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Digital therapeutic care (DTC) programs are unsupervised appbased treatments that provide video exercises and educational material to patients with nonspecific low back pain during episodes of pain and functional disability. German statutory health insurance can reimburse DTC programs since 2019, but evidence on efficacy and reasonable pricing remains scarce. This paper presents a probabilistic sensitivity analysis (PSA) to evaluate the efficacy and costutility of a DTC app against treatment as usual (TAU) in Germany.
The aim of this study was to perform a PSA in the form of a Monte Carlo simulation based on the deterministic base case analysis to account for model assumptions and parameter uncertainty. We also intend to explore to what extent the results in this probabilistic analysis differ from the results in the base case analysis and to what extent a shortage of outcome data concerning qualityoflife (QoL) metrics impacts the overall results.
The PSA builds upon a statetransition Markov chain with a 4week cycle length over a model time horizon of 3 years from a recently published deterministic costutility analysis. A Monte Carlo simulation with 10,000 iterations and a cohort size of 10,000 was employed to evaluate the costutility from a societal perspective. Qualityadjusted life years (QALYs) were derived from Veterans RAND 6Dimension (VR6D) and ShortForm 6Dimension (SF6D) single utility scores. Finally, we also simulated reducing the price for a 3month app prescription to analyze at which price threshold DTC would result in being the dominant strategy over TAU in Germany.
The Monte Carlo simulation yielded on average a €135.97 (a currency exchange rate of EUR €1=US $1.069 is applicable) incremental cost and 0.004 incremental QALYs per person and year for the unsupervised DTC app strategy compared to inperson physiotherapy in Germany. The corresponding incremental costutility ratio (ICUR) amounts to an additional €34,315.19 per additional QALY. DTC yielded more QALYs in 54.96% of the iterations. DTC dominates TAU in 24.04% of the iterations for QALYs. Reducing the app price in the simulation from currently €239.96 to €164.61 for a 3month prescription could yield a negative ICUR and thus make DTC the dominant strategy, even though the estimated probability of DTC being more effective than TAU is only 54.96%.
Decisionmakers should be cautious when considering the reimbursement of DTC apps since no significant treatment effect was found, and the probability of costeffectiveness remains below 60% even for an infinite willingnesstopay threshold. More appbased studies involving the utilization of QoL outcome parameters are urgently needed to account for the low and limited precision of the available QoL input parameters, which are crucial to making profound recommendations concerning the costutility of novel apps.
Low back pain (LBP) poses a tremendous health burden for patients and health care systems worldwide, with a lifetime prevalence of up to 85% [
In Germany, the
We applied a probabilistic sensitivity analysis (PSA) to address uncertainties in the transition probabilities, attrition rates, cost components, and healthrelated quality of life (QoL) scores, which were beyond the scope of the deterministic analysis recently published by Lewkowicz et al [
Because this was a simulation study with no human participants, ethics approval was not sought.
This paper builds on a recent analysis of the costutility of a DTC program for patients with nonacute LBP in Germany from a societal perspective [
Like Lewkowicz et al [
The transition probabilities for states 3, 4, and 5 were derived from the attrition rates reported in the Kaia Health app study [
Discrete health statetransition Markov chain with 7 health states (adapted and reprinted from Lewkowicz et al [
Lewkowicz et al [
Lewkowicz et al [
Transition matrix of the Markov chain.
To and from  Low impact (state 1)  High impact (state 2)  Treatment weeks 14 (state 3)  Treatment weeks 58 (state 4)  Treatment weeks 912 (state 5)  Remission (state 6)  Healthy (state 7)  



