Network Meta-analysis with MARS
mars authors
2026-04-02
Network-Meta-Analysis.RmdThis vignette shows how to run a network meta-analysis with
network_meta() using both multilevel and multivariate
fitting strategies, and how to extract:
- Direct effects
- Indirect effects
- Total effects
- Standard errors for direct, indirect, and total effects
- Normal-approximation confidence intervals for direct, indirect, and total effects
- Number of direct and indirect effects and contributing studies by comparison
- Heterogeneity summaries (
QandI^2, total and within) - Between-study variance (
tau^2) by model component/level - Incoherence-factor assessment (per-comparison and global)
- Contribution matrix (% information from direct comparisons)
- Treatment ranking/order and rank probabilities
- Node-splitting direct-vs-indirect comparisons
- Fit-stat summaries and lightweight model comparison helper
library(mars)Example Network Data
Each row is an observed contrast with effect defined as
treatment_2 - treatment_1.
nma_dat <- data.frame(
study = c("s1", "s1", "s2", "s3", "s4", "s5", "s6", "s7", "s8", "s9", "s10", "s11"),
trt1 = c("A", "A", "A", "B", "A", "B", "C", "A", "B", "C", "A", "B"),
trt2 = c("B", "C", "B", "C", "D", "D", "D", "C", "D", "D", "B", "C"),
yi = c(0.22, 0.41, 0.18, 0.19, 0.61, 0.39, 0.23, 0.37, 0.43, 0.18, 0.24, 0.20),
vi = c(0.04, 0.05, 0.03, 0.04, 0.06, 0.05, 0.05, 0.04, 0.06, 0.05, 0.04, 0.04),
stringsAsFactors = FALSE
)
nma_dat
#> study trt1 trt2 yi vi
#> 1 s1 A B 0.22 0.04
#> 2 s1 A C 0.41 0.05
#> 3 s2 A B 0.18 0.03
#> 4 s3 B C 0.19 0.04
#> 5 s4 A D 0.61 0.06
#> 6 s5 B D 0.39 0.05
#> 7 s6 C D 0.23 0.05
#> 8 s7 A C 0.37 0.04
#> 9 s8 B D 0.43 0.06
#> 10 s9 C D 0.18 0.05
#> 11 s10 A B 0.24 0.04
#> 12 s11 B C 0.20 0.04Multilevel Network Meta-analysis
Multilevel network meta-analysis always estimates flexible
heterogeneity by random level. tau_components chooses the
component definition.
nma_ml_flexible <- network_meta(
data = nma_dat,
study_id = "study",
treatment_1 = "trt1",
treatment_2 = "trt2",
effect = "yi",
variance = "vi",
reference = "A",
model_type = "multilevel",
tau_components = "comparison",
ci_level = 0.90,
estimation_method = "MLE"
)
summary(nma_ml_flexible)
#> Network Meta-analysis (MARS)
#> Model Type: multilevel
#> Heterogeneity: flexible
#> Tau components: comparison
#> Reference: A
#> Treatments: A, B, C, D
#>
#> Evidence Summary:
#> $n_comparisons_total
#> [1] 6
#>
#> $n_comparisons_with_direct
#> [1] 6
#>
#> $n_comparisons_with_indirect
#> [1] 6
#>
#> $n_comparisons_indirect_only
#> [1] 0
#>
#> $n_direct_effects
#> [1] 12
#>
#> $n_indirect_effects
#> [1] 48
#>
#>
#> Incoherence-Factor Assessment:
#> Global test:
#> Q_incoherence df p_value
#> 10.7599 6 0.09608667
#>
#> Per-comparison incoherence factors:
#> treatment_1 treatment_2 incoherence_factor if_se z p_value
