Introduction
Methodology
Treatment data
Cost data
Simulation
Output | Equation |
---|---|
TOPuB1 | if(round(LEX-AFIa) > (LEX-MIA),round(LEX-AFIb),round(LEX-AFIa)) |
TOPuB2 | if(TOPuB1 > 77;round(LEX-AFIc);TOPuB1) |
TOPlB1 | if(TOPuB2 < 1;round(LEX-AFIb);TOPuB2) |
TOPlB2 | if(TOPlB1 < 1;round(LEX-AFIc);TOPlB1) |
TOPlB3 | if(TOPlB2 < 1;1;TOPlB2) |
TOPuB3 | if(TOPlB3 > (LEX-MIA);(LEX-MIA);TOPlB3) |
TOP | TOPuB3 |
AFI | LEX-TOP |
LTS1lB | if(LTS1 < 0;0;LTS1) |
LTS2lB | if(LTS2 < 0;0;LTS2) |
LTS3lB | if(LTS3 < 0;0;LTS3) |
EP_LTS_G1 | TOP-LTS1lB-LTS2lB-LTS3lB [upper spec limit = 0] |
DR_LTS1 | round(LTS1lB-0,5) [lower spec limit = 1] |
DR_LTS10 | round(LTS1lB-0,5) [lower spec limit = 10] |
DR_LTS25 | round(LTS1lB-0,5) lower spec limit = 25] |
NOI_G1 | 1 + if(LTS1lB > = TOP;0;1) + if((LTS1lB + LTS2lB) > = TOP;0;1) |
TTR1lB | if(TTR1 < 0;0;TTR1) |
TTR2lB | if(TTR2 < 0;0;TTR2) |
TTR3lB | if(TTR3 < 0;0;TTR3) |
TTR4lB | if(TTR4 < 0;0;TTR4) |
TTR1uB | TTR1lB |
TTR2uB | TTR2lB |
TTR3uB | TTR3lB |
TTR4uB | TTR4lB |
EP_TTR_G1 | TOP-TTR1uB-TTR2uB-TTR3uB-TTR4uB [upper spec limit = 0] |
DR_TTR1 | round(TTR1uB-0.5) [lower spec limit = 1] |
DR_TTR5 | round(TTR1uB-0.5) [lower spec limit = 5] |
DR_TTR10 | round(TTR1uB-0.5) [lower spec limit = 10] |
NOR_G1 | if(TTR1uB > = TOP;0;1) + if((TTR1uB + TTR2uB) > = TOP;0;1) + if((TTR1uB + TTR2uB + TTR3uB) > = TOP;0;1) |
TTU | TTUa + TTUb |
TAP | round(TTU) |
NOP_G1 | if(TOP > = TAP;1;0) + if(TOP > = (2*TAP);1;0) + if(TOP > = (3*TAP);1;0) + if(TOP > = (4*TAP);1;0) + if(TOP > = (5*TAP);1;0) + if(TOP > = (6*TAP);1;0) + if(TOP > = (7*TAP);1;0) + if(TOP > = (8*TAP);1;0) + if(TOP > = (9*TAP);1;0) + if(TOP > = (10*TAP);1;0) + if(TOP > = (11*TAP);1;0) + if(TOP > = (12*TAP);1;0) |
G1_CFI | (ISB + 3*FOA)/((1 + DIR)^0) |
G1_CRI | if(LTS1lB < TOP;1;0)*((ISB + 2*FOA)/((1 + DIR)^(round(LTS1lB-0.5)))) + if((LTS1lB + LTS2lB) < TOP;1;0)*((ISB + 2*FOA)/((1 + DIR)^((round(LTS1lB + LTS2lB-0.5))))) |
G1_CRE | if(TTR1uB < TOP;1;0)*((REV + FOA)/((1 + DIR)^(round(TTR1uB-0.5)))) + if((TTR1uB + TTR2uB) < TOP;1;0)*((REV + FOA)/((1 + DIR)^((round(TTR1uB + TTR2uB-0.5))))) + if((TTR1uB + TTR2uB + TTR3uB) < TOP;1;0)*((REV + FOA)/((1 + DIR)^((round(TTR1uB + TTR2uB + TTR3uB-0.5))))) |
G1_APU | if(TOP > = TAP;1;0)*(APU/((1 + DIR)^TAP)) + if(TOP > = (2*TAP);1;0)*(APU/((1 + DIR)^(2*TAP))) + if(TOP > = (3*TAP);1;0)*(APU/((1 + DIR)^(3*TAP))) + if(TOP > = (4*TAP);1;0)*(APU/((1 + DIR)^(4*TAP))) + if(TOP > = (5*TAP);1;0)*(APU/((1 + DIR)^(5*TAP))) + if(TOP > = (6*TAP);1;0)*(APU/((1 + DIR)^(6*TAP))) + if(TOP > = (7*TAP);1;0)*(APU/((1 + DIR)^(7*TAP))) + if(TOP > = (8*TAP);1;0)*(APU/((1 + DIR)^(8*TAP))) + if(TOP > = (9*TAP);1;0)*(APU/((1 + DIR)^(9*TAP))) + if(TOP > = (10*TAP);1;0)*(APU/((1 + DIR)^(10*TAP))) + if(TOP > = (11*TAP);1;0)*(APU/((1 + DIR)^(11*TAP))) + if(TOP > = (12*TAP);1;0)*(APU/((1 + DIR)^(12*TAP))) |