DTC^{a}  0.2  0.0125  0.75^{b}  0  0  0.0375  0  

TAU^{c}  0.2  0.0125  0.75^{b}  0  0  0.0375  0  



DTC  0.042  0.158  0.8^{b}  0  0  0  0  

TAU  0.042  0.158  0.8^{b}  0  0  0  0  



DTC  0.0513  0.0111  0  0.87 ^{b}  0  0.0625  0  

TAU  0.0267  0.0057  0  0.935^{b}  0  0.0325  0  



DTC  0.0513  0.0111  0  0  0.875^{b}  0.0625  0  

TAU  0.0176  0.0038  0  0  0.957^{b}  0.0215  0  



DTC  0.2350  0.0509  0  0  0  0.614^{b}  0.1^{b}  

TAU  0.2761  0.0598  0  0  0  0.614^{b}  0.05^{b}  



DTC  0.5047  0.1092  0  0  0  0.386  0  

TAU  0.5047  0.1092  0  0  0  0.386  0  



DTC  0  0  0  0  0  0  1  

TAU  0  0  0  0  0  0  1 
^{a}DTC: digital therapeutic care.
^{b}Transition probabilities taken from the literature. All other transition probabilities in the respective rows are calculated from conditional probabilities given the respective event based on [
^{c}TAU: treatment as usual.
For the PSA, which is a robust method to evaluate the impact of parameter uncertainties [
We considered the input parameters for transition probabilities and QoL outcomes from the literature as “most likely” values and applied the Program Evaluation and Review Technique (PERT) approximation [
We applied the gamma distribution for all cost components, which requires the mean and SD of the cost components as input parameters. We used the results for direct and indirect cost components of chronic LBP over a 6month period reported in a large German costofillness study [
where
We deviated from the assumption in [
We derived costeffectiveness acceptability curves (CEACs) to illustrate the probability of DTC apps being a costeffective measure given a certain willingnesstopay (WTP) threshold. The CEAC indicated the fraction of iterations considered to be costeffective given a specific WTP. Graphically, the WTP threshold was a line through the origin with a slope equal to the respective WTP, and the outcome of an iteration in the Monte Carlo simulation was considered to be costeffective if it lies below the WTP threshold in the costutility plane [
Some health care systems may only adopt novel technologies which are more effective than TAU, (ie, if its incremental effect is nonnegative). We derived an additional CEAC where we included only outcomes that lay in the southeast quadrant or in the northeast quadrant under the WTP threshold in the costutility plane to account for this constraint. Moreover, we computed the number of iterations where DTC strictly dominates TAU (ie, where cost__{DTC}<cost__{TAU} and effect__{DTC}>effect__{TAU}, and viceversa).
Transition probabilities and beta parameters for simulation after PERT^{q} transformation.
Transition probability  Expected value^{b}  SD^{c}  α^{d}  β^{d}  