#> A B 0.2143952 0.1826015 1.1741152 0.24034887
#> A C 0.3762058 0.2368238 1.5885474 0.11216261
#> A D 0.6124295 0.3638213 1.6833250 0.09231219
#> B C 0.1962550 0.2255820 0.8699938 0.38430377
#> B D 0.4143979 0.2564005 1.6162133 0.10604821
#> C D 0.2017792 0.2492718 0.8094749 0.41824205
#> ci_lower ci_upper
#> -0.14349719 0.5722877
#> -0.08796027 0.8403719
#> -0.10064714 1.3255061
#> -0.24587769 0.6383877
#> -0.08813784 0.9169335
#> -0.28678445 0.6903429
#>
#> Contribution Matrix (% information from direct comparisons):
#> A vs B A vs C A vs D B vs C B vs D C vs D
#> A vs B 90.37 4.42 0.29 3.82 1.04 0.06
#> A vs C 41.34 36.50 0.66 16.71 0.59 4.21
#> A vs D 50.86 12.36 3.52 0.64 16.35 16.26
#> B vs C 29.11 13.62 0.03 46.64 4.49 6.11
#> B vs D 24.22 1.45 2.15 13.68 38.74 19.76
#> C vs D 1.08 8.82 1.80 15.68 16.64 55.98
#>
#> Model Fixed Effects (SE fallback applied when needed):
#> term estimate std_error z_value p_value se_source
#> d_B 0.2056048 0.06449319 3.188007 1.432571e-03 hessian
#> d_C 0.3993498 0.07557253 5.284324 1.261696e-07 hessian
#> d_D 0.6075705 0.08147836 7.456833 8.862676e-14 hessian
#>
#> Fit Statistics:
#> model_type heterogeneity n_treatments n_edges estimator QE QE_df QE_p logLik
#> <NA> <NA> 0 NA <NA> NA NA NA 3.204918
#> Dev AIC BIC AICc
#> 9.590164 3.590164 6.014697 223.5902
#>
#> Node-Splitting Assessment:
#> Q_node_split df p_value
#> 10.7599 6 0.09608667
#>
#> treatment_1 treatment_2 direct indirect direct_indirect_diff diff_se
#> A B 0.2100000 -0.004395249 0.2143952 0.1826015
#> A C 0.3877778 0.011571989 0.3762058 0.2368238
#> A D 0.6100000 -0.002429464 0.6124295 0.3638213
#> B C 0.1950000 -0.001254985 0.1962550 0.2255820
#> B D 0.4081818 -0.006216033 0.4143979 0.2564005
#> C D 0.2050000 0.003220770 0.2017792 0.2492718
#> z p_value ci_lower ci_upper
#> 1.1741152 0.24034887 -0.14349719 0.5722877
#> 1.5885474 0.11216261 -0.08796027 0.8403719
#> 1.6833250 0.09231219 -0.10064714 1.3255061
#> 0.8699938 0.38430377 -0.24587769 0.6383877
#> 1.6162133 0.10604821 -0.08813784 0.9169335
#> 0.8094749 0.41824205 -0.28678445 0.6903429
#>
#> Treatment Ranking:
#> treatment mean_effect std_error mean_rank median_rank sucra sucr_a
#> D 0.6075705 0.11120217 1.03100 1 98.96667 98.96667
#> C 0.3993498 0.10789372 1.99725 2 66.75833 66.75833
#> B 0.2056048 0.09666086 2.98825 3 33.72500 33.72500
#> A 0.0000000 0.00000000 3.98350 4 0.55000 0.55000
#> p_best
#> 0.969
#> 0.031
#> 0.000
#> 0.000
#>
#> Contribution Decomposition (top rows):
#> Fixed-Effect Design Diagnostics:
#> $rank
#> [1] NA
#>
#> $ncol
#> [1] 3
#>
#> $condition_number
#> [1] 4.269992
#>
#> $info_condition_number
#> [1] NA
#>
#> $singular
#> [1] TRUE
#>
#> $near_singular
#> [1] FALSE
#>
#> $recommendation
#> [1] "Fixed-effect information matrix is rank-deficient/ill-conditioned; consider simplifying contrasts, merging sparse levels, or adding regularization."
