library(multinma)
options(mc.cores = parallel::detectCores())
This vignette describes the analysis of 50 trials of 8 thrombolytic
drugs (streptokinase, SK; alteplase, t-PA; accelerated alteplase, Acc
t-PA; streptokinase plus alteplase, SK+tPA; reteplase, r-PA;
tenocteplase, TNK; urokinase, UK; anistreptilase, ASPAC) plus
per-cutaneous transluminal coronary angioplasty (PTCA) (Boland
et al. 2003; Lu and Ades
2006; Dias et al. 2011,
2010). The
number of deaths in 30 or 35 days following acute myocardial infarction
are recorded. The data are available in this package as
thrombolytics
:
head(thrombolytics)
#> studyn trtn trtc r n
#> 1 1 1 SK 1472 20251
#> 2 1 3 Acc t-PA 652 10396
#> 3 1 4 SK + t-PA 723 10374
#> 4 2 1 SK 9 130
#> 5 2 2 t-PA 6 123
#> 6 3 1 SK 5 63
We begin by setting up the network. We have arm-level count data
giving the number of deaths (r
) out of the total
(n
) in each arm, so we use the function
set_agd_arm()
. By default, SK is set as the network
reference treatment.
<- set_agd_arm(thrombolytics,
thrombo_net study = studyn,
trt = trtc,
r = r,
n = n)
thrombo_net#> A network with 50 AgD studies (arm-based).
#>
#> ------------------------------------------------------- AgD studies (arm-based) ----
#> Study Treatment arms
#> 1 3: SK | Acc t-PA | SK + t-PA
#> 2 2: SK | t-PA
#> 3 2: SK | t-PA
#> 4 2: SK | t-PA
#> 5 2: SK | t-PA
#> 6 3: SK | ASPAC | t-PA
#> 7 2: SK | t-PA
#> 8 2: SK | t-PA
#> 9 2: SK | t-PA
#> 10 2: SK | SK + t-PA
#> ... plus 40 more studies
#>
#> Outcome type: count
#> ------------------------------------------------------------------------------------
#> Total number of treatments: 9
#> Total number of studies: 50
#> Reference treatment is: SK
#> Network is connected
Plot the network structure.
plot(thrombo_net, weight_edges = TRUE, weight_nodes = TRUE)
Following TSD 4 (Dias et al. 2011), we fit a fixed
effects NMA model, using the nma()
function with
trt_effects = "fixed"
. We use \(\mathrm{N}(0, 100^2)\) prior distributions
for the treatment effects \(d_k\) and
study-specific intercepts \(\mu_j\). 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.
The model is fitted using the nma()
function. By
default, this will use a Binomial likelihood and a logit link function,
auto-detected from the data.
<- nma(thrombo_net,
thrombo_fit trt_effects = "fixed",
prior_intercept = normal(scale = 100),
prior_trt = normal(scale = 100))
#> Note: Setting "SK" as the network reference treatment.
Basic parameter summaries are given by the print()
method:
thrombo_fit#> A fixed 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% 75% 97.5% n_eff Rhat
#> d[Acc t-PA] -0.18 0.00 0.04 -0.26 -0.21 -0.18 -0.15 -0.10 2797 1
#> d[ASPAC] 0.02 0.00 0.04 -0.05 -0.01 0.02 0.04 0.09 4743 1
#> d[PTCA] -0.48 0.00 0.10 -0.67 -0.55 -0.47 -0.41 -0.28 4449 1
#> d[r-PA] -0.12 0.00 0.06 -0.24 -0.16 -0.12 -0.08 -0.01 4056 1
#> d[SK + t-PA] -0.05 0.00 0.05 -0.14 -0.08 -0.05 -0.02 0.04 5889 1
#> d[t-PA] 0.00 0.00 0.03 -0.05 -0.02 0.00 0.02 0.06 4672 1
#> d[TNK] -0.17 0.00 0.08 -0.33 -0.22 -0.17 -0.12 -0.02 3843 1
#> d[UK] -0.20 0.00 0.22 -0.64 -0.35 -0.21 -0.05 0.23 5138 1
#> lp__ -43043.04 0.14 5.44 -43054.58 -43046.51 -43042.70 -43039.21 -43033.41 1490 1
#>
#> Samples were drawn using NUTS(diag_e) at Tue May 23 11:29:30 2023.
