- Email: [email protected]
Use of a neural network to predict stone growth after shock wave lithotripsy
PRELIMINARY COMMUNICATION
ELSEVIER
USE OF A NEURAL NETWORK TO PREDICT STONE GROWTH AFTER SHOCK WAVE LITHOTRIPSY ELI K. MICHAELS, CRAIG S. NIEDERBERGER, RICHARD M. GOLDEN, BRUCE BROWN, LUKE CHO, AND YOUNG HONG
ABSTRACT Objectives. To determine whether a neural network is ,superior to standard computational methods in predicting stone regrowth after shock wave lithotripsy (SWL) and to determine whether the presence of residual fragments, as an independent variable, increases risk. Methods. We reviewed the records of 98 patients with renal or ureteral calculi treated by primary SWL at a single institution and followed up for at least 1 year; residual stone fragment growth or new stone occurrence was determined from abdominal radiographs. A neural network was programmed and trained to predict an increased stone volume over time utilizing input variables, including previous stone events, metabolic abnormality, directed medical therapy, infection, caliectasis, and residual fragments after SWL. Patient data were partitioned into a training set of 65 examples and a test set of 33. The neural network did not encounter the test set until training was complete. Results. The average follow-up period was 3.5 years (range 1 to 10). Of 98 patients, 47 had residual stone fragments 3 months after SWL; of these 47, 8 had increased stone volume at last follow-up visit. Of 51 patients stone free after SWL, 4 had stone recurrence. Coexisting risk factors were incorporated into a neural computational model to determine which of the risk factors was individually predictive of stone growth. The classification accuracy of the neural model in the test set was 9 1%, with a sensitivity of 9 l%, a specificity of 92%, and a receiver operating characteristic curve area of 0.964, results significantly better than those yielded by linear and quadratic discriminant function analysis. Conclusions. A computational tool was developed to predict accurately the risk of future stone activity in patients treated by SWL. Use of the neural network demonstrates that none of the risk factors for stone growth, including the presence of residual fragments, is individually predictive of continuing stone formation. UROLOGY 51: 335-338, 1998. 0 1998, Elsevier Science Inc. All rights reserved.
stone-free kidney has historically been the goal of any procedure used to treat renal calculi. The desire for a stone-free result derives from the general ineffectiveness of medical treatments for calcium stone dissolution and the belief that any stone material remaining might act as a nidus
A
Supported in part by NIH grant HD 30155. This study was presented in part at the annual Meeting of the American Urological Association, Orlando, Florida, May 2996. From the Department of Urology, College of Medicine, and Department of Electrical Engineering and Computer Sciences, University of Illinois at Chicago, Chicago, Illinois; and School of Human Development, University of Texas at Dallas, Dallas, Texas Reprint requests: Eli K. Michaels, M.D., Department of Urology, University of Illinois at Chicago, 820 South Wood Street, Chicago, IL 60612-7316 Submitted (Rapid Communication): July 1, 1997, accepted (with revisions): September 3, 1997 0 1998, ELSEVIERSCIENCE INC. ALL RIGHTS RESERVED
for regrowth of the stone. The difficulty encountered with reoperation made any such regrowth problematic. Using currently available techniques, for most patients the chance of a stone-free result depends on the invasiveness of the initial procedures.lJ Our experience with primary shock wave lithotripsy (SWL) mirrors that of other investigators who have found that many patients, especially those with larger stones and/or a dilated collecting system, will not be rendered stone free324 and that residual stone after SWL may facilitate stone recurrence.5-* In the current study, we report our experience with 98 patients treated by primary SWL and with follow-up data for at least 1 year. We compared stone formation in patients with or without residual fragments and, using a novel computational modeling approach, tested the predictive 0090-4295/98/$19.00 PII SOO90-4295(97)00611-O
335
