Djang R, Stahl JE and Pais VM Jr: Informing the management of asymptomatic nephrolithiasis: Markov decision analysis for the 1 cm renal stone. Urol Pract 2021; 8: 495.

Asymptomatic renal calculi have an estimated prevalence of up to 7.8%.^1,2 Such stones can remain asymptomatic indefinitely, although 20–50% may progress to a symptomatic state and potentially require intervention.³

The management of incidentally discovered, asymptomatic renal stones is controversial. While some choose watchful waiting, others recommend preemptive surgical treatments. Of the available surgical options, shock wave lithotripsy (SWL) is considered the least invasive and has purported highest initial postoperative quality of life (QOL), although it has inferior stone-free rates (SFRs) compared with ureteroscopy with basket extraction of fragmented stones (URS-B).^4,5 More recently, ureteroscopy with laser “dusting” (URS-D), generating very fine fragments left in situ to pass, has enjoyed growing acceptance as it reduces the need for a ureteral stent and thus may offer improved QOL. Literature, though, suggests inferior SFR compared with URS-B.⁶

As each intervention is associated with different rates of success and associated benefits tempered by rates of failure including residual stones, need for repeat procedures, unscheduled visits to the emergency department and variable patient tolerance for these risks, the optimal management for a patient confronting this increasingly common scenario remains undefined.

To address such issues, we constructed a Markov decision analysis model to show which management option would optimally preserve the highest quality adjusted life years (QALYs).⁷

Markov decision processes simplify analysis of complex, real world scenarios whereby uncertain events are modeled as transitions between different states based on known existing or estimated probabilities for transition. This statistical methodology is frequently employed in the legal, statistical, engineering and medical disciplines to help determine optimal strategies of action given probabilities of ongoing risk over time. For example, Markov models have been employed to assess colon cancer screening⁸ and cardiac stents.⁹

In our Markov decision process (fig. 1, table), we examined the quality of life preserved as a function of probability of success of each of the 4 possible interventions of interest (watchful waiting, URS-B, URS-D and SWL) for a solitary 1 cm asymptomatic stone in a hypothetical otherwise healthy middle-aged patient. Decision analysis trees were constructed using TreeAge Pro software (TreeAge Software, Inc., Williamstown, Massachussetts; 2019). Failures of watchful waiting (ie, an asymptomatic stone becoming symptomatic) or failed interventions with residual stones realize penalties that reduce the overall QALYs that a hypothetical patient would preserve at the end of a 3-year period. We derived probabilities, utilities and toll-penalties from existing literature whenever possible and clinical extrapolation when no published data were available. Additionally, penalties for receiving a ureteral stent and undergoing surgery were standardized and incorporated into each subtree when indicated. We also performed 1-way sensitivity analyses to determine threshold probabilities and utilities that may alter preferred options.

Figure 1. Markov decision tree, global view.

Employing baseline published SFRs (92% after URS-B,¹⁰ 74% after SWL,¹⁰ and 58% after URS-D⁶), we found that watchful waiting is the overall short-term preferred management strategy for an asymptomatic stone, preserving 2.82 QALYs over the 3-year period. The remaining options had similar but decreasing QALYs—URS-B provided 2.78 QALYs, SWL provided 2.72 QALYs and URS-D provided 2.67 QALYs.

Other interventions varied in superiority based upon their respective SFRs and this can be appreciated when interpreting 1-way sensitivity data. URS-D is only superior as an intervention when URS-B is encumbered with poor SFR; specifically, intervention success less than 37% (fig. 2). But with increasing SFR of URS-B, specifically at a value >62% in our Markov analysis, URS-B becomes the preferred interventional-specific option for an asymptomatic stone as it preserves the highest QALYs of any surgical option, even in the setting of a toll penalty for ureteral stent placement and the subsequent decrease in quality of life as previously estimated in the literature. As SFR probabilities and utility/disutility values remain in flux, 1-way sensitivity analyses represent the most useful aspect of this Markov analysis as the probability of stone-free URS-B varies between surgeon and is unlikely to be a single, static value for each patient.

Figure 2. URS-B, 1-way sensitivity analysis.

In addition, clinical experience informs that stent tolerance varies widely between patients with variable detriment to QOL. Therefore, 1-way sensitivity analysis was performed to assess the effect of varying disutility attributed to stent pain (fig. 3). This revealed that despite high stent disutility (penalty) values, URS-B remained the preferred option for intervention. We found that URS-B remains the preferred intervention at the highest levels of stent penalty because of the high stone-free success rates of URS-B, specifically at 92%. In other words, URS-B with stent penalties still preserves quality of life compared to procedures (eg SWL and URS-D) which may initially be less burdensome to the patient, but have a significantly higher proportion of repeat surgery.

Figure 3. Disutility (penalty) related to ureteral stents, 1-way sensitivity analysis.

In summary, when accounting for SFR, QOL penalties for ureteral stent placement, and anticipated utilities of associated health states over a 3-year period, watchful waiting is the preferred management modality in our Markov decision model for an asymptomatic 1 cm solitary renal stone in a healthy hypothetical patient, over 3 years. Sensitivity analyses further described threshold levels when one intervention becomes superior to the other based upon observed variance in real world stone-free probabilities and patient-derived utilities.

Overall, these analyses demonstrate variability in preserved QALYs based on how stents are tolerated and the surgeon’s SFRs per modality, underscoring the importance of regular review of surgeon-specific SFRs and counseling of patients. Notably, several variables were not included in our model including cost-effectiveness, patient anxiety related to harboring a stone, comorbidity, stone location, and stone type, amongst others. We plan to incorporate such parameters in a future study. Future iterations would also benefit from improved utility and disutility measures, which likely can be best derived from available and future stone-specific quality of life measures such as the Wisconsin stone QOL (WISQOL) questionnaire. Once the “dust” settles, a unified Markov model incorporating all these variables as well as surgeon-specific SFRs and patient-specific variables to QOL may provide clarity to the debate for managing an asymptomatic renal stone.