#> 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 \(\mu_j\) are hidden, but could be examined
by changing the pars
argument:
# Not run
print(thrombo_fit, pars = c("d", "mu"))
The prior and posterior distributions can be compared visually using
the plot_prior_posterior()
function:
plot_prior_posterior(thrombo_fit, prior = "trt")
Model fit can be checked using the dic()
function
<- dic(thrombo_fit))
(dic_consistency #> Residual deviance: 106.2 (on 102 data points)
#> pD: 59.1
#> DIC: 165.3
and the residual deviance contributions examined with the
corresponding plot()
method.
plot(dic_consistency)
There are a number of points which are not very well fit by the model, having posterior mean residual deviance contributions greater than 1.
Note: The results of the inconsistency models here are slightly different to those of Dias et al. (2010, 2011), although the overall conclusions are the same. This is due to the presence of multi-arm trials and a different ordering of treatments, meaning that inconsistency is parameterised differently within the multi-arm trials. The same results as Dias et al. are obtained if the network is instead set up with
trtn
as the treatment variable.
Another method for assessing inconsistency is node-splitting (Dias et al. 2011, 2010). Whereas the UME model assesses inconsistency globally, node-splitting assesses inconsistency locally for each potentially inconsistent comparison (those with both direct and indirect evidence) in turn.
Node-splitting can be performed using the nma()
function
with the argument consistency = "nodesplit"
. By default,
all possible comparisons will be split (as determined by the
get_nodesplits()
function). Alternatively, a specific
comparison or comparisons to split can be provided to the
nodesplit
argument.
<- nma(thrombo_net,
thrombo_nodesplit consistency = "nodesplit",
trt_effects = "fixed",
prior_intercept = normal(scale = 100),
prior_trt = normal(scale = 100))
#> Fitting model 1 of 15, node-split: Acc t-PA vs. SK
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 2 of 15, node-split: ASPAC vs. SK
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 3 of 15, node-split: PTCA vs. SK
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 4 of 15, node-split: r-PA vs. SK
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 5 of 15, node-split: t-PA vs. SK
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 6 of 15, node-split: UK vs. SK
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 7 of 15, node-split: ASPAC vs. Acc t-PA
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 8 of 15, node-split: PTCA vs. Acc t-PA
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 9 of 15, node-split: r-PA vs. Acc t-PA
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 10 of 15, node-split: SK + t-PA vs. Acc t-PA
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 11 of 15, node-split: UK vs. Acc t-PA
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 12 of 15, node-split: t-PA vs. ASPAC
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 13 of 15, node-split: t-PA vs. PTCA
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 14 of 15, node-split: UK vs. t-PA
#> Note: Setting "SK" as the network reference treatment.
#> Fitting model 15 of 15, consistency model
#> Note: Setting "SK" as the network reference treatment.
The summary()
method summarises the node-splitting
results, displaying the direct and indirect estimates \(d_\mathrm{dir}\) and \(d_\mathrm{ind}\) from each node-split
model, the network estimate \(d_\mathrm{net}\) from the consistency
model, the inconsistency factor \(\omega =
d_\mathrm{dir} - d_\mathrm{ind}\), and a Bayesian \(p\)-value for inconsistency on each
comparison. The DIC model fit statistics are also provided. (If a random
effects model was fitted, the heterogeneity standard deviation \(\tau\) under each node-split model and
under the consistency model would also be displayed.)
summary(thrombo_nodesplit)
#> Node-splitting models fitted for 14 comparisons.
