The present invention relates to the field of medical diagnosis, and in particular to systems and methods for estimating the state of disease(s) in a patient based upon the outcomes of tests that are subject to error. The method may be scaled in parallel across a plurality of tests and a plurality of diseases to achieve the clinical impression of the patient.
Medical diagnosis is the process of translating clinical findings into judgments about the health of a person. Medical diagnosis is complex because the quality and relevance of clinical data must inform an evolving impression of a person's health within an adaptive strategy for generating new data. Medical diagnosis requires reasoning based on incomplete, uncertain, and changing information since medical testing is constrained by concerns about time, cost, and safety; since tests can produce erroneous outcomes; and since the patient condition and patient data can evolve. These, along with the explosion of information that is available from advances in biomedical research, laboratory medicine, imaging studies, and high-throughput “omic” methods—genomic, proteonomic, metabolomic—challenge our capacity to distill clinical information into an understanding of the patient, especially one that is transparent to clinicians, nurses, the patient, care givers, insurers, and others. This challenge is a barrier to two imperatives in modern medicine: applying population-based evidence to patient-specific diagnosis (so called evidence-based medicine) and implementing a comprehensive electronic medical record (EMR) system that treats the value of the information about a person.
Since the 1950's, investigators have sought a paradigm where the computer can function as a quantitative tool to support the cognitive processes of clinicians who are engaged in large-scale medical diagnosis—the simultaneous diagnosis of multiple diseases among the complete inventory of medical diseases. The paradigm should support an approach to medical diagnosis with 4 characteristics: Medical diagnosis is a dynamic real-time process; the clinician's disease impression of disease is probabilistic rather than deterministic; the disease impression is updated given new clinical findings; and medical tests are subject to error. Despite over five decades of research, investigators have been unable to define a paradigm that is both computationally tractable and implements the four characteristics of medical diagnosis. Early models of medical diagnosis supported deterministic reasoning. These included hypothetico-deductive models, decision trees, and heuristic pattern recognition models. Deterministic models were adapted to support probabilistic reasoning: Decision trees were extended using fuzzy set theory; heuristic models were extended using confirmation theory and recast as Bayesian networks. Among these, Bayesian networks seemed most promising, but solving for the probabilities of interest is not feasible for large systems, whether the solution is exact or approximate. Modified (or reduced) networks of the parent Bayesian network were sought. These were attempts to discover alternative probability-based models that treated the temporal, iterative, and adaptive nature of diagnosis and were also computationally tractable. Previous research has not addressed the forth characteristic of medical diagnosis—that medical tests are subject of error. Thus, there exists a need for a computationally tractable method that implement the four characteristics of medical diagnosis and which may be practically implemented in computer software and systems.
Developments in ontologies as building blocks for semantic webs offer new approaches for scientific analysis and for translational research in biomedicine. Here, embodiments of the present invention provide a system and method for medical diagnosis that implement the four characteristics of medical diagnosis, including the problem of test error and its effect on the reliability of diagnoses. The logic of large-scale medical diagnosis is shown to be a Diagnostic Semantic Web (DSW) that is assembled from the semantic triples (ontologies) of different disease/test combinations. The DSW is a quantitative model that may be implemented in software and distributed across computer networks and systems to clinicians engaged in medical diagnosis. A clinician's estimate of the state of a disease in a person (called the disease impression) is a probability distribution that evolves in response to test outcomes. When tests are conditionally independent, the DSW is equivalent to a set of hidden Markov models, where each hidden Markov model governs the evolution of its disease-specific disease impression. In this way, embodiments of the present invention treat medical diagnosis as a parallel stochastic filtering problem. Medical diagnosis becomes computationally tractable since it is trivially parallelizable. When tests are not conditionally independent, the approach provides satisfactory results but is computationally more complex.
The principles of the present invention result in quantitative methods for two essential tasks in medical diagnosis: inference and prediction. The inference method quantifies in real time the diagnostic value of test outcomes as they arrive. The prediction method provides the expected diagnostic benefit of a putative test given the current state of the diagnostic evaluation. As a layer of logic within a next generation EMR system, these methods support an easily understandable and self-documenting account of the strategy and reasoning that led to the current view of a patient's state of health, including diagnoses and confidence in the diagnoses. The clinical impression—the set of disease impressions for all diseases in the medical lexicon—provides a unified, quantitative, and transferable best estimate of a patient's state of health.
One embodiment of a method of the present invention comprises inferring the impression of the state of a disease in a patient, for a disease with a set of possible disease conditions, comprising identifying a current disease impression of the patient; obtaining the outcome of a test performed with respect to the disease in the patient; and updating the current disease impression to a new disease impression based upon the conditional probabilities of obtaining the test outcome given each of said disease conditions. A test has a set of possible outcomes, and therefore a likelihood matrix can be comprising the conditional probability distribution of obtaining each test outcome given each of the disease conditions. These conditional probabilities are used in updating the disease impression. The method can be extended to a plurality of tests for a plurality of diseases, in which case a likelihood matrix is provided with the conditional probability distribution of each test outcome given each disease condition for each disease. The disease impression preferably updated from test results until it is within a predetermined threshold of confidence with respect to one of the disease conditions for the disease of interest. If repeated with respect to a plurality of diseases, the clinical impression of the patient is obtained.