Low impact (state 1)  0.30000  0.16667  1.96800  4.59200 


High impact (state 2)  0.02439  0.01234  3.78404  151.36171 


Treatment weeks 14 (state 3)  0.66667  0.16667  4.66667  2.33333 


Remission (state 6)  0.06977  0.03612  3.40097  45.34629 





Low Impact (state 1)  0.07749  0.04027  3.33817  39.74008 


High Impact (state 2)  0.27200  0.16667  1.66697  4.46160 


Treatment weeks 14 (state 3)  0.70000  0.16667  4.59200  1.96800 





Low impact (state 1)  0.50314  0.16667  4.02493  3.97471 


High impact (state 2)  0.17938  0.09793  2.57361  11.77401 


Remission (state 6)  0.42400  0.16667  3.30384  4.48823 







Low impact (state 1)  0.09318  0.04880  3.21274  31.26755 


High impact (state 2)  0.02177  0.01100  3.80694  171.09847 


Treatment weeks 58 (state 4)  0.80000  0.11024  9.73257  2.43314 


Remission (state 6)  0.11111  0.05871  3.07279  24.58235 





Low impact (state 1)  0.09318  0.04880  3.21274  31.26755 


High impact (state 2)  0.02177  0.01100  3.80694  171.09847 


Treatment weeks 912 (state 5)  0.80000  0.11024  9.73257  2.43314 


Remission (state 6)  0.11111  0.05871  3.07279  24.58235 





Low impact (state 1)  0.32339  0.16667  2.22404  4.65314 


High impact (state 2)  0.09241  0.04838  3.21882  31.61410 


Remission (state 6)  0.57600  0.16667  4.48823  3.30384 


Healthy (state 7)  0.16667  0.09045  2.66255  13.31276 






Low impact (state 1)  0.05072  0.02601  3.55883  66.60730 


High impact (state 2)  0.01144  0.00575  3.89784  336.89235 


Treatment weeks 58  0.88496  0.06090  23.40459  3.04260 


Remission  0.06103  0.03146  3.47283  53.42822 





Low impact (state 1)  0.03414  0.01736  3.69970  104.67097 


High impact (state 2)  0.00760  0.00381  3.93198  513.71610 


Treatment weeks 912  0.92081  0.04119  38.65633  3.32444 


Remission (state 6)  0.04123  0.02104  3.63908  84.62987 





Low impact (state 1)  0.35079  0.16667  2.52522  4.67334 


High impact (state 2)  0.10684  0.05633  3.10581  25.96486 


Remission (state 6)  0.57600  0.16667  4.48823  3.30384 


Healthy (state 7)  0.09091  0.04756  3.23069  32.30693 
^{a}PERT: Program Evaluation and Review Technique.
^{b}First moment: “Most likely” (expected) value taken from [
^{c}SD for calculation of the second moment taken from [
^{d}Shape parameters α and β for beta distribution were calculated using the method of moments.
^{e}DTC: digital therapeutic care.
^{f}TAU: treatment as usual.
Cost components.
Cost components (health state)  Mean^{a} (SD^{b})  α^{c}  β^{c}  
Low impact (state 1)  441.74 (476.74)  0.8584  514.5364  
High impact (state 2)  588.96 (476.74)  1.5261  385.9023  


GP^{d} consultation  20.47 (43.93)  0.2171  94.2767  
Medication  16.81 (35.36)  0.226  74.3801  
Diagnostic procedure  29.24 (53.72)  0.2962  98.6948  
Indirect cost  147.74 (476.74)  0.0953  1543.6092  
App price (only DTC^{e})  239.96 (N/A^{f})  N/A  N/A  
4 × physiotherapy (only TAU^{g})  102.88 (44.4266)  5.363  19.184  


Medication  16.81 (35.36)  0.226  74.3801  
2 × physiotherapy (only TAU)  46.44 (22.2133)  4.3711  10.6249  
Medication  16.81 (35.36)  0.226  74.3801 
^{a}Mean values taken from [
^{b}SD calculated from 95% CIs reported in [
^{c}Parameters α and β for Gamma distribution calculated from mean and SD values.
^{d}GP: general practitioner.
^{e}DTC: digital therapeutic care.
^{f}N/A: not applicable.
^{g}TAU: treatment as usual.
Healthrelated QoL^{a} utility scores after PERT^{b} transformation.
Healthrelated QoL (QALY^{c} weight)  Expected value^{d}  SD  α^{e}  β^{e}  



