NMA with no covariates
We fit a random effects model using the nma() function with trt_effects = "random". We use \(\mathrm{N}(0, 100^2)\) prior distributions for the treatment effects \(d_k\) and study-specific intercepts \(\mu_j\), and a \(\textrm{half-N}(5^2)\) prior for the heterogeneity standard deviation \(\tau\). We can examine the range of parameter values implied by these prior distributions with the summary() method:
summary(normal(scale = 100))
#> A Normal prior distribution: location = 0, scale = 100.
#> 50% of the prior density lies between -67.45 and 67.45.
#> 95% of the prior density lies between -196 and 196.
summary(half_normal(scale = 5))
#> A half-Normal prior distribution: location = 0, scale = 5.
#> 50% of the prior density lies between 0 and 3.37.
#> 95% of the prior density lies between 0 and 9.8.
Fitting the model with the nma() function. We increase the target acceptance rate adapt_delta = 0.99 to minimise divergent transition warnings.
af_fit_1 <- nma(af_net,
trt_effects = "random",
prior_intercept = normal(scale = 100),
prior_trt = normal(scale = 100),
prior_het = half_normal(scale = 5),
adapt_delta = 0.99)
#> Note: Setting "Standard adjusted dose anti-coagulant" as the network reference treatment.
Basic parameter summaries are given by the print() method:
af_fit_1
#> A random effects NMA with a binomial likelihood (logit link).
#> Inference for Stan model: binomial_1par.
#> 4 chains, each with iter=2000; warmup=1000; thin=1;
#> post-warmup draws per chain=1000, total post-warmup draws=4000.
#>
#> mean se_mean sd 2.5% 25% 50%
#> d[Acenocoumarol] -0.79 0.02 0.82 -2.48 -1.31 -0.75
#> d[Alternate day aspirin] -1.04 0.03 1.38 -4.22 -1.81 -0.87
#> d[Dipyridamole] 0.58 0.01 0.47 -0.36 0.29 0.59
#> d[Fixed dose warfarin] 0.93 0.01 0.41 0.11 0.66 0.93
#> d[Fixed dose warfarin + low dose aspirin] 0.47 0.01 0.44 -0.40 0.18 0.48
#> d[Fixed dose warfarin + medium dose aspirin] 0.89 0.01 0.32 0.22 0.69 0.91
#> d[High dose aspirin] 0.50 0.01 0.78 -1.05 -0.01 0.49
#> d[Indobufen] 0.25 0.01 0.46 -0.64 -0.04 0.24
#> d[Low adjusted dose anti-coagulant] -0.30 0.01 0.39 -1.06 -0.56 -0.29
#> d[Low dose aspirin] 0.61 0.01 0.23 0.16 0.47 0.61
#> d[Low dose aspirin + copidogrel] 0.51 0.01 0.35 -0.22 0.31 0.52
#> d[Low dose aspirin + dipyridamole] 0.27 0.01 0.49 -0.73 -0.04 0.26
#> d[Medium dose aspirin] 0.38 0.00 0.20 -0.04 0.26 0.39
#> d[Placebo/Standard care] 0.75 0.01 0.19 0.37 0.62 0.75
#> d[Triflusal] 0.65 0.01 0.61 -0.54 0.25 0.63
#> d[Ximelagatran] -0.08 0.00 0.27 -0.63 -0.24 -0.08
#> lp__ -4771.60 0.20 7.16 -4786.63 -4776.35 -4771.23
#> tau 0.29 0.01 0.14 0.04 0.20 0.28
#> 75% 97.5% n_eff Rhat
#> d[Acenocoumarol] -0.22 0.77 2831 1.00
#> d[Alternate day aspirin] -0.11 1.24 2649 1.00
#> d[Dipyridamole] 0.89 1.48 2312 1.00
#> d[Fixed dose warfarin] 1.19 1.73 3407 1.00
#> d[Fixed dose warfarin + low dose aspirin] 0.75 1.32 2316 1.00
#> d[Fixed dose warfarin + medium dose aspirin] 1.11 1.48 3215 1.00
#> d[High dose aspirin] 1.01 2.01 3559 1.00
#> d[Indobufen] 0.54 1.17 3523 1.00
#> d[Low adjusted dose anti-coagulant] -0.05 0.47 2262 1.00
#> d[Low dose aspirin] 0.76 1.06 1878 1.00
#> d[Low dose aspirin + copidogrel] 0.72 1.20 3278 1.00
#> d[Low dose aspirin + dipyridamole] 0.58 1.23 3083 1.00
#> d[Medium dose aspirin] 0.51 0.75 2420 1.00
#> d[Placebo/Standard care] 0.88 1.13 1242 1.01
#> d[Triflusal] 1.04 1.85 2604 1.00
#> d[Ximelagatran] 0.07 0.47 3119 1.00
#> lp__ -4766.66 -4758.50 1248 1.00
#> tau 0.37 0.58 704 1.00
#>
#> Samples were drawn using NUTS(diag_e) at Thu Feb 24 09:06:33 2022.
#> For each parameter, n_eff is a crude measure of effective sample size,
#> and Rhat is the potential scale reduction factor on split chains (at
#> convergence, Rhat=1).
By default, summaries of the study-specific intercepts \(\mu_j\) and study-specific relative effects \(\delta_{jk}\) are hidden, but could be examined by changing the pars argument:
# Not run
print(af_fit_1, pars = c("d", "mu", "delta"))
The prior and posterior distributions can be compared visually using the plot_prior_posterior() function:
plot_prior_posterior(af_fit_1, prior = c("trt", "het"))
We can compute relative effects against placebo/standard care with the relative_effects() function with the trt_ref argument:
(af_1_releff <- relative_effects(af_fit_1, trt_ref = "Placebo/Standard care"))
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> d[Standard adjusted dose anti-coagulant] -0.75 0.19 -1.13 -0.88 -0.75 -0.62 -0.37 1264
#> d[Acenocoumarol] -1.54 0.84 -3.26 -2.10 -1.51 -0.96 0.09 2669
#> d[Alternate day aspirin] -1.79 1.37 -4.97 -2.53 -1.63 -0.84 0.44 3429
#> d[Dipyridamole] -0.17 0.44 -1.05 -0.46 -0.16 0.12 0.68 3822
#> d[Fixed dose warfarin] 0.17 0.44 -0.71 -0.12 0.17 0.47 1.03 3309
#> d[Fixed dose warfarin + low dose aspirin] -0.28 0.39 -1.08 -0.53 -0.28 -0.03 0.51 3665
#> d[Fixed dose warfarin + medium dose aspirin] 0.14 0.36 -0.61 -0.09 0.15 0.38 0.83 2741
#> d[High dose aspirin] -0.25 0.77 -1.80 -0.75 -0.25 0.26 1.24 4109
#> d[Indobufen] -0.50 0.50 -1.46 -0.82 -0.50 -0.20 0.50 3060
#> d[Low adjusted dose anti-coagulant] -1.05 0.36 -1.74 -1.29 -1.05 -0.82 -0.34 4084
#> d[Low dose aspirin] -0.14 0.21 -0.58 -0.28 -0.14 0.00 0.27 3878
#> d[Low dose aspirin + copidogrel] -0.24 0.39 -1.05 -0.48 -0.24 0.00 0.58 2581
#> d[Low dose aspirin + dipyridamole] -0.48 0.46 -1.42 -0.78 -0.48 -0.19 0.44 4514
#> d[Medium dose aspirin] -0.37 0.23 -0.84 -0.51 -0.36 -0.22 0.06 2571
#> d[Triflusal] -0.10 0.64 -1.34 -0.53 -0.12 0.32 1.19 2398
#> d[Ximelagatran] -0.83 0.34 -1.48 -1.04 -0.84 -0.63 -0.12 2080
#> Tail_ESS Rhat
#> d[Standard adjusted dose anti-coagulant] 1619 1.01
#> d[Acenocoumarol] 2785 1.00
#> d[Alternate day aspirin] 2464 1.00
#> d[Dipyridamole] 3084 1.00
#> d[Fixed dose warfarin] 3039 1.00
#> d[Fixed dose warfarin + low dose aspirin] 2763 1.00
#> d[Fixed dose warfarin + medium dose aspirin] 2686 1.00
#> d[High dose aspirin] 2800 1.00
#> d[Indobufen] 2835 1.00
#> d[Low adjusted dose anti-coagulant] 3028 1.00
#> d[Low dose aspirin] 2892 1.00
#> d[Low dose aspirin + copidogrel] 2426 1.00
#> d[Low dose aspirin + dipyridamole] 2945 1.00
#> d[Medium dose aspirin] 2547 1.00
#> d[Triflusal] 2559 1.00
#> d[Ximelagatran] 2174 1.00
These estimates can easily be plotted with the plot() method:
plot(af_1_releff, ref_line = 0)
We can also produce treatment rankings, rank probabilities, and cumulative rank probabilities.
