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Algorithms for robust nonlinear regression with heteroscedastic errors.

Nonlinear regression algorithms were compared by Monte-Carlo simulations when the measurement error was dependent on the measured values (heteroscedasticity) and possibly contaminated with outliers. The tested leastsquares (LSQ) algorithms either required user-supplied weights to accommodate heteroscedasticity or the weights were estimated within the procedures. Robust versions of the LSQ algorithms, namely robust iteratively reweighted (IRR) and least absolute value (LAV) regressions, were also considered. The comparisons were based on the efficiency of the estimated parameters and their resistance to outliers. Based on these criteria, among the tested LSQ algorithms, extended least squares (ELSQ) was found to be the most reliable. The IRR versions of these algorithms were slightly more efficient than the LAV versions when there were no outliers but they provided weaker protection to outliers than the LAV variants.

Algorithms↗

Mathematical characterization of Chaos Game Representation. New algorithms for nucleotide sequence analysis.

Chaos Game Representation (CGR) can recognize patterns in the nucleotide sequences, obtained from databases, of a class of genes using the techniques of fractal structures and by considering DNA sequences as strings composed of four units, G, A, T and C. Such recognition of patterns relies only on visual identification and no mathematical characterization of CGR is known. The present report describes two algorithms that can predict the presence or absence of a stretch of nucleotides in any gene family. The first algorithm can be used to generate DNA sequences represented by any point in the CGR. The second algorithm can simulate known CGR patterns for different gene families by setting the probabilities of occurrence of different di- or trinucleotides by a trial and error process using some guidelines and approximate rules-of-thumb. The validity of the second algorithm has been tested by simulating sequences that can mimic the CGRs of vertebrate non-oncogenes, proto-oncogenes and oncogenes. These algorithms can provide a mathematical basis of the CGR patterns obtained using nucleotide sequences from databases.

Algorithms↗

A simulation algorithm for ultrasound liver backscattered signals.

In this study, we present a simulation algorithm for the backscattered ultrasound signal from liver tissue. The algorithm simulates backscattered signals from normal liver and three different liver abnormalities. The performance of the algorithm has been tested by statistically comparing the simulated signals with corresponding signals obtained from a previous in vivo study. To verify that the simulated signals can be classified correctly we have applied a classification technique based on an artificial neural network. The acoustic features extracted from the spectrum over a 2.5 MHz bandwidth are the attenuation coefficient and the change of speed of sound with frequency (dispersion). Our results show that the algorithm performs satisfactorily. Further testing of the algorithm is conducted by the use of a data acquisition and analysis system designed by the authors, where several simulated signals are stored in memory chips and classified according to their abnormalities.

Acoustics↗

Dynamic programming algorithms for biological sequence comparison.

Efficient dynamic programming algorithms are available for a broad class of protein and DNA sequence comparison problems. These algorithms require computer time proportional to the product of the lengths of the two sequences being compared [O(N2)] but require memory space proportional only to the sum of these lengths [O(N)]. Although the requirement for O(N2) time limits use of the algorithms to the largest computers when searching protein and DNA sequence databases, many other applications of these algorithms, such as calculation of distances for evolutionary trees and comparison of a new sequence to a library of sequence profiles, are well within the capabilities of desktop computers. In particular, the results of library searches with rapid searching programs, such as FASTA or BLAST, should be confirmed by performing a rigorous optimal alignment. Whereas rapid methods do not overlook significant sequence similarities, FASTA limits the number of gaps that can be inserted into an alignment, so that a rigorous alignment may extend the alignment substantially in some cases. BLAST does not allow gaps in the local regions that it reports; a calculation that allows gaps is very likely to extend the alignment substantially. Although a Monte Carlo evaluation of the statistical significance of a similarity score with a rigorous algorithm is much slower than the heuristic approach used by the RDF2 program, the dynamic programming approach should take less than 1 hr on a 386-based PC or desktop Unix workstation. For descriptive purposes, we have limited our discussion to methods for calculating similarity scores and distances that use gap penalties of the form g = rk. Nevertheless, programs for the more general case (g = q+rk) are readily available. Versions of these programs that run either on Unix workstations, IBM-PC class computers, or the Macintosh can be obtained from either of the authors.

Algorithms↗

Hypermedia and randomized algorithms for medical expert systems.