value of different variables, including pre-existing metabolic abnormalities, infection, stone size, caliectasis, and directed medical therapy. We analyzed our data using the backpropagation artificial neural network, a computational modeling technique by which the computer performs tasks of pattern recognition by first “training” the neural network with observed input-output pairs and then “testing” the resulting model with other observed input-output pairs not previously used in training.9 We then used the neural network to predict the likelihood of whether individual patients would experience stone regrowth or recurrence. MATERIAL AND METHODS Ninety-eight patients with renal or ureteral calculi were treated by primary SWL at a single institution and followed up for at least 1 year (mean 3.5, range 1 to 10). The presence of residual fragments and/or stone recurrence was determined from abdominal radiographs obtained 3 months after SWL and periodically until the last follow-up visit and was evaluated by one urologist (E.M.). The presence of urinary infection by urea-splitting bacteria was documented from clean catch urine samples. Patients with struvite stones were considered for this review only if there was evidence of metabolic abnormality (ie, stone analysis revealing calcium oxalate mixed with struvite) A dilated collecting system (caliectasis) was considered a stone growth risk factor and was usually a result of prolonged obstruction by a renal or ureteral stone; urinary diversion or neurogenic bladder was infrequent. Metabolic abnormalities were determined by 24-hour urine collections and included hypercalciuria and hyperuricosuria. Crystallographic stone analysis was available for most patients; individuals with cystine stones were excluded. A history of previous stone events was obtained from the patient or medical records. Medical therapy consisted of oral thiazides, citrate, or allopurinol, alone or in combinations. STATISTICAL ANALYSIS A feed-forward neural network with one hidden layer, one output unit, and a cross-entropy error function was programmed in C using our neUROn (neural computation environment for UROlogical numericals) environment, in which network topology is tailored to a specific urologic application.10 The training method was backpropagation.gJl The 98 patient examples were randomly divided into a training set of 65 examples and a test set of 33 using an algorithm that maintained equal frequency of outcomes in both sets. The test set was not used in training. Sixteen input variables were encoded into 37 binary, categoric, and continuous nodes in the input layer, depending on the specific type of input variable represented in the training set. The single discrete predicted binary output represented either (1) if no fragments were present on final follow-up, or if fragments were present, but did not grow; or (2) if new stones were found on follow-up, or if existing fragments grew. Networks were built with 10 nodes in a single hidden layer, and the number of hidden nodes was reduced until overlearning ceased, at which time 5 hidden nodes remained in the network. The properties of the error surface were then checked to see if the parameter estimates were a strict local minimum of the cross-entropy error function. Linear and quadratic discriminant function analysis were applied to both training and test sets for comparison with the results of the neural model.r2 336
TABLE I. Characteristics of 98 patients treated by shock wave Iithotripsy
Stone location Kidney Normal Caliectasis Ureter Stone growth Kidney Normal Caliectasis Stone analysis Calcium oxalate Struvitekalcium oxalate Previous stone(s) Metabolic abnormality* Medical therapy+ Follow-up (yr)
Stone Free [n = 51)
Residual Fragments (n = 47)
32 5 15 4 (7.8%)
22 21 8 8 (17.0%) 2 6
3 1 41 1 21 12124 tested 14 3.5
35 5 22 7/l 5 tested 10 3.5
* Hypercalciuria and/or hypemricosuria. ’ Thiazide andlor votassium citrate and/or allomrinol.
To determine the significance of individual input variables on the neural network model, Wilk’s generalized likelihood ratio test (GLRT) was used to examine the final trained network as a nonlinear regression model.rr When using Wilk’s GLRT, each input node is sequentially removed from the neural network by setting its connection weights to 0; the network is retrained and the final error of the feature-deficient network recorded. This error is compared with the full networks error, resulting in a statistical probability allowing rejection of the null hypothesis that the feature-deficient network and the full network result classify with the same error. This probability thus indicates whether an individual feature is required for the full models accuracy.
