CONTENTS:
Complex medical decisions require careful consideration of each potential decision and each decision element. This consideration may proceed by a pairwise comparison of all input elements or all potential output decisions in a matrix mechanism of cognition. Matrix cognition provides a mathematical mechanism to yield the principal eigenvalue and its containing eigenvector, which in turn provides a numerical weighting of each element for each potential decision. Consultants can be similarly weighted, based on the measured effectiveness of their previous decisions.
Complex medical decisions are central in each of the phases of clinical care (1), and are usually based on decision elements or findings derived from a single patient by the clinical team (2). The discovery of decision elements or findings particular to a given patient is a major task for the clinical team, and is a necessary prelude to initiating medical action for the patient (3). The triad of discovery, decision and action constitutes a core for the analysis of each phase of clinical care (2), and can be greatly facilitated by the mathematical techniques of matrix cognition (4).
Recent studies (5) have compared clinicians' reasoning with a decision analysis of the same problem. In contrast to decision analysis, the physicians did not generate global outlines of their decisions (5). Rather, they chained together a sequence of decisions based on available and incomplete information (5). The cognitive method for clinical decision-making under uncertainty appears to be incremental, subdividing the overall problem into subproblems, solved on the basis of a few attributes (5).
Decision-making may be defined as the considered selection of one of several potential decisions, on the basis of available information, knowledge and wisdom, either explicit in the presentation or implicit in the decision-maker (6), while cognition has been defined as the experience of knowledge and how it is used (6).
The cognitive methods of physicians, subdividing an overall decision into subproblems (5), often parallels the distinct phases of clinical care of a patient, such as diagnosis before therapy, or prevention of disease before onset of disease, or rehabilitation of the patient after therapy of the patient (1). The analysis of queueing and renewal within human systems (7) has permited the identification of both decision elements and potential decisions in at least 10 such distinct phases of clinical care, including: prediction of disease; prevention of disease; diagnosis of disease; staging of disease; therapy of the patient; rehabilitation of the patient; health of the patient; counseling of the patient; advocacy for the patient; and financing for the patient (2). Although occasionally overlapping, these phases of clinical care are most often distinct and sequential, as is the cognition of the physicians making the decisions during the phases of clinical care (1). This partition perhaps reflects the limited attention span of all human subjects, and the limited capacity for processing information, as revealed by the early studies of Miller (8). Computer systems, by contrast, permit a reduction of many evaluations by humans to a long series of pairwise comparisons, in which the accumulating results are stored for later calculation while the user can focus serially on distinguishing only two qualities or quantities at any one time (9).
The development by Saaty (4) of a mathematical analysis of pairwise comparisons of user responses has continued to exert a profound influence on computer applications designed to enhance interactive human cognition (10). Saaty discovered that if users are asked to measure the contribution of one or more decision elements to two or more potential decisions, and if the decision element evaluations are entered pairwise in a two-dimensional matrix as they are obtained from the user, then the response matrix can be solved for its principal eigenvalue and for the eigenvector containing this principal eigenvalue. These mathematical solutions yield direct estimates of data consistency within the response matrix, and a normalized estimate of the contribution of each decision element to each potential decision (4). The use of the eigenvector method also preserves the ordinal rank of each of the decision elements when data within the response matrix are incomplete or inconsistent (10), a situation often encountered during the clinical evaluation of a patient (5).
The practical effect of such matrix cognition during clinical evaluation is to record the user's choices of potential decisions for consideration, the user's choices of decision elements for analysis, and the user's choices of consultants for participation in the analysis (1,2). Each consultant is then asked to estimate the quantitative contribution of each decision element to each potential decision, and this estimate is then weighted by the calculated eigenvector obtained by solving the response matrix of each consultant (1,2). Each consultant's quantitative scaling of each potential decision is then calculated, ranked in order, and combined with the results of the other consultants to yield a consensus best decision and ranking of alternative decisions (1,2).
If consultants are employed in serial cases of patients, the results and effects of their previous decisions may be recorded and used to calculate a weighting factor for the new evaluations offered by the consultant. In this way, the response matrix, and eventually the original user, learns which consultants are effective decision-makers and which are not. As the original user becomes more adept in formulating the potential decisions for consideration and the decision elements for evaluation, the resulting response matrices of each consultant will reflect a greater focus on the critical decision points in each evaluation. With use, decision elements will be recognized for greater or lesser influence on particular potential decisions, and this new information can be incorporated in new formulations of the choices, or directly into the shell of the program (1,2).
It will be recognized that the ability of such clinical programs to be re-formulated with each use, and the ability of the contained response matrix mechanism to learn of past performance for future evaluations, constitute the core of an open system (1), in contrast to the fixed character and dated opinion of expert systems (2,9).
Saaty has also discovered that the response matrix may be deliberately perturbed by one or more alterations in the cellular data, without necessarily altering either the ranking of the choices, or the quantitative contribution to each of the choices (4,10). This is partly explained by the non-linear character of the response matrix (12), partly by the particular type of perturbation employed (13), and partly by the important role being recognized for adaptive matrix integration in real-time simulation of a variety of systems (14).
Hilary Putnam has declared: "The notional task of artificial intelligence is to simulate intelligence, not to duplicate it." (15). Simulation of physical systems has often been achieved by coupled linear and non-linear differential equations (16), or even in computer hardware (17), but increasingly, matrix methods are being employed for simulation of truly complex systems (18) or in hybrid analyses with differential equations (14).
Computer simulation of medical systems of interest promises to assist us in better decision-making, as well as in revealing new details of our systems for our study (19,20).
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