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Evidence synthesis # Comparative analysis of Stanmore & Charnley incorporating all evidence n = 10000 updates (1 per simulated set of parameter values) are required for this model; For hazard ratio estimates, monitor HR. monitor C.incr, BQ.incr, BL.incr ICER, INB and P.CEA Sections of the code that have changed from Model 1 are shown in pink model { # Cost-effectiveness model ###################### for(n in 1:2) { # loop over protheses # Costs for(t in 1:N) { ct[n,t] <- inprod(pi[n,t,], c[n,])/pow((1+delta.c), (t-1)) } C[n] <- C0[n] + sum(ct[n,]) # Benefits - life expectancy for(t in 1:N) { blt[n,t] <- inprod(pi[n,t,], bl[])/pow((1+delta.b), (t-1)) } BL[n] <- sum(blt[n,]) # Benefits - QALYs for(t in 1:N) { bqt[n,t] <- inprod(pi[n,t,], bq[])/pow((1+delta.b), (t-1)) } BQ[n] <- sum(bqt[n,]) # Markov model probabilities: ####################### # Transition matrix for(t in 1:N) { Lambda[n,t,1,1] <- 1 - gamma[n,t] - lambda[t] Lambda[n,t,1,2] <- gamma[n,t] * lambda.op Lambda[n,t,1,3] <- gamma[n,t] *(1-lambda.op) Lambda[n,t,1,4] <- 0 Lambda[n,t,1,5] <- lambda[t] Lambda[n,t,2,1] <- 0 Lambda[n,t,2,2] <- 0 Lambda[n,t,2,3] <- 0 Lambda[n,t,2,4] <- 0 Lambda[n,t,2,5] <- 1 Lambda[n,t,3,1] <- 0 Lambda[n,t,3,2] <- 0 Lambda[n,t,3,3] <- 0 Lambda[n,t,3,4] <- 1 - lambda[t] Lambda[n,t,3,5] <- lambda[t] Lambda[n,t,4,1] <- 0 Lambda[n,t,4,2] <- rho * lambda.op Lambda[n,t,4,3] <- rho * (1- lambda.op) Lambda[n,t,4,4] <- 1 - rho - lambda[t] Lambda[n,t,4,5] <- lambda[t] Lambda[n,t,5,1] <- 0 Lambda[n,t,5,2] <- 0 Lambda[n,t,5,3] <- 0 Lambda[n,t,5,4] <- 0 Lambda[n,t,5,5] <- 1 gamma[n,t] <- h[n] * (t-1) } # Marginal probability of being in each state at time 1 pi[n,1,1] <- 1-lambda.op ; pi[n,1,2]<-0 ; pi[n,1,3] <- 0 ; pi[n,1,4]<-0; pi[n,1,5] <- lambda.op # Marginal probability of being in each state at time t>1 for(s in 1:S) { for(t in 2:N) { pi[n,t,s] <- inprod(pi[n,(t-1),], Lambda[n,t,,s]) } } } # Evidence ######### for (i in 1:M){ # loop over studies rC[i] ~ dbin(pC[i],nC[i]) # number of revisions on Charnley rS[i] ~ dbin(pS[i],nS[i]) # number of revisions on Stanmore # logit(pC[i]) <- base[i] -logHR[i]/2 # # logit(pS[i]) <- base[i]+logHR[i]/2 cloglog(pC[i]) <- base[i] -logHR[i]/2 # cloglog does not seem to work. cloglog(pS[i]) <- base[i]+logHR[i]/2 base[i] ~ dunif(-5,0) # need sensible prior restriction # log hazard ration for ith study logHR[i] ~ dnorm(LHR,tauHR[i]) tauHR[i]<-qualweights[i]*tauh # precision for ith study weighted by quality weights } LHR~ dunif(-100,100) log(HR)<-LHR tauh<-1/ (sigmah*sigmah) sigmah~dnorm( .2, 400)I(0,) # between-trial sd = 0.05 (prior constrained to be positive) # age-sex specific revision hazard logh ~ dnorm(logh0, tau) logh0 <- log(h0) h[1] <- exp(logh) # revision hazard for Charnley h[2] <- HR * h[1] # revision hazard for Stanmore # Incremental costs and benefits ########################## C.incr <- C[2] - C[1] BL.incr <- BL[2] - BL[1] BQ.incr <- BQ[2] - BQ[1] ICER <- C.incr / BQ.incr # Probability of cost effectiveness @ KK pounds per QALY # (values of KK considered range from 500 to 20000 in 500 pound increments) (m=12 for 6000, m=20 for 10000) for(m in 1:40) { KK[m] <- 500*m # Amount health care provider is willing to pay for each additional QALY INB[m] <- KK[m] * BQ.incr - C.incr P.CEA[m] <- step(INB[m]) } } Data list(N = 25, # Number of cycles S = 5, # Number of states in Markov model M = 3, # Number of studies in evidence synthesis rho = 0.04, # re-revision rate lambda.op = 0.01, # post-operative mortality rate # age-sex specific revision hazard: # age-sex specific revision hazard: tau = 25, # sd of 1/sqrt(25) = .2 on log-scale corresponds to 95% interval including +/- 50% hazard uncertainty h0 = 0.0016, C0 = c(4052, 4402), # set-up costs of primary operation c = structure(.Data = c(0, 5290, 5290, 0, 0, 0, 5640, 5640, 0, 0), .Dim=c(2,5)), # additional costs associated with each state and prothesis # (zero except for revision states 2 and 3) bl = c(1,0,1,1,0), # life-expectancy benefits associated with each state (one except for death states 2 and 5) bq = c(0.938, -0.622, -0.3387, 0.938, 0), # QALYs associated with each state delta.c = 0.06, # cost discount delta.b = 0.06, # health discount # delta.b = 0.015, # alternative health discount (for sensitivity analysis) # delta.b = 0.0, # alternative health discount (for sensitivity analysis) lambda = c( 0.0379, 0.0379, 0.0379, 0.0379, 0.0379, 0.0912, 0.0912, 0.0912, 0.0912, 0.0912, 0.0912, 0.0912, 0.0912, 0.0912, 0.0912, 0.1958, 0.1958, 0.1958, 0.1958, 0.1958, 0.1958, 0.1958, 0.1958, 0.1958, 0.1958 ), # Evidence rC = c(1683, 7, 33), # number of revisions for each study (Charnley) nC = c(28525, 200, 208), # number of operations for each study (Charnley) rS = c(28, 9, 69), # number of revisions for each study (Stanmore) nS = c(865, 213, 982), # number of operations for each study (Stanmore) # Quality weights for each study qualweights = c(0.5, 1, 0.2) # qualweights = c(0.1, 1, 0.05) # alternative quality weights for sensitivity