RESULTS Although continuing stone formation appears to be more common in patients with residual fragments (17% [n = 81) than in those stone free (7.8% [n = 41) after SWL, further examination of the data (Table I) reveals that the two patient groups were not equivalent, the major difference being the much greater incidence of collecting system dilation (caliectasis) present in the residual fragment group. Although it is known that renal dilation may result in higher residual fragment rates after SWL, it has not been shown which of the two factors is responsible for subsequent stone growth. The classification accuracy of the neural model in the test set was 91%, sensitivity 91%, specificity 92%, and receiver operating characteristic (ROC) curve area 0.964 (1 .O would be a perfect classifier, 0.5 would result from chance guessing). In comparison, classification accuracy for both linear and quadratic discriminant function analysis was 36%, UROLOGY 51 (2), 1998
and although specificity was lOO%, sensitivity was 0% and ROC area 0.524. Using Wilk’s GLRT, no single variable (including residual fragments) was found (all P BO.9) that, when removed, significantly deteriorated the networks classification accuracy; this implies that the presence or absence of residual fragments, per se, is not predictive of continuing stone formation. The final network may be investigated fully by any person using a JavaScript-capable World Wide Web browser (such as Netscape 2.0 and above) at http://godot.urol.uic.edu. As JavaScript code is loaded into the client browser, the entire neural architecture, including trained weights and biases, may be observed (“View Source” in Netscape). We offer this resource because the resulting trained neural network code is too lengthy to be presented here. COMMENT A discussion of stone “recurrence” must allow that this term is often used inappropriately to describe regrowth or enlargement of identifiable calculus (or fragments), as opposed to its strict definition of new stone formation from a radiographically stone-free kidney. In the current study, we used the term “active (or continuing) stone formation” to describe both situations: that is, new stone formation as well as enlargement of existing stone. Initial studies of stone formation rates after SWL treatment focused on residual fragments as a risk factor for future growth. A large number of patients with primarily calcium oxalate stones were evaluated at 1 and 2 years after SWL by Newman et al. ,5 who found that patients with residual fragments had a stone formation rate of 21% compared with a recurrence rate of 8.4% at 1 year in patients stone free after SWL. Further analysis of the data shows that patients who had residual fragments were more commonly those with multiple stones, larger stones, or caliectasis, suggesting that these patients were more “metabolically active” than those who became stone free, and bringing into question the validity of stone-free status as an independent variable. Studies by Fine et al.6 and Yu et al7 showed that patients with residual fragments after SWL more frequently had a larger initial stone burden, as well as a history of more frequent previous stone events, suggesting that stone formation rate differences may result from pre-existing factors rather than merely the presence of fragments after SWL. The importance of normal urinary tract anatomy is shown by Streem,* who followed up patients with infection stones for 3.5 years after percutaneous nephrostolithotomy or SWL and found that stone recurrence is statistically related to the presence of UROLOGY 51 (21, 1998
anatomic or functional urinary tract abnormality and not to the presence of residual stone fragments or the number of recurrent urinary infections.13 Studies by Parks and Coe14 on stone recurrence suggest that the number of previous stone events was the major determinant of new stone formation and postulate that tiny nucleation centers from previous stones may remain in renal tubules to initiate new stone formation. This is predicated on the fact that nucleation of calcium oxalate requires higher supersaturation levels than that needed for crystal growth and aggregation and that presence of these residual nuclei enhances new stone formation, given similar urinary chemistry. They conclude that the relapse rate is