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Produce posterior treatment rankings and rank probabilities from a fitted NMA model. When a meta-regression is fitted with effect modifier interactions with treatment, these will differ by study population.

Usage

posterior_ranks(
  x,
  newdata = NULL,
  study = NULL,
  lower_better = TRUE,
  probs = c(0.025, 0.25, 0.5, 0.75, 0.975),
  sucra = FALSE,
  summary = TRUE
)

posterior_rank_probs(
  x,
  newdata = NULL,
  study = NULL,
  lower_better = TRUE,
  cumulative = FALSE,
  sucra = FALSE
)

Arguments

x

A stan_nma object created by nma()

newdata

Only used if a regression model is fitted. A data frame of study details, one row per study, giving the covariate values at which to produce relative effects. Column names must match variables in the regression model. If NULL, relative effects are produced for all studies in the network.

study

Column of newdata which specifies study names, otherwise studies will be labelled by row number.

lower_better

Logical, are lower treatment effects better (TRUE; default) or higher better (FALSE)? See details.

probs

Numeric vector of quantiles of interest to present in computed summary, default c(0.025, 0.25, 0.5, 0.75, 0.975)

sucra

Logical, calculate the surface under the cumulative ranking curve (SUCRA) for each treatment? Default FALSE.

summary

Logical, calculate posterior summaries? Default TRUE.

cumulative

Logical, return cumulative rank probabilities? Default is FALSE, return posterior probabilities of each treatment having a given rank. If TRUE, cumulative posterior rank probabilities are returned for each treatment having a given rank or better.

Value

A nma_summary object if summary = TRUE, otherwise a list containing a 3D MCMC array of samples and (for regression models) a data frame of study information.

Details

The function posterior_ranks() produces posterior rankings, which have a distribution (e.g. mean/median rank and 95% Credible Interval). The function posterior_rank_probs() produces rank probabilities, which give the posterior probabilities of being ranked first, second, etc. out of all treatments.

The argument lower_better specifies whether lower treatment effects or higher treatment effects are preferred. For example, with a negative binary outcome lower (more negative) log odds ratios are preferred, so lower_better = TRUE. Conversely, for example, if treatments aim to increase the rate of a positive outcome then lower_better = FALSE.

See also

plot.nma_summary() for plotting the ranks and rank probabilities.

Examples

## Smoking cessation
# \donttest{
# Run smoking RE NMA example if not already available
if (!exists("smk_fit_RE")) example("example_smk_re", run.donttest = TRUE)
# }
# \donttest{
# Produce posterior ranks
smk_rank_RE <- posterior_ranks(smk_fit_RE, lower_better = FALSE)
smk_rank_RE
#>                              mean   sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> rank[No intervention]        3.89 0.32    3   4   4   4     4     2434       NA
#> rank[Group counselling]      1.37 0.63    1   1   1   2     3     3066     3101
#> rank[Individual counselling] 1.91 0.62    1   2   2   2     3     2635     2915
#> rank[Self-help]              2.83 0.68    1   3   3   3     4     2447       NA
#>                              Rhat
#> rank[No intervention]           1
#> rank[Group counselling]         1
#> rank[Individual counselling]    1
#> rank[Self-help]                 1
plot(smk_rank_RE)


# Produce rank probabilities
smk_rankprob_RE <- posterior_rank_probs(smk_fit_RE, lower_better = FALSE)
smk_rankprob_RE
#>                           p_rank[1] p_rank[2] p_rank[3] p_rank[4]
#> d[No intervention]             0.00      0.00      0.10      0.89
#> d[Group counselling]           0.71      0.22      0.07      0.00
#> d[Individual counselling]      0.24      0.61      0.15      0.00
#> d[Self-help]                   0.06      0.17      0.68      0.10
plot(smk_rankprob_RE)


# Produce cumulative rank probabilities
smk_cumrankprob_RE <- posterior_rank_probs(smk_fit_RE, lower_better = FALSE,
                                           cumulative = TRUE)
smk_cumrankprob_RE
#>                           p_rank[1] p_rank[2] p_rank[3] p_rank[4]
#> d[No intervention]             0.00      0.00      0.11         1
#> d[Group counselling]           0.71      0.93      1.00         1
#> d[Individual counselling]      0.24      0.85      1.00         1
#> d[Self-help]                   0.06      0.22      0.90         1
plot(smk_cumrankprob_RE)