G1_TSC | FOA*((((1 + DIR)^(TOP-1))-1)/(((1 + DIR)^(TOP-1))*DIR)) |
G1_LTC | G1_CFI + G1_CRI + G1_CRE + G1_APU + G1_TSC |
Output | Equation |
---|---|
THIlB | if(round(THIt) < TOP,round(THIt),TOP) |
THI | if(THIlB < 25,THIlB,25) |
TSB | TOP-THI |
NHI_G2 | 1 + if(DSH1 < THI,1,0) + if((DSH1 + DSH2) < THI,1,0) + if((DSH1 + DSH2 + DSH3) < THI,1,0) + if((DSH1 + DSH2 + DSH3 + DSH4) < THI,1,0) + if((DSH1 + DSH2 + DSH3 + DSH4 + DSH5) < THI,1,0) |
EP_NHI_G2 | THI-DSH1-DSH2-DSH3-DSH4-DSH5-DSH6 |
G2_CFI | (HIS1 + 2*FOA)/((1 + DIR)^0) |
G2_CFS | if(DSH1 < THI,1,0)*((HIS2 + FOA)/((1 + DIR)^round(DSH1-0,5))) + if((round(DSH1 + DSH2)) < THI,1,0)*((HIS3 + FOA)/((1 + DIR)^round(DSH1 + DSH2-0,5))) + if((round(DSH1 + DSH2 + DSH3)) < THI,1,0)*((HIS4 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3-0,5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4)) < THI,1,0)*((HIS5 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4-0,5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5)) < THI,1,0)*((HIS6 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5-0,5))) |
G2_VSB | (ISB + 2*FOA)/((1 + DIR)^THI) |
G2_CRI | if(LTS1lB < TSB;1;0)*((ISB + 2*FOA)/((1 + DIR)^round(THI + LTS1lB-0,5))) + if((LTS1lB + LTS2lB) < TSB;1;0)*((ISB + 2*FOA)/((1 + DIR)^round(THI + LTS1lB + LTS2lB-0,5))) |
NOI_G2 | 1 + if(LTS1lB > = TSB,0,1) + if((LTS1lB + LTS2lB) > = TSB,0,1) |
G2_CRE | if(TTR1uB < TSB,1,0)*((REV + FOA)/((1 + DIR)^round(THI + TTR1uB-0,5))) + if((TTR1uB + TTR2uB) < TSB,1,0)*((REV + FOA)/((1 + DIR)^round(THI + TTR1uB + TTR2uB-0,5))) + if((TTR1uB + TTR2uB + TTR3uB) < TSB,1,0)*((REV + FOA)/((1 + DIR)^round(THI + TTR1uB + TTR2uB + TTR3uB-0,5))) |
NOR_G2 | if(TTR1uB > = TSB,0,1) + if((TTR1uB + TTR2uB) > = TSB,0,1) + if((TTR1uB + TTR2uB + TTR3uB) > = TSB,0,1) |
G2_TSC | G1_TSC |
G2_APU | if(TSB > = TAP;1;0)*(APU/((1 + DIR)^(TAP + THI))) + if(TSB > = (2*TAP);1;0)*(APU/((1 + DIR)^(2*TAP + THI))) + if(TSB > = (3*TAP);1;0)*(APU/((1 + DIR)^(3*TAP + THI))) + if(TSB > = (4*TAP);1;0)*(APU/((1 + DIR)^(4*TAP + THI))) + if(TSB > = (5*TAP);1;0)*(APU/((1 + DIR)^(5*TAP + THI))) + if(TSB > = (6*TAP);1;0)*(APU/((1 + DIR)^(6*TAP + THI))) + if(TSB > = (7*TAP);1;0)*(APU/((1 + DIR)^(7*TAP + THI))) + if(TSB > = (8*TAP);1;0)*(APU/((1 + DIR)^(8*TAP + THI))) + if(TSB > = (9*TAP);1;0)*(APU/((1 + DIR)^(9*TAP + THI))) + if(TSB > = (10*TAP);1;0)*(APU/((1 + DIR)^(10*TAP + THI))) + if(TSB > = (11*TAP);1;0)*(APU/((1 + DIR)^(11*TAP + THI))) + if(TSB > = (12*TAP);1;0)*(APU/((1 + DIR)^(12*TAP + THI))) |