KNET is an environment for constructing probabilistic, knowledge-intensive systems within the axiomatic framework of decision theory. The KNET architecture defines a complete separation between the hypermedia user interface on the one hand, and the representation and management of expert opinion on the other. KNET offers a choice of algorithms for probabilistic inference. We and our coworkers have used KNET to build consultation systems for lymph-node pathology, bone-marrow transplantation therapy, clinical epidemiology, and alarm management in the intensive-care unit. Most important, KNET contains a randomized approximation scheme (RAS) for the difficult and almost certainly intractable problem of Bayesian inference. Our algorithm can, in many circumstances, perform efficient approximate inference in large and richly interconnected models of medical diagnosis. In this article, we describe the architecture of KNET, construct a randomized algorithm for probabilistic inference, and analyze the algorithm's performance. Finally, we characterize our algorithms' empiric behavior and explore its potential for parallel speedups. From design to implementation, then, KNET demonstrates the crucial interaction between theoretical computer science and medical informatics.

Algorithms↗

BIO-SPEAD: a parallel computing environment to accelerate development of biologic signal processing algorithms.

We have created BIO-SPEAD (pronounced speed), a BIOlogical Signal Processing Environment for Algorithm Development. BIO-SPEAD is designed to accelerate development of complex algorithms which integrate information derived from single or multiple physiologic waveforms. BIO-SPEAD currently performs all of the basic analyses of several arterial blood pressure waveforms, and allows the user to utilize the results of those low-level analyses for development of more complex algorithms. We utilized a parallel programming architecture called the Process Trellis which keeps the different tasks, or processes, within BIO-SPEAD independent of each other. Additionally, we have developed a graphics interface to enable the user to visualize the waveform under analysis, the low-level system analysis, and the internal workings of the algorithm under development. The system has been used for several algorithm development projects and has demonstrated its utility.

Algorithms↗

Development and validation of a logistic regression-derived algorithm for estimating the incremental probability of coronary artery disease before and after exercise testing.

OBJECTIVES: Our goals were to develop and validate a multivariate algorithm for estimating the incremental probability of the presence of coronary artery disease. BACKGROUND: Multivariate methods, including logistic regression analysis, have been extensively applied to diagnostic exercise testing. However, few previous studies have included both an incremental design and external validation. METHODS: A retrospective collection of clinical, exercise test and catheterization data was performed involving four U.S. referral medical centers. All patients had no prior history of coronary disease and had undergone coronary angiography < or = 3 months after exercise stress testing. An algorithm was developed in one center (590 patients with a 41% prevalence of coronary artery disease) with the use of logistic regression analysis and was validated in the other three centers (1,234 patients, 70% prevalence). The algorithm incorporated pretest variables (age, gender, symptoms, diabetes, cholesterol), exercise electrocardiographic (ECG) variables (mm of ST segment depression, ST slope, peak heart rate, metabolic equivalents [METs], exercise angina) and one thallium variable. Discrimination was measured with receiver operating characteristic curve analysis. Calibration (that is, reliability) was assessed from a comparison of probability estimates and the actual prevalence of disease. RESULTS: The overall incremental receiver operating characteristic curve areas for the validation group were pretest, -0.738 +/- 0.016; postexercise ECG, 0.78 (SE 0.017); and postthallium, 0.82 (SE 0.016); p < 0.01 for both increments. Within the three validation institutions, the institution with a disease prevalence closest to that of the derivation institution had the best incremental receiver operating characteristic curve areas. There was a stepwise incremental improvement in calibration especially from exercise ECG to thallium testing. CONCLUSIONS: An incremental multivariate algorithm derived in one center reliably estimated disease probability in patients from three other centers. The incremental value of testing was best demonstrated when the derivation and validation groups had a similar disease prevalence. This algorithm may be useful in decision making that relates to the diagnosis of coronary disease.

Algorithms↗

A new algorithm for the initial evaluation and management of supraventricular tachycardia.