(af_1_ranks <- posterior_ranks(af_fit_1))
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> rank[Standard adjusted dose anti-coagulant] 5.36 1.49 3.00 4 5 6 8 2100 3222
#> rank[Acenocoumarol] 3.02 3.05 1.00 1 2 3 13 2930 3191
#> rank[Alternate day aspirin] 3.62 4.19 1.00 1 2 4 16 4812 3776
#> rank[Dipyridamole] 11.25 3.90 3.00 8 12 15 17 3235 NA
#> rank[Fixed dose warfarin] 14.06 3.08 6.98 12 15 16 17 3083 NA
#> rank[Fixed dose warfarin + low dose aspirin] 10.12 3.85 3.00 7 10 13 17 3191 2775
#> rank[Fixed dose warfarin + medium dose aspirin] 14.11 2.67 8.00 13 15 16 17 2637 NA
#> rank[High dose aspirin] 10.16 5.28 1.00 5 10 15 17 3817 NA
#> rank[Indobufen] 8.10 3.99 2.00 5 8 11 16 3235 3120
#> rank[Low adjusted dose anti-coagulant] 3.77 2.24 1.00 2 3 5 10 2553 3150
#> rank[Low dose aspirin] 11.68 2.28 7.00 10 12 13 16 3224 2975
#> rank[Low dose aspirin + copidogrel] 10.59 3.39 4.00 8 11 13 17 2962 2531
#> rank[Low dose aspirin + dipyridamole] 8.23 3.95 2.00 5 8 11 16 3639 2864
#> rank[Medium dose aspirin] 9.15 2.16 5.00 8 9 11 14 3291 3327
#> rank[Placebo/Standard care] 13.37 1.83 9.98 12 13 15 17 2910 3279
#> rank[Triflusal] 11.47 4.51 3.00 8 12 16 17 2579 NA
#> rank[Ximelagatran] 4.97 2.37 2.00 3 5 6 11 2307 2430
#> Rhat
#> rank[Standard adjusted dose anti-coagulant] 1
#> rank[Acenocoumarol] 1
#> rank[Alternate day aspirin] 1
#> rank[Dipyridamole] 1
#> rank[Fixed dose warfarin] 1
#> rank[Fixed dose warfarin + low dose aspirin] 1
#> rank[Fixed dose warfarin + medium dose aspirin] 1
#> rank[High dose aspirin] 1
#> rank[Indobufen] 1
#> rank[Low adjusted dose anti-coagulant] 1
#> rank[Low dose aspirin] 1
#> rank[Low dose aspirin + copidogrel] 1
#> rank[Low dose aspirin + dipyridamole] 1
#> rank[Medium dose aspirin] 1
#> rank[Placebo/Standard care] 1
#> rank[Triflusal] 1
#> rank[Ximelagatran] 1
plot(af_1_ranks)
(af_1_rankprobs <- posterior_rank_probs(af_fit_1))
#> p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5]
#> d[Standard adjusted dose anti-coagulant] 0.00 0.02 0.07 0.19 0.28
#> d[Acenocoumarol] 0.37 0.30 0.10 0.05 0.04
#> d[Alternate day aspirin] 0.47 0.17 0.07 0.04 0.03
#> d[Dipyridamole] 0.00 0.01 0.02 0.03 0.03
#> d[Fixed dose warfarin] 0.00 0.00 0.00 0.01 0.01
#> d[Fixed dose warfarin + low dose aspirin] 0.00 0.01 0.03 0.04 0.04
#> d[Fixed dose warfarin + medium dose aspirin] 0.00 0.00 0.00 0.00 0.01
#> d[High dose aspirin] 0.03 0.05 0.07 0.06 0.05
#> d[Indobufen] 0.01 0.04 0.07 0.09 0.08
#> d[Low adjusted dose anti-coagulant] 0.08 0.25 0.26 0.14 0.09
#> d[Low dose aspirin] 0.00 0.00 0.00 0.00 0.00
#> d[Low dose aspirin + copidogrel] 0.00 0.01 0.01 0.02 0.03
#> d[Low dose aspirin + dipyridamole] 0.01 0.04 0.07 0.08 0.07
#> d[Medium dose aspirin] 0.00 0.00 0.00 0.01 0.03
#> d[Placebo/Standard care] 0.00 0.00 0.00 0.00 0.00
#> d[Triflusal] 0.00 0.01 0.03 0.04 0.04
#> d[Ximelagatran] 0.02 0.09 0.18 0.21 0.17
#> p_rank[6] p_rank[7] p_rank[8] p_rank[9] p_rank[10]
#> d[Standard adjusted dose anti-coagulant] 0.23 0.13 0.05 0.02 0.00
#> d[Acenocoumarol] 0.03 0.02 0.02 0.01 0.01
#> d[Alternate day aspirin] 0.03 0.03 0.02 0.02 0.01
#> d[Dipyridamole] 0.04 0.06 0.07 0.07 0.08
#> d[Fixed dose warfarin] 0.01 0.02 0.02 0.04 0.04
#> d[Fixed dose warfarin + low dose aspirin] 0.07 0.08 0.08 0.09 0.09
#> d[Fixed dose warfarin + medium dose aspirin] 0.01 0.01 0.02 0.03 0.04
#> d[High dose aspirin] 0.05 0.06 0.05 0.05 0.05
#> d[Indobufen] 0.10 0.10 0.09 0.07 0.07
#> d[Low adjusted dose anti-coagulant] 0.07 0.04 0.03 0.02 0.01
#> d[Low dose aspirin] 0.01 0.02 0.05 0.09 0.12
#> d[Low dose aspirin + copidogrel] 0.05 0.07 0.09 0.11 0.11
#> d[Low dose aspirin + dipyridamole] 0.09 0.10 0.10 0.08 0.07
#> d[Medium dose aspirin] 0.06 0.12 0.18 0.18 0.17
#> d[Placebo/Standard care] 0.00 0.00 0.00 0.02 0.04
#> d[Triflusal] 0.05 0.05 0.06 0.06 0.06
#> d[Ximelagatran] 0.12 0.08 0.05 0.03 0.02
#> p_rank[11] p_rank[12] p_rank[13] p_rank[14] p_rank[15]
#> d[Standard adjusted dose anti-coagulant] 0.00 0.00 0.00 0.00 0.00
#> d[Acenocoumarol] 0.01 0.01 0.01 0.01 0.01
#> d[Alternate day aspirin] 0.01 0.01 0.01 0.01 0.01
#> d[Dipyridamole] 0.08 0.08 0.07 0.09 0.09
#> d[Fixed dose warfarin] 0.05 0.06 0.07 0.10 0.13
#> d[Fixed dose warfarin + low dose aspirin] 0.08 0.08 0.07 0.07 0.06
#> d[Fixed dose warfarin + medium dose aspirin] 0.06 0.07 0.08 0.12 0.17
#> d[High dose aspirin] 0.04 0.05 0.04 0.05 0.06
#> d[Indobufen] 0.06 0.05 0.05 0.04 0.04
#> d[Low adjusted dose anti-coagulant] 0.01 0.00 0.00 0.00 0.00
#> d[Low dose aspirin] 0.17 0.16 0.16 0.10 0.07
#> d[Low dose aspirin + copidogrel] 0.10 0.10 0.09 0.08 0.06
#> d[Low dose aspirin + dipyridamole] 0.06 0.05 0.04 0.04 0.03
#> d[Medium dose aspirin] 0.12 0.07 0.04 0.02 0.01
#> d[Placebo/Standard care] 0.09 0.14 0.21 0.21 0.17
#> d[Triflusal] 0.06 0.06 0.06 0.06 0.08
#> d[Ximelagatran] 0.01 0.01 0.00 0.00 0.00
#> p_rank[16] p_rank[17]
#> d[Standard adjusted dose anti-coagulant] 0.00 0.00
#> d[Acenocoumarol] 0.01 0.00
#> d[Alternate day aspirin] 0.02 0.02
#> d[Dipyridamole] 0.10 0.07
#> d[Fixed dose warfarin] 0.20 0.25
#> d[Fixed dose warfarin + low dose aspirin] 0.06 0.04
#> d[Fixed dose warfarin + medium dose aspirin] 0.23 0.17
#> d[High dose aspirin] 0.08 0.17
#> d[Indobufen] 0.02 0.02
#> d[Low adjusted dose anti-coagulant] 0.00 0.00
#> d[Low dose aspirin] 0.03 0.01
#> d[Low dose aspirin + copidogrel] 0.05 0.03
#> d[Low dose aspirin + dipyridamole] 0.03 0.02
#> d[Medium dose aspirin] 0.00 0.00
#> d[Placebo/Standard care] 0.08 0.03
#> d[Triflusal] 0.10 0.17
#> d[Ximelagatran] 0.00 0.00
plot(af_1_rankprobs)
(af_1_cumrankprobs <- posterior_rank_probs(af_fit_1, cumulative = TRUE))
#> p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5]
#> d[Standard adjusted dose anti-coagulant] 0.00 0.02 0.09 0.28 0.56
#> d[Acenocoumarol] 0.37 0.67 0.76 0.81 0.86
#> d[Alternate day aspirin] 0.47 0.65 0.72 0.76 0.79
#> d[Dipyridamole] 0.00 0.01 0.03 0.06 0.09
#> d[Fixed dose warfarin] 0.00 0.00 0.00 0.01 0.02
#> d[Fixed dose warfarin + low dose aspirin] 0.00 0.01 0.04 0.08 0.13
#> d[Fixed dose warfarin + medium dose aspirin] 0.00 0.00 0.00 0.00 0.01
#> d[High dose aspirin] 0.03 0.08 0.15 0.21 0.26
#> d[Indobufen] 0.01 0.06 0.13 0.21 0.29
#> d[Low adjusted dose anti-coagulant] 0.08 0.32 0.59 0.73 0.82
#> d[Low dose aspirin] 0.00 0.00 0.00 0.00 0.00
#> d[Low dose aspirin + copidogrel] 0.00 0.01 0.02 0.04 0.07
#> d[Low dose aspirin + dipyridamole] 0.01 0.05 0.12 0.20 0.28
#> d[Medium dose aspirin] 0.00 0.00 0.00 0.01 0.04
#> d[Placebo/Standard care] 0.00 0.00 0.00 0.00 0.00
#> d[Triflusal] 0.00 0.02 0.05 0.09 0.13
#> d[Ximelagatran] 0.02 0.11 0.29 0.50 0.67
#> p_rank[6] p_rank[7] p_rank[8] p_rank[9] p_rank[10]
#> d[Standard adjusted dose anti-coagulant] 0.79 0.92 0.98 0.99 1.00
#> d[Acenocoumarol] 0.89 0.91 0.93 0.94 0.95
#> d[Alternate day aspirin] 0.82 0.85 0.87 0.89 0.90
#> d[Dipyridamole] 0.13 0.19 0.26 0.34 0.42
#> d[Fixed dose warfarin] 0.03 0.04 0.07 0.10 0.15
#> d[Fixed dose warfarin + low dose aspirin] 0.19 0.27 0.36 0.45 0.54