proportional to the length of time (and thereby number of stone events) sustained before institution of medical treatment rather than the presence of specific metabolic abnormalities or the time to most recent stone event. Based on these observations, one might predict that the greatly expanded surface area of stone fragments resulting from SWL would cause an explosion of stone growth; yet it is clear from all available data that a great majority of patients (at least 80%) with residual fragments after SWL do not have stone growth or formation of new stones. This finding is confirmed in a recent study by Chen and Streem,ls who demonstrated stone growth in only 11% of patients with post-SWL fragments followed up for a mean of 33.3 months. Other factors, predating SWL treatment, are clearly operative. Use of a neural network in the current study allowed prediction of continuing active stone formation in patients followed up after primary SWL; this model outperformed traditional linear statistical classification methods. Additionally, this method demonstrated that none of the tested risk factors, including the presence of residual fragments, was predictive of continuing stone formation when considered individually. We caution that the lack of significance of the residual stone fragment predictor variable could be attributed to the lack of statistical power in the Wilk’s GLRT analysis for the given sample size, model, and data. However, we note that even if a larger sample size did result in a significant predictor variable effect, the corresponding change in classification accuracy of the model would be too small (based on the current sample size estimates) to continue to warrant the conclusion that the predictor variable was clinically relevant. The irrelevance of residual stone fragments as a strong predictor of recurrence was suspected in studies of specific patient groups using Kaplan-Meier estimates8J3 but not investigated using a robust nonlinear model for multiple variables in a diverse stone population that would 337
result in high classification accuracy. Use of the neural network allowed such analysis. Since the initiation of the neUROn project, we have endeavored to make available to physicians the modeling tools thus created. At first, we provided a common gateway interface (cgi) to trained neural networks executable on our server. In the spirit of distributed computing, we provided this trained neural network as JavaScript code. Any JavaScript-capable World Wide Web browser, such as Netscape version 2.0 and higher, that is directed to our site (http://godot.urol.uic.edu) may load and execute this trained neural network on the local, client machine. This globally available neural network serves not only physicians wishing to predict outcomes for real patients, but also as a learning tool, for the browsing physician may alter individual input variables and view the network’s prediction. Such interaction often yields intriguing results. CONCLUSIONS We demonstrated the use of a computational tool to accurately predict the risk of future stone growth after SWL. The possibility that residual stone fragments may not increase stone formation risk compels us to re-examine our treatment goals for patients with stones and consider treatment options with lesser morbidity than those required to achieve a stone-free result. The ultimate goals should be prevention of stone recurrence and preservation of renal function, and our data provide further evidence that a stone-free result after SWL is not necessarily an independent factor in achieving these goals. REFERENCES 1. Segura JW, Preminger GM, Assimos DG, Dretler SP, Kahn RI, Lingeman JE, Macaluso JN Jr, and McCullough DL: Nephrolithiasis Clinical Guidelines Panel summary report on the management of staghorn calculi. J Urol 151: 1648-1651, 1994. 2. Winfield HN, Clayman RV, Chaussy CG, Weyman PJ,
338