#>
#>
#> Treatment Order:
#> rank treatment effect_vs_reference
#> 1 D 0.6076
#> 2 C 0.3993
#> 3 B 0.2056
#> 4 A 0.0000
#>
#> Direct / Indirect / Total Effects:
#> treatment_1 treatment_2 direct direct_se direct_n_studies direct_n_effects
#> A B 0.2100 0.1095 3 3
#> A C 0.3878 0.1491 2 2
#> A D 0.6100 0.2449 1 1
#> B C 0.1950 0.1414 2 2
#> B D 0.4082 0.1651 2 2
#> C D 0.2050 0.1581 2 2
#> direct_observed direct_observed_se indirect indirect_se indirect_n_paths
#> 0.2100 0.1095 -0.0044 0.1461 2
#> 0.3878 0.1491 0.0116 0.1840 2
#> 0.6100 0.2449 -0.0024 0.2690 2
#> 0.1950 0.1414 -0.0013 0.1757 2
#> 0.4082 0.1651 -0.0062 0.1961 2
#> 0.2050 0.1581 0.0032 0.1927 2
#> indirect_n_studies indirect_n_effects total total_se total_n_studies
#> 7 7 0.2056 0.0967 9
#> 8 8 0.3993 0.1079 9
#> 8 9 0.6076 0.1112 9
#> 8 9 0.1937 0.1043 10
#> 8 8 0.4020 0.1058 10
#> 7 7 0.2082 0.1102 9
#> total_n_effects direct_ci_lower direct_ci_upper direct_observed_ci_lower
#> 10 0.0298 0.3902 0.0298
#> 10 0.1426 0.6330 0.1426
#> 10 0.2071 1.0129 0.2071
#> 11 -0.0376 0.4276 -0.0376
#> 10 0.1365 0.6798 0.1365
#> 9 -0.0551 0.4651 -0.0551
#> direct_observed_ci_upper indirect_ci_lower indirect_ci_upper total_ci_lower
#> 0.3902 -0.2447 0.2359 0.0466
#> 0.6330 -0.2911 0.3143 0.2219
#> 1.0129 -0.4449 0.4401 0.4247
#> 0.4276 -0.2903 0.2878 0.0221
#> 0.6798 -0.3288 0.3164 0.2279
#> 0.4651 -0.3138 0.3202 0.0270
#> total_ci_upper
#> 0.3646
#> 0.5768
#> 0.7905
#> 0.3654
#> 0.5760
#> 0.3894
#>
#> Indirect SE note:
#> Indirect SEs are approximate; for mixed direct+indirect comparisons, var(indirect) is computed as var(total) + var(direct) assuming zero covariance.
#>
#> Heterogeneity Summary:
#> Overall Q:
#> $value
#> [,1]
#> [1,] 0.1092282
#>
#> $df
#> [1] 9
#>
#> $p
#> [,1]
#> [1,] 1
#>
#>
#> Q by random effect level:
#> level Q df p_value n_groups
#> study_id 0.000155828 1 0.9900402 1
#> component_id 0.000000000 0 NA 0
#>
#> Level-specific I2 / Tau2:
#> component tau2 Q df p_value n_groups I2
#> component_id 1e-06 0.000000000 0 NA 0 0.002867794
#> study_id 1e-06 0.000155828 1 0.9900402 1 0.002867794
#>
#> Total I^2:
#> [1] 0.001147137
#>
#> Within I^2:
#> [1] 0.002867794 0.002867794
#>
#> Between-study variance (tau^2):
#> component tau2
#> study_id 1e-06
#> component_id 1e-06League table of total effects:
nma_ml_flexible$league_table
#> A B C D
#> A 0.0000000 0.2056048 0.3993498 0.6075705
#> B -0.2056048 0.0000000 0.1937450 0.4019658
#> C -0.3993498 -0.1937450 0.0000000 0.2082208
#> D -0.6075705 -0.4019658 -0.2082208 0.0000000Per-comparison study contributions and indirect SEs:
nma_ml_flexible$effects[, c(
"treatment_1", "treatment_2",
"direct_n_studies", "indirect_n_studies", "total_n_studies",
"indirect", "indirect_se", "indirect_ci_lower", "indirect_ci_upper",
"total", "total_se", "total_ci_lower", "total_ci_upper"
)]
#> treatment_1 treatment_2 direct_n_studies indirect_n_studies total_n_studies
#> 1 A B 3 7 9
#> 2 A C 2 8 9
#> 3 A D 1 8 9