#>
#> ---------------------------------------------------- Node-split Acc t-PA vs. SK ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net -0.18 0.04 -0.26 -0.21 -0.18 -0.15 -0.09 2521 3141 1
#> d_dir -0.16 0.05 -0.25 -0.19 -0.16 -0.12 -0.06 4551 3852 1
#> d_ind -0.25 0.09 -0.42 -0.31 -0.25 -0.19 -0.07 630 1212 1
#> omega 0.09 0.10 -0.11 0.02 0.09 0.16 0.29 772 1396 1
#>
#> Residual deviance: 106.3 (on 102 data points)
#> pD: 59.8
#> DIC: 166.1
#>
#> Bayesian p-value: 0.38
#>
#> ------------------------------------------------------- Node-split ASPAC vs. SK ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net 0.02 0.04 -0.06 -0.01 0.02 0.04 0.09 5295 3456 1
#> d_dir 0.01 0.04 -0.07 -0.02 0.01 0.03 0.08 4535 3493 1
#> d_ind 0.42 0.25 -0.06 0.25 0.41 0.58 0.92 2746 2609 1
#> omega -0.41 0.25 -0.92 -0.58 -0.41 -0.24 0.08 2793 2726 1
#>
#> Residual deviance: 104.8 (on 102 data points)
#> pD: 60.2
#> DIC: 165.1
#>
#> Bayesian p-value: 0.1
#>
#> -------------------------------------------------------- Node-split PTCA vs. SK ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net -0.47 0.10 -0.67 -0.54 -0.47 -0.40 -0.27 3926 3359 1
#> d_dir -0.66 0.18 -1.03 -0.79 -0.66 -0.54 -0.31 4503 3800 1
#> d_ind -0.39 0.12 -0.62 -0.47 -0.39 -0.31 -0.16 3489 3105 1
#> omega -0.27 0.22 -0.70 -0.42 -0.27 -0.12 0.18 3825 3197 1
#>
#> Residual deviance: 105.6 (on 102 data points)
#> pD: 59.9
#> DIC: 165.5
#>
#> Bayesian p-value: 0.22
#>
#> -------------------------------------------------------- Node-split r-PA vs. SK ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net -0.12 0.06 -0.24 -0.16 -0.12 -0.08 0.00 3802 3353 1
#> d_dir -0.06 0.09 -0.24 -0.12 -0.06 0.00 0.11 5975 3549 1
#> d_ind -0.18 0.08 -0.33 -0.23 -0.18 -0.12 -0.02 2087 2702 1
#> omega 0.11 0.12 -0.12 0.03 0.11 0.20 0.35 2868 2988 1
#>
#> Residual deviance: 106.3 (on 102 data points)
#> pD: 60
#> DIC: 166.3
#>
#> Bayesian p-value: 0.34
#>
#> -------------------------------------------------------- Node-split t-PA vs. SK ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net 0.00 0.03 -0.06 -0.02 0.00 0.02 0.06 4941 3656 1
#> d_dir 0.00 0.03 -0.06 -0.02 0.00 0.02 0.06 3754 3571 1
#> d_ind 0.17 0.23 -0.26 0.02 0.18 0.34 0.60 1252 2003 1
#> omega -0.17 0.23 -0.60 -0.34 -0.18 -0.01 0.27 1273 2201 1
#>
#> Residual deviance: 105.9 (on 102 data points)
#> pD: 59.4
#> DIC: 165.3
#>
#> Bayesian p-value: 0.46
#>
#> ---------------------------------------------------------- Node-split UK vs. SK ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net -0.20 0.22 -0.63 -0.34 -0.20 -0.05 0.23 4501 3364 1
#> d_dir -0.36 0.53 -1.43 -0.71 -0.37 0.00 0.65 5612 2999 1
#> d_ind -0.17 0.25 -0.65 -0.34 -0.17 -0.01 0.33 3854 3133 1