#> d[Fixed dose warfarin + medium dose aspirin] 0.01 0.02 0.05 0.08 0.12
#> d[High dose aspirin] 0.30 0.36 0.41 0.46 0.51
#> d[Indobufen] 0.39 0.49 0.58 0.66 0.73
#> d[Low adjusted dose anti-coagulant] 0.89 0.92 0.95 0.97 0.98
#> d[Low dose aspirin] 0.01 0.03 0.09 0.17 0.29
#> d[Low dose aspirin + copidogrel] 0.11 0.19 0.28 0.39 0.50
#> d[Low dose aspirin + dipyridamole] 0.37 0.47 0.57 0.65 0.72
#> d[Medium dose aspirin] 0.10 0.22 0.39 0.58 0.75
#> d[Placebo/Standard care] 0.00 0.00 0.01 0.02 0.07
#> d[Triflusal] 0.18 0.23 0.29 0.35 0.41
#> d[Ximelagatran] 0.79 0.87 0.92 0.95 0.97
#> p_rank[11] p_rank[12] p_rank[13] p_rank[14] p_rank[15]
#> d[Standard adjusted dose anti-coagulant] 1.00 1.00 1.00 1.00 1.00
#> d[Acenocoumarol] 0.96 0.97 0.98 0.99 0.99
#> d[Alternate day aspirin] 0.92 0.92 0.94 0.95 0.96
#> d[Dipyridamole] 0.50 0.58 0.65 0.74 0.83
#> d[Fixed dose warfarin] 0.20 0.26 0.33 0.43 0.56
#> d[Fixed dose warfarin + low dose aspirin] 0.62 0.70 0.77 0.84 0.90
#> d[Fixed dose warfarin + medium dose aspirin] 0.17 0.24 0.32 0.44 0.61
#> d[High dose aspirin] 0.55 0.60 0.64 0.69 0.75
#> d[Indobufen] 0.78 0.83 0.88 0.92 0.95
#> d[Low adjusted dose anti-coagulant] 0.99 1.00 1.00 1.00 1.00
#> d[Low dose aspirin] 0.46 0.63 0.79 0.89 0.96
#> d[Low dose aspirin + copidogrel] 0.59 0.69 0.78 0.86 0.92
#> d[Low dose aspirin + dipyridamole] 0.78 0.83 0.88 0.92 0.95
#> d[Medium dose aspirin] 0.87 0.94 0.97 0.99 1.00
#> d[Placebo/Standard care] 0.16 0.30 0.51 0.72 0.89
#> d[Triflusal] 0.47 0.53 0.58 0.65 0.73
#> d[Ximelagatran] 0.98 0.99 0.99 1.00 1.00
#> p_rank[16] p_rank[17]
#> d[Standard adjusted dose anti-coagulant] 1.00 1
#> d[Acenocoumarol] 1.00 1
#> d[Alternate day aspirin] 0.98 1
#> d[Dipyridamole] 0.93 1
#> d[Fixed dose warfarin] 0.75 1
#> d[Fixed dose warfarin + low dose aspirin] 0.96 1
#> d[Fixed dose warfarin + medium dose aspirin] 0.83 1
#> d[High dose aspirin] 0.83 1
#> d[Indobufen] 0.98 1
#> d[Low adjusted dose anti-coagulant] 1.00 1
#> d[Low dose aspirin] 0.99 1
#> d[Low dose aspirin + copidogrel] 0.97 1
#> d[Low dose aspirin + dipyridamole] 0.98 1
#> d[Medium dose aspirin] 1.00 1
#> d[Placebo/Standard care] 0.97 1
#> d[Triflusal] 0.83 1
#> d[Ximelagatran] 1.00 1
plot(af_1_cumrankprobs)
Network meta-regression adjusting for proportion of prior stroke
We now consider a meta-regression model adjusting for the proportion of individuals in each study with prior stroke, with shared interaction coefficients by treatment class. The regression model is specified in the nma() function using a formula in the regression argument. The formula ~ .trt:stroke means that interactions of prior stroke with treatment will be included; the .trt special variable indicates treatment, and stroke is in the original data set. We specify class_interactions = "common" to denote that the interaction parameters are to be common (i.e. shared) between treatments within each class. (Setting class_interactions = "independent" would fit model 2 of Cooper et al. (2009) with separate interactions for each treatment, data permitting.) We use the same prior distributions as above, but additionally require a prior distribution for the regression coefficients prior_reg; we use a \(\mathrm{N}(0, 100^2)\) prior distribution. The QR decomposition can greatly improve the efficiency of sampling for regression models by decorrelating the sampling space; we specify that this should be used with QR = TRUE, and increase the target acceptance rate adapt_delta = 0.99 to minimise divergent transition warnings.
af_fit_4b <- nma(af_net,
trt_effects = "random",
regression = ~ .trt:stroke,
class_interactions = "common",
QR = TRUE,
prior_intercept = normal(scale = 100),
prior_trt = normal(scale = 100),
prior_reg = normal(scale = 100),
prior_het = half_normal(scale = 5),
adapt_delta = 0.99)
#> Note: Setting "Standard adjusted dose anti-coagulant" as the network reference treatment.
Basic parameter summaries are given by the print() method:
af_fit_4b
#> A random effects NMA with a binomial likelihood (logit link).
#> Regression model: ~.trt:stroke.
#> Centred covariates at the following overall mean values:
#> stroke
#> 0.2957377
#> Inference for Stan model: binomial_1par.
#> 4 chains, each with iter=2000; warmup=1000; thin=1;
#> post-warmup draws per chain=1000, total post-warmup draws=4000.
#>
#> mean se_mean sd 2.5% 25% 50%
#> beta[.trtclassControl:stroke] 0.70 0.01 0.42 -0.15 0.43 0.69
#> beta[.trtclassAnti-platelet:stroke] 0.93 0.01 0.41 0.11 0.68 0.92
#> beta[.trtclassMixed:stroke] 3.94 0.03 2.12 -0.20 2.50 3.94
#> d[Acenocoumarol] 0.37 0.02 1.00 -1.60 -0.30 0.40
#> d[Alternate day aspirin] -0.90 0.03 1.37 -4.16 -1.64 -0.72
#> d[Dipyridamole] 0.57 0.01 0.40 -0.22 0.32 0.58
#> d[Fixed dose warfarin] 0.64 0.01 0.38 -0.12 0.38 0.64
#> d[Fixed dose warfarin + low dose aspirin] 1.46 0.01 0.74 0.03 0.98 1.46
#> d[Fixed dose warfarin + medium dose aspirin] 1.00 0.00 0.30 0.39 0.80 0.99
#> d[High dose aspirin] 0.42 0.01 0.74 -1.04 -0.07 0.43
#> d[Indobufen] -0.40 0.01 0.48 -1.37 -0.71 -0.41
#> d[Low adjusted dose anti-coagulant] -0.42 0.01 0.37 -1.16 -0.67 -0.42
#> d[Low dose aspirin] 0.72 0.00 0.20 0.32 0.59 0.72
#> d[Low dose aspirin + copidogrel] 0.65 0.01 0.28 0.09 0.49 0.65
#> d[Low dose aspirin + dipyridamole] 0.25 0.01 0.44 -0.61 -0.04 0.25
#> d[Medium dose aspirin] 0.35 0.00 0.18 -0.01 0.24 0.35
#> d[Placebo/Standard care] 0.79 0.00 0.19 0.43 0.67 0.79
#> d[Triflusal] 0.92 0.01 0.58 -0.16 0.52 0.90
#> d[Ximelagatran] -0.07 0.00 0.22 -0.48 -0.20 -0.08
#> lp__ -4771.21 0.20 7.07 -4786.27 -4775.75 -4770.95
#> tau 0.18 0.01 0.12 0.01 0.09 0.17
#> 75% 97.5% n_eff Rhat
#> beta[.trtclassControl:stroke] 0.97 1.55 4158 1
#> beta[.trtclassAnti-platelet:stroke] 1.19 1.74 3436 1
#> beta[.trtclassMixed:stroke] 5.34 8.09 4463 1
#> d[Acenocoumarol] 1.03 2.32 4098 1
#> d[Alternate day aspirin] 0.04 1.28 2654 1
#> d[Dipyridamole] 0.83 1.38 5543 1
#> d[Fixed dose warfarin] 0.89 1.39 4117 1
#> d[Fixed dose warfarin + low dose aspirin] 1.95 2.93 4575 1
#> d[Fixed dose warfarin + medium dose aspirin] 1.19 1.61 4749 1
#> d[High dose aspirin] 0.91 1.89 5818 1
#> d[Indobufen] -0.09 0.56 4131 1
#> d[Low adjusted dose anti-coagulant] -0.17 0.31 4345 1
#> d[Low dose aspirin] 0.85 1.10 4737 1
#> d[Low dose aspirin + copidogrel] 0.82 1.23 3080 1
#> d[Low dose aspirin + dipyridamole] 0.54 1.10 6410 1
#> d[Medium dose aspirin] 0.46 0.69 3643 1
#> d[Placebo/Standard care] 0.91 1.16 4649 1
#> d[Triflusal] 1.31 2.10 4880 1
#> d[Ximelagatran] 0.05 0.39 2951 1
#> lp__ -4766.34 -4758.34 1233 1
#> tau 0.26 0.48 429 1
#>
#> Samples were drawn using NUTS(diag_e) at Thu Feb 24 09:07:08 2022.
#> For each parameter, n_eff is a crude measure of effective sample size,
#> and Rhat is the potential scale reduction factor on split chains (at
#> convergence, Rhat=1).
The estimated treatment effects d[] shown here correspond to relative effects at the reference level of the covariate, here proportion of prior stroke centered at the network mean value 0.296.
