcare tasks, and discussed the motivation behind our settings. We also presented preliminary statistics of the sets of analogical proportions that we built from MIMIC-III. The main contribution of our work is the formalization of settings that are meaningful in healthcare, and that guide the process of building sets of analogies in healthcare. We discuss the pertinence of certain widely used postulates in this healthcare context. Lastly, we also illustrated the Identity setting on which we addressed a preliminary experiment on the analogy detection task. These ifrst results pave the way to conducting further experiments on the other two settings, and to an in depth analysis of the potential of coupling representation learning and analogical reasoning in healthcare.
We thank IARML reviewers for their constructive and positive feedback. Experiments presented in this paper were carried out using computational clusters equipped with GPU from the Grid’5000 testbed (see https://www.grid5000.fr).
The research work of the second named author is partially supported by TAILOR, a EU Horizon 2020 project (GA No 952215), and the Inria Project Lab “Hybrid Approaches for Interpretable AI” (HyAIAI).