Low impact (state 1)  0.655  0.0743^{f}  26.1445  13.7708 

High impact (state 2)  0.61  0.1248^{g}  8.7032  5.5643 

Remission (state 6)  0.806  0.0713^{g}  23.9639  5.7679 

Healthy (state 7)  0.806  0.0713^{g}  23.9639  5.7679 



Treatment weeks 14 (state 3)  0.655  0.0766^{f}  24.5159  12.9129 

Treatment weeks 58 (4)  0.699  0.0695^{f}  29.6712  12.7768 

Treatment weeks 912 (5)  0.748  0.0699^{f}  28.1058  9.4687 



Treatment weeks 14 (3)  0.655  0.0691^{f}  30.2894  15.954 

Treatment weeks 58 (4)  0.717  0.0834^{f}  20.1705  7.9613 

Treatment weeks 912 (5)  0.729  0.0862^{f}  18.6139  6.9196 
^{a}QoL: quality of life.
^{b}PERT: Program Evaluation and Review Technique.
^{c}QALY: qualityadjusted life year.
^{d}First moment: “most likely” (expected) value taken from [
^{e}Shape parameters α and β for beta distribution were calculated using the method of moments.
^{f}SD calculated from [
^{g}SD calculated from [
^{h}DTC: digital therapeutic care.
^{i}TAU: treatment as usual.
The 10,000 iterations of the Monte Carlo simulation yielded average costs of €2263.96 with an average of 0.6941 QALYs per person and year for DTC and an average cost of €2127.99 with an average of 0.6902 QALYs per person and year for TAU. Thus, the mean incremental cost is €135.97, and the mean incremental QALYs are 0.004 per person and year for the DTC app. The corresponding incremental costutility ratio (ICUR) amounts to an additional €34,315.19 per additional QALY.
Summary statistics of the relevant cost and effectiveness outcomes^{a}.
Parameter  Mean (SD)  Median  Min^{b}  Max^{c} 
DTC^{d} cost (€)  2263.96 (1467.69)  1853.92  413.53  22108.91 
DTC cost (€) (hypothetical if app price is € 0)  1830.94 (1456.95)  1420.13  99.77  21544.24 
DTC QALYs^{e}  0.6941 (0.0321)  0.6944  0.5608  0.8223 
TAU^{f} cost (€)  2127.99 (1459.20)  1736.76  251.55  21033.72 
TAU QALYs  0.6902 (0.0309)  0.6909  0.5711  0.7997 
Incremental cost (€)  135.97 (484.54)  149.88  −4748.22  4551.22 
Incremental cost (€) (hypothetical, if app price is 0)  1830.9 (1456.9)  1420.1  99.7704  21544.2 
Incremental QALYs  0.0040 (0.0296)  0.0038  −0.0950  0.1484 
^{a}Table shows summary statistics of the simulation results for the regular app price of €239 (a currency exchange rate of EUR €1=US $1.069 is applicable) and the hypothetical scenario with an app price of €0 per person and year.
^{b}Min: minimum.
^{c}Max: maximum.
^{d}DTC: digital therapeutic care.
^{e}QALY: qualityadjusted life year.
^{f}TAU: treatment as usual.
Monte Carlo simulation results per person and year in the costutility plane. Each dot represents incremental qualityadjusted life years (QALYs) and incremental costs for one simulated outcome in the costutilityplane. Histograms on axes visualize the marginal distributions of incremental costs and incremental QALYs.
DTC was costlier than TAU in 66.53% of the iterations but also yielded more QALYs in 54.96% of the iterations. DTC dominated TAU in 24.04% of the iterations, whereas TAU dominated DTC in 35.61% of the iterations.
The CEAC in
Overview of the numbers of iterations, which indicate the different outcomes.
Parameter  Current app price (€239), %  Hypothetical app price (€0), % 
Positive incremental treatment outcome  54.96  54.96 
Negative incremental treatment outcome  45.04  45.04 
Positive incremental cost  66.53  17.64 
Negative incremental cost  33.47  82.36 
DTC^{a} dominant  24.04  48.85 
TAU^{b} dominant  35.61  11.53 
^{a}DTC: digital therapeutic care.
^{b}TAU: treatment as usual.
Costeffectiveness acceptability curve (CEAC) for qualityadjusted life years (QALYs).
When including iterations with negative incremental effects, the minimum probability of DTC being effective was 33.47%, corresponding to the fraction of iterations with negative incremental costs. The CEAC reached 50% at a WTP of approximately €41,000, flattened at a WTP of around €80,000, and approximated the maximum possible probability of costeffectiveness of 54.96% when the WTP tended to infinity. When excluding outcomes with negative incremental effects, DTC was only considered to be costeffective with a probability of 24.04% for a WTP of €0, corresponding to the fraction of iterations in which DTC strictly dominated TAU. The restricted CEAC reached a probability of costeffectiveness of 50% only at a WTP of approximately €60,000. Like the unrestricted CEAC, the restricted CEAC flattened around a WTP of €80,000 and approximated the maximum possible probability of costeffectiveness of 54.96% when WTP tended to infinity.
We reran the Monte Carlo simulation using the same aforementioned figures but with the app cost set to €0 to assess the costeffectiveness of DTC if the app was available free of charge. Decreasing the app price to €0 yielded a decrease in the incremental cost to €−297.04 and thus a decrease in the ICUR to €−74,964.87. Note that using the same random seed in both simulations assured that the effects and simulated courses of treatment and compliance remained unchanged. Comparing the ICUR with app prices of €239 and €0 allowed us to determine the association between app price and ICUR, which amounts to an increase in the ICUR of €455.41 for each additional Euro charged for a 3month period. Although the ICUR would be negative for an app price below €164,61, the estimated probability of DTC being more effective than TAU was only 54.96%.
This paper presents a PSA to evaluate the potential benefits of an appbased DTC program for patients with LBP in comparison to the TAU in Germany. We found the resulting ICUR to be substantially higher compared to the ICUR in the deterministic base case analysis, indicating that DTC apps are not clearly costeffective at the current app price of €239 compared to TAU in Germany. The PSA yielded incremental costs of €135.97 and 0.004 incremental QALYs per patient and year for the DTC app. The resulting ICUR was €34,315.19 per QALY gained, as compared to €5,486 reported in [
The large difference between the ICUR of 34,315.19 found in the PSA and the ICUR of 5,486 reported in [