One embodiment of a system of the present invention comprises a database stored in a computer readable memory comprising a plurality of likelihood matrices for a plurality of diseases and a plurality of tests, each such disease comprising a set of disease conditions and each such test comprising a set of possible test outcomes, so that each likelihood matrix comprises, for one of the diseases and one of the tests, the conditional probability distribution of each test outcome given each disease condition. The system also includes a processor in communication with the database, the processor having a computer readable memory storing instructions executable by said processor that identify a current disease impression of a patient; obtain the outcome of a test performed with respect to the disease in the patient; retrieve from the database the conditional probabilities of obtaining the test outcome given each of the disease conditions; and update the current disease impression to a new disease impression based upon the conditional probabilities. The database may contain likelihood matrices for a plurality of diseases and a plurality of tests, in which case the system can update the clinical impression of the patient in response to one or more test outcomes.
The present invention will be explained, by way of example only, with reference to certain embodiments and the attached Figures, in which:
a) is a diagram of the process of medical diagnosis as a diagnostic web, which is a bipartite semantic web.
b) illustrates an embodiment of one aspect of a method of the present invention, showing that each disease impression pj in the diagnostic web updates as a hidden Markov model;
Allopathic medicine flows from a fundamental axiom: A disease causes (a set of) observable clinical features,
disease→{features}. (1)
This statement roots medicine in empirical science. The task of biomedical research is to characterize the details of the statement. An important task in electronic medical record systems is to translate natural language expressions of diseases and observable clinical features into expressions that involve standardized medical terminology such as ICD-9, ICD-10, SNOMED-CT. The task of medical diagnosis is to evaluate Eq. 1 in the reverse direction—to infer the state of disease in a person from tests that measure the features of a disease. When causality is not absolute but suggestive, Eq. 1 is understood as a probabilistic expression. Methods in probabilistic inference invariably make use of Bayes theorem, but the methods differ in how Bayes theorem is applied.
Large-scale medical diagnosis is concerned with the simultaneous diagnosis of multiple diseases. To be able to quantitatively support medical diagnosis, we must first define elementary data types. Here, the state of a particular disease in a person is described by the state variable X. The state variable X is in one of n≧2, preferably mutually exclusive and exhaustive, disease conditions ΩX={x0, . . . , xn-1}={xi}. The disease conditions are dictated by current standards in medical practice. They are ordered in ascending severity beginning with the null disease condition x0. Examples:
1. Infection: not infected (x0), infected (x1).
2. Hypertension: normotensive (x0), mild (x1), moderate (x2), severe (x3).
Example 1 illustrates the classical yes-no (binary) description of disease, where a person either suffers from the disease (x1) or does not suffer from the disease (x0). Including the null disease condition x0 in the set of disease conditions Ωx supports strong conclusions. The conclusion “infection has been ruled-out” requires appeal to the null disease condition x0. This conclusion is a stronger than the conclusion “infection has not been ruled-in,” which requires appeal only to the non-null disease condition x1. Example 2 illustrates diseases that are more finely resolved on a pathophysiologic spectrum. Here, disease is n-ary, where ΩX has n≧2 disease conditions. The number of disease conditions n is subject to revision from improved understanding of the disease, improved tests, or when improved treatment may result. Hypertension is a good example. Its four disease conditions grew out of two—normotensive, and hypertensive.
People get sick, get better, etc. at times that are difficult to predict and for reasons that are not always clear. Accordingly, the state variable for a disease X(t) is a time-dependent random variable, also called a stochastic variable. Thus, the time-evolution of disease in a person is viewed as a random jump process, where a person spends some time in a disease condition then jumps to another disease condition, and so on. Unlike many prior art attempts at processes for quantitative medical diagnosis, the present invention does not require a model the dynamics of the disease state X(t). Instead, embodiments of the present invention provide an estimate of X(t) that depends upon data gathered from the patient through testing. The estimate of disease in a person is called the disease impression.
Here, a medical test is broadly defined as any question, assay, or study that can clarify the condition of a clinical feature (Eq. 1). Preferably, disease conditions of a particular disease are defined to be mutually exclusive and exhaustive. In contrast with other prior art Bayesian approaches, embodiments of the present invention do not require that diseases themselves be mutually exclusive. In fact, the present invention accommodates a reality faced in medical diagnosis that two or more diseases can be completely redundant.