By default, summaries of the study-specific intercepts \(\mu_j\) and study-specific relative effects \(\delta_{jk}\) are hidden, but could be examined by changing the pars argument:
# Not run
print(af_fit_4b, pars = c("d", "mu", "delta"))
The prior and posterior distributions can be compared visually using the plot_prior_posterior() function:
plot_prior_posterior(af_fit_4b, prior = c("reg", "het"))
We can compute relative effects against placebo/standard care with the relative_effects() function with the trt_ref argument, which by default produces relative effects for the observed proportions of prior stroke in each study:
# Not run
(af_4b_releff <- relative_effects(af_fit_4b, trt_ref = "Placebo/Standard care"))
plot(af_4b_releff, ref_line = 0)
We can produce estimated treatment effects for particular covariate values using the newdata argument. For example, treatment effects when no individuals or all individuals have prior stroke are produced by
(af_4b_releff_01 <- relative_effects(af_fit_4b,
trt_ref = "Placebo/Standard care",
newdata = data.frame(stroke = c(0, 1),
label = c("stroke = 0", "stroke = 1")),
study = label))
#> ------------------------------------------------------------- Study: stroke = 0 ----
#>
#> Covariate values:
#> stroke
#> 0
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> d[stroke = 0: Standard adjusted dose anti-coagulant] -0.58 0.24 -1.05 -0.74 -0.59 -0.43 -0.11
#> d[stroke = 0: Acenocoumarol] -1.38 0.83 -3.11 -1.91 -1.35 -0.81 0.16
#> d[stroke = 0: Alternate day aspirin] -1.76 1.36 -5.06 -2.52 -1.57 -0.82 0.44
#> d[stroke = 0: Dipyridamole] -0.29 0.43 -1.13 -0.57 -0.28 -0.02 0.59
#> d[stroke = 0: Fixed dose warfarin] 0.05 0.44 -0.81 -0.24 0.05 0.34 0.90
#> d[stroke = 0: Fixed dose warfarin + low dose aspirin] -0.29 0.34 -0.97 -0.51 -0.29 -0.07 0.36
#> d[stroke = 0: Fixed dose warfarin + medium dose aspirin] -0.75 0.65 -2.06 -1.18 -0.75 -0.33 0.56
#> d[stroke = 0: High dose aspirin] -0.44 0.76 -1.96 -0.95 -0.43 0.04 1.09
#> d[stroke = 0: Indobufen] -1.26 0.58 -2.38 -1.63 -1.27 -0.90 -0.05
#> d[stroke = 0: Low adjusted dose anti-coagulant] -1.01 0.33 -1.66 -1.23 -1.00 -0.78 -0.36
#> d[stroke = 0: Low dose aspirin] -0.14 0.22 -0.58 -0.28 -0.14 0.00 0.29
#> d[stroke = 0: Low dose aspirin + copidogrel] -0.21 0.36 -0.93 -0.43 -0.21 0.01 0.51
#> d[stroke = 0: Low dose aspirin + dipyridamole] -0.61 0.46 -1.53 -0.90 -0.60 -0.30 0.29
#> d[stroke = 0: Medium dose aspirin] -0.51 0.26 -1.03 -0.68 -0.51 -0.34 -0.02
#> d[stroke = 0: Triflusal] 0.06 0.61 -1.08 -0.35 0.04 0.46 1.32
#> d[stroke = 0: Ximelagatran] -0.66 0.33 -1.30 -0.87 -0.66 -0.44 -0.03
#> Bulk_ESS Tail_ESS Rhat
#> d[stroke = 0: Standard adjusted dose anti-coagulant] 4270 2916 1
#> d[stroke = 0: Acenocoumarol] 4467 2570 1
#> d[stroke = 0: Alternate day aspirin] 3324 1966 1
#> d[stroke = 0: Dipyridamole] 5248 2778 1
#> d[stroke = 0: Fixed dose warfarin] 4811 3163 1
#> d[stroke = 0: Fixed dose warfarin + low dose aspirin] 4259 2549 1
#> d[stroke = 0: Fixed dose warfarin + medium dose aspirin] 4607 2884 1
#> d[stroke = 0: High dose aspirin] 5792 3028 1
#> d[stroke = 0: Indobufen] 4439 2334 1
#> d[stroke = 0: Low adjusted dose anti-coagulant] 5086 3216 1
#> d[stroke = 0: Low dose aspirin] 4186 2558 1
#> d[stroke = 0: Low dose aspirin + copidogrel] 3761 2265 1
#> d[stroke = 0: Low dose aspirin + dipyridamole] 5465 2728 1
#> d[stroke = 0: Medium dose aspirin] 4044 2679 1
#> d[stroke = 0: Triflusal] 4995 3060 1
#> d[stroke = 0: Ximelagatran] 3492 2415 1
#>
#> ------------------------------------------------------------- Study: stroke = 1 ----
#>
#> Covariate values:
#> stroke
#> 1
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> d[stroke = 1: Standard adjusted dose anti-coagulant] -1.28 0.33 -1.95 -1.49 -1.28 -1.06 -0.64
#> d[stroke = 1: Acenocoumarol] 1.87 2.26 -2.58 0.39 1.88 3.34 6.28
#> d[stroke = 1: Alternate day aspirin] -1.53 1.38 -4.79 -2.29 -1.36 -0.58 0.70
#> d[stroke = 1: Dipyridamole] -0.06 0.39 -0.84 -0.30 -0.06 0.20 0.69
#> d[stroke = 1: Fixed dose warfarin] -0.65 0.51 -1.67 -0.98 -0.65 -0.30 0.37
#> d[stroke = 1: Fixed dose warfarin + low dose aspirin] 2.96 2.16 -1.22 1.49 2.97 4.36 7.18
#> d[stroke = 1: Fixed dose warfarin + medium dose aspirin] 2.49 1.62 -0.60 1.40 2.47 3.54 5.70
#> d[stroke = 1: High dose aspirin] -0.21 0.72 -1.65 -0.69 -0.20 0.27 1.20
#> d[stroke = 1: Indobufen] -1.03 0.51 -2.02 -1.37 -1.04 -0.70 -0.03
#> d[stroke = 1: Low adjusted dose anti-coagulant] -1.70 0.50 -2.73 -2.04 -1.70 -1.38 -0.73
#> d[stroke = 1: Low dose aspirin] 0.09 0.28 -0.47 -0.09 0.09 0.27 0.62
#> d[stroke = 1: Low dose aspirin + copidogrel] 0.02 0.39 -0.77 -0.21 0.02 0.26 0.79
#> d[stroke = 1: Low dose aspirin + dipyridamole] -0.38 0.41 -1.22 -0.65 -0.37 -0.10 0.42
#> d[stroke = 1: Medium dose aspirin] -0.28 0.25 -0.79 -0.44 -0.27 -0.13 0.18
#> d[stroke = 1: Triflusal] 0.29 0.64 -0.92 -0.14 0.29 0.72 1.58
#> d[stroke = 1: Ximelagatran] -1.35 0.40 -2.15 -1.61 -1.35 -1.09 -0.55
#> Bulk_ESS Tail_ESS Rhat
#> d[stroke = 1: Standard adjusted dose anti-coagulant] 4607 2676 1
#> d[stroke = 1: Acenocoumarol] 4229 2860 1
#> d[stroke = 1: Alternate day aspirin] 3302 2111 1
#> d[stroke = 1: Dipyridamole] 5663 2578 1
#> d[stroke = 1: Fixed dose warfarin] 4777 3095 1
#> d[stroke = 1: Fixed dose warfarin + low dose aspirin] 4577 2928 1
#> d[stroke = 1: Fixed dose warfarin + medium dose aspirin] 4739 2691 1
#> d[stroke = 1: High dose aspirin] 5641 2914 1
#> d[stroke = 1: Indobufen] 4939 3187 1
#> d[stroke = 1: Low adjusted dose anti-coagulant] 4394 2763 1
#> d[stroke = 1: Low dose aspirin] 4835 2949 1
#> d[stroke = 1: Low dose aspirin + copidogrel] 3649 2399 1
#> d[stroke = 1: Low dose aspirin + dipyridamole] 5770 2884 1
#> d[stroke = 1: Medium dose aspirin] 4549 2282 1
#> d[stroke = 1: Triflusal] 4788 2801 1
#> d[stroke = 1: Ximelagatran] 4035 2492 1
plot(af_4b_releff_01, ref_line = 0)
The estimated class interactions (against the reference “Mixed” class) are very uncertain.
plot(af_fit_4b, pars = "beta", stat = "halfeye", ref_line = 0)
The interactions are more straightforward to interpret if we transform the interaction coefficients (using the consistency equations) so that they are against the control class:
af_4b_beta <- as.array(af_fit_4b, pars = "beta")
# Subtract beta[Control:stroke] from the other class interactions
af_4b_beta[ , , 2:3] <- sweep(af_4b_beta[ , , 2:3], 1:2,
af_4b_beta[ , , "beta[.trtclassControl:stroke]"], FUN = "-")
# Set beta[Anti-coagulant:stroke] = -beta[Control:stroke]
af_4b_beta[ , , "beta[.trtclassControl:stroke]"] <- -af_4b_beta[ , , "beta[.trtclassControl:stroke]"]
names(af_4b_beta)[1] <- "beta[.trtclassAnti-coagulant:stroke]"
# Summarise
summary(af_4b_beta)
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> beta[.trtclassAnti-coagulant:stroke] -0.70 0.42 -1.55 -0.97 -0.69 -0.43 0.15 4210 3025
#> beta[.trtclassAnti-platelet:stroke] 0.23 0.34 -0.44 0.01 0.24 0.45 0.86 4465 2391
#> beta[.trtclassMixed:stroke] 3.24 2.15 -0.96 1.81 3.25 4.65 7.41 4623 2777
#> Rhat
#> beta[.trtclassAnti-coagulant:stroke] 1
#> beta[.trtclassAnti-platelet:stroke] 1
#> beta[.trtclassMixed:stroke] 1
plot(summary(af_4b_beta), stat = "halfeye", ref_line = 0)
There is some evidence that the effect of anti-coagulants increases (compared to control) with prior stroke. There is little evidence the effect of anti-platelets reduces with prior stroke, although the point estimate represents a substantial reduction in effectiveness, and the 95% Credible Interval includes values that correspond to substantial increases in treatment effect. The interaction effect of stroke on mixed treatments is very uncertain, but potentially indicates a substantial reduction in treatment effects with prior stroke.
We can also produce treatment rankings, rank probabilities, and cumulative rank probabilities. By default (without the newdata argument specified), these are produced at the value of stroke for each study in the network in turn. To instead produce rankings for when no individuals or all individuals have prior stroke, we specify the newdata argument.