NOP_G2 | if(TSB > = TAP;1;0) + if(TSB > = (2*TAP);1;0) + if(TSB > = (3*TAP);1;0) + if(TSB > = (4*TAP);1;0) + if(TSB > = (5*TAP);1;0) + if(TSB > = (6*TAP);1;0) + if(TSB > = (7*TAP);1;0) + if(TSB > = (8*TAP);1;0) + if(TSB > = (9*TAP);1;0) + if(TSB > = (10*TAP);1;0) + if(TSB > = (11*TAP);1;0) + if(TSB > = (12*TAP);1;0) |
G2_LTC | G2_CFI + G2_CFS + G2_VSB + G2_CRI + G2_CRE + G2_APU + G2_TSC |
EP_LTS_G2 | TSB-LTS1lB-LTS2lB-LTS3lB |
EP_TTR_G2 | TSB-TTR1uB-TTR2uB-TTR3uB-TTR4uB |
Output | Equation |
---|---|
G3_CFI | (HIS1 + 2*FOA)/((1 + DIR)^0) |
G3_CFS | if(DSH1 < TOP;1;0)*((HIS2 + FOA)/((1 + DIR)^round(DSH1-0.5))) + if((round(DSH1 + DSH2)) < TOP;1;0)*((HIS3 + FOA)/((1 + DIR)^round(DSH1 + DSH2-0.5))) + if((round(DSH1 + DSH2 + DSH3)) < TOP;1;0)*((HIS4 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3-0.5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4)) < TOP;1;0)*((HIS5 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4-0.5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5)) < TOP;1;0)*((HIS6 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5-0.5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6)) < TOP;1;0)*((HIS7 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6-0.5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7)) < TOP;1;0)*((HIS8 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7-0.5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8)) < TOP;1;0)*((HIS9 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8-0.5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9)) < TOP;1;0)*((HIS10 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9-0.5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10)) < TOP;1;0)*((HIS11 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10-0.5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10 + DSH11)) < TOP;1;0)*((HIS12 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10 + DSH11-0.5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10 + DSH11 + DSH12)) < TOP;1;0)*((HIS13 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10 + DSH11 + DSH12-0.5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10 + DSH11 + DSH12 + DSH13)) < TOP;1;0)*((HIS14 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10 + DSH11 + DSH12 + DSH13-0.5))) + if((round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10 + DSH11 + DSH12 + DSH13 + DSH14)) < TOP;1;0)*((HIS15 + FOA)/((1 + DIR)^round(DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10 + DSH11 + DSH12 + DSH13 + DSH14-0.5))) |
G3_TSC | G1_TSC |
EP_NHI_G3 | TOP-DSH1-DSH2-DSH3-DSH4-DSH5-DSH6-DSH7-DSH8-DSH9-DSH10-DSH11-DSH12-DSH13-DSH14-DSH15 |
G3_LTC | G3_CFI + G3_CFS + G3_TSC |