For each disease, we define a discrete probability distribution p=(p0, . . . , pn-1), also called a probability mass function or probability density, as the n-tuple of probability elements pi=p(i)=Pr[X=xi], ∀xiεΩX. The element pi is the probability that the state variable X is equal to the disease condition xi. As shown in
p,ej=ejipi=∥p∥∥ej∥cos φj. (2)
Furthermore, pi=∥p∥cos φi/∥ei∥=∥p∥ cos φi, where ∥p∥=1/Σ{j} cos φj. The length of the disease impression p is a function of all angles φ0, . . . , φn-1, which makes each probability element pj—the projection of p onto ej—a function of all angles φ0,K, φn-1. Diagnostic progress towards axis ej is expressed more simply and directly in terms of the angle φj rather than the probability element pj. Using the coordinate transform for φipi,
the disease impression p can be equivalently represented as an n-tuple of probability elements (p0, . . . pn-1) or as an n-tuple of angles (φ0, . . . , φn-1). The angles φi range from 0 to π/2. For convenience, we define normalized angles
Consider a test whose output is reported as an integer α that assumes some value {circumflex over (α)} among m possible outcomes, {circumflex over (α)}εΩα={0,1, . . . , m−1}. For some disease, we will discuss the test where the number of possible test outcomes m of the test equals the number of disease conditions n of the disease. See the Appendix for how to treat the case m≠n. A test Tk can inform the disease impressions of multiple diseases D0, D1, . . . . Focus on the test Tk with respect to disease Dj, and denote the disease-referenced test Tk←j. An (n×n)-test has joint probability distribution T given as an n×n matrix with elements Tiα=Pr(α={circumflex over (α)},X=xi)=p(α,i). The element Tiα is the statistical correlation between test outcome {circumflex over (α)} and disease condition i. To avoid confusion, we consistently index the outcomes of a test by the Greek letter α and index the disease conditions of a test by the Latin letter i. T is normalized, |T|=Σ{α,i}Tiα=1. Off-diagonal elements Tiα, i≠α that are greater than zero quantify the statistical error, also called the internal noise, of the test. The internal noise of a test is important since it introduces random error into the disease impression p. This makes p a random variable; specifically p is a vector-valued random variable. Note that the state of disease X(t) and the impression p of the state of disease X(t) are different quantities. Both are random variables: X(t) is random because the evolution of disease in a person is a random process, but p is random because it depends on tests that produce error randomly. It is not possible to say when a test will produce its next erroneous outcome. Consequently, internal noise can be described only statistically. A binary test, or (2×2)-test, produces either a negative outcome (α=0) or a positive outcome (α=1). Binary tests are encountered so often that the elements Tiα of the joint probability distribution T have common names: T00 (true negative), T01 (false positive), T10 (false negative), T11 (true positive).
The conditional probability distribution of the disease-referenced test Tk←j is the likelihood matrix L with elements Liα=Pr(α={circumflex over (α)}|X=xi)=p(α|i). The element p(α|i) is the probability of obtaining test outcome {circumflex over (α)} given that a person is in disease condition xi. The conditional probability distribution L is obtained by renormalizing the joint probability distribution T,
This equation follows from the definition of conditional probability p(α|i)=p(α,i)/p(i), where p(i) is the marginal probability p(i)=Σ{α}p(α,i). The denominator in Eq. 4,
which is the sum over all elements {α} in row i of T, is the prevalence of disease condition xi in the patient population. Eq. 4 guarantees that each row i of the likelihood matrix L is unit normalized, Σ{α}Liα=1. For a (2×2)-test, the diagonal elements of L have common names: L11 (sensitivity) and L00 (specificity).
An ontology is an expression that relates two elements and conveys the meaning of the relationship. The semantic triple, the 3-tuple (subject, object, influence), is the ontology for directionally associating a subject with an object. Having defined the disease impression p of disease Dj, the output α of the disease-referenced test Tj←k, and the likelihood matrix L of the disease-referenced test Tj←k, the fundamental axiom of allopathic medicine (Eq. 1) may now be expressed quantitatively as a semantic triple (p, α, L). We call this semantic triple a diagnostic triple. The variables of the diagnostic triple and the element that the variable quantifies—disease (box) and its causal influence (arrow) on a test (circle)—are represented as an elementary graph,
Each variable in the diagnostic triple is a different type. The disease impression p is a probability distribution; the test output α is a random variable; the likelihood L is a matrix.
Embodiments of the present invention apply the diagnostic triple to the problem of large-scale diagnosis involving multiple diseases Dj and multiple disease-referenced tests Tk←j. Let pj=(p0j, . . . , pn-1j) be the disease impression of disease Dj; let Ljk be the likelihood matrix of test Tk←j; and let αk, be the output of test Tk←j. The disease triples for all desired disease/test combinations {(pj, αk, Ljk)} are assembled as a semantic web (
One might be tempted to define the overall clinical impression of a person's state of health as the set of the disease impressions {pj} for all diseases in a standardized medical lexicon. However, some diseases—derived diseases—are defined as logical operations of elementary diseases. For example, infectious endocarditis D3 involves both persistent bacteremia D1 AND cardiac valvular pathology D2 (D3=D1D2). And for example, a person has chronic obstructive pulmonary disease D3 if s/he has either emphysema D1
p
1
p2≡maxφ
The disjunction {hacek over (p)}=p1p2 is defined,
p
1
p2≡minφ
In other words, the conjunction {circumflex over (p)} is assigned to whichever disease impression p1, p2 has the largest angle φn-1. The disjunction {hacek over (p)} is assigned to whichever disease impression p1, p2 has the smallest angle φn-1. The angle φn-1 is the angle for the most severe disease condition. The clinical impression {pj,} is defined as the set of all elementary diseases and all logically derived diseases. During diagnosis, the clinical impression is updated by independently updating the elementary disease impressions pj then processing the pj to obtain the disease impressions of all derived diseases. This representation of disease is consistent with the cognitive model of medical diagnosis, where elementary diseases are called disease facets (
The DSW (
as the outcomes of tests become available. As demonstrated below, when tests are conditionally independent, the disease impression for each disease not only updates as new test outcomes arrive (Eq. 7), but it updates recursively.