(af_4b_ranks <- posterior_ranks(af_fit_4b,
newdata = data.frame(stroke = c(0, 1),
label = c("stroke = 0", "stroke = 1")),
study = label))
#> ------------------------------------------------------------- Study: stroke = 0 ----
#>
#> Covariate values:
#> stroke
#> 0
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> rank[stroke = 0: Standard adjusted dose anti-coagulant] 7.71 1.91 4 6 8 9 12
#> rank[stroke = 0: Acenocoumarol] 3.98 3.68 1 1 3 5 15
#> rank[stroke = 0: Alternate day aspirin] 4.01 4.46 1 1 2 5 17
#> rank[stroke = 0: Dipyridamole] 11.09 3.66 4 8 11 14 17
#> rank[stroke = 0: Fixed dose warfarin] 14.09 2.94 6 12 15 16 17
#> rank[stroke = 0: Fixed dose warfarin + low dose aspirin] 11.07 3.65 4 8 11 14 17
#> rank[stroke = 0: Fixed dose warfarin + medium dose aspirin] 7.09 4.52 1 3 6 10 17
#> rank[stroke = 0: High dose aspirin] 9.57 5.26 1 5 10 15 17
#> rank[stroke = 0: Indobufen] 3.65 2.81 1 2 3 4 12
#> rank[stroke = 0: Low adjusted dose anti-coagulant] 4.52 2.40 1 3 4 6 11
#> rank[stroke = 0: Low dose aspirin] 12.92 1.95 9 12 13 14 16
#> rank[stroke = 0: Low dose aspirin + copidogrel] 12.03 2.94 5 10 12 14 17
#> rank[stroke = 0: Low dose aspirin + dipyridamole] 7.86 3.70 2 5 7 11 16
#> rank[stroke = 0: Medium dose aspirin] 8.58 2.18 5 7 9 10 13
#> rank[stroke = 0: Placebo/Standard care] 14.32 1.88 10 13 15 16 17
#> rank[stroke = 0: Triflusal] 13.47 3.89 4 11 15 17 17
#> rank[stroke = 0: Ximelagatran] 7.04 2.68 3 5 7 9 13
#> Bulk_ESS Tail_ESS Rhat
#> rank[stroke = 0: Standard adjusted dose anti-coagulant] 4059 3552 1
#> rank[stroke = 0: Acenocoumarol] 4258 3252 1
#> rank[stroke = 0: Alternate day aspirin] 4503 3239 1
#> rank[stroke = 0: Dipyridamole] 4673 NA 1
#> rank[stroke = 0: Fixed dose warfarin] 4080 NA 1
#> rank[stroke = 0: Fixed dose warfarin + low dose aspirin] 4399 2787 1
#> rank[stroke = 0: Fixed dose warfarin + medium dose aspirin] 4002 2969 1
#> rank[stroke = 0: High dose aspirin] 5785 NA 1
#> rank[stroke = 0: Indobufen] 3684 2277 1
#> rank[stroke = 0: Low adjusted dose anti-coagulant] 4038 3235 1
#> rank[stroke = 0: Low dose aspirin] 3714 3621 1
#> rank[stroke = 0: Low dose aspirin + copidogrel] 3263 2541 1
#> rank[stroke = 0: Low dose aspirin + dipyridamole] 5319 3057 1
#> rank[stroke = 0: Medium dose aspirin] 4847 2822 1
#> rank[stroke = 0: Placebo/Standard care] 3304 NA 1
#> rank[stroke = 0: Triflusal] 4808 NA 1
#> rank[stroke = 0: Ximelagatran] 3042 2909 1
#>
#> ------------------------------------------------------------- Study: stroke = 1 ----
#>
#> Covariate values:
#> stroke
#> 1
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> rank[stroke = 1: Standard adjusted dose anti-coagulant] 3.64 1.13 2 3 4 4 6
#> rank[stroke = 1: Acenocoumarol] 13.28 4.34 1 14 15 16 17
#> rank[stroke = 1: Alternate day aspirin] 4.47 3.99 1 1 3 6 14
#> rank[stroke = 1: Dipyridamole] 10.53 2.73 5 9 11 13 15
#> rank[stroke = 1: Fixed dose warfarin] 7.05 2.72 3 5 6 8 14
#> rank[stroke = 1: Fixed dose warfarin + low dose aspirin] 15.84 2.88 5 16 17 17 17
#> rank[stroke = 1: Fixed dose warfarin + medium dose aspirin] 15.43 1.94 8 15 16 16 17
#> rank[stroke = 1: High dose aspirin] 9.40 3.97 2 6 9 13 16
#> rank[stroke = 1: Indobufen] 4.98 2.21 1 4 5 6 10
#> rank[stroke = 1: Low adjusted dose anti-coagulant] 2.04 1.32 1 1 2 2 5
#> rank[stroke = 1: Low dose aspirin] 11.90 1.78 8 11 12 13 15
#> rank[stroke = 1: Low dose aspirin + copidogrel] 11.14 2.41 6 9 11 13 15
#> rank[stroke = 1: Low dose aspirin + dipyridamole] 8.19 2.65 3 6 8 10 14
#> rank[stroke = 1: Medium dose aspirin] 8.60 1.70 6 7 8 10 12
#> rank[stroke = 1: Placebo/Standard care] 11.16 1.90 7 10 11 12 15
#> rank[stroke = 1: Triflusal] 12.18 3.02 5 10 13 14 17
#> rank[stroke = 1: Ximelagatran] 3.19 1.46 1 2 3 4 6
#> Bulk_ESS Tail_ESS Rhat
#> rank[stroke = 1: Standard adjusted dose anti-coagulant] 3145 2407 1
#> rank[stroke = 1: Acenocoumarol] 3877 NA 1
#> rank[stroke = 1: Alternate day aspirin] 4551 3054 1
#> rank[stroke = 1: Dipyridamole] 4822 2777 1
#> rank[stroke = 1: Fixed dose warfarin] 3913 3068 1
#> rank[stroke = 1: Fixed dose warfarin + low dose aspirin] 3822 NA 1
#> rank[stroke = 1: Fixed dose warfarin + medium dose aspirin] 3156 NA 1
#> rank[stroke = 1: High dose aspirin] 5301 2933 1
#> rank[stroke = 1: Indobufen] 3961 2217 1
#> rank[stroke = 1: Low adjusted dose anti-coagulant] 3348 3413 1
#> rank[stroke = 1: Low dose aspirin] 3778 3582 1
#> rank[stroke = 1: Low dose aspirin + copidogrel] 3579 2801 1
#> rank[stroke = 1: Low dose aspirin + dipyridamole] 5517 3013 1
#> rank[stroke = 1: Medium dose aspirin] 4263 3705 1
#> rank[stroke = 1: Placebo/Standard care] 4322 3060 1
#> rank[stroke = 1: Triflusal] 4124 NA 1
#> rank[stroke = 1: Ximelagatran] 2674 2247 1
plot(af_4b_ranks)
(af_4b_rankprobs <- posterior_rank_probs(af_fit_4b,
newdata = data.frame(stroke = c(0, 1),
label = c("stroke = 0", "stroke = 1")),
study = label))
#> ------------------------------------------------------------- Study: stroke = 0 ----
#>
#> Covariate values:
#> stroke
#> 0
#>
#> p_rank[1] p_rank[2] p_rank[3] p_rank[4]
#> d[stroke = 0: Standard adjusted dose anti-coagulant] 0.00 0.00 0.01 0.03
#> d[stroke = 0: Acenocoumarol] 0.26 0.24 0.14 0.08
#> d[stroke = 0: Alternate day aspirin] 0.44 0.14 0.09 0.06
#> d[stroke = 0: Dipyridamole] 0.00 0.00 0.01 0.03
#> d[stroke = 0: Fixed dose warfarin] 0.00 0.00 0.00 0.00
#> d[stroke = 0: Fixed dose warfarin + low dose aspirin] 0.00 0.01 0.01 0.03
#> d[stroke = 0: Fixed dose warfarin + medium dose aspirin] 0.05 0.10 0.12 0.11
#> d[stroke = 0: High dose aspirin] 0.03 0.06 0.07 0.08
#> d[stroke = 0: Indobufen] 0.17 0.26 0.20 0.13
#> d[stroke = 0: Low adjusted dose anti-coagulant] 0.04 0.14 0.21 0.21
#> d[stroke = 0: Low dose aspirin] 0.00 0.00 0.00 0.00
#> d[stroke = 0: Low dose aspirin + copidogrel] 0.00 0.00 0.00 0.01
#> d[stroke = 0: Low dose aspirin + dipyridamole] 0.01 0.03 0.06 0.10
#> d[stroke = 0: Medium dose aspirin] 0.00 0.00 0.01 0.02
#> d[stroke = 0: Placebo/Standard care] 0.00 0.00 0.00 0.00
#> d[stroke = 0: Triflusal] 0.00 0.00 0.01 0.02
#> d[stroke = 0: Ximelagatran] 0.00 0.02 0.05 0.10
#> p_rank[5] p_rank[6] p_rank[7] p_rank[8]
#> d[stroke = 0: Standard adjusted dose anti-coagulant] 0.08 0.15 0.20 0.19
#> d[stroke = 0: Acenocoumarol] 0.06 0.04 0.03 0.02
#> d[stroke = 0: Alternate day aspirin] 0.04 0.03 0.02 0.02
#> d[stroke = 0: Dipyridamole] 0.04 0.05 0.06 0.07
#> d[stroke = 0: Fixed dose warfarin] 0.01 0.01 0.01 0.02
#> d[stroke = 0: Fixed dose warfarin + low dose aspirin] 0.04 0.05 0.05 0.07
#> d[stroke = 0: Fixed dose warfarin + medium dose aspirin] 0.10 0.08 0.06 0.05