#> omega -0.19 0.59 -1.39 -0.59 -0.18 0.21 0.93 5006 2822 1
#>
#> Residual deviance: 107.1 (on 102 data points)
#> pD: 60
#> DIC: 167.2
#>
#> Bayesian p-value: 0.75
#>
#> ------------------------------------------------- Node-split ASPAC vs. Acc t-PA ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net 0.19 0.06 0.08 0.15 0.19 0.23 0.30 3229 3158 1
#> d_dir 1.40 0.41 0.63 1.11 1.39 1.66 2.25 3683 2856 1
#> d_ind 0.16 0.06 0.05 0.12 0.16 0.20 0.28 2851 3010 1
#> omega 1.23 0.41 0.48 0.95 1.22 1.50 2.09 3525 2658 1
#>
#> Residual deviance: 96.8 (on 102 data points)
#> pD: 59.7
#> DIC: 156.5
#>
#> Bayesian p-value: <0.01
#>
#> -------------------------------------------------- Node-split PTCA vs. Acc t-PA ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net -0.30 0.10 -0.49 -0.37 -0.30 -0.23 -0.10 5422 3485 1
#> d_dir -0.22 0.12 -0.44 -0.30 -0.22 -0.14 0.02 4788 3685 1
#> d_ind -0.47 0.17 -0.82 -0.59 -0.48 -0.36 -0.14 3208 3305 1
#> omega 0.26 0.21 -0.14 0.12 0.26 0.40 0.66 3408 3077 1
#>
#> Residual deviance: 105.1 (on 102 data points)
#> pD: 59.4
#> DIC: 164.5
#>
#> Bayesian p-value: 0.22
#>
#> -------------------------------------------------- Node-split r-PA vs. Acc t-PA ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net 0.05 0.06 -0.06 0.02 0.05 0.09 0.16 5889 3168 1
#> d_dir 0.02 0.07 -0.11 -0.03 0.02 0.06 0.15 5343 3910 1
#> d_ind 0.13 0.10 -0.07 0.06 0.13 0.20 0.34 1867 2746 1
#> omega -0.11 0.12 -0.35 -0.20 -0.12 -0.03 0.12 1943 2521 1
#>
#> Residual deviance: 106.1 (on 102 data points)
#> pD: 59.9
#> DIC: 166
#>
#> Bayesian p-value: 0.36
#>
#> --------------------------------------------- Node-split SK + t-PA vs. Acc t-PA ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net 0.13 0.05 0.02 0.09 0.13 0.17 0.23 5277 3247 1
#> d_dir 0.13 0.05 0.02 0.09 0.13 0.16 0.23 3551 3485 1
#> d_ind 0.63 0.69 -0.71 0.16 0.61 1.07 2.03 2928 2351 1
#> omega -0.50 0.69 -1.91 -0.95 -0.49 -0.04 0.84 2939 2464 1
#>
#> Residual deviance: 106.6 (on 102 data points)
#> pD: 59.9
#> DIC: 166.5
#>
#> Bayesian p-value: 0.47
#>
#> ---------------------------------------------------- Node-split UK vs. Acc t-PA ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net -0.02 0.22 -0.47 -0.17 -0.02 0.13 0.41 4277 3064 1
#> d_dir 0.13 0.35 -0.57 -0.11 0.13 0.37 0.82 4832 3421 1
#> d_ind -0.14 0.28 -0.70 -0.32 -0.13 0.06 0.42 4221 3376 1
#> omega 0.27 0.46 -0.61 -0.05 0.26 0.57 1.19 3940 2953 1
#>
#> Residual deviance: 106.5 (on 102 data points)
#> pD: 59.7
#> DIC: 166.2
#>
#> Bayesian p-value: 0.56
#>
#> ----------------------------------------------------- Node-split t-PA vs. ASPAC ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net -0.01 0.04 -0.09 -0.04 -0.01 0.01 0.06 7086 3248 1