Fuchs GJ, and Lupu AN: Monotherapy of staghom renal calculi: a comparative study between percutaneous nephrolithotomy and extracorporeal shock wave lithotripsy. J Urol 139: 895-899,1988. 3. Lam HS, Lingeman JE, Barron M, Newman DM, Mosbaugh PG, Steele RE, Knapp PM, Scott JW, Nyhuis A, and Woods JR: Staghorn calculi: analysis of treatment results between initial percutaneous nephrostolithotomy and extracorporeal shock wave lithotripsy monotherapy with reference to surface area. J Urol 147: 1219-1225, 1992. 4. Michaels EK, and Fowler JE Jr: ESWL monotherapy for large-volume renal calculi: efficacy and morbidity. Urology 34: 96-99,1989. 5. Newman DM, Scott JW, and Lingeman JE: Two-year follow-up of patients treated with extracorporeal shock wave lithotripsy. J Endouro12: 163-171, 1988. 6. Fine JK, Pak CY, and Preminger GM: Effect of medical management and residual fragments on recurrent stone formation following shock wave lithotripsy. J Urol 153: 27-33, 1995. 7. Yu CC, Lee YH, Huang JK, Chen MT, Chen KK, Lin AT, and Chang LS: Long-term stone regrowth and recurrence rates after extracorporeal shock wave lithotripsy. Br J Uro172: 688691, 1993. 8. Streem SB: Long-term incidence and risk factors for recurrent stones following percutaneous nephrostolithotomy or percutaneous nephrostolithotomy/extracorporeal shock wave lithotripsy for infection related calculi. J Urol153: 584587, 1995. 9. Werbos P: Beyond regression: new tools for prediction and analysis in the behavioral sciences (PhD thesis). Cambridge, Massachusetts, Harvard University, 1974. 10. Fiesler E, Beale R, Axelrod T, Blayo F, Cios KJ, Doerschuk PI, Jain S, Murphy GL, Niederberger C, Torkkola K, and Wellekens CJ: Handbook of Neural Computation. Oxford, IOP Publishing and Oxford University Press, 1997, pp G5 4:1-6. 11. Golden RM: Mathematical Methodsfor Neural Network Analysis and Design. Cambridge, Massachusetts, MIT Press, 1996. 12. James M: Classification Algorithms. London, William Collins and Sons, 1986, pp 15-55. 13. Cohen TD, Streem SB, and Lammert G: Long-term incidence and risks for recurrent stones following contemporary management of upper tract calculi in patients with urinary diversion. J Urol 155: 62-65, 1996. 14. Parks JH, and Coe FL: An increasing number of calcium oxalate stone events worsens treatment outcome. Kidney Int 45: 1722-1730,1994. 15. Chen RN, and Streem SB: Extracorporeal shock wave lithotripsy for lower pole calculi: long-term radiographic and clinical outcome. J Urol 156: 1572-1575, 1996.
UROLOGY 51 (2),1998
ELSEVIER
USE OF A NEURAL NETWORK TO PREDICT STONE GROWTH AFTER SHOCK WAVE LITHOTRIPSY ELI K. MICHAELS, CRAIG S. NIEDERBERGER, RICHARD M. GOLDEN, BRUCE BROWN, LUKE CHO, AND YOUNG HONG
ABSTRACT Objectives. To determine whether a neural network is ,superior to standard computational methods in predicting stone regrowth after shock wave lithotripsy (SWL) and to determine whether the presence of residual fragments, as an independent variable, increases risk. Methods. We reviewed the records of 98 patients with renal or ureteral calculi treated by primary SWL at a single institution and followed up for at least 1 year; residual stone fragment growth or new stone occurrence was determined from abdominal radiographs. A neural network was programmed and trained to predict an increased stone volume over time utilizing input variables, including previous stone events, metabolic abnormality, directed medical therapy, infection, caliectasis, and residual fragments after SWL. Patient data were partitioned into a training set of 65 examples and a test set of 33. The neural network did not encounter the test set until training was complete. Results. The average follow-up period was 3.5 years (range 1 to 10). Of 98 patients, 47 had residual stone fragments 3 months after SWL; of these 47, 8 had increased stone volume at last follow-up visit. Of 51 patients stone free after SWL, 4 had stone recurrence. Coexisting risk factors were incorporated into a neural computational model to determine which of the risk factors was individually predictive of stone growth. The classification accuracy of the neural model in the test set was 9 1%, with a sensitivity of 9 l%, a specificity of 92%, and a receiver operating characteristic curve area of 0.964, results significantly better than those yielded by linear and quadratic discriminant function analysis. Conclusions. A computational tool was developed to predict accurately the risk of future stone activity in patients treated by SWL. Use of the neural network demonstrates that none of the risk factors for stone growth, including the presence of residual fragments, is individually predictive of continuing stone formation. UROLOGY 51: 335-338, 1998. 0 1998, Elsevier Science Inc. All rights reserved.