#> 4 B C 2 8 10
#> 5 B D 2 8 10
#> 6 C D 2 7 9
#> indirect indirect_se indirect_ci_lower indirect_ci_upper total
#> 1 -0.004395249 0.1460935 -0.2446977 0.2359072 0.2056048
#> 2 0.011571989 0.1840198 -0.2911136 0.3142576 0.3993498
#> 3 -0.002429464 0.2690092 -0.4449101 0.4400512 0.6075705
#> 4 -0.001254985 0.1757477 -0.2903342 0.2878243 0.1937450
#> 5 -0.006216033 0.1961338 -0.3288275 0.3163954 0.4019658
#> 6 0.003220770 0.1927081 -0.3137559 0.3201974 0.2082208
#> total_se total_ci_lower total_ci_upper
#> 1 0.09666086 0.04661178 0.3645977
#> 2 0.10789372 0.22188039 0.5768191
#> 3 0.11120217 0.42465924 0.7904818
#> 4 0.10434202 0.02211767 0.3653724
#> 5 0.10580996 0.22792389 0.5760077
#> 6 0.11016539 0.02701483 0.3894267For flexible multilevel models, tau^2 is reported by
random level/component:
nma_ml_flexible$heterogeneity_summary$tau2
#> component tau2
#> 1 study_id 1e-06
#> 2 component_id 1e-06For multilevel models, Q is also broken out by
random/nested level:
nma_ml_flexible$heterogeneity_summary$Q_by_level
#> level Q df p_value n_groups
#> 1 study_id 0.000155828 1 0.9900402 1
#> 2 component_id 0.000000000 0 NA 0Incoherence-factor assessment for multilevel NMA:
nma_ml_flexible$incoherence_assessment$global
#> Q_incoherence df p_value
#> 1 10.7599 6 0.09608667
nma_ml_flexible$incoherence_assessment$per_comparison
#> treatment_1 treatment_2 incoherence_factor if_se z p_value
#> 1 A B 0.2143952 0.1826015 1.1741152 0.24034887
#> 2 A C 0.3762058 0.2368238 1.5885474 0.11216261
#> 3 A D 0.6124295 0.3638213 1.6833250 0.09231219
#> 4 B C 0.1962550 0.2255820 0.8699938 0.38430377
#> 5 B D 0.4143979 0.2564005 1.6162133 0.10604821
#> 6 C D 0.2017792 0.2492718 0.8094749 0.41824205
#> ci_lower ci_upper
#> 1 -0.14349719 0.5722877
#> 2 -0.08796027 0.8403719
#> 3 -0.10064714 1.3255061
#> 4 -0.24587769 0.6383877
#> 5 -0.08813784 0.9169335
#> 6 -0.28678445 0.6903429Node-splitting for key direct/indirect contrasts:
nma_ml_flexible$node_splitting$global
#> Q_node_split df p_value
#> 1 10.7599 6 0.09608667
head(nma_ml_flexible$node_splitting$per_comparison)
#> treatment_1 treatment_2 direct indirect direct_indirect_diff diff_se
#> 1 A B 0.2100000 -0.004395249 0.2143952 0.1826015
#> 2 A C 0.3877778 0.011571989 0.3762058 0.2368238
#> 3 A D 0.6100000 -0.002429464 0.6124295 0.3638213
#> 4 B C 0.1950000 -0.001254985 0.1962550 0.2255820
#> 5 B D 0.4081818 -0.006216033 0.4143979 0.2564005
#> 6 C D 0.2050000 0.003220770 0.2017792 0.2492718
#> z p_value ci_lower ci_upper
#> 1 1.1741152 0.24034887 -0.14349719 0.5722877
#> 2 1.5885474 0.11216261 -0.08796027 0.8403719
#> 3 1.6833250 0.09231219 -0.10064714 1.3255061
#> 4 0.8699938 0.38430377 -0.24587769 0.6383877
#> 5 1.6162133 0.10604821 -0.08813784 0.9169335
#> 6 0.8094749 0.41824205 -0.28678445 0.6903429Contribution decomposition by study/source block:
head(nma_ml_flexible$contribution_decomposition$by_study)
#> [1] treatment_1 treatment_2 source_edge study
#> [5] effect_percentage