Assume tests T0, T1, . . . , Tτ do not interact so that the outputs α0, α1, . . . , ατ, respectively, of the tests are conditionally independent,
p(ατ, . . . ,α1,α0|i)=p(ατ|i) . . . p(α1|i)p(α0|i). (8)
The disease impression of each disease in the diagnostic web (
Eq. 8 demands that tests be conditionally independent. Whether test findings are conditionally independent is a question about the knowledge base (see discussion, Eq. 13). In other words, Eq. 8 is valid as long as each test provides a measurement of a disease that is blind to the outcomes of previous tests. Thus, the ordered list of tests T0, T1 . . . may include a test that has been repeated (e.g., blood cultures in triplicate).
Having proven the foregoing, disease impression becomes a piecewise continuous time-dependent function p(t)=p(t0),p(t1), . . . , where p(tτ)=p(i|α(tτ−1), . . . , α(t0)) is the disease impression during the time interval [tτ,tτ+1). The time interval Δti=ti+1−ti is not fixed. In our revised notation, α(tτ) is the outcome â of a noisy measurement δαα(t
In the final expression, the numerator is the simple product of element Liα(t
Eq. 9a is evolution equation for the disease impression. This and other properties become clearer when Eq. 9a is written in operator form:
p(tτ+1)=W(tτ)p(tτ) (9b)
where Wi(tτ)=Liα(t
according to the hidden Markov model shown in
The evolution of disease impression is illustrated graphically in
Embodiments of the present invention, therefore, allow the simultaneous diagnosis of multiple diseases—large-scale medical diagnosis—via solving a parallel stochastic filtering problem, where the disease impressions of all elementary diseases are independently updated as test outcomes α(ts) arrive. Eq. 9 provides the updating, but the process must begin with some initial condition p(t0). One may assume complete ignorance and adopt an equivocal disease impression—the uniform distribution pi(t0)=1/n. A better alternative is to use the prevalence of disease in the population demographic, that is the age-classified, gender-classified, and if appropriate geography- and racial/ethnic-classified, population from which the patient comes, pi(t0)=ri, where ri is given by Eq. 5.
In addition to estimating the state of disease from the outcomes of tests, it is useful to predict how a test could change the clinical impression. Prediction is important when designing a diagnostic strategy since the predicted change in the clinical impression is the anticipated diagnostic benefit in a cost/benefit analysis of test options. Bearing in mind that tests are subject to random error, the desired quantity is the most probable effect that a test will have on the clinical impression. The following example is of a binary disease, but the method illustrated is applicable to diseases of any dimension.
Begin by assuming that a person is in some disease condition X=xj, or, equivalently, p*=ej. If the goal is to rule-in the disease (we think that X=x1) then p*=(0,1). If the goal is to rule-out the disease (we think that X=x0) then p*=(1,0). For a person who is known or assumed to be in disease condition p*, the probability of obtaining result α of some test with likelihood matrix L is the inner product of L and p*, ρα=L,p*=Lαip*i. The unit-normalized rows of Liα guarantee that ρα is a probability distribution, so ρα can be represented as a point on the manifold M (
The term in parentheses is a vector over α, which, when left-multiplied by Liα produces a vector over i. Eq. 10 provides the expected projected disease impression after performing a test T(tτ) for a person in disease condition p*. To predict behavior beyond the average, one simulates the measurement δα{circumflex over (α)}(t) by Monte Carlo sampling from ρα then applies the measurement to Eq. 9. This approach provides higher moments of the distribution p(p(tτ+1)) of the projected disease impression. Since Eq. 10 depends on pi(tτ) nonlinearly, exact prediction with two or more tests requires calculation of the full distribution p(p(t)). But, making the approximation pi(tτ)≈pi(tτ) on the right hand side of Eq. 10, we obtain the expression
to recursively to calculate, approximately, the expected disease impression after a succession of tests. In terms of the diagnostic space, the expected projected disease impression p(tτ) is a point on the manifold M, while the full distribution p(p(tτ)) of projected disease impression is a probability density on M.
We conclude methods development by answering two important questions. First, we ask, “What is the average predicted long-term (stationary) disease estimate ps=p(t∞) after repeatedly testing a person whose disease state is the disease condition p*?” For a person in the time-independent disease condition p*, applying Eq. 10 an infinite number of times causes the average disease estimate to either not change, ps=p(0) (trivial case, where tests are non-informative, Liα=1/n), or to converge on the disease-distribution, ps=p*.