Interpretations by physicians and those generated by electrocardiograph computer softwares have poor ability to recognize different types of supraventricular tachycardia (SVT). Therefore, we developed and tested a new SVT algorithm based on easily identifiable morphological characteristics and a simple dichotomous yes/no format regarding initial electrocardiographic manifestation and response pattern. The algorithm was then tested by medical house staff during the initial evaluation of 50 adult ED and cardiac intensive care unit patients suspected of having SVT. For a wide representation of SVTs, the new algorithm gave an overall diagnostic accuracy rate of 90%. Adenosine use was limited to 54% of the cases. No patient developed hemodynamic instability after algorithm-dictated interventions were carried out. Electrocardiograph computer-generated diagnoses correctly identified the specific type of SVT in 38% of the cases. This study shows the effectiveness of the proposed new algorithm in the rapid bedside evaluation and management of SVTs and confirms that computer-generated diagnoses are unreliable.

Adult↗

Value of electrocardiographic algorithm based on "ups and downs" of ST in assessment of a culprit artery in evolving inferior wall acute myocardial infarction.

Acute myocardial infarction (AMI) of the inferoposterior wall is due to occlusion of the right coronary artery (RCA) or the left circumflex (LCx) coronary artery. The outcome of patients depends mainly on the culprit artery. Therefore, the presumptive prediction of a culprit artery based on the electrocardiogram recorded at admission is of clinical importance. The aim of this study was to develop a sequential algorithm based on the "ups and downs" of the ST segment in different leads to predict the culprit artery (RCA vs LCx) in cases of inferoposterior AMI. We analyzed electrocardiographic and angiographic findings of 63 consecutive patients with an evolving AMI with ST elevation in the inferior leads (II, III, and aVF) and a single-vessel occlusion. Specificity, sensitivity, and positive and negative predictive values of different electrocardiographic criteria (ups and downs of the ST segment) were studied individually and in combination to find an algorithm that would best predict the culprit artery. The following electrocardiographic criteria were included in the 3-step algorithm: (1) ST changes in lead I, (2) the ratio of ST elevation in lead III to that in lead II, and (3) the ratio of the sum of ST depression in precordial leads to the sum of ST elevation in inferior leads [( summation operator downward arrow ST in leads V(1) to V(3))/( summation operator upward arrow ST in leads II, III, and aVF)]. Application of this sensitive algorithm suggested the location of the culprit coronary artery (RCA vs LCx) in 60 of 63 patients (>95%). The few patients in whom this algorithm did not work were those with a very dominant LCx that presented ST depression of > or =0.5 mm in lead I. In conclusion, careful sequential analysis of an electrocardiogram of an inferoposterior AMI with ST elevation may lead to the identification of a culprit artery.

Algorithms↗

[Postoperative nausea and vomiting: cost and therapeutic algorithm. Part II: high-risk patients and late PONV].

OBJECTIVES: To evaluate in high-risk patients and in usual clinical conditions, the efficiency of treatments based on an algorithm on late (24 h) postoperative nausea and vomiting (PONV). STUDY DESIGN: Prospective and descriptive. METHODS: The nature and efficiency of prophylactic and curative PONV treatments was evaluated 24 h after surgery under general anesthesia in patients at high risk of PONV, one and 15 month after the introduction of a clinical and therapeutic algorithm. A risk score based on the type of surgery and patients characteristics determined the prophylactic treatment: high risk = droperidol 1.25 mg + ondansetron 4 mg; moderate risk = droperidol 1.25 mg. Cost of prophylactic and curative treatment was calculated according to the exact number of vials of antiemetics used. RESULTS: The use of the therapeutic algorithm leads to a reduction of PONV by a half (47.7% of 109 patients in 1999 vs. 24.5% of 102 patients in 2001) while twice more patients received a prophylactic treatment (32.1% vs. 75.5%). The number of patients needed to be treated (NNT) according to the algorithm to avoid PONV was 1.8 in this high-risk population. However, the relative risk to have PONV was only reduced by 66% with the combination of two antiemetics in 2001 and 22.5% patients still suffered from PONV despite the double prophylactic treatments. The relative risk of PONV without prophylactic treatment was spontaneously reduced by 25% between the two study periods (54% vs. 40%). After 15 months, the recommendations were followed in 43.1% of patients. A curative treatment was given in the same percentage of patients in 2001 and 1999 (63.4% vs. 68%), but followed the recommendations in fivefold more patients (47% vs. 9.1%). The cost of PONV treatment (prophylactic and curative) was increased by 3.5-fold between the two periods ( 55 for 109 patients vs. 190 for 102 patients). CONCLUSION: The use of a PONV therapeutic algorithm based on a scored risk was associated to a lower reduction of late PONV than already published in the literature while the cost was increased as expected. This suggests the efficacy of antiemetic prophylactic treatment might have been overestimated by large multicenter trials and is less in usual clinical conditions. Thus local evaluation of practice is required by performing quality insurance programs.