stone-free kidney has historically been the goal of any procedure used to treat renal calculi. The desire for a stone-free result derives from the general ineffectiveness of medical treatments for calcium stone dissolution and the belief that any stone material remaining might act as a nidus
A
Supported in part by NIH grant HD 30155. This study was presented in part at the annual Meeting of the American Urological Association, Orlando, Florida, May 2996. From the Department of Urology, College of Medicine, and Department of Electrical Engineering and Computer Sciences, University of Illinois at Chicago, Chicago, Illinois; and School of Human Development, University of Texas at Dallas, Dallas, Texas Reprint requests: Eli K. Michaels, M.D., Department of Urology, University of Illinois at Chicago, 820 South Wood Street, Chicago, IL 60612-7316 Submitted (Rapid Communication): July 1, 1997, accepted (with revisions): September 3, 1997 0 1998, ELSEVIERSCIENCE INC. ALL RIGHTS RESERVED
for regrowth of the stone. The difficulty encountered with reoperation made any such regrowth problematic. Using currently available techniques, for most patients the chance of a stone-free result depends on the invasiveness of the initial procedures.lJ Our experience with primary shock wave lithotripsy (SWL) mirrors that of other investigators who have found that many patients, especially those with larger stones and/or a dilated collecting system, will not be rendered stone free324 and that residual stone after SWL may facilitate stone recurrence.5-* In the current study, we report our experience with 98 patients treated by primary SWL and with follow-up data for at least 1 year. We compared stone formation in patients with or without residual fragments and, using a novel computational modeling approach, tested the predictive 0090-4295/98/$19.00 PII SOO90-4295(97)00611-O
335
value of different variables, including pre-existing metabolic abnormalities, infection, stone size, caliectasis, and directed medical therapy. We analyzed our data using the backpropagation artificial neural network, a computational modeling technique by which the computer performs tasks of pattern recognition by first “training” the neural network with observed input-output pairs and then “testing” the resulting model with other observed input-output pairs not previously used in training.9 We then used the neural network to predict the likelihood of whether individual patients would experience stone regrowth or recurrence. MATERIAL AND METHODS Ninety-eight patients with renal or ureteral calculi were treated by primary SWL at a single institution and followed up for at least 1 year (mean 3.5, range 1 to 10). The presence of residual fragments and/or stone recurrence was determined from abdominal radiographs obtained 3 months after SWL and periodically until the last follow-up visit and was evaluated by one urologist (E.M.). The presence of urinary infection by urea-splitting bacteria was documented from clean catch urine samples. Patients with struvite stones were considered for this review only if there was evidence of metabolic abnormality (ie, stone analysis revealing calcium oxalate mixed with struvite) A dilated collecting system (caliectasis) was considered a stone growth risk factor and was usually a result of prolonged obstruction by a renal or ureteral stone; urinary diversion or neurogenic bladder was infrequent. Metabolic abnormalities were determined by 24-hour urine collections and included hypercalciuria and hyperuricosuria. Crystallographic stone analysis was available for most patients; individuals with cystine stones were excluded. A history of previous stone events was obtained from the patient or medical records. Medical therapy consisted of oral thiazides, citrate, or allopurinol, alone or in combinations. STATISTICAL ANALYSIS A feed-forward neural network with one hidden layer, one output unit, and a cross-entropy error function was programmed in C using our neUROn (neural computation environment for UROlogical numericals) environment, in which network topology is tailored to a specific urologic application.10 The training method was backpropagation.gJl The 98 patient examples were randomly divided into a training set of 65 examples and a test set of 33 using an algorithm that maintained equal frequency of outcomes in both sets. The test set was not used in training. Sixteen input variables were encoded into 37 binary, categoric, and continuous nodes in the input layer, depending on the specific type of input variable represented in the training set. The single discrete predicted binary output represented either (1) if no fragments were present on final follow-up, or if fragments were present, but did not grow; or (2) if new stones were found on follow-up, or if existing fragments grew. Networks were built with 10 nodes in a single hidden layer, and the number of hidden nodes was reduced until overlearning ceased, at which time 5 hidden nodes remained in the network. The properties of the error surface were then checked to see if the parameter estimates were a strict local minimum of the cross-entropy error function. Linear and quadratic discriminant function analysis were applied to both training and test sets for comparison with the results of the neural model.r2 336
TABLE I. Characteristics of 98 patients treated by shock wave Iithotripsy
Stone location Kidney Normal Caliectasis Ureter Stone growth Kidney Normal Caliectasis Stone analysis Calcium oxalate Struvitekalcium oxalate Previous stone(s) Metabolic abnormality* Medical therapy+ Follow-up (yr)
Stone Free [n = 51)
Residual Fragments (n = 47)
32 5 15 4 (7.8%)
22 21 8 8 (17.0%) 2 6
3 1 41 1 21 12124 tested 14 3.5
35 5 22 7/l 5 tested 10 3.5
* Hypercalciuria and/or hypemricosuria. ’ Thiazide andlor votassium citrate and/or allomrinol.