Second, we ask, “Does the disease estimate p(tτ) depend on the order that test outcomes α(t0),α(t1), . . . , α(tτ−1) are applied to propagate p(t)?” Eq. 9 satisfies the commutative property, p(i|α1,α2)=p(i|α2,α1). By extension, the inferred disease impression p(tτ) depends on the accumulated test outcomes {α(t0),α(t1), . . . , α(tτ−1)} but not their sequence. Therefore, when tests are conditionally independent (Eq. 8), the final disease impression is independent of the diagnostic path. In other words, the disease impression depends only on the starting estimate and the accumulated evidence.
The method of prediction was examined with an example of the diagnosis of infection (example 1 above). The example involved a patient who was infected at times t0, t1, t2 (p*=e1) then recovered between times t2 and t3 (p*=e0) and remained uninfected. This example, where the patient is initially infected then recovers, was chosen to illustrate how an embodiment of the method of the present invention perform temporal reasoning—reasoning as the patient condition itself changes, also called patient dynamics.
When any angle φj becomes smaller than its associated threshold angle φj† (
Diagnosis: xj if φj<φj†
with confidence pj. In the example shown in
Some think of medical diagnosis as an attempt to reduce uncertainty in the mind of the clinician, where reduced uncertainty is quantified as a loss of Shannon entropy or, equivalently, the gain of Shannon information. The example in
The measure of progress towards the diagnosis of disease condition xj should quantify progress of the disease impression towards axis ej. Furthermore, diagnostic progress should not be influenced by changes in the length of the disease impression p that are required to keep the disease impression unit-normalized, |p|=1. Two measures for quantifying diagnostic progress are appropriate: (i) the angular change in the disease impression Δφj(tτ)=φj(tτ+1)−φj(t96) due to the test outcome α(tτ) and (ii) the rotational strain
Ú
j(tτ)=−Δφj(tτ)/φj(tτ) (12)
due to the test outcome α(tτ). Rotational strain is dimensionless and bounded, Újε[0,1], with Új=0 being no progress and Új=1 being maximum progress. The predicted utility of a test can be measured using the average predicted angular strain Új(tτ), which is based on the average projected disease impression (Eq. 10 or 11).
A practical measure of predicted test utility is the expected number of times NNDi (number needed to diagnose) that a test must be repeated to diagnose disease condition xi given the current disease impression p(tτ). A test with low NNDi is more powerful for diagnosing disease condition xi than a test with a high NNDi, NNDi depends on three factors: (i) the likelihood matrix Liα of the test, (ii) the threshold for diagnosis φi†, and (iii) the current disease impression p(tτ). NNDi is not a constant; its dependence on p(tτ) makes NND, a time-dependent function NNDi(tτ). For the example in
A rule in medical diagnosis is that high sensitivity tests should be used to rule-in disease (diagnose disease condition x1) while high specificity tests should be used to rule-out disease (diagnose disease condition x0). The example shown in
As shown above, large-scale medical diagnosis—the simultaneous diagnosis of all diseases in the standardized medical lexicon—is modeled as a Diagnostic Semantic Web (DSW). The DSW is a special kind of bipartite semantic web with a layer of diseases of fixed size and a layer of tests that grows as tests are performed (
Each disease preferably constitutes an exhaustive set of n≦2 non-overlapping disease conditions that are arranged in order of increasing severity. The disease-free condition is preferably included as the first disease condition. Thus, diseases with any number of disease conditions are treated. A test is defined broadly as any time-resolved source of clinical information. This includes information from the history (e.g., family history, social history, review of systems) and the physical (e.g. physical exam, preliminary laboratory results, imaging studies). The disease impression is represented as a vector that is confined to a manifold within a Hilbert space (
Prior art approaches to quantifying medical diagnosis have been unable to provide a solution that is computationally tractable and implements the three characteristics of medical diagnosis. Medical diagnosis is a dynamic real-time process; the clinician's disease impression of disease is probabilistic; and the disease impression is updated given new clinical findings. Early models of medical diagnosis supported deterministic reasoning. Deterministic models included hypothetico-deductive models, decision trees, and heuristic pattern recognition models. Deterministic models were adapted to support probabilistic reasoning. Heuristic models were extended using confirmation theory and as Bayesian networks, and decision trees were extended using fuzzy set theory. Among these, Bayesian networks seemed most promising, but solving for the probabilities of interest is not feasible for large systems, whether the solution is exact or approximate. Modified (or reduced) networks of the parent Bayesian network were sought. The latter were, essentially, attempts to discover alternative probability-based models for computer-aided medical diagnosis that were computationally tractable and also treated the temporal, iterative, and adaptive nature of diagnosis.
Historically, large-scale medical diagnosis has been viewed as a pattern recognition problem. Large-scale medical diagnosis has been modeled (treated computationally) as a heuristic Bayesian problem, as a Bayesian network, using heuristic Bayesian sequential decision theory, and, most recently, using Dynamic Bayesian network (DBN)-based sequential decision theory.