#> d_dir -0.02 0.04 -0.10 -0.05 -0.02 0.00 0.05 4822 3243 1
#> d_ind 0.02 0.06 -0.10 -0.02 0.03 0.07 0.15 2950 3120 1
#> omega -0.05 0.06 -0.17 -0.09 -0.05 -0.01 0.07 3041 3089 1
#>
#> Residual deviance: 106.5 (on 102 data points)
#> pD: 60
#> DIC: 166.5
#>
#> Bayesian p-value: 0.44
#>
#> ------------------------------------------------------ Node-split t-PA vs. PTCA ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net 0.48 0.11 0.27 0.40 0.48 0.55 0.69 4207 3416 1
#> d_dir 0.55 0.43 -0.27 0.26 0.55 0.82 1.40 4256 3356 1
#> d_ind 0.47 0.11 0.26 0.40 0.47 0.55 0.68 3440 3047 1
#> omega 0.08 0.44 -0.77 -0.22 0.07 0.37 0.96 3842 3243 1
#>
#> Residual deviance: 107.1 (on 102 data points)
#> pD: 59.9
#> DIC: 167.1
#>
#> Bayesian p-value: 0.86
#>
#> -------------------------------------------------------- Node-split UK vs. t-PA ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d_net -0.20 0.22 -0.64 -0.35 -0.20 -0.05 0.23 4599 3160 1
#> d_dir -0.30 0.34 -0.97 -0.52 -0.30 -0.06 0.36 4567 3797 1
#> d_ind -0.14 0.29 -0.72 -0.34 -0.14 0.05 0.42 3970 3038 1
#> omega -0.16 0.44 -1.07 -0.44 -0.15 0.14 0.68 4252 3498 1
#>
#> Residual deviance: 107.1 (on 102 data points)
#> pD: 60
#> DIC: 167.1
#>
#> Bayesian p-value: 0.74
Node-splitting the ASPAC vs. Acc t-PA comparison results the lowest DIC, and this is lower than the consistency model. The posterior distribution for the inconsistency factor \(\omega\) for this comparison lies far from 0 and the Bayesian \(p\)-value for inconsistency is small (< 0.01), meaning that there is substantial disagreement between the direct and indirect evidence on this comparison.
We can visually compare the direct, indirect, and network estimates
using the plot()
method.
plot(thrombo_nodesplit)
We can also plot the posterior distributions of the inconsistency
factors \(\omega\), again using the
plot()
method. Here, we specify a “halfeye” plot of the
posterior density with median and credible intervals, and customise the
plot layout with standard ggplot2
functions.
plot(thrombo_nodesplit, pars = "omega", stat = "halfeye", ref_line = 0) +
::aes(y = comparison) +
ggplot2::facet_null() ggplot2
Notice again that the posterior distribution of the inconsistency factor for the ASPAC vs. Acc t-PA comparison lies far from 0, indicating substantial inconsistency between the direct and indirect evidence on this comparison.
Relative effects for all pairwise contrasts between treatments can be
produced using the relative_effects()
function, with
all_contrasts = TRUE
.
<- relative_effects(thrombo_fit, all_contrasts = TRUE))