To determine the significance of individual input variables on the neural network model, Wilk’s generalized likelihood ratio test (GLRT) was used to examine the final trained network as a nonlinear regression model.rr When using Wilk’s GLRT, each input node is sequentially removed from the neural network by setting its connection weights to 0; the network is retrained and the final error of the feature-deficient network recorded. This error is compared with the full networks error, resulting in a statistical probability allowing rejection of the null hypothesis that the feature-deficient network and the full network result classify with the same error. This probability thus indicates whether an individual feature is required for the full models accuracy.
RESULTS Although continuing stone formation appears to be more common in patients with residual fragments (17% [n = 81) than in those stone free (7.8% [n = 41) after SWL, further examination of the data (Table I) reveals that the two patient groups were not equivalent, the major difference being the much greater incidence of collecting system dilation (caliectasis) present in the residual fragment group. Although it is known that renal dilation may result in higher residual fragment rates after SWL, it has not been shown which of the two factors is responsible for subsequent stone growth. The classification accuracy of the neural model in the test set was 91%, sensitivity 91%, specificity 92%, and receiver operating characteristic (ROC) curve area 0.964 (1 .O would be a perfect classifier, 0.5 would result from chance guessing). In comparison, classification accuracy for both linear and quadratic discriminant function analysis was 36%, UROLOGY 51 (2), 1998
and although specificity was lOO%, sensitivity was 0% and ROC area 0.524. Using Wilk’s GLRT, no single variable (including residual fragments) was found (all P BO.9) that, when removed, significantly deteriorated the networks classification accuracy; this implies that the presence or absence of residual fragments, per se, is not predictive of continuing stone formation. The final network may be investigated fully by any person using a JavaScript-capable World Wide Web browser (such as Netscape 2.0 and above) at http://godot.urol.uic.edu. As JavaScript code is loaded into the client browser, the entire neural architecture, including trained weights and biases, may be observed (“View Source” in Netscape). We offer this resource because the resulting trained neural network code is too lengthy to be presented here. COMMENT A discussion of stone “recurrence” must allow that this term is often used inappropriately to describe regrowth or enlargement of identifiable calculus (or fragments), as opposed to its strict definition of new stone formation from a radiographically stone-free kidney. In the current study, we used the term “active (or continuing) stone formation” to describe both situations: that is, new stone formation as well as enlargement of existing stone. Initial studies of stone formation rates after SWL treatment focused on residual fragments as a risk factor for future growth. A large number of patients with primarily calcium oxalate stones were evaluated at 1 and 2 years after SWL by Newman et al. ,5 who found that patients with residual fragments had a stone formation rate of 21% compared with a recurrence rate of 8.4% at 1 year in patients stone free after SWL. Further analysis of the data shows that patients who had residual fragments were more commonly those with multiple stones, larger stones, or caliectasis, suggesting that these patients were more “metabolically active” than those who became stone free, and bringing into question the validity of stone-free status as an independent variable. Studies by Fine et al.6 and Yu et al7 showed that patients with residual fragments after SWL more frequently had a larger initial stone burden, as well as a history of more frequent previous stone events, suggesting that stone formation rate differences may result from pre-existing factors rather than merely the presence of fragments after SWL. The importance of normal urinary tract anatomy is shown by Streem,* who followed up patients with infection stones for 3.5 years after percutaneous nephrostolithotomy or SWL and found that stone recurrence is statistically related to the presence of UROLOGY 51 (21, 1998