Sequential diagnosis—Many approaches in computer-aided diagnosis analyze clinical information retrospectively. An alternative strategy, which follows the normal clinical workflow, is to perform a sequential diagnosis, considering new test results as they arrive. Gorry and Barnett recognized the potential to apply Bayes rule recursively to propagate belief. DBN address the temporal nature of diagnostic reasoning by replicating a stationary Bayesian network, also called a belief network, and adding temporal transitions between the stationary Bayesian networks. DBN, however, are not practical. The amount of computing time that is needed to exactly calculate the marginal probability density for each disease limits the size of Bayesian networks in medical diagnosis. Approximate methods reduce calculation times, but approximation methods are limited to Bayesian networks that treat binary diseases.
Here, by treating medical diagnosis as a filtering problem, the number of disease conditions that can be treated is practically unlimited. The disease impression of each disease is updated independently, making medical diagnosis trivially parallelizable. Others have addressed the limited time-scope of a test result (e.g., a person's age is accurate for only one year) by recasting the fixed conditional probabilities in the knowledge base as time-dependent quantities. When medical diagnosis is viewed as a filtering problem, such manipulation is unnecessary. Any change in the result of a test is viewed as a new outcome of the test, and the disease impression is updated using either Eq. 9 or, in certain cases, using Eq. S5 (see below). In this way, the limited time-scope of a test output is treated automatically, and repeated tests are treated seamlessly.
Also, the time-evolution of a dynamic network, be it a dynamic Bayesian network, Markov network, Markov random field, artificial neural network, or semantic web, is governed by a discrete-time (Eq. 9b) or continuous-time master equation. The properties of the master equation depend on the properties of the propagation operator W. The propagation operator for the DSW has an attractive property: it depends only on the knowledge base, which is stationary, and the current disease impression p(tτ). Consequently, the time-evolution of the disease impression is a non-linear (in p) Markov chain. W is a time-dependent operator since it depends on the current disease impression.
The non-linear dependence on the disease impression can produce counter-intuitive results. A rule in medical diagnosis is that high sensitivity tests should be used to rule-in disease while high specificity tests should be used to rule-out disease. Due to the non-linear dependence on the disease impression, we showed above that this rule does not hold universally. Eqs. 10 and 11 provide the average predicted the utility of a test to further the diagnosis of some disease. When crafting a diagnostic strategy, the predicted utility of a test is the expected benefit in a cost-benefit analysis of test options. It may be helpful to re-label the cost-benefit analysis as a cost-benefit-quality analysis, where cost means monetary cost and other factors like the possibility of a missed diagnosis are categorized under benefit.
Structural differences in graphical models—differences between the present invention and the prior art create important structural differences between the DSW and other graphical models of medical diagnosis, which include the Markov network, the Markov random field, the artificial neural network, and the Bayesian network. Semantic webs, Markov random fields, and Markov networks have numerical expressions associated with the edges of their graph. In a Markov network, the expression is a scalar that governs the probability that the system will transition along the edge. In the Markov random field, a potential energy function is defined for sets of nodes. In the DSW, the edge-associated expression is the matrix L′, that quantifies the statistical correlation between the outcomes of a test and conditions of a disease. Bayesian networks and artificial neural networks have no parameters associated with their edges. In Bayesian networks, conditional probabilities are absorbed into the nodes. In artificial neural networks, non-linear activation functions govern the state of nodes.
For convenience, we first list features that distinguish certain embodiments of the present invention from the prior art; then each is discussed. (i) Tests are assumed to be error prone. (ii) Diseases are n-ary: State of a disease is one of n≦2 mutually exclusive conditions, ordered in increasing severity. The null disease condition (n=0) is included. (iii) Diseases need not be mutually exclusive; they may even be redundant. (iv) Knowledge base relies on coarse-graining, rather than causal independence. (v) Probability distributions are defined locally for a particular disease. The estimate of the state of each disease is the probability distribution. (vi) Equitable treatment of positive and negative findings.
Tests are error-prone—Prior art methods typically assume that no errors are made in performing tests and do not make allowance for possible error. As a result, inferred (posterior) probabilities are regarded as subjective measures of belief. Conclusions are drawn from the inferred probabilities though Bayesian hypothesis testing or some kind of decision theoretic optimization. Here, the present invention utilizes the traditional frequencist interpretation of probability and allows for tests to be error prone.
Diseases are n-ary—-Previous Bayesian treatments required diseases to be binary. Positive findings and negative findings in these systems require unique nodes. There is a big difference between the two statements (i) aortic dissection has not been diagnosed and (ii) aortic dissection has been ruled-out.
Diseases need not be mutually exclusive—Other Bayesian approaches require diseases to be mutually exclusive; i.e., all diseases must be defined so that there is no overlap among them. This is an unrealistic assumption. Consider: How does one define as mutually exclusive diseases disseminated intravascular coagulation, HELLP syndrome, hypertension, pre-eclampsia, nephritic syndrome, thrombocytopenia? A woman with HELLP syndrome has all the above. Solving the joint probability distribution is NP-hard. The probability of the patient being disease-free with respect to some disease is a complicated function of the global distribution function. Here, diseases need not be mutually exclusive. We showed above how to the present invention is capable of treating diseases that are defined as logical operations of more elementary diseases.
Local vs. global probability distribution—Previous approaches regard probability as a global quantity—a (joint) probability distribution is defined over the positive disease conditions of all diseases. Treating probability as a global quantity limits how diseases must be defined, makes the problem computationally intractable, and creates conceptual problems that produce wrong conclusions.