# Further customisation is possible with ggplot commands
plot(smk_cumrankprob_RE) +
  ggplot2::facet_null() +
  ggplot2::aes(colour = Treatment)

# }

## Plaque psoriasis ML-NMR
# \donttest{
# Run plaque psoriasis ML-NMR example if not already available
if (!exists("pso_fit")) example("example_pso_mlnmr", run.donttest = TRUE)
# }
# \donttest{
# Produce population-adjusted rankings for all study populations in
# the network

# Ranks
pso_rank <- posterior_ranks(pso_fit)
pso_rank
#> ---------------------------------------------------------------- Study: FIXTURE ---- 
#> 
#> Covariate values:
#>  durnpso prevsys  bsa weight  psa
#>      1.6    0.62 0.34   8.34 0.14
#> 
#>                        mean   sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> rank[FIXTURE: PBO]     1.00 0.00    1   1   1   1     1       NA       NA   NA
#> rank[FIXTURE: ETN]     2.00 0.00    2   2   2   2     2       NA       NA   NA
#> rank[FIXTURE: IXE_Q2W] 6.00 0.02    6   6   6   6     6     4016       NA    1
#> rank[FIXTURE: IXE_Q4W] 4.78 0.41    4   5   5   5     5     4442       NA    1
#> rank[FIXTURE: SEC_150] 3.00 0.06    3   3   3   3     3     3188     3188    1
#> rank[FIXTURE: SEC_300] 4.21 0.42    4   4   4   4     5     4643     4016    1
#> 
#> -------------------------------------------------------------- Study: UNCOVER-1 ---- 
#> 
#> Covariate values:
#>  durnpso prevsys  bsa weight  psa
#>        2    0.73 0.28   9.24 0.28
#> 
#>                          mean   sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> rank[UNCOVER-1: PBO]     1.00 0.00    1   1   1   1     1       NA       NA
#> rank[UNCOVER-1: ETN]     2.00 0.00    2   2   2   2     2       NA       NA
#> rank[UNCOVER-1: IXE_Q2W] 6.00 0.02    6   6   6   6     6     4016       NA
#> rank[UNCOVER-1: IXE_Q4W] 4.78 0.41    4   5   5   5     5     4442       NA
#> rank[UNCOVER-1: SEC_150] 3.00 0.06    3   3   3   3     3     3188     3188
#> rank[UNCOVER-1: SEC_300] 4.21 0.42    4   4   4   4     5     4643     4016
#>                          Rhat
#> rank[UNCOVER-1: PBO]       NA
#> rank[UNCOVER-1: ETN]       NA
#> rank[UNCOVER-1: IXE_Q2W]    1
#> rank[UNCOVER-1: IXE_Q4W]    1
#> rank[UNCOVER-1: SEC_150]    1
#> rank[UNCOVER-1: SEC_300]    1
#> 
#> -------------------------------------------------------------- Study: UNCOVER-2 ---- 
#> 
#> Covariate values:
#>  durnpso prevsys  bsa weight  psa
#>     1.87    0.64 0.27   9.17 0.24
#> 
#>                          mean   sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> rank[UNCOVER-2: PBO]     1.00 0.00    1   1   1   1     1       NA       NA
#> rank[UNCOVER-2: ETN]     2.00 0.00    2   2   2   2     2       NA       NA
#> rank[UNCOVER-2: IXE_Q2W] 6.00 0.02    6   6   6   6     6     4016       NA
#> rank[UNCOVER-2: IXE_Q4W] 4.78 0.41    4   5   5   5     5     4442       NA
#> rank[UNCOVER-2: SEC_150] 3.00 0.06    3   3   3   3     3     3188     3188
#> rank[UNCOVER-2: SEC_300] 4.21 0.42    4   4   4   4     5     4643     4016
#>                          Rhat
#> rank[UNCOVER-2: PBO]       NA
#> rank[UNCOVER-2: ETN]       NA
#> rank[UNCOVER-2: IXE_Q2W]    1
#> rank[UNCOVER-2: IXE_Q4W]    1
#> rank[UNCOVER-2: SEC_150]    1
#> rank[UNCOVER-2: SEC_300]    1
#> 
#> -------------------------------------------------------------- Study: UNCOVER-3 ---- 
#> 
#> Covariate values:
#>  durnpso prevsys  bsa weight psa
#>     1.78    0.59 0.28   9.01 0.2
#> 
#>                          mean   sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> rank[UNCOVER-3: PBO]     1.00 0.00    1   1   1   1     1       NA       NA
#> rank[UNCOVER-3: ETN]     2.00 0.00    2   2   2   2     2       NA       NA
#> rank[UNCOVER-3: IXE_Q2W] 6.00 0.02    6   6   6   6     6     4016       NA
#> rank[UNCOVER-3: IXE_Q4W] 4.78 0.41    4   5   5   5     5     4442       NA
#> rank[UNCOVER-3: SEC_150] 3.00 0.06    3   3   3   3     3     3188     3188
#> rank[UNCOVER-3: SEC_300] 4.21 0.42    4   4   4   4     5     4643     4016
#>                          Rhat
#> rank[UNCOVER-3: PBO]       NA
#> rank[UNCOVER-3: ETN]       NA
#> rank[UNCOVER-3: IXE_Q2W]    1
#> rank[UNCOVER-3: IXE_Q4W]    1
#> rank[UNCOVER-3: SEC_150]    1
#> rank[UNCOVER-3: SEC_300]    1
#> 
plot(pso_rank)