#> <0 rows> (or 0-length row.names)
head(nma_ml_flexible$contribution_decomposition$by_edge_block)
#> source_edge treatment_1 treatment_2 effect_percentage n_studies n_effects
#> 1 A vs B A B 90.368175 3 3
#> 2 A vs B B C 29.107446 3 3
#> 3 A vs B A C 41.342442 3 3
#> 4 A vs B B D 24.217443 3 3
#> 5 A vs B C D 1.076873 3 3
#> 6 A vs B A D 50.864110 3 3
#> sum_inverse_variance effective_information weighted_effective_information
#> 1 83.33333 2.941176 2.65788751
#> 2 83.33333 2.941176 0.85610134
#> 3 83.33333 2.941176 1.21595416
#> 4 83.33333 2.941176 0.71227773
#> 5 83.33333 2.941176 0.03167274
#> 6 83.33333 2.941176 1.49600324
head(nma_ml_flexible$contribution_decomposition$effective_information$by_edge)
#> source_edge n_studies n_effects sum_inverse_variance effective_information
#> 1 A vs B 3 3 83.33333 2.941176
#> 2 A vs C 2 2 45.00000 1.975610
#> 3 A vs D 1 1 16.66667 1.000000
#> 4 B vs C 2 2 50.00000 2.000000
#> 5 B vs D 2 2 36.66667 1.983607
#> 6 C vs D 2 2 40.00000 2.000000
head(nma_ml_flexible$contribution_decomposition$effective_information$by_edge_study)
#> source_edge study n_effects sum_inverse_variance effective_information
#> 1 A vs B s1 1 25.00000 1
#> 2 A vs B s10 1 25.00000 1
#> 3 A vs B s2 1 33.33333 1
#> 4 A vs C s1 1 20.00000 1
#> 5 A vs C s7 1 25.00000 1
#> 6 A vs D s4 1 16.66667 1
head(nma_ml_flexible$contribution_decomposition$effective_information$by_comparison)
#> treatment_1 treatment_2 weighted_effective_information
#> 1 A B NA
#> 2 B C NA
#> 3 A C NA
#> 4 B D NA
#> 5 C D NA
#> 6 A D NAFit statistics:
nma_ml_flexible$fit_stats
#> model_type heterogeneity n_treatments n_edges estimator QE QE_df QE_p
#> 1 <NA> <NA> 0 NA <NA> NA NA NA
#> logLik Dev AIC BIC AICc
#> 1 3.204918 9.590164 3.590164 6.014697 223.5902Ranking output:
nma_ml_flexible$ranking$rankings
#> treatment mean_effect std_error mean_rank median_rank sucra sucr_a
#> D D 0.6075705 0.11120217 1.03100 1 98.96667 98.96667
#> C C 0.3993498 0.10789372 1.99725 2 66.75833 66.75833
#> B B 0.2056048 0.09666086 2.98825 3 33.72500 33.72500
#> A A 0.0000000 0.00000000 3.98350 4 0.55000 0.55000
#> p_best
#> D 0.969
#> C 0.031
#> B 0.000
#> A 0.000
nma_ml_flexible$ranking$rank_probability[1:4, , drop = FALSE]
#> rank_1 rank_2 rank_3 rank_4
#> A 0.000 0.00000 0.01650 0.9835
#> B 0.000 0.02825 0.95525 0.0165
#> C 0.031 0.94075 0.02825 0.0000
#> D 0.969 0.03100 0.00000 0.0000
nma_ml_flexible$league_table_ordered
#> treatment_1 treatment_2 total total_se total_ci_lower total_ci_upper
#> 3 A D 0.6075705 0.11120217 0.42465924 0.7904818
#> 5 B D 0.4019658 0.10580996 0.22792389 0.5760077
#> 2 A C 0.3993498 0.10789372 0.22188039 0.5768191
#> 6 C D 0.2082208 0.11016539 0.02701483 0.3894267
#> 1 A B 0.2056048 0.09666086 0.04661178 0.3645977
#> 4 B C 0.1937450 0.10434202 0.02211767 0.3653724
head(nma_ml_flexible$league_table_se)
#> A B C D
#> A 0 0 0 0
#> B 0 0 0 0
#> C 0 0 0 0
#> D 0 0 0 0Level-specific heterogeneity:
nma_ml_flexible$heterogeneity_summary$level_heterogeneity