Tests are Error-prone—The reader may be left with the impression that the diagnostic uncertainty is fundamentally due to incomplete information about a patient. Here, diagnostic uncertainty is fundamentally due to uncertainty stemming from the fact that tests are error-prone. A property of random error is that you never know when errors will appear. It is possible that a test with a specificity of 99% could produce three false positives in a row (on the same patient), which lead to an incorrect diagnosis and incorrect treatment that damaged the patient. These cases will occur because tests are fundamentally error-prone. There is nothing that can be done. The present invention accepts this fact of clinical life.
Equitable treatment of positive and negative findings—Previous models treated diseases as positive quantities—as in, you have a disease as a hypothesis. To claim that one did not have a disease (i.e. to rule-out a disease) was treated as the compliment of the hypothesis. This is a problem for two reasons. First, taking the compliment is non trivial. Second, one can only treat binary diseases; n-ary diseases are not accessible.
Local vs. global—Here, we regard probability as a local quantity—each disease has its own probability distribution. The summary impression of a patient, the clinical impression, is the set of disease impressions for each disease in a standard medical lexicon. Diseases need not be mutually exclusive. In the extreme case of diseases that are completely redundant, one simple obtains identical disease impressions for the redundantly defined diseases, as it should be.
One limiting factor in computer-aided medical diagnosis is the knowledge base for diagnosis, which consists of the statistical correlations (likelihood coefficients) Liα=p(α|i) for each disease-test pair. In some cases, the Liα are available in the medical literature. In other cases, the Liα can be obtained from the analysis of historical data. It is noteworthy that the likelihood coefficients in the literature suffer two limitations. First, the Liα are coarse-grained, also called marginalized, versions of the more finely resolved joint conditional probabilities p(α|i,j) of a test T with respect to two diseases Di, Dj. The marginal probability density p(α|i) for a test T and disease Di is obtained by averaging over all disease conditions of the co-morbid disease Dj,
p(α|i)=Σp(α|j,i)p(j|i). (13)
Eq. 13 is easily generalized for multiple co-morbid diseases {Dj}≠Di. If the joint conditional probabilities p(α|i,j) are available then the marginal likelihoods p(α|i) can be calculated during diagnosis from the joint conditional density p(α|i,j) and the current disease impressions p(i), p(j) of diseases Di, Dj using
Eq. 14 is derived in the Appendix. A second limitation of the marginal likelihoods in the literature is that they may not reflect the conditions for a particular location/region. Despite their limitations, marginal likelihoods p(α|i) comprise the population-based evidence in evidence-based medical diagnosis. These coefficients provide a starting knowledge base for conducting quantitative medical diagnosis. Expert diagnosticians will distinguish themselves by supplying joint conditional probabilities like p(α|i,j) and p(α2|α1,i) that are derived from experience. Expert diagnosticians will also use likelihood coefficients that are appropriate for the location, time, and circumstance. One embodiment of the system of the present invention allows a clinician to adjust elements of the likelihood matrices, and also supply joint conditional probabilities, based on experience.
By employing a coarse-grained knowledge base, we avoid the noisy-OR assumption and its limitations. In the noisy-OR assumption, causal independence is assumed between diseases on findings.
The major simplifying assumption in Bayesian approaches in medical diagnosis, including in the discussion above, is that tests T1, T2, . . . , Tτ are conditionally independent (Eq. 8). The conditional independence assumption is a zero-order approximation that can be replaced with higher-order approximations where appropriate. Through an example, we clarify the meaning of the conditional independence of tests. Then we consider what if tests are not conditionally independent. We show how to treat tests that are pair-wise conditionally dependent (so-called first-order approximation).
Consider the cause of elevated body temperature—the outcome of the test T2. One can claim that elevated body temperature is more likely to be caused by infection (disease Di) than, say, hyperthyroidism (disease D2) because a cardiac echocardiogram (test Ti) showed a valvular vegetation, which suggests that the patient has infective endocarditis. Here, the clinician reasons correctly that the interpretation of fever (test T2) should depend on the outcome of the echocardiogram (previous test T1). But what does “interpret test T2” mean? The interpretation of test T2 means drawing an inference about a patient's disease condition based on the outcome of test T2 and, perhaps, also on the outcome of a previous test T1−p(i|α2,α1). While true, this statement about dependencies when inferring the state of disease from two tests is entirely separate from statements about whether two tests independently measure the state of disease in a person, namely that “tests T1 and T2 are conditionally independent” p(α2,α1|i)p(α1|i). Another way of stating that test T2 is conditionally independent from test T1 (Eq. 8) is to say that the outcome of test T2 depends on the disease condition of the patient but does not depend on the outcome of some other test T1, p(α2|α1,i)=p(α2|i)}. See the Appendix for proof that this equation (Eq. S1) is equivalent to Eq. 8. A counter example: If a pathologist based his reading of a biopsy on some other study (say an imaging study) instead of the sample at hand, this would be fraudulent result and would flagrantly violate of Eq, S1 (and hence Eq. 8). Thus, the conditional independence assumption can be regarded as an assumption of honesty—tests can't peek at each other; they offer independent “readings” of the patient.