Overall, the stark difference between the outcome from the PSA and from [
Although a recent review found 12 studies on 6 different DTC apps with implemented decision support interventions, the control groups in those studies received no specific treatment [
The incremental costs of €135.97 found in the PSA are fairly similar to the €121.59 reported in [
Our scenario analysis focused on the effects of the app cost and investigated how the reimbursement price could be updated to render appbased treatment as a costeffective alternative. The results suggest that an adjusted app reimbursement price less than €164.61, which would be slightly higher than the presumed costs for physiotherapy in the TAU, could lead to negative incremental costs, thus yielding a negative ICUR for the DTC app. Therefore, according to our model, a reimbursement price below €54.87 per month could make DTC somewhat less costly than facetoface physiotherapy, while the health outcomes cannot be considered to differ significantly between TAU and DTC.
Different DTC programs with different app components and divergently progressed decision support interventions are associated with different overall costutility outcomes. While the core components and the core method of health care delivery are similar among these apps, further implementations such as virtual reality guidance during exercises or personalized feedback interventions through push notifications may improve the efficacy of DTC programs and generate increased effects on the QoL of LBP patients. Extended capabilities of decision support interventions may have a significantly positive impact on the longterm outcome [
To the best of our knowledge, along with [
The shortage of data may involve potential biases in the parameters of the distributions. We applied the PERT approach to derive probability density functions for the transition probabilities and considered the basecase values from [
For the gamma distribution, the input values for the standard deviation parameter were derived from a German costofillness study and adopted for the cost components in the PSA. Since we found no information in the literature on potential correlations between different cost components, we sampled each cost component independently in the PSA. The cost outcome may thus be biased either upward or downward, depending on whether higher costs in 1 component increase (eg, if more physician visits trigger more prescriptions) or decrease (eg, if seeing the physician more often avoids costs in other components) the costs in other components. However, since indirect costs make up the largest part of total cost and all cost parameters except for the app reimbursement price and cost of facetoface physiotherapy are equally included in both strategies, we argue that the missing correlations may have only a relatively small impact on our overall findings.
Our model focused on the direct comparison between the cost of unsupervised DTC and personal physiotherapy, and we excluded inpatient and rehabilitation care, as well as minor ambulatory treatment modalities. Overall, only 81% of total LBPrelated health care expenditures were considered in our simulation [
Finally, measuring QoL through 2 different metrics (ie, the SF6D and VR6D) is another potential limitation. We acknowledge that using different outcome metrics for 1 simulation is not recommended but argue that SF6D and VR6D tend to be highly correlated and yield comparable outcomes, so they may be used interchangeably [
Allowing for parameter uncertainty yielded a significantly higher ICUR than the previously published deterministic approach. The CEACs indicate that the DTC approach is not very likely to be costeffective, as the probability of costeffectiveness remains below 55% even for an infinite WTP. One reason for the inconclusive result for QoL may be the high uncertainty, especially in health outcomes. At present, decisionmakers should be cautious when considering the reimbursement of DTC apps, since no significant incremental effect on health was found. However, future developments of DTC apps may involve further decision support interventions, which may improve compliance, decrease attrition, and eventually yield better health outcomes. Future evaluations of DTC programs should strive to improve the precision of QoL outcome data and preferably aim to evaluate DTC apps with decision support interventions in a reallife environment.
A. Applying Program Evaluation and Review Technique (PERT) and Method of Moments (MoM) methods. B. Summary of probabilistic sensitivity analysis (PSA) input parameters and probability density functions.
Histogram: cost parameter.
Histogram: quality of life (QoL) parameter.
Histogram: digital therapeutic care (DTC) transition matrix.
Histogram: treatmentasusual (TAU) transition matrix.
costeffectiveness acceptability curve
Digital Health Applications
digital therapeutic care
International Classification of Diseases 10th revision
incremental costutility ratio
low back pain
Program Evaluation and Review Technique
probabilistic sensitivity analysis
qualityadjusted life year
quality of life
randomized controlled trial
ShortForm 6Dimension
treatment as usual
Veterans RAND 12Item Health Survey
Veterans RAND 6Dimension
willingness to pay
This work has received funding from the European Union’s Horizon 2020 research and innovation program Smart4Health (grant 826117). It was also funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Projektnummer 491466077
All data generated or analyzed during this study are included in this published paper and its Multimedia Appendix files.
DL and MS conceptualized the study. DL and MS were in charge of the Monte Carlo simulation and analyses, interpretation of the results, and writing of the manuscript. DL, MS, and EB contributed to refining all sections and critically editing the manuscript. All authors approved the submitted manuscript.
None declared.