anatomic or functional urinary tract abnormality and not to the presence of residual stone fragments or the number of recurrent urinary infections.13 Studies by Parks and Coe14 on stone recurrence suggest that the number of previous stone events was the major determinant of new stone formation and postulate that tiny nucleation centers from previous stones may remain in renal tubules to initiate new stone formation. This is predicated on the fact that nucleation of calcium oxalate requires higher supersaturation levels than that needed for crystal growth and aggregation and that presence of these residual nuclei enhances new stone formation, given similar urinary chemistry. They conclude that the relapse rate is proportional to the length of time (and thereby number of stone events) sustained before institution of medical treatment rather than the presence of specific metabolic abnormalities or the time to most recent stone event. Based on these observations, one might predict that the greatly expanded surface area of stone fragments resulting from SWL would cause an explosion of stone growth; yet it is clear from all available data that a great majority of patients (at least 80%) with residual fragments after SWL do not have stone growth or formation of new stones. This finding is confirmed in a recent study by Chen and Streem,ls who demonstrated stone growth in only 11% of patients with post-SWL fragments followed up for a mean of 33.3 months. Other factors, predating SWL treatment, are clearly operative. Use of a neural network in the current study allowed prediction of continuing active stone formation in patients followed up after primary SWL; this model outperformed traditional linear statistical classification methods. Additionally, this method demonstrated that none of the tested risk factors, including the presence of residual fragments, was predictive of continuing stone formation when considered individually. We caution that the lack of significance of the residual stone fragment predictor variable could be attributed to the lack of statistical power in the Wilk’s GLRT analysis for the given sample size, model, and data. However, we note that even if a larger sample size did result in a significant predictor variable effect, the corresponding change in classification accuracy of the model would be too small (based on the current sample size estimates) to continue to warrant the conclusion that the predictor variable was clinically relevant. The irrelevance of residual stone fragments as a strong predictor of recurrence was suspected in studies of specific patient groups using Kaplan-Meier estimates8J3 but not investigated using a robust nonlinear model for multiple variables in a diverse stone population that would 337
result in high classification accuracy. Use of the neural network allowed such analysis. Since the initiation of the neUROn project, we have endeavored to make available to physicians the modeling tools thus created. At first, we provided a common gateway interface (cgi) to trained neural networks executable on our server. In the spirit of distributed computing, we provided this trained neural network as JavaScript code. Any JavaScript-capable World Wide Web browser, such as Netscape version 2.0 and higher, that is directed to our site (http://godot.urol.uic.edu) may load and execute this trained neural network on the local, client machine. This globally available neural network serves not only physicians wishing to predict outcomes for real patients, but also as a learning tool, for the browsing physician may alter individual input variables and view the network’s prediction. Such interaction often yields intriguing results. CONCLUSIONS We demonstrated the use of a computational tool to accurately predict the risk of future stone growth after SWL. The possibility that residual stone fragments may not increase stone formation risk compels us to re-examine our treatment goals for patients with stones and consider treatment options with lesser morbidity than those required to achieve a stone-free result. The ultimate goals should be prevention of stone recurrence and preservation of renal function, and our data provide further evidence that a stone-free result after SWL is not necessarily an independent factor in achieving these goals. REFERENCES 1. Segura JW, Preminger GM, Assimos DG, Dretler SP, Kahn RI, Lingeman JE, Macaluso JN Jr, and McCullough DL: Nephrolithiasis Clinical Guidelines Panel summary report on the management of staghorn calculi. J Urol 151: 1648-1651, 1994. 2. Winfield HN, Clayman RV, Chaussy CG, Weyman PJ,
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UROLOGY 51 (2),1998