The inference algorithm (Eq. 9) and prediction algorithm (Eq. 10) can be modified in a straightforward manner to accommodate cases where Eq. 8 or, equivalently, Eq. S1 does not hold. When Eq. S1 is not valid, one uses a propagation operator W that depends on a previous test, p(α2|α1,i), instead of an operator that does not depend on other tests, p(α2|i). Now, the disease impression evolves according to a lesser update rule,
that is derived in the appendix (Eq. A5). This equation deals explicitly with the pair-wise conditional dependence of two tests.
In some cases, the temporal sequence of observations can provide strong clues for a diagnosis. For example, abdominal pain T1 followed by gastrointestinal distress T2 suggests appendicitis, while gastrointestinal distress followed by pain suggests gastroenteritis, p(α2|i,α1)≠P(α1|i,α2). Medical diagnosis remains Markovian under the first-order approximation (when pair-wise conditional dependencies are admitted), but the commutative property is lost. Whether it is feasible to populate a knowledge base of conditional probabilities p(α2|i,α1) for pair-wise conditionally dependent tests is a separate issue.
In certain extreme cases, two tests are completely conditionally dependent, meaning that the second test is redundant of the first. A good example would be repeatedly asking (testing) a person's age or gender. For redundant tests, which tend to appear in the patient history rather than the physical exam, collecting data more than once is useless. Here,
p(αs, . . . , α1,α0|i)=p(α0|i),
where α0, α1, . . . , αs are the outputs of a test that has been repeated s times. For redundant tests, we define a switchable likelihood matrix Liα (t)=Liα+F(t)(1/n−Liα) where F(t) is a Boolean flag that is set, 0→1, once the outcome of this test has been used to update the disease impression. When F(t) is 1, the outcome of a repeated test is non-informative since a test with all likelihood coefficients set equal to 1/n is non-informative. This is verified by direct substitution into Eq. 9.
It will be understood by those skilled in the art that the foregoing may implemented in a computer-based medical information and record system. Such a system may consist of a single computer or comprise multiple computers in communication over a network, including a local area network, a wide area network, the Internet, or any combination of the foregoing.
As shown in
The tasks and processes described herein may be distributed across computer systems as most advantageously suits a particular implementation, as would be understood by those skilled in the art. For example, in one embodiment, the processor programmed to perform the analysis may reside in the same system as the database, and input is received from and output is provided to the user via a thin client over a network. In another embodiment, it may be preferable to distribute the computational processes of updating disease and clinical impression as described herein to a local computer system, with the likelihood matrices residing in a database on a separate server accessible to each such system. Finally, it may be advantageous to have a standalone system, for example in a notebook or tablet computer, that contains the processor, the database, and all necessary instructions to receive data and perform the processes described herein. The computer systems may be general purpose programmable computers or they may contain hardware specially designed to perform the probabilistic methods described herein in parallel on a large scale to achieve very rapid simultaneous estimation of multiple disease conditions.
In one embodiment, the processor 84 is in communication with a computer memory having instructions to execute the prediction process herein. Prior to the clinician's performing a test or otherwise receiving a test outcome, the processor analyzes the likely effect of the available tests on a current disease impression of interest of the patient, in accordance with the prediction process. The processor then identifies to the clinician at least one test that is predicted to have diagnostic value with respect to the disease impression, and in a preferred embodiment, a plurality of tests having diagnostic value with respect to the disease impression with an indication of the predicted diagnostic progress achieved by each test. In yet another embodiment, the processor performs this process with respect to the clinical impression of the patient, that is, the collection of all disease impressions of interest for the patient, and provides an array of tests with predicted diagnostic value and the predicted diagnostic progress for each such test with respect to each disease impression for which the test has meaningful diagnostic value.
As a layer of medical logic within an electronic medical record system, the methods of the present invention support both computer-aided medical diagnosis and evidence-based medicine. A comprehensive discussion of how the methods of the present invention can address the escalating costs of healthcare is beyond the scope of this application. Briefly, the methods of the present invention allow the value of clinical information to be inferred and predicted in real time. Reduced cost may be possible when these methods operate as a supporting layer of logic within a electronic medical record system. The ability to calculate the expected change in the clinical impression from a test permits a real time cost-benefit analysis of test options. The prevalence of such analyses will only increase as we enter an era of “accountable healthcare” with medical reimbursements transitioning from pay for performance to bundled payments and other novel payment schemes.
Although the present invention has been described and shown with reference to certain preferred embodiments thereof, other embodiments are possible. The foregoing description is therefore considered in all respects to be illustrative and not restrictive. Therefore, the present invention should be defined with reference to the claims and their equivalents, and the spirit and scope of the claims should not be limited to the description of the preferred embodiments contained herein.
This application claims priority to and the benefit of the provisional patent application entitled Optimal Estimation in Medical Diagnosis, application Ser. No. 61/260,641, filed Nov. 12, 2009.
Number | Date | Country | |
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61260641 | Nov 2009 | US |