#> d[stroke = 0: High dose aspirin] 0.07 0.05 0.05 0.04
#> d[stroke = 0: Indobufen] 0.07 0.05 0.03 0.02
#> d[stroke = 0: Low adjusted dose anti-coagulant] 0.14 0.09 0.06 0.04
#> d[stroke = 0: Low dose aspirin] 0.00 0.00 0.00 0.01
#> d[stroke = 0: Low dose aspirin + copidogrel] 0.01 0.02 0.03 0.04
#> d[stroke = 0: Low dose aspirin + dipyridamole] 0.11 0.10 0.09 0.08
#> d[stroke = 0: Medium dose aspirin] 0.06 0.09 0.13 0.18
#> d[stroke = 0: Placebo/Standard care] 0.00 0.00 0.00 0.00
#> d[stroke = 0: Triflusal] 0.02 0.03 0.03 0.03
#> d[stroke = 0: Ximelagatran] 0.15 0.16 0.14 0.11
#> p_rank[9] p_rank[10] p_rank[11] p_rank[12]
#> d[stroke = 0: Standard adjusted dose anti-coagulant] 0.16 0.10 0.05 0.02
#> d[stroke = 0: Acenocoumarol] 0.02 0.02 0.02 0.02
#> d[stroke = 0: Alternate day aspirin] 0.02 0.02 0.02 0.01
#> d[stroke = 0: Dipyridamole] 0.07 0.09 0.11 0.10
#> d[stroke = 0: Fixed dose warfarin] 0.03 0.04 0.05 0.07
#> d[stroke = 0: Fixed dose warfarin + low dose aspirin] 0.07 0.09 0.09 0.10
#> d[stroke = 0: Fixed dose warfarin + medium dose aspirin] 0.05 0.05 0.05 0.04
#> d[stroke = 0: High dose aspirin] 0.04 0.04 0.05 0.05
#> d[stroke = 0: Indobufen] 0.02 0.01 0.01 0.01
#> d[stroke = 0: Low adjusted dose anti-coagulant] 0.03 0.02 0.01 0.01
#> d[stroke = 0: Low dose aspirin] 0.03 0.06 0.11 0.17
#> d[stroke = 0: Low dose aspirin + copidogrel] 0.07 0.10 0.12 0.13
#> d[stroke = 0: Low dose aspirin + dipyridamole] 0.08 0.08 0.06 0.06
#> d[stroke = 0: Medium dose aspirin] 0.18 0.15 0.10 0.05
#> d[stroke = 0: Placebo/Standard care] 0.01 0.02 0.04 0.08
#> d[stroke = 0: Triflusal] 0.03 0.04 0.06 0.06
#> d[stroke = 0: Ximelagatran] 0.09 0.07 0.05 0.03
#> p_rank[13] p_rank[14] p_rank[15]
#> d[stroke = 0: Standard adjusted dose anti-coagulant] 0.01 0.00 0.00
#> d[stroke = 0: Acenocoumarol] 0.01 0.01 0.01
#> d[stroke = 0: Alternate day aspirin] 0.01 0.02 0.01
#> d[stroke = 0: Dipyridamole] 0.09 0.09 0.08
#> d[stroke = 0: Fixed dose warfarin] 0.07 0.10 0.14
#> d[stroke = 0: Fixed dose warfarin + low dose aspirin] 0.09 0.10 0.09
#> d[stroke = 0: Fixed dose warfarin + medium dose aspirin] 0.04 0.03 0.04
#> d[stroke = 0: High dose aspirin] 0.05 0.05 0.05
#> d[stroke = 0: Indobufen] 0.01 0.00 0.00
#> d[stroke = 0: Low adjusted dose anti-coagulant] 0.01 0.00 0.00
#> d[stroke = 0: Low dose aspirin] 0.20 0.19 0.14
#> d[stroke = 0: Low dose aspirin + copidogrel] 0.13 0.11 0.11
#> d[stroke = 0: Low dose aspirin + dipyridamole] 0.05 0.03 0.02
#> d[stroke = 0: Medium dose aspirin] 0.02 0.01 0.00
#> d[stroke = 0: Placebo/Standard care] 0.13 0.19 0.22
#> d[stroke = 0: Triflusal] 0.06 0.07 0.09
#> d[stroke = 0: Ximelagatran] 0.02 0.01 0.00
#> p_rank[16] p_rank[17]
#> d[stroke = 0: Standard adjusted dose anti-coagulant] 0.00 0.00
#> d[stroke = 0: Acenocoumarol] 0.02 0.00
#> d[stroke = 0: Alternate day aspirin] 0.02 0.03
#> d[stroke = 0: Dipyridamole] 0.07 0.06
#> d[stroke = 0: Fixed dose warfarin] 0.21 0.22
#> d[stroke = 0: Fixed dose warfarin + low dose aspirin] 0.06 0.05
#> d[stroke = 0: Fixed dose warfarin + medium dose aspirin] 0.03 0.03
#> d[stroke = 0: High dose aspirin] 0.07 0.14
#> d[stroke = 0: Indobufen] 0.00 0.00
#> d[stroke = 0: Low adjusted dose anti-coagulant] 0.00 0.00
#> d[stroke = 0: Low dose aspirin] 0.06 0.02
#> d[stroke = 0: Low dose aspirin + copidogrel] 0.08 0.04
#> d[stroke = 0: Low dose aspirin + dipyridamole] 0.02 0.01
#> d[stroke = 0: Medium dose aspirin] 0.00 0.00
#> d[stroke = 0: Placebo/Standard care] 0.21 0.10
#> d[stroke = 0: Triflusal] 0.14 0.32
#> d[stroke = 0: Ximelagatran] 0.00 0.00
#>
#> ------------------------------------------------------------- Study: stroke = 1 ----
#>
#> Covariate values:
#> stroke
#> 1
#>
#> p_rank[1] p_rank[2] p_rank[3] p_rank[4]
#> d[stroke = 1: Standard adjusted dose anti-coagulant] 0.01 0.13 0.34 0.33
#> d[stroke = 1: Acenocoumarol] 0.04 0.02 0.01 0.01
#> d[stroke = 1: Alternate day aspirin] 0.37 0.10 0.05 0.06
#> d[stroke = 1: Dipyridamole] 0.00 0.00 0.00 0.01
#> d[stroke = 1: Fixed dose warfarin] 0.01 0.01 0.03 0.07
#> d[stroke = 1: Fixed dose warfarin + low dose aspirin] 0.00 0.01 0.01 0.00
#> d[stroke = 1: Fixed dose warfarin + medium dose aspirin] 0.00 0.00 0.00 0.00
#> d[stroke = 1: High dose aspirin] 0.02 0.03 0.02 0.03
#> d[stroke = 1: Indobufen] 0.04 0.09 0.11 0.17
#> d[stroke = 1: Low adjusted dose anti-coagulant] 0.44 0.32 0.11 0.07
#> d[stroke = 1: Low dose aspirin] 0.00 0.00 0.00 0.00
#> d[stroke = 1: Low dose aspirin + copidogrel] 0.00 0.00 0.00 0.00
#> d[stroke = 1: Low dose aspirin + dipyridamole] 0.00 0.01 0.02 0.03
#> d[stroke = 1: Medium dose aspirin] 0.00 0.00 0.00 0.00
#> d[stroke = 1: Placebo/Standard care] 0.00 0.00 0.00 0.00
#> d[stroke = 1: Triflusal] 0.00 0.00 0.00 0.01
#> d[stroke = 1: Ximelagatran] 0.07 0.27 0.30 0.20
#> p_rank[5] p_rank[6] p_rank[7] p_rank[8]
#> d[stroke = 1: Standard adjusted dose anti-coagulant] 0.14 0.03 0.01 0.00
#> d[stroke = 1: Acenocoumarol] 0.02 0.02 0.02 0.02
#> d[stroke = 1: Alternate day aspirin] 0.09 0.09 0.05 0.04
#> d[stroke = 1: Dipyridamole] 0.02 0.04 0.08 0.10
#> d[stroke = 1: Fixed dose warfarin] 0.16 0.25 0.15 0.10
#> d[stroke = 1: Fixed dose warfarin + low dose aspirin] 0.00 0.01 0.01 0.01
#> d[stroke = 1: Fixed dose warfarin + medium dose aspirin] 0.00 0.00 0.01 0.01
#> d[stroke = 1: High dose aspirin] 0.06 0.10 0.11 0.08
#> d[stroke = 1: Indobufen] 0.25 0.17 0.07 0.04
#> d[stroke = 1: Low adjusted dose anti-coagulant] 0.04 0.01 0.00 0.00
#> d[stroke = 1: Low dose aspirin] 0.00 0.00 0.01 0.02
#> d[stroke = 1: Low dose aspirin + copidogrel] 0.01 0.02 0.05 0.07
#> d[stroke = 1: Low dose aspirin + dipyridamole] 0.07 0.13 0.18 0.15
#> d[stroke = 1: Medium dose aspirin] 0.01 0.06 0.18 0.25
#> d[stroke = 1: Placebo/Standard care] 0.00 0.00 0.02 0.05
#> d[stroke = 1: Triflusal] 0.02 0.03 0.04 0.05
#> d[stroke = 1: Ximelagatran] 0.09 0.04 0.01 0.00
#> p_rank[9] p_rank[10] p_rank[11] p_rank[12]
#> d[stroke = 1: Standard adjusted dose anti-coagulant] 0.00 0.00 0.00 0.00
#> d[stroke = 1: Acenocoumarol] 0.02 0.01 0.01 0.02
#> d[stroke = 1: Alternate day aspirin] 0.03 0.02 0.02 0.02
#> d[stroke = 1: Dipyridamole] 0.12 0.12 0.12 0.12
#> d[stroke = 1: Fixed dose warfarin] 0.06 0.04 0.04 0.02
#> d[stroke = 1: Fixed dose warfarin + low dose aspirin] 0.01 0.01 0.00 0.01
#> d[stroke = 1: Fixed dose warfarin + medium dose aspirin] 0.00 0.01 0.01 0.01
#> d[stroke = 1: High dose aspirin] 0.07 0.06 0.05 0.06
#> d[stroke = 1: Indobufen] 0.02 0.02 0.01 0.00
#> d[stroke = 1: Low adjusted dose anti-coagulant] 0.00 0.00 0.00 0.00
#> d[stroke = 1: Low dose aspirin] 0.06 0.11 0.19 0.23