NHI_G3 | 1 + if(DSH1 < TOP;1;0) + if((DSH1 + DSH2) < TOP;1;0) + if((DSH1 + DSH2 + DSH3) < TOP;1;0) + if((DSH1 + DSH2 + DSH3 + DSH4) < TOP;1;0) + if((DSH1 + DSH2 + DSH3 + DSH4 + DSH5) < TOP;1;0) + if((DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6) < TOP;1;0) + if((DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7) < TOP;1;0) + if((DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8) < TOP;1;0) + if((DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9) < TOP;1;0) + if((DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10) < TOP;1;0) + if((DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10 + DSH11) < TOP;1;0) + if((DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10 + DSH11 + DSH12) < TOP;1;0) + if((DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10 + DSH11 + DSH12 + DSH13) < TOP;1;0) + if((DSH1 + DSH2 + DSH3 + DSH4 + DSH5 + DSH6 + DSH7 + DSH8 + DSH9 + DSH10 + DSH11 + DSH12 + DSH13 + DSH14) < TOP;1;0) |
Model parameters
Input name | Distribution | Parameters | Source |
---|---|---|---|
LEX – life expectancy | Fixed | Value: 81 | [24] (mean value man and woman) |
MIA – minimum implantation age | Fixed | Value: 5 | [25] |
AFIa, AFIb, AFIc – age at first intervention (for lower/upper bound correction) | Weibull | Shape: 244.32323 Scale: 2866.73542 Threshold: -2806.08613 | own, based on medical data |
FOA – flat-rate outpatient appointments | Fixed | Value: 145 | own, based on MHH cost data |
DIR – discount rate | Fixed | Value: 0.05 | [22] |
ISB – cost of implantation of Vibrant Soundbridge | Lognormal | Location: 9.57283 Scale: 0.07429 | own, based on medical data and cost data mentioned before |
LTS1, LTS2, LTS3 – lifetime Vibrant Soundbridge | Triangular | Lower: -3 Mode: 0 Upper: 400 | own, based on medical data |
TTR1, TTR2, TTR3 – time to revision | Triangular | Lower: -3 Mode: 0 Upper: 140 | own, based on medical data |
REV – cost revision | Lognormal | Location: 8.29047 Scale: 0.20121 | own, based on medical data and cost data set |
APU – cost audio processor | Fixed | Value: 5719.9 | [26] |
TTUa – time to upgrade APU minimum | Fixed | Value: 6 | [23] |
TTUb – additional time to upgrade APU | Exponential | Rate: 1.41988 | own, based on medical data |
THIt – Time of hearing-improving intervention total (for lower/upper bound correction) | Lognormal | Location: 0.70939 Scale: 1.3453 | own, based on medical data |
DSH1, DSH2, … DSH15 – duration of success of hearing-improving surgery | Weibull | Shape: 0.68361 Scale: 1.74601 Threshold: 0.28273 | own, based on medical data |
HIS1, HIS2, … HIS15 – cost of hearing-improving surgery | Lognormal | Location: 8.2339 Scale: 0.25662 | own, based on medical data and cost data set |
Results
Treatment duration (“TOP”)
Model results of group 1
-
Rate after one year: 1.12%
-
Rate after ten years: 5.65%
-
Rate after 25 years: 12.62%.
