This study aimed to evaluate the performance of a model to predict for the outcome of SWL treatment using both patient and stone related variables. The resulting model showed moderate predictive ability (AUC of 0.64–0.67) in terms of the ability to discriminate between a successful or unsuccessful outcome after SWL treatment. Predictive ability in terms of calibration was poor based on a significant Hosmer–Lemeshow test, meaning that the observed and expected outcomes in tested subgroups of our sample were not similar. Including variables calculated from CTTA did not increase the predictive ability of the model. There could be several reasons for this including bias in the data collection and classification of outcome, and not having selected the most influential factors for SWL efficacy as variables in the model. Our results suggest there is not enough current understanding of the important predictive factors for SWL efficacy to be able to produce a useful model to aid clinical decision making for which cases are most suitable for SWL treatment.

This is the first study that has examined a wide range of both patient and stone related variables using three different methods of multivariable analyses. Several studies have found the significance of single factors to predict for SWL success4,11,15,20,23. Of the studies which produced a predictive model using a combination of different factors thought to affect SWL success rate12,17,18,19,28, only three studies (which both used logistic regression) have presented ROC analysis on the predictive performance of these models10,16,21. Our AUC values (0.64–0.67) were lower than the AUC of 0.75 to 0.87 found using logistic regression models in these three previous studies10,16,21 - even though there were variables in agreement between our study and the above three studies, in terms of finding that age, SSD, stone size and number of stones were significant predictors in a multivariable model. This may be explained due to the problems of overfitting and the inclusion of related or co-correlated variables when using logistic regression. The LASSO method reduces this problem by shrinking the weight of each predictor, and the PLS method also has the advantage of not using univariate results for the pre-selection of variables into the multivariable analysis. These methods used in our study therefore reduces the overestimation of variable significance, and overall predictive ability. We also kept continuous data as continuous (to avoid loss of information through categorization which three other studies have done with some variables before statistical analysis)10,13,16,28.

Furthermore, unlike previous studies, we also performed several multivariable analyses. A comparison of the performance of predictive models for the outcome of ‘Completely Stone Free’ or ‘Stone Free with CIRFs’ using three methods of multivariable analyses in Table 4, shows that, neither the LASSO method nor the Random Forests method produced an AUC of more than 0.7. At this predictive level, the models produced in this study are unlikely to be useful in discriminating for cases most likely to succeed or fail SWL.

Use of CTTA on stone imaging

Recent interest in extracting more information from CT images of the stone have produced results suggesting the importance of stone heterogeneity, in addition to stone attenuation, as a predictive factor for successful SWL14,15,22,23,24,25,28. Stone attenuation is a well-researched predictive factor for SWL outcome. Stone attenuation, as measured in this study using the mean HU value, was a significant predictor for SWL outcome on univariate analyses but was not chosen to be included in the multivariable analyses, suggesting that size may have had more weight in our model. Previous studies have used a variety of methods to quantify stone heterogeneity from use of subjective visualization to statistical methods14,15,22,23,24,25,28. The CTTA method used in this study calculates variables which have been previously validated in tumor imaging26. This method also reduces measurement bias as there is no user-dependent variability in drawing the region of interest (ROI) or interpreting the results. Our study has the advantage of using objective measures of stone heterogeneity by using textural analysis of the distribution of all of the pixels in a cross-section of stone, rather than subjective observation of stone appearance on CT which can be difficult to differentiate14,23. One study found that they were unable to view the internal structure of stones on non-contrast CT to classify as hyper-or hypodense centre or homogeneous19. Rather than subjecting patients to higher resolution CT scans, textural analysis may provide a more practical way of assessing stone heterogeneity. However, in our study, the addition of textural analysis variables did not significantly improve the predictive ability of the multivariable model, although many textural features were significant on univariate analysis. It is likely that variables related to the size of the stone, including total number of pixels, and entropy which is correlated to stone size, are the most influential factors. However, as methods of CT image analysis develop, it is foreseeable that we will gain more information on stone characteristics, including architecture and composition to aid treatment.

Study limitations

Limitations of our study include: its retrospective nature and the measurement of some variables on the largest stone only if there was more than one stone. Retrospective collection of variable and outcome data may have led to bias and reduced the predictive ability of a multivariable model. However, this also allowed a more pragmatic approach, by including cases with more than one stone and repeated SWL sessions, our results may be more applicable to clinical practice. A previous study has found that the size and HU density of the largest stone was a better predictor than the mean where more than one stone was treated18. Our analysis of the solitary stones showed similar predictive ability and suggests that our measurements based on the largest stone have not biased the data.

In summary, analysis of clinical and stone imaging factors, including more novel variables of CTTA in this study has not produced a useful model for predicting the outcome of SWL. This study supports findings from previous studies on the importance of predictor factors relating to patient age and stone size, as well as contradicting some popular beliefs on the importance of skin-to-stone distance and the lower pole position. However, our results do not support previous study findings which suggest CTTA variables have additional predictive value above traditional factors related to stone size.