#> d[stroke = 1: Low dose aspirin + copidogrel] 0.10 0.13 0.13 0.16
#> d[stroke = 1: Low dose aspirin + dipyridamole] 0.12 0.09 0.07 0.05
#> d[stroke = 1: Medium dose aspirin] 0.23 0.13 0.07 0.03
#> d[stroke = 1: Placebo/Standard care] 0.11 0.18 0.20 0.19
#> d[stroke = 1: Triflusal] 0.06 0.07 0.06 0.07
#> d[stroke = 1: Ximelagatran] 0.00 0.00 0.00 0.00
#> p_rank[13] p_rank[14] p_rank[15]
#> d[stroke = 1: Standard adjusted dose anti-coagulant] 0.00 0.00 0.00
#> d[stroke = 1: Acenocoumarol] 0.02 0.05 0.44
#> d[stroke = 1: Alternate day aspirin] 0.02 0.03 0.01
#> d[stroke = 1: Dipyridamole] 0.13 0.09 0.03
#> d[stroke = 1: Fixed dose warfarin] 0.02 0.02 0.01
#> d[stroke = 1: Fixed dose warfarin + low dose aspirin] 0.01 0.01 0.05
#> d[stroke = 1: Fixed dose warfarin + medium dose aspirin] 0.01 0.01 0.27
#> d[stroke = 1: High dose aspirin] 0.09 0.14 0.04
#> d[stroke = 1: Indobufen] 0.00 0.00 0.00
#> d[stroke = 1: Low adjusted dose anti-coagulant] 0.00 0.00 0.00
#> d[stroke = 1: Low dose aspirin] 0.21 0.12 0.03
#> d[stroke = 1: Low dose aspirin + copidogrel] 0.17 0.11 0.03
#> d[stroke = 1: Low dose aspirin + dipyridamole] 0.04 0.02 0.01
#> d[stroke = 1: Medium dose aspirin] 0.01 0.00 0.00
#> d[stroke = 1: Placebo/Standard care] 0.14 0.07 0.02
#> d[stroke = 1: Triflusal] 0.13 0.32 0.06
#> d[stroke = 1: Ximelagatran] 0.00 0.00 0.00
#> p_rank[16] p_rank[17]
#> d[stroke = 1: Standard adjusted dose anti-coagulant] 0.00 0.00
#> d[stroke = 1: Acenocoumarol] 0.20 0.07
#> d[stroke = 1: Alternate day aspirin] 0.01 0.00
#> d[stroke = 1: Dipyridamole] 0.01 0.01
#> d[stroke = 1: Fixed dose warfarin] 0.00 0.00
#> d[stroke = 1: Fixed dose warfarin + low dose aspirin] 0.19 0.66
#> d[stroke = 1: Fixed dose warfarin + medium dose aspirin] 0.50 0.16
#> d[stroke = 1: High dose aspirin] 0.02 0.02
#> d[stroke = 1: Indobufen] 0.00 0.00
#> d[stroke = 1: Low adjusted dose anti-coagulant] 0.00 0.00
#> d[stroke = 1: Low dose aspirin] 0.01 0.00
#> d[stroke = 1: Low dose aspirin + copidogrel] 0.01 0.01
#> d[stroke = 1: Low dose aspirin + dipyridamole] 0.00 0.00
#> d[stroke = 1: Medium dose aspirin] 0.00 0.00
#> d[stroke = 1: Placebo/Standard care] 0.01 0.00
#> d[stroke = 1: Triflusal] 0.03 0.05
#> d[stroke = 1: Ximelagatran] 0.00 0.00
# Modify the default output with ggplot2 functionality
library(ggplot2)
plot(af_4b_rankprobs) +
facet_grid(Treatment~Study, labeller = label_wrap_gen(20)) +
theme(strip.text.y = element_text(angle = 0))
(af_4b_cumrankprobs <- posterior_rank_probs(af_fit_4b, cumulative = TRUE,
newdata = data.frame(stroke = c(0, 1),
label = c("stroke = 0", "stroke = 1")),
study = label))
#> ------------------------------------------------------------- Study: stroke = 0 ----
#>
#> Covariate values:
#> stroke
#> 0
#>
#> p_rank[1] p_rank[2] p_rank[3] p_rank[4]
#> d[stroke = 0: Standard adjusted dose anti-coagulant] 0.00 0.00 0.01 0.04
#> d[stroke = 0: Acenocoumarol] 0.26 0.50 0.64 0.72
#> d[stroke = 0: Alternate day aspirin] 0.44 0.58 0.67 0.73
#> d[stroke = 0: Dipyridamole] 0.00 0.00 0.02 0.05
#> d[stroke = 0: Fixed dose warfarin] 0.00 0.00 0.00 0.01
#> d[stroke = 0: Fixed dose warfarin + low dose aspirin] 0.00 0.01 0.02 0.05
#> d[stroke = 0: Fixed dose warfarin + medium dose aspirin] 0.05 0.15 0.27 0.38
#> d[stroke = 0: High dose aspirin] 0.03 0.09 0.16 0.24
#> d[stroke = 0: Indobufen] 0.17 0.43 0.63 0.76
#> d[stroke = 0: Low adjusted dose anti-coagulant] 0.04 0.18 0.39 0.60
#> d[stroke = 0: Low dose aspirin] 0.00 0.00 0.00 0.00
#> d[stroke = 0: Low dose aspirin + copidogrel] 0.00 0.00 0.00 0.01
#> d[stroke = 0: Low dose aspirin + dipyridamole] 0.01 0.04 0.11 0.21
#> d[stroke = 0: Medium dose aspirin] 0.00 0.00 0.01 0.02
#> d[stroke = 0: Placebo/Standard care] 0.00 0.00 0.00 0.00
#> d[stroke = 0: Triflusal] 0.00 0.00 0.01 0.03
#> d[stroke = 0: Ximelagatran] 0.00 0.02 0.07 0.16
#> p_rank[5] p_rank[6] p_rank[7] p_rank[8]
#> d[stroke = 0: Standard adjusted dose anti-coagulant] 0.12 0.27 0.48 0.67
#> d[stroke = 0: Acenocoumarol] 0.78 0.82 0.84 0.87
#> d[stroke = 0: Alternate day aspirin] 0.77 0.80 0.82 0.84
#> d[stroke = 0: Dipyridamole] 0.09 0.13 0.19 0.25
#> d[stroke = 0: Fixed dose warfarin] 0.01 0.03 0.04 0.06
#> d[stroke = 0: Fixed dose warfarin + low dose aspirin] 0.09 0.13 0.18 0.25
#> d[stroke = 0: Fixed dose warfarin + medium dose aspirin] 0.47 0.55 0.61 0.66
#> d[stroke = 0: High dose aspirin] 0.31 0.36 0.41 0.46
#> d[stroke = 0: Indobufen] 0.83 0.88 0.91 0.93
#> d[stroke = 0: Low adjusted dose anti-coagulant] 0.74 0.83 0.89 0.92
#> d[stroke = 0: Low dose aspirin] 0.00 0.00 0.01 0.02
#> d[stroke = 0: Low dose aspirin + copidogrel] 0.03 0.04 0.07 0.12
#> d[stroke = 0: Low dose aspirin + dipyridamole] 0.32 0.42 0.51 0.59
#> d[stroke = 0: Medium dose aspirin] 0.08 0.17 0.31 0.48
#> d[stroke = 0: Placebo/Standard care] 0.00 0.00 0.00 0.01
#> d[stroke = 0: Triflusal] 0.05 0.08 0.11 0.14
#> d[stroke = 0: Ximelagatran] 0.31 0.48 0.62 0.73
#> p_rank[9] p_rank[10] p_rank[11] p_rank[12]
#> d[stroke = 0: Standard adjusted dose anti-coagulant] 0.82 0.92 0.97 0.99
#> d[stroke = 0: Acenocoumarol] 0.89 0.92 0.93 0.95
#> d[stroke = 0: Alternate day aspirin] 0.86 0.88 0.90 0.91
#> d[stroke = 0: Dipyridamole] 0.32 0.41 0.52 0.61
#> d[stroke = 0: Fixed dose warfarin] 0.09 0.13 0.18 0.26
#> d[stroke = 0: Fixed dose warfarin + low dose aspirin] 0.32 0.41 0.51 0.61
#> d[stroke = 0: Fixed dose warfarin + medium dose aspirin] 0.71 0.75 0.80 0.83
#> d[stroke = 0: High dose aspirin] 0.50 0.54 0.59 0.64
#> d[stroke = 0: Indobufen] 0.95 0.96 0.97 0.98
#> d[stroke = 0: Low adjusted dose anti-coagulant] 0.95 0.97 0.98 0.99
#> d[stroke = 0: Low dose aspirin] 0.05 0.11 0.22 0.39
#> d[stroke = 0: Low dose aspirin + copidogrel] 0.19 0.29 0.41 0.53
#> d[stroke = 0: Low dose aspirin + dipyridamole] 0.67 0.75 0.81 0.87
#> d[stroke = 0: Medium dose aspirin] 0.66 0.81 0.91 0.96
#> d[stroke = 0: Placebo/Standard care] 0.02 0.04 0.08 0.16
#> d[stroke = 0: Triflusal] 0.18 0.22 0.28 0.34
#> d[stroke = 0: Ximelagatran] 0.82 0.89 0.93 0.96
#> p_rank[13] p_rank[14] p_rank[15]
#> d[stroke = 0: Standard adjusted dose anti-coagulant] 1.00 1.00 1.00
#> d[stroke = 0: Acenocoumarol] 0.96 0.97 0.98
#> d[stroke = 0: Alternate day aspirin] 0.92 0.94 0.95
#> d[stroke = 0: Dipyridamole] 0.70 0.80 0.87
#> d[stroke = 0: Fixed dose warfarin] 0.33 0.43 0.57
#> d[stroke = 0: Fixed dose warfarin + low dose aspirin] 0.70 0.80 0.89
#> d[stroke = 0: Fixed dose warfarin + medium dose aspirin] 0.87 0.90 0.94
#> d[stroke = 0: High dose aspirin] 0.69 0.74 0.79
#> d[stroke = 0: Indobufen] 0.99 0.99 0.99
#> d[stroke = 0: Low adjusted dose anti-coagulant] 1.00 1.00 1.00