Adult↗

Benchmarking a memetic algorithm for ordering microarray data.

This work introduces a new algorithm for "gene ordering". Given a matrix of gene expression data values, the task is to find a permutation of the gene names list such that genes with similar expression patterns should be relatively close in the permutation. The algorithm is based on a combined approach that integrates a constructive heuristic with evolutionary and Tabu Search techniques in a single methodology. To evaluate the benefits of this method, we compared our results with the current outputs provided by several widely used algorithms in functional genomics. We also compared the results with our own hierarchical clustering method when used in isolation. We show that the use of images, corrupted with known levels of noise, helps to illustrate some aspects of the performance of the algorithms and provide a complementary benchmark for the analysis. The use of these images, with known high-quality solutions, facilitates in some cases the assessment of the methods and helps the software development, validation and reproducibility of results. We also propose two quantitative measures of performance for gene ordering. Using these measures, we make a comparison with probably the most used algorithm (due to Eisen and collaborators, PNAS 1998) using a microarray dataset available on the public domain (the complete yeast cell cycle dataset).

Algorithms↗

MRS algorithm: a new method for searching myocardial region in SPECT myocardial perfusion images.

First, the necessity of automatically segmenting myocardium from myocardial SPECT image is discussed in Section 1. To eliminate the influence of the background, the optimal threshold segmentation method modified for the MRS algorithm is explained in Section 2. Then, the image erosion structure is applied to identify the myocardium region and the liver region. The contour tracing method is introduced to extract the myocardial contour. To locate the centriod of the myocardium, the myocardial centriod searching method is developed. The protocol of the MRS algorithm is summarized in Section 6. The performance of the MRS algorithm is investigated and the conclusion is drawn in Section 7. Finally, the importance of the MRS algorithm and the improvement of the MRS algorithm are discussed.

Algorithms↗

Bleeding after use of the levonorgestrel regimen of emergency contraception: concordance between women's reports of their menstrual periods and an objective algorithm.

OBJECTIVE: To compare concordance between periods as recorded by women on daily diaries with those determined objectively by an algorithm used in an earlier study to assess bleeding patterns after taking the emergency contraceptive pill (ECP) regimen consisting of 1.5 mg levonorgestrel. METHODS: We asked 120 women who had been treated with the regimen to keep daily bleeding diaries for 9 weeks. We compared menstrual periods recorded on the diary cards and reported in follow-up interviews with those determined by an algorithm adapted from the World Health Organization (WHO). RESULTS: Altogether, 111 subjects contributed diary cards on which the algorithm could identify at least one period; a total of 261 periods were identified by the algorithm. In 87% of these periods, women recorded on the diary a start date that was the same as or only 1 day later, but in 8% their recorded start day was more than 7 days later. For the first period following use of the regimen, concordance was lower: 81% and 14%, respectively. CONCLUSION: We found generally good concordance between the starts of menstrual periods as determined by an algorithm adapted from the WHO and the date of the start of a period as reported by participants on diary cards. In our earlier study, we found that the earlier in the cycle a woman took 1.5 mg levonorgestrel, the earlier was the next period. Had we relied on women's recording of the first period on the diary card, we would not have reached that conclusion.

Adolescent↗

A practical insulin infusion algorithm for the establishment of euglycaemia in both lean and obese patients with type 1 and type 2 diabetes.