(thrombo_releff #> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> d[Acc t-PA vs. SK] -0.18 0.04 -0.26 -0.21 -0.18 -0.15 -0.10 2787 2902 1
#> d[ASPAC vs. SK] 0.02 0.04 -0.05 -0.01 0.02 0.04 0.09 4882 3323 1
#> d[PTCA vs. SK] -0.48 0.10 -0.67 -0.55 -0.47 -0.41 -0.28 4458 3124 1
#> d[r-PA vs. SK] -0.12 0.06 -0.24 -0.16 -0.12 -0.08 -0.01 4104 3362 1
#> d[SK + t-PA vs. SK] -0.05 0.05 -0.14 -0.08 -0.05 -0.02 0.04 5956 2726 1
#> d[t-PA vs. SK] 0.00 0.03 -0.05 -0.02 0.00 0.02 0.06 4715 3221 1
#> d[TNK vs. SK] -0.17 0.08 -0.33 -0.22 -0.17 -0.12 -0.02 3912 2912 1
#> d[UK vs. SK] -0.20 0.22 -0.64 -0.35 -0.21 -0.05 0.23 5190 3606 1
#> d[ASPAC vs. Acc t-PA] 0.19 0.06 0.08 0.16 0.19 0.23 0.30 3265 3187 1
#> d[PTCA vs. Acc t-PA] -0.30 0.10 -0.48 -0.36 -0.30 -0.23 -0.11 5685 3538 1
#> d[r-PA vs. Acc t-PA] 0.05 0.06 -0.06 0.02 0.05 0.09 0.16 5474 3708 1
#> d[SK + t-PA vs. Acc t-PA] 0.13 0.05 0.02 0.09 0.13 0.17 0.23 5195 3166 1
#> d[t-PA vs. Acc t-PA] 0.18 0.05 0.08 0.15 0.18 0.22 0.28 3277 3466 1
#> d[TNK vs. Acc t-PA] 0.01 0.06 -0.12 -0.04 0.01 0.05 0.13 5682 3836 1
#> d[UK vs. Acc t-PA] -0.03 0.22 -0.46 -0.18 -0.03 0.13 0.41 5249 3612 1
#> d[PTCA vs. ASPAC] -0.49 0.11 -0.69 -0.57 -0.49 -0.42 -0.29 4510 3429 1
#> d[r-PA vs. ASPAC] -0.14 0.07 -0.28 -0.19 -0.14 -0.09 0.00 4158 3396 1
#> d[SK + t-PA vs. ASPAC] -0.06 0.06 -0.18 -0.10 -0.06 -0.02 0.05 5529 3127 1
#> d[t-PA vs. ASPAC] -0.01 0.04 -0.08 -0.04 -0.01 0.01 0.06 6265 3193 1
#> d[TNK vs. ASPAC] -0.19 0.09 -0.35 -0.25 -0.19 -0.13 -0.02 4030 3025 1
#> d[UK vs. ASPAC] -0.22 0.23 -0.66 -0.37 -0.22 -0.07 0.23 5290 3385 1
#> d[r-PA vs. PTCA] 0.35 0.11 0.14 0.28 0.35 0.42 0.56 5839 3792 1
#> d[SK + t-PA vs. PTCA] 0.43 0.11 0.22 0.36 0.43 0.50 0.63 5556 3400 1
#> d[t-PA vs. PTCA] 0.48 0.10 0.28 0.41 0.48 0.55 0.68 4474 3187 1
#> d[TNK vs. PTCA] 0.30 0.12 0.08 0.22 0.31 0.38 0.53 6395 3267 1
#> d[UK vs. PTCA] 0.27 0.24 -0.20 0.11 0.26 0.44 0.75 5336 3466 1
#> d[SK + t-PA vs. r-PA] 0.08 0.07 -0.06 0.03 0.07 0.12 0.21 5975 3297 1
#> d[t-PA vs. r-PA] 0.13 0.07 0.00 0.08 0.13 0.17 0.26 4018 3209 1
#> d[TNK vs. r-PA] -0.05 0.09 -0.22 -0.11 -0.05 0.01 0.12 6506 2948 1
#> d[UK vs. r-PA] -0.08 0.23 -0.52 -0.24 -0.08 0.08 0.38 5161 3397 1
#> d[t-PA vs. SK + t-PA] 0.05 0.06 -0.06 0.01 0.05 0.09 0.16 5763 3209 1
#> d[TNK vs. SK + t-PA] -0.12 0.08 -0.29 -0.18 -0.12 -0.07 0.04 5837 2839 1
#> d[UK vs. SK + t-PA] -0.15 0.23 -0.58 -0.31 -0.16 0.00 0.29 5225 3477 1
#> d[TNK vs. t-PA] -0.17 0.08 -0.34 -0.23 -0.17 -0.12 -0.01 4156 3355 1
#> d[UK vs. t-PA] -0.21 0.22 -0.63 -0.35 -0.21 -0.05 0.24 5186 3373 1
#> d[UK vs. TNK] -0.03 0.23 -0.48 -0.19 -0.03 0.13 0.42 5506 3248 1
plot(thrombo_releff, ref_line = 0)
Treatment rankings, rank probabilities, and cumulative rank probabilities.