#> d[stroke = 0: Low dose aspirin] 0.59 0.78 0.92
#> d[stroke = 0: Low dose aspirin + copidogrel] 0.66 0.77 0.88
#> d[stroke = 0: Low dose aspirin + dipyridamole] 0.92 0.95 0.97
#> d[stroke = 0: Medium dose aspirin] 0.99 1.00 1.00
#> d[stroke = 0: Placebo/Standard care] 0.29 0.48 0.70
#> d[stroke = 0: Triflusal] 0.40 0.46 0.55
#> d[stroke = 0: Ximelagatran] 0.98 0.99 1.00
#> p_rank[16] p_rank[17]
#> d[stroke = 0: Standard adjusted dose anti-coagulant] 1.00 1
#> d[stroke = 0: Acenocoumarol] 1.00 1
#> d[stroke = 0: Alternate day aspirin] 0.97 1
#> d[stroke = 0: Dipyridamole] 0.94 1
#> d[stroke = 0: Fixed dose warfarin] 0.78 1
#> d[stroke = 0: Fixed dose warfarin + low dose aspirin] 0.95 1
#> d[stroke = 0: Fixed dose warfarin + medium dose aspirin] 0.97 1
#> d[stroke = 0: High dose aspirin] 0.86 1
#> d[stroke = 0: Indobufen] 1.00 1
#> d[stroke = 0: Low adjusted dose anti-coagulant] 1.00 1
#> d[stroke = 0: Low dose aspirin] 0.98 1
#> d[stroke = 0: Low dose aspirin + copidogrel] 0.96 1
#> d[stroke = 0: Low dose aspirin + dipyridamole] 0.99 1
#> d[stroke = 0: Medium dose aspirin] 1.00 1
#> d[stroke = 0: Placebo/Standard care] 0.90 1
#> d[stroke = 0: Triflusal] 0.68 1
#> d[stroke = 0: Ximelagatran] 1.00 1
#>
#> ------------------------------------------------------------- Study: stroke = 1 ----
#>
#> Covariate values:
#> stroke
#> 1
#>
#> p_rank[1] p_rank[2] p_rank[3] p_rank[4]
#> d[stroke = 1: Standard adjusted dose anti-coagulant] 0.01 0.14 0.48 0.81
#> d[stroke = 1: Acenocoumarol] 0.04 0.06 0.08 0.09
#> d[stroke = 1: Alternate day aspirin] 0.37 0.47 0.52 0.58
#> d[stroke = 1: Dipyridamole] 0.00 0.00 0.01 0.01
#> d[stroke = 1: Fixed dose warfarin] 0.01 0.02 0.04 0.11
#> d[stroke = 1: Fixed dose warfarin + low dose aspirin] 0.00 0.01 0.02 0.02
#> d[stroke = 1: Fixed dose warfarin + medium dose aspirin] 0.00 0.00 0.00 0.01
#> d[stroke = 1: High dose aspirin] 0.02 0.05 0.07 0.10
#> d[stroke = 1: Indobufen] 0.04 0.13 0.24 0.40
#> d[stroke = 1: Low adjusted dose anti-coagulant] 0.44 0.76 0.87 0.94
#> d[stroke = 1: Low dose aspirin] 0.00 0.00 0.00 0.00
#> d[stroke = 1: Low dose aspirin + copidogrel] 0.00 0.00 0.00 0.01
#> d[stroke = 1: Low dose aspirin + dipyridamole] 0.00 0.01 0.03 0.06
#> d[stroke = 1: Medium dose aspirin] 0.00 0.00 0.00 0.00
#> d[stroke = 1: Placebo/Standard care] 0.00 0.00 0.00 0.00
#> d[stroke = 1: Triflusal] 0.00 0.00 0.00 0.01
#> d[stroke = 1: Ximelagatran] 0.07 0.35 0.65 0.85
#> p_rank[5] p_rank[6] p_rank[7] p_rank[8]
#> d[stroke = 1: Standard adjusted dose anti-coagulant] 0.95 0.99 1.00 1.00
#> d[stroke = 1: Acenocoumarol] 0.10 0.12 0.14 0.16
#> d[stroke = 1: Alternate day aspirin] 0.67 0.75 0.81 0.84
#> d[stroke = 1: Dipyridamole] 0.03 0.07 0.15 0.25
#> d[stroke = 1: Fixed dose warfarin] 0.28 0.53 0.68 0.78
#> d[stroke = 1: Fixed dose warfarin + low dose aspirin] 0.03 0.04 0.04 0.05
#> d[stroke = 1: Fixed dose warfarin + medium dose aspirin] 0.01 0.01 0.02 0.03
#> d[stroke = 1: High dose aspirin] 0.17 0.27 0.37 0.45
#> d[stroke = 1: Indobufen] 0.65 0.82 0.90 0.94
#> d[stroke = 1: Low adjusted dose anti-coagulant] 0.98 0.99 1.00 1.00
#> d[stroke = 1: Low dose aspirin] 0.00 0.00 0.01 0.03
#> d[stroke = 1: Low dose aspirin + copidogrel] 0.01 0.03 0.08 0.15
#> d[stroke = 1: Low dose aspirin + dipyridamole] 0.13 0.26 0.44 0.60
#> d[stroke = 1: Medium dose aspirin] 0.02 0.08 0.26 0.51
#> d[stroke = 1: Placebo/Standard care] 0.00 0.01 0.03 0.08
#> d[stroke = 1: Triflusal] 0.03 0.06 0.10 0.15
#> d[stroke = 1: Ximelagatran] 0.94 0.98 0.99 0.99
#> p_rank[9] p_rank[10] p_rank[11] p_rank[12]
#> d[stroke = 1: Standard adjusted dose anti-coagulant] 1.00 1.00 1.00 1.00
#> d[stroke = 1: Acenocoumarol] 0.17 0.18 0.20 0.22
#> d[stroke = 1: Alternate day aspirin] 0.87 0.89 0.91 0.93
#> d[stroke = 1: Dipyridamole] 0.36 0.49 0.61 0.73
#> d[stroke = 1: Fixed dose warfarin] 0.84 0.88 0.92 0.94
#> d[stroke = 1: Fixed dose warfarin + low dose aspirin] 0.06 0.07 0.07 0.08
#> d[stroke = 1: Fixed dose warfarin + medium dose aspirin] 0.03 0.04 0.05 0.05
#> d[stroke = 1: High dose aspirin] 0.52 0.58 0.64 0.70
#> d[stroke = 1: Indobufen] 0.96 0.98 0.99 0.99
#> d[stroke = 1: Low adjusted dose anti-coagulant] 1.00 1.00 1.00 1.00
#> d[stroke = 1: Low dose aspirin] 0.09 0.20 0.39 0.62
#> d[stroke = 1: Low dose aspirin + copidogrel] 0.25 0.38 0.51 0.67
#> d[stroke = 1: Low dose aspirin + dipyridamole] 0.72 0.80 0.88 0.93
#> d[stroke = 1: Medium dose aspirin] 0.74 0.87 0.95 0.98
#> d[stroke = 1: Placebo/Standard care] 0.19 0.37 0.57 0.76
#> d[stroke = 1: Triflusal] 0.20 0.27 0.33 0.41
#> d[stroke = 1: Ximelagatran] 1.00 1.00 1.00 1.00
#> p_rank[13] p_rank[14] p_rank[15]
#> d[stroke = 1: Standard adjusted dose anti-coagulant] 1.00 1.00 1.00
#> d[stroke = 1: Acenocoumarol] 0.23 0.28 0.72
#> d[stroke = 1: Alternate day aspirin] 0.95 0.98 0.99
#> d[stroke = 1: Dipyridamole] 0.86 0.95 0.98
#> d[stroke = 1: Fixed dose warfarin] 0.96 0.98 0.99
#> d[stroke = 1: Fixed dose warfarin + low dose aspirin] 0.09 0.10 0.15
#> d[stroke = 1: Fixed dose warfarin + medium dose aspirin] 0.06 0.08 0.35
#> d[stroke = 1: High dose aspirin] 0.79 0.92 0.96
#> d[stroke = 1: Indobufen] 0.99 1.00 1.00
#> d[stroke = 1: Low adjusted dose anti-coagulant] 1.00 1.00 1.00
#> d[stroke = 1: Low dose aspirin] 0.82 0.95 0.98
#> d[stroke = 1: Low dose aspirin + copidogrel] 0.84 0.95 0.98
#> d[stroke = 1: Low dose aspirin + dipyridamole] 0.97 0.99 1.00
#> d[stroke = 1: Medium dose aspirin] 0.99 1.00 1.00
#> d[stroke = 1: Placebo/Standard care] 0.90 0.97 0.99
#> d[stroke = 1: Triflusal] 0.54 0.86 0.92
#> d[stroke = 1: Ximelagatran] 1.00 1.00 1.00
#> p_rank[16] p_rank[17]
#> d[stroke = 1: Standard adjusted dose anti-coagulant] 1.00 1
#> d[stroke = 1: Acenocoumarol] 0.93 1
#> d[stroke = 1: Alternate day aspirin] 1.00 1
#> d[stroke = 1: Dipyridamole] 0.99 1
#> d[stroke = 1: Fixed dose warfarin] 1.00 1
#> d[stroke = 1: Fixed dose warfarin + low dose aspirin] 0.34 1
#> d[stroke = 1: Fixed dose warfarin + medium dose aspirin] 0.84 1
#> d[stroke = 1: High dose aspirin] 0.98 1
#> d[stroke = 1: Indobufen] 1.00 1
#> d[stroke = 1: Low adjusted dose anti-coagulant] 1.00 1
#> d[stroke = 1: Low dose aspirin] 1.00 1
#> d[stroke = 1: Low dose aspirin + copidogrel] 0.99 1
#> d[stroke = 1: Low dose aspirin + dipyridamole] 1.00 1
#> d[stroke = 1: Medium dose aspirin] 1.00 1
#> d[stroke = 1: Placebo/Standard care] 1.00 1
#> d[stroke = 1: Triflusal] 0.95 1
#> d[stroke = 1: Ximelagatran] 1.00 1
plot(af_4b_cumrankprobs) +
facet_grid(Treatment~Study, labeller = label_wrap_gen(20)) +
theme(strip.text.y = element_text(angle = 0))