BACKGROUND: Both in research and in various clinical situations, prolonged euglycaemia can be desirable. In recent years, its benefit in (critically) ill patients and patients with acute myocardial infarction has been established. The objective of this study was to assess safety and efficacy of a practical, bodyweight-dependent algorithm to establish euglycaemia in both lean and obese patients with type 1 and type 2 diabetes. METHODS: In 43 patients with type 1 diabetes and 17 patients with type 2 diabetes insulin were infused overnight to establish euglycaemia. Plasma glucose concentration was determined at 45 min intervals, and the insulin infusion rate was altered according to the algorithm. RESULTS: Baseline plasma glucose concentrations were 13.1+/- 4.4 and 12.7 +/- 4.0 mmol/l in type 1 and type 2 diabetic patients, respectively. In both groups mean plasma glucose was reduced below 8.0 mmol/l within 3 h, and averaged 7.4 +/- 1.4 and 7.2 +/- 1.0 mmol/l (P = 0.11) over the next 7 h. Five (11.6%) patients with type 1 diabetes required administration of glucose because plasma glucose concentrations fell below 4.4 mmol/l. Consequently, type 1 diabetic patients were hypoglycaemic during 0.89% of the total study period. The lowest plasma glucose recorded was 3.9 mmol/l. In the type 2 diabetic patients the lowest plasma glucose was 5.5 mmol/l and no glucose administration was required for near-hypoglycaemia. The algorithm was equally effective in both lean and obese patients. CONCLUSIONS: Euglycaemia was established simply, swiftly and safely during the study period with the practical weight-based algorithm used in this study, in both lean and obese type 1 and type 2 diabetic patients, with a very low rate of mild hypoglycaemia. The algorithm is applicable in research and various several clinical settings. Its validity for a prolonged period of time and in critically ill patients needs to be further evaluated.

Adult↗

Cost-saving effect of treatment algorithm for chronic anal fissure: a prospective analysis.

Evidence-based medicine suggests that in the management of chronic anal fissure (CAF), lateral internal sphincterotomy (LIS) is far more effective than medical treatment in lowering the anal sphincter tone and curing the fissure. In the current study, we developed a treatment algorithm from topical nitroglycerin (NTG) to botulinum toxin type A (Botox [BTX]) to LIS and analyzed its cost benefit by calculating the effective and potential costs based on the treatment success and the rate of avoided surgeries. Patients presenting between November 2003 and December 2004 with CAF and symptoms for greater than 3 months were prospectively treated according to a treatment algorithm which started with (1) topical NTG, in case of failure (2) injection of BTX, thus limiting (3) surgery to those who failed both nonsurgical options or at any point chose the surgical approach. Based on the primary end points of fissure healing or surgery, we calculated the true cost (algorithm) and the potential incremental cost (BTX plus surgery or surgery in all patients, respectively). Sixty-seven patients with CAF (25 men and 42 women; median duration of symptoms, 16 weeks) were treated according to the algorithm. NTG alone was successful in fissure healing in 31 of 67 patients (46.2%). Two developed a recurrent fissure and then received BTX as part of the protocol. Of the 36 patients who failed NTG trial, 3 requested surgery; the others were treated with BTX, which was successful in 84.8%. Five patients (15.2%) failed BTX and subsequently required surgery. The overall surgery rate in the whole study group was 11.9%, whereas CAF healed in 88.1% of our patients with medical treatment alone. Cost for NTG is $10; for 100 units BTX, $528; and for outpatient surgery, $1119. The total cost for these 67 patients therefore was $33,252 ($290 for NTG, $20,580 for NTG plus BTX, $3,357 for NTG plus LIS, and $9,025 for NTG plus BTX plus LIS). If all patients had received BTX with a 15% failure rate, the total cost would have been $56,688 (70.3% cost increase). If all patients had undergone surgery as initial/only treatment, the total cost would have been $74,973 (125% cost increase). Our treatment algorithm for CAF with stepwise escalation can avoid surgery in 88% of the patients. It is highly cost-efficient and resulted in savings of 41% (compared with BTX plus LIS) and up to 70% (compared with surgery in all patients), respectively.

Adult↗

An automated scoring algorithm for computerized clinical vignettes: evaluating physician performance against explicit quality criteria.