analysis # qualweights = c(1, 1, 1) # alternative quality weights for sensitivity analysis) ) Initial values list(base=c(-3.09,-3.25,-2.12),logHR=c(-.63,.15,-.92),LHR=-0.35) list(base= -1.4, logHR = -.92 ) Results node mean sd MC error 2.5% median 97.5% start sample BL.incr 0.001489 6.986E-4 1.837E-5 4.668E-5 0.001521 0.002796 5001 10000 BQ.incr 0.03708 0.01733 4.588E-4 0.001161 0.03791 0.06943 5001 10000 C.incr 218.8 72.35 1.953 87.07 214.5 372.0 5001 10000 ICER 10330.0 2.57E+5 2609.0 234.3 5431.0 44860.0 5001 10000 INB[1] -200.2 81.01 2.182 -370.9 -195.5 -52.11 5001 10000 INB[2] -181.7 89.66 2.412 -369.9 -176.5 -17.29 5001 10000 INB[3] -163.2 98.32 2.641 -369.4 -157.6 17.22 5001 10000 INB[4] -144.6 107.0 2.87 -368.8 -138.6 51.67 5001 10000 INB[5] -126.1 115.6 3.1 -368.3 -119.7 86.12 5001 10000 INB[6] -107.6 124.3 3.329 -367.8 -100.7 120.8 5001 10000 INB[7] -89.02 133.0 3.558 -367.1 -81.77 155.3 5001 10000 INB[8] -70.48 141.6 3.788 -366.4 -62.8 189.9 5001 10000 INB[9] -51.94 150.3 4.017 -365.7 -43.81 224.6 5001 10000 INB[10] -33.4 158.9 4.246 -365.0 -24.84 259.4 5001 10000 INB[11] -14.86 167.6 4.476 -364.3 -5.73 294.1 5001 10000 INB[12] 3.681 176.3 4.705 -363.9 13.25 328.9 5001 10000 INB[13] 22.22 184.9 4.935 -363.5 32.18 363.6 5001 10000 INB[14] 40.76 193.6 5.164 -362.8 51.04 398.6 5001 10000 INB[15] 59.3 202.3 5.393 -362.1 70.02 433.4 5001 10000 INB[16] 77.84 210.9 5.623 -361.4 88.93 467.9 5001 10000 INB[17] 96.38 219.6 5.852 -360.5 108.1 502.6 5001 10000 INB[18] 114.9 228.3 6.081 -359.9 127.0 537.3 5001 10000 INB[19] 133.5 236.9 6.311 -359.2 145.8 572.0 5001 10000 INB[20] 152.0 245.6 6.54 -358.6 164.7 606.6 5001 10000 INB[21] 170.5 254.2 6.77 -358.0 183.6 641.3 5001 10000 INB[22] 189.1 262.9 6.999 -357.5 202.5 675.9 5001 10000 INB[23] 207.6 271.6 7.228 -357.2 221.5 710.6 5001 10000 INB[24] 226.2 280.2 7.458 -356.8 240.5 745.2 5001 10000 INB[25] 244.7 288.9 7.687 -356.1 259.6 779.9 5001 10000 INB[26] 263.2 297.6 7.916 -355.4 278.4 814.5 5001 10000 INB[27] 281.8 306.2 8.146 -354.7 297.3 849.2 5001 10000 INB[28] 300.3 314.9 8.375 -354.1 316.2 883.8 5001 10000 INB[29] 318.8 323.6 8.605 -353.6 335.2 918.5 5001 10000 INB[30] 337.4 332.2 8.834 -353.0 354.1 953.1 5001 10000 INB[31] 355.9 340.9 9.063 -352.4 373.1 987.7 5001 10000 INB[32] 374.5 349.6 9.293 -351.9 391.9 1022.0 5001 10000 INB[33] 393.0 358.2 9.522 -351.3 410.9 1057.0 5001 10000 INB[34] 411.5 366.9 9.751 -350.8 429.9 1092.0 5001 10000 INB[35] 430.1 375.6 9.981 -350.2 448.8 1126.0 5001 10000 INB[36] 448.6 384.2 10.21 -349.6 467.8 1161.0 5001 10000 INB[37] 467.2 392.9 10.44 -349.1 486.7 1196.0 5001 10000 INB[38] 485.7 401.6 10.67 -348.5 505.8 1231.0 5001 10000 INB[39] 504.2 410.2 10.9 -347.9 524.8 1266.0 5001 10000 INB[40] 522.8 418.9 11.13 -347.4 543.7 1301.0 5001 10000 P.CEA[1] 0.0052 0.07192 8.817E-4 0.0 0.0 0.0 5001 10000 P.CEA[2] 0.0157 0.1243 0.001695 0.0 0.0 0.0 5001 10000 P.CEA[3] 0.0366 0.1878 0.002822 0.0 0.0 1.0 5001 10000 P.CEA[4] 0.0723 0.259 0.004483 0.0 0.0 1.0 5001 10000 P.CEA[5] 0.1205 0.3255 0.005611 0.0 0.0 1.0 5001 10000 P.CEA[6] 0.1736 0.3788 0.006767 0.0 0.0 1.0 5001 10000 P.CEA[7] 0.2393 0.4267 0.00854 0.0 0.0 1.0 5001 10000 P.CEA[8] 0.3055 0.4606 0.009709 0.0 0.0 1.0 5001 10000 P.CEA[9] 0.3702 0.4829 0.01032 0.0 0.0 1.0 5001 10000 P.CEA[10] 0.4277 0.4947 0.01077 0.0 0.0 1.0 5001 10000 P.CEA[11] 0.485 0.4998 0.01126 0.0 0.0 1.0 5001 10000 P.CEA[12] 0.5318 0.499 0.01115 0.0 1.0 1.0 5001 10000 P.CEA[13] 0.5761 0.4942 0.01104 0.0 1.0 1.0 5001 10000 P.CEA[14] 0.6116 0.4874 0.01084 0.0 1.0 1.0 5001 10000 P.CEA[15] 0.6461 0.4782 0.01067 0.0 1.0 1.0 5001 10000 P.CEA[16] 0.674 0.4687 0.01065 0.0 1.0 1.0 5001 10000 P.CEA[17] 0.701 0.4578 0.0106 0.0 1.0 1.0 5001 10000 P.CEA[18] 0.723 0.4475 0.01013 0.0 1.0 1.0 5001 10000 P.CEA[19] 0.7435 0.4367 0.009737 0.0 1.0 1.0 5001 10000 P.CEA[20] 0.7612 0.4264 0.009515 0.0 1.0 1.0 5001 10000 P.CEA[21] 0.7752 0.4175 0.009414 0.0 1.0 1.0 5001 10000 P.CEA[22] 0.7886 0.4083 0.009193 0.0 1.0 1.0 5001 10000 P.CEA[23] 0.8022 0.3983 0.008909 0.0 1.0 1.0 5001 10000 P.CEA[24] 0.8136 0.3894 0.008682 0.0 1.0 1.0 5001 10000 P.CEA[25] 0.8242 0.3806 0.008397 0.0 1.0 1.0 5001 10000 P.CEA[26] 0.8318 0.374 0.008182 0.0 1.0 1.0 5001 10000 P.CEA[27] 0.8407 0.366 0.008014 0.0 1.0 1.0 5001 10000 P.CEA[28] 0.8482 0.3588 0.0078 0.0 1.0 1.0 5001 10000 P.CEA[29] 0.8555 0.3516 0.007453 0.0 1.0 1.0 5001 10000 P.CEA[30] 0.8618 0.3451 0.007371 0.0 1.0 1.0 5001 10000 P.CEA[31] 0.8679 0.3386 0.007144 0.0 1.0 1.0 5001 10000 P.CEA[32] 0.8742 0.3316 0.006882 0.0 1.0 1.0 5001 10000 P.CEA[33] 0.8778 0.3275 0.006729 0.0 1.0 1.0 5001 10000 P.CEA[34] 0.882 0.3226 0.006607 0.0 1.0 1.0 5001 10000 P.CEA[35] 0.885 0.319 0.00648 0.0 1.0 1.0 5001 10000 P.CEA[36] 0.889 0.3141 0.006567 0.0 1.0 1.0 5001 10000 P.CEA[37] 0.8936 0.3083 0.006362 0.0 1.0 1.0 5001 10000 P.CEA[38] 0.8971 0.3038 0.006167 0.0 1.0 1.0 5001 10000 P.CEA[39] 0.9002 0.2997 0.006108 0.0 1.0 1.0 5001 10000 P.CEA[40] 0.9043 0.2942 0.005933 0.0 1.0 1.0 5001 10000 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