<- posterior_ranks(thrombo_fit))
(thrombo_ranks #> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> rank[SK] 7.44 0.95 6 7 7 8 9 3578 NA 1
#> rank[Acc t-PA] 3.20 0.81 2 3 3 4 5 4327 3751 1
#> rank[ASPAC] 7.98 1.14 5 7 8 9 9 4684 NA 1
#> rank[PTCA] 1.13 0.35 1 1 1 1 2 3764 3831 1
#> rank[r-PA] 4.40 1.16 2 4 4 5 7 4505 3328 1
#> rank[SK + t-PA] 5.98 1.22 4 5 6 6 9 5388 NA 1
#> rank[t-PA] 7.50 1.10 5 7 8 8 9 4778 NA 1
#> rank[TNK] 3.49 1.27 2 3 3 4 6 5358 3134 1
#> rank[UK] 3.88 2.69 1 2 2 5 9 5234 NA 1
plot(thrombo_ranks)
<- posterior_rank_probs(thrombo_fit))
(thrombo_rankprobs #> p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5] p_rank[6] p_rank[7] p_rank[8]
#> d[SK] 0.00 0.00 0.00 0.00 0.02 0.13 0.40 0.31
#> d[Acc t-PA] 0.00 0.19 0.46 0.30 0.05 0.00 0.00 0.00
#> d[ASPAC] 0.00 0.00 0.00 0.00 0.03 0.10 0.17 0.26
#> d[PTCA] 0.87 0.12 0.00 0.00 0.00 0.00 0.00 0.00
#> d[r-PA] 0.00 0.06 0.15 0.30 0.38 0.08 0.02 0.01
#> d[SK + t-PA] 0.00 0.00 0.01 0.06 0.25 0.46 0.10 0.06
#> d[t-PA] 0.00 0.00 0.00 0.01 0.04 0.14 0.29 0.33
#> d[TNK] 0.00 0.24 0.32 0.24 0.15 0.03 0.01 0.01
#> d[UK] 0.12 0.39 0.07 0.08 0.09 0.06 0.02 0.02
#> p_rank[9]
#> d[SK] 0.14
#> d[Acc t-PA] 0.00
#> d[ASPAC] 0.44
#> d[PTCA] 0.00
#> d[r-PA] 0.01
#> d[SK + t-PA] 0.06
#> d[t-PA] 0.20
#> d[TNK] 0.01
#> d[UK] 0.15
plot(thrombo_rankprobs)
<- posterior_rank_probs(thrombo_fit, cumulative = TRUE))
(thrombo_cumrankprobs #> p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5] p_rank[6] p_rank[7] p_rank[8]
#> d[SK] 0.00 0.00 0.00 0.00 0.02 0.15 0.54 0.86
#> d[Acc t-PA] 0.00 0.19 0.65 0.95 1.00 1.00 1.00 1.00
#> d[ASPAC] 0.00 0.00 0.00 0.00 0.03 0.13 0.30 0.56
#> d[PTCA] 0.87 1.00 1.00 1.00 1.00 1.00 1.00 1.00
#> d[r-PA] 0.00 0.06 0.20 0.50 0.89 0.97 0.99 0.99
#> d[SK + t-PA] 0.00 0.00 0.01 0.08 0.32 0.79 0.88 0.94
#> d[t-PA] 0.00 0.00 0.00 0.01 0.04 0.18 0.47 0.80
#> d[TNK] 0.00 0.24 0.56 0.80 0.95 0.98 0.99 0.99
#> d[UK] 0.12 0.51 0.57 0.66 0.75 0.81 0.83 0.85
#> p_rank[9]
#> d[SK] 1
#> d[Acc t-PA] 1
#> d[ASPAC] 1
#> d[PTCA] 1
#> d[r-PA] 1
#> d[SK + t-PA] 1
#> d[t-PA] 1
#> d[TNK] 1
#> d[UK] 1
plot(thrombo_cumrankprobs)