OBJECTIVE: To evaluate the accuracy of an automated algorithm for scoring physicians' responses to open-ended clinical vignettes against explicit, evidence-based quality criteria. METHODS: One hundred sixteen physicians completed a total of 915 computerized clinical vignettes at 4 sites. Each vignette simulated an outpatient primary care visit for one of 8 different clinical cases. The automated algorithm scored disease-specific quality criterion as done or not done by recognizing the presence or absence of predefined patterns in the physician's text response to the vignette. Scores generated by the automated algorithm for each criterion were compared to scores generated by trained human abstractors. Vignette responses were divided into development and test sets. Percentage agreement between automated and manual scores was computed separately for the development and test sets. Sensitivity and specificity were calculated. Costs of automated and manual scoring were compared. RESULTS: Accuracy of the algorithm exceeds 90% for both the development and test sets, and is high for care items that were deemed either necessary or unnecessary, across diverse clinical cases, and for all domains of the outpatient clinical encounter. The sensitivity of the automated scoring algorithm is 89.0%, and specificity is 93.5%. Automated scoring is approximately 84% less expensive than manual scoring. CONCLUSION: Automated scoring of computerized vignettes appears feasible and accurate. Computerized vignettes incorporating accurate automated scoring offer the promise of a highly standardized but relatively inexpensive measurement tool for a wide range of quality assessments within and across health systems.

Algorithms↗

An algorithm to predict implantable cardioverter-defibrillator lead failure.

OBJECTIVES: The goal of this analysis was to test an algorithm that identifies implantable cardioverter-defibrillator (ICD) lead problems before clinical failure and/or inappropriate therapy. BACKGROUND: The ICD lead failures typically present as inappropriate shock therapy. Identifying lead failures before their clinical presentation may prevent patient discomfort, improve device longevity, and avoid device-induced proarrhythmia. METHODS: We tested an algorithm that uses two measures of oversensing and one measure of abnormal impedance to detect a lead failure. The oversensing measures consisted of a counter for RR intervals <140 ms and nonsustained ventricular tachycardia episodes with mean RR interval <200 ms. The impedance measure tracked lead impedances every day and each week. Abnormal impedance was defined as a decrease in impedances or an outlier value compared with baseline. Lead failures were identified when both oversensing measures were met or abnormal impedance and one oversensing measure occurred. The stored data from 696 patients with an ICD were analyzed to determine the sensitivity and specificity of the algorithm to detect lead failures. RESULTS: Twenty-nine patients demonstrated clinical lead failures with an average of 6 +/- 9 inappropriate shocks per patient. The two oversensing measures used in the algorithm predicted 72% (21 of 29) of the lead failures. Fulfilling at least two of the three impedance and oversensing measures, the sensitivity of our algorithm was 83% (24 of 29) with a 100% (667 of 667) specificity. CONCLUSION: Oversensing combined with abnormal impedance trends may be used to identify ICD lead failures with high sensitivity and very high specificity.

Algorithms↗

P-wave morphology in focal atrial tachycardia: development of an algorithm to predict the anatomic site of origin.

OBJECTIVES: The purpose of this study was to perform a detailed analysis of the P-wave morphology (PWM) in focal atrial tachycardia (AT) and construct and prospectively evaluate an algorithm for identification of the anatomic site of origin. BACKGROUND: Although smaller studies have described the PWM from particular anatomic locations, a detailed algorithm characterizing the likely location of a tachycardia associated with a P-wave of unknown origin has been lacking. METHODS: The PWMs for 126 consecutive patients undergoing successful radiofrequency ablation of 130 ATs are reported. P waves were included only when the onset was preceded by a discernible isoelectric segment. P waves were classified as positive (+), negative (-), isoelectric, or biphasic. Sensitivity, specificity, and predictive values were calculated. On the basis of these results, an algorithm was constructed and prospectively evaluated in 30 new consecutive ATs. RESULTS: The distribution of ATs was right atrial (RA) in 82 of 130 (63%) and left atrial (LA) in 48 of 130 (37%). Right atrial sites included crista (n = 28), tricuspid annulus (n = 29), coronary sinus (CS) ostium (n = 14), perinodal (n = 7), right septum (n = 1), and RA appendage (n= 3). Left atrial sites included pulmonary veins (n = 32), mitral annulus (n = 8), CS body (n= 3), left septum (n = 3), and LA appendage (n = 2). In electrocardiographic lead V1, a negative or +/- P-wave demonstrated a specificity of 100% for a RA focus, and a + or -/+ P-wave demonstrated a sensitivity of 100% for a LA focus. A characteristic PWM was associated with high sensitivity and specificity at common atrial sites for tachycardia foci. A P-wave algorithm correctly identified the focus in 93%. CONCLUSIONS: Characteristic PWMs corresponding to known anatomic sites for focal AT are associated with high specificity and sensitivity. A P-wave algorithm correctly identified the site of tachycardia origin in 93%.

Adolescent↗