# Rank probabilities
pso_rankprobs <- posterior_rank_probs(pso_fit)
pso_rankprobs
#> ---------------------------------------------------------------- Study: FIXTURE ---- 
#> 
#> Covariate values:
#>  durnpso prevsys  bsa weight  psa
#>      1.6    0.62 0.34   8.34 0.14
#> 
#>                     p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5] p_rank[6]
#> d[FIXTURE: PBO]             1         0         0      0.00      0.00         0
#> d[FIXTURE: ETN]             0         1         0      0.00      0.00         0
#> d[FIXTURE: IXE_Q2W]         0         0         0      0.00      0.00         1
#> d[FIXTURE: IXE_Q4W]         0         0         0      0.22      0.78         0
#> d[FIXTURE: SEC_150]         0         0         1      0.00      0.00         0
#> d[FIXTURE: SEC_300]         0         0         0      0.78      0.22         0
#> 
#> -------------------------------------------------------------- Study: UNCOVER-1 ---- 
#> 
#> Covariate values:
#>  durnpso prevsys  bsa weight  psa
#>        2    0.73 0.28   9.24 0.28
#> 
#>                       p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5]
#> d[UNCOVER-1: PBO]             1         0         0      0.00      0.00
#> d[UNCOVER-1: ETN]             0         1         0      0.00      0.00
#> d[UNCOVER-1: IXE_Q2W]         0         0         0      0.00      0.00
#> d[UNCOVER-1: IXE_Q4W]         0         0         0      0.22      0.78
#> d[UNCOVER-1: SEC_150]         0         0         1      0.00      0.00
#> d[UNCOVER-1: SEC_300]         0         0         0      0.78      0.22
#>                       p_rank[6]
#> d[UNCOVER-1: PBO]             0
#> d[UNCOVER-1: ETN]             0
#> d[UNCOVER-1: IXE_Q2W]         1
#> d[UNCOVER-1: IXE_Q4W]         0
#> d[UNCOVER-1: SEC_150]         0
#> d[UNCOVER-1: SEC_300]         0
#> 
#> -------------------------------------------------------------- Study: UNCOVER-2 ---- 
#> 
#> Covariate values:
#>  durnpso prevsys  bsa weight  psa
#>     1.87    0.64 0.27   9.17 0.24
#> 
#>                       p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5]
#> d[UNCOVER-2: PBO]             1         0         0      0.00      0.00
#> d[UNCOVER-2: ETN]             0         1         0      0.00      0.00
#> d[UNCOVER-2: IXE_Q2W]         0         0         0      0.00      0.00
#> d[UNCOVER-2: IXE_Q4W]         0         0         0      0.22      0.78
#> d[UNCOVER-2: SEC_150]         0         0         1      0.00      0.00
#> d[UNCOVER-2: SEC_300]         0         0         0      0.78      0.22
#>                       p_rank[6]
#> d[UNCOVER-2: PBO]             0
#> d[UNCOVER-2: ETN]             0
#> d[UNCOVER-2: IXE_Q2W]         1
#> d[UNCOVER-2: IXE_Q4W]         0
#> d[UNCOVER-2: SEC_150]         0
#> d[UNCOVER-2: SEC_300]         0
#> 
#> -------------------------------------------------------------- Study: UNCOVER-3 ---- 
#> 
#> Covariate values:
#>  durnpso prevsys  bsa weight psa
#>     1.78    0.59 0.28   9.01 0.2
#> 
#>                       p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5]
#> d[UNCOVER-3: PBO]             1         0         0      0.00      0.00
#> d[UNCOVER-3: ETN]             0         1         0      0.00      0.00
#> d[UNCOVER-3: IXE_Q2W]         0         0         0      0.00      0.00
#> d[UNCOVER-3: IXE_Q4W]         0         0         0      0.22      0.78
#> d[UNCOVER-3: SEC_150]         0         0         1      0.00      0.00
#> d[UNCOVER-3: SEC_300]         0         0         0      0.78      0.22
#>                       p_rank[6]
#> d[UNCOVER-3: PBO]             0
#> d[UNCOVER-3: ETN]             0
#> d[UNCOVER-3: IXE_Q2W]         1
#> d[UNCOVER-3: IXE_Q4W]         0
#> d[UNCOVER-3: SEC_150]         0
#> d[UNCOVER-3: SEC_300]         0
#> 
plot(pso_rankprobs)