-
Rate after one year: 1.00%
-
Rate after ten years: 4.80%
-
Rate after 25 years: 4.80% - No implant failures across all patients after the tenth year of use.
-
Revision rate after one year: 3.32%.
-
Revision rate after five years: 8.64%.
-
Revision rate after ten years: 15.57%.
-
Revision rate after one year: 3.00%.
-
Revision rate after five years: 7.90%
-
Revision rate after ten years: 13.80%.
Model results group 2
Model results group 3
-
Group 1: VSB direct 28,324.51€ (± 6120.84€).
-
Group 2: hearing-improvement surgery, then VSB 32,187.07€ (± 6901.79€)
-
Group 3: only hearing-improvement surgery 28,381.09€ (± 10,326.73€)
-
Rank 1: VSB direct 1059.61€ per year
-
Rank 2: Only hearing-improvement surgery 1212.55€ per year
-
Rask 3: Hearing-improvement surgery, then VSB 1229.14€ per year
Discussion
Influence of the duration of treatment (TOP)
-
When considering the duration of care and taking into account a successful treatment, VSB implantation seems to be a reasonable to option for remaining lifetimes of more than 13 years.
-
For shorter treatment durations, hearing-improvement surgery appears to make sense from an economical perspective.
-
If the remaining lifetime is more than 35 years, successful treatment with hearing-improving interventions alone becomes less likely, as even with the maximum number of 15 hearing-improving operations defined in the model, an increasing proportion of people in this group cannot be treated for the remaining time. Thus, from a cost perspective, alternative treatment options must be considered. The VSB seems to be a reasonable choice due to its lower lifetime costs.
Homogeneity of costs
Total simulation set (TOP) | 10 years | 20 years | 30 years | |
---|---|---|---|---|
n in simulation | 10,000 | 196 | 323 | 258 |
Group 1 | ||||
Average cost in € | 28,325 | 21,123 | 27,037 | 30,842 |
Standard deviation in € | 6121 | 3249 | 4258 | 4652 |
Cost homogeneity | 0.82 | 0.87 | 0.86 | 0.87 |
Group 2 | ||||
Average cost in € | 32,187 | 25,321 | 31,096 | 34,232 |
Standard deviation in € | 6902 | 4496 | 5662 | 5975 |
Cost homogeneity | 0.82 | 0.85 | 0.85 | 0.85 |
Group 3 | ||||
Average cost in € | 28,381 | 18,471 | 27,409 | 32,552 |
Standard deviation in € | 10327 | 8018 | 9690 | 8037 |
Cost homogeneity | 0.73 | 0.70 | 0.74 | 0.80 |
t-test–mean cost | ||||
G1 vs. G2 | < 0.001 | < 0.001 | < 0.001 | < 0.001 |
G1 vs. G3 | 0.637 | < 0.001 | 0.528 | 0.003 |
G2 vs. G3 | < 0.001 | < 0.001 | < 0.001 | 0.007 |
Bonnet-test - standard deviation | ||||
G1 vs. G2 | < 0.001 | 0.013 | 0.002 | 0.031 |
G1 vs. G3 | < 0.001 | < 0.001 | < 0.001 | < 0.001 |
G2 vs. G3 | < 0.001 | < 0.001 | < 0.001 | < 0.001 |
-
– The use of a middle ear implant makes future costs significantly easier to plan, since there is a higher degree of cost homogeneity.
Influence of the number of hearing-improvement surgeries
NHI (G1 or G2 data) | Mean in € | Standard deviation | Cost increased? |
---|---|---|---|
“0” = G1_LTC | 28,325 | 6121 | – |
“1” | 30,606 | 6499 | < 0.001 |
“2” | 32,347 | 6493 | < 0.001 |
“3” | 32,796 | 6953 | 0.030 |
“4” | 34,067 | 7567 | < 0.001 |
“5” | 35,394 | 7361 | < 0.001 |