# Cumulative rank probabilities
pso_cumrankprobs <- posterior_rank_probs(pso_fit, cumulative = TRUE)
pso_cumrankprobs
#> ---------------------------------------------------------------- Study: FIXTURE ---- 
#> 
#> Covariate values:
#>  durnpso prevsys  bsa weight  psa
#>      1.6    0.62 0.34   8.34 0.14
#> 
#>                     p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5] p_rank[6]
#> d[FIXTURE: PBO]             1         1         1      1.00         1         1
#> d[FIXTURE: ETN]             0         1         1      1.00         1         1
#> d[FIXTURE: IXE_Q2W]         0         0         0      0.00         0         1
#> d[FIXTURE: IXE_Q4W]         0         0         0      0.22         1         1
#> d[FIXTURE: SEC_150]         0         0         1      1.00         1         1
#> d[FIXTURE: SEC_300]         0         0         0      0.78         1         1
#> 
#> -------------------------------------------------------------- Study: UNCOVER-1 ---- 
#> 
#> Covariate values:
#>  durnpso prevsys  bsa weight  psa
#>        2    0.73 0.28   9.24 0.28
#> 
#>                       p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5]
#> d[UNCOVER-1: PBO]             1         1         1      1.00         1
#> d[UNCOVER-1: ETN]             0         1         1      1.00         1
#> d[UNCOVER-1: IXE_Q2W]         0         0         0      0.00         0
#> d[UNCOVER-1: IXE_Q4W]         0         0         0      0.22         1
#> d[UNCOVER-1: SEC_150]         0         0         1      1.00         1
#> d[UNCOVER-1: SEC_300]         0         0         0      0.78         1
#>                       p_rank[6]
#> d[UNCOVER-1: PBO]             1
#> d[UNCOVER-1: ETN]             1
#> d[UNCOVER-1: IXE_Q2W]         1
#> d[UNCOVER-1: IXE_Q4W]         1
#> d[UNCOVER-1: SEC_150]         1
#> d[UNCOVER-1: SEC_300]         1
#> 
#> -------------------------------------------------------------- Study: UNCOVER-2 ---- 
#> 
#> Covariate values:
#>  durnpso prevsys  bsa weight  psa
#>     1.87    0.64 0.27   9.17 0.24
#> 
#>                       p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5]
#> d[UNCOVER-2: PBO]             1         1         1      1.00         1
#> d[UNCOVER-2: ETN]             0         1         1      1.00         1
#> d[UNCOVER-2: IXE_Q2W]         0         0         0      0.00         0
#> d[UNCOVER-2: IXE_Q4W]         0         0         0      0.22         1
#> d[UNCOVER-2: SEC_150]         0         0         1      1.00         1
#> d[UNCOVER-2: SEC_300]         0         0         0      0.78         1
#>                       p_rank[6]
#> d[UNCOVER-2: PBO]             1
#> d[UNCOVER-2: ETN]             1
#> d[UNCOVER-2: IXE_Q2W]         1
#> d[UNCOVER-2: IXE_Q4W]         1
#> d[UNCOVER-2: SEC_150]         1
#> d[UNCOVER-2: SEC_300]         1
#> 
#> -------------------------------------------------------------- Study: UNCOVER-3 ---- 
#> 
#> Covariate values:
#>  durnpso prevsys  bsa weight psa
#>     1.78    0.59 0.28   9.01 0.2
#> 
#>                       p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5]
#> d[UNCOVER-3: PBO]             1         1         1      1.00         1
#> d[UNCOVER-3: ETN]             0         1         1      1.00         1
#> d[UNCOVER-3: IXE_Q2W]         0         0         0      0.00         0
#> d[UNCOVER-3: IXE_Q4W]         0         0         0      0.22         1
#> d[UNCOVER-3: SEC_150]         0         0         1      1.00         1
#> d[UNCOVER-3: SEC_300]         0         0         0      0.78         1
#>                       p_rank[6]
#> d[UNCOVER-3: PBO]             1
#> d[UNCOVER-3: ETN]             1
#> d[UNCOVER-3: IXE_Q2W]         1
#> d[UNCOVER-3: IXE_Q4W]         1
#> d[UNCOVER-3: SEC_150]         1
#> d[UNCOVER-3: SEC_300]         1
#> 
plot(pso_cumrankprobs)


# Produce population-adjusted rankings for a different target
# population
new_agd_means <- data.frame(
  bsa = 0.6,
  prevsys = 0.1,
  psa = 0.2,
  weight = 10,
  durnpso = 3)

# Ranks
posterior_ranks(pso_fit, newdata = new_agd_means)
#> ------------------------------------------------------------------ Study: New 1 ---- 
#> 
#> Covariate values:
#>  durnpso prevsys bsa weight psa
#>        3     0.1 0.6     10 0.2
#> 
#>                      mean   sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> rank[New 1: PBO]     1.00 0.00    1   1   1   1     1       NA       NA   NA
#> rank[New 1: ETN]     2.00 0.00    2   2   2   2     2       NA       NA   NA
#> rank[New 1: IXE_Q2W] 6.00 0.02    6   6   6   6     6     4016       NA    1
#> rank[New 1: IXE_Q4W] 4.78 0.41    4   5   5   5     5     4442       NA    1
#> rank[New 1: SEC_150] 3.00 0.06    3   3   3   3     3     3188     3188    1
#> rank[New 1: SEC_300] 4.21 0.42    4   4   4   4     5     4643     4016    1
#> 

# Rank probabilities
posterior_rank_probs(pso_fit, newdata = new_agd_means)
#> ------------------------------------------------------------------ Study: New 1 ---- 
#> 
#> Covariate values:
#>  durnpso prevsys bsa weight psa
#>        3     0.1 0.6     10 0.2
#> 
#>                   p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5] p_rank[6]
#> d[New 1: PBO]             1         0         0      0.00      0.00         0
#> d[New 1: ETN]             0         1         0      0.00      0.00         0
#> d[New 1: IXE_Q2W]         0         0         0      0.00      0.00         1
#> d[New 1: IXE_Q4W]         0         0         0      0.22      0.78         0
#> d[New 1: SEC_150]         0         0         1      0.00      0.00         0
#> d[New 1: SEC_300]         0         0         0      0.78      0.22         0
#> 

# Cumulative rank probabilities
posterior_rank_probs(pso_fit, newdata = new_agd_means,
                     cumulative = TRUE)
#> ------------------------------------------------------------------ Study: New 1 ---- 
#> 
#> Covariate values:
#>  durnpso prevsys bsa weight psa
#>        3     0.1 0.6     10 0.2
#> 
#>                   p_rank[1] p_rank[2] p_rank[3] p_rank[4] p_rank[5] p_rank[6]
#> d[New 1: PBO]             1         1         1      1.00         1         1
#> d[New 1: ETN]             0         1         1      1.00         1         1
#> d[New 1: IXE_Q2W]         0         0         0      0.00         0         1
#> d[New 1: IXE_Q4W]         0         0         0      0.22         1         1
#> d[New 1: SEC_150]         0         0         1      1.00         1         1
#> d[New 1: SEC_300]         0         0         0      0.78         1         1
#> 
# }