#> component tau2 Q df p_value n_groups I2
#> 1 component_id 1e-06 0.000000000 0 NA 0 0.002867794
#> 2 study_id 1e-06 0.000155828 1 0.9900402 1 0.002867794Contribution matrix for multilevel NMA:
nma_ml_flexible$contribution_matrix
#> A vs B A vs C A vs D B vs C B vs D C vs D
#> A vs B 90.368175 4.423892 0.28859562 3.8207366 1.0435139 0.05508629
#> A vs C 41.342442 36.496433 0.65531482 16.7057362 0.5851147 4.21495961
#> A vs D 50.864110 12.358909 3.52304713 0.6445192 16.3481046 16.26130979
#> B vs C 29.107446 13.618556 0.02785936 46.6434337 4.4913978 6.11130750
#> B vs D 24.217443 1.453047 2.15266159 13.6821576 38.7374037 19.75728756
#> C vs D 1.076873 8.817042 1.80366089 15.6818831 16.6424910 55.97804929Multilevel with Moderators
nma_dat$severity <- rep(c(0.2, 0.5, 0.8), length.out = nrow(nma_dat))
nma_dat$followup_months <- rep(c(3, 6, 12), length.out = nrow(nma_dat))
nma_ml_mod <- network_meta(
data = nma_dat,
study_id = "study",
treatment_1 = "trt1",
treatment_2 = "trt2",
effect = "yi",
variance = "vi",
reference = "A",
model_type = "multilevel",
tau_components = "comparison",
moderators = ~ severity + followup_months,
estimation_method = "MLE"
)
summary(nma_ml_mod)
#> Network Meta-analysis (MARS)
#> Model Type: multilevel
#> Heterogeneity: flexible
#> Tau components: comparison
#> Moderators: severity, followup_months
#> Reference: A
#> Treatments: A, B, C, D
#>
#> Evidence Summary:
#> $n_comparisons_total
#> [1] 6
#>
#> $n_comparisons_with_direct
#> [1] 6
#>
#> $n_comparisons_with_indirect
#> [1] 6
#>
#> $n_comparisons_indirect_only
#> [1] 0
#>
#> $n_direct_effects
#> [1] 12
#>
#> $n_indirect_effects
#> [1] 48
#>
#>
#> Incoherence-Factor Assessment:
#> Global test:
#> Q_incoherence df p_value
#> 9.934809 6 0.1274243
#>
#> Per-comparison incoherence factors:
#> treatment_1 treatment_2 incoherence_factor if_se z p_value
#> A B 0.2682828 0.4318174 0.6212876 0.5344104
#> A C -0.3675848 0.3107142 -1.1830320 0.2367965
#> A D -0.5633491 0.3546417 -1.5885022 0.1121728
#> B C 0.1833121 0.4221084 0.4342773 0.6640871
#> B D -0.3921116 0.2060007 -1.9034481 0.0569821
#> C D -0.1668590 0.1238819 -1.3469207 0.1780058
#> ci_lower ci_upper
#> -0.5780638 1.11462940
#> -0.9765735 0.24140380
#> -1.2584341 0.13173582
#> -0.6440051 1.01062924
#> -0.7958655 0.01164232
#> -0.4096630 0.07594494
#>
#> Contribution Matrix (% information from direct comparisons):
#> A vs B A vs C A vs D B vs C B vs D C vs D
#> A vs B 0 0.16 2.14 0 97.69 0.01
#> A vs C 0 99.87 0.11 0 0.00 0.02
#> A vs D 0 6.76 92.80 0 0.00 0.43
#> B vs C 0 4.89 1.81 0 93.29 0.02
#> B vs D 0 0.00 0.00 0 100.00 0.00
#> C vs D 0 72.80 26.93 0 0.00 0.27
#>
#> Model Fixed Effects (SE fallback applied when needed):
#> term estimate std_error z_value p_value se_source
#> d_B 0.198383855 0.1124218 1.76463798 0.077624628 hessian
#> d_C 0.388405127 0.1925867 2.01678029 0.043718447 hessian
#> d_D 0.596100819 0.2222841 2.68170722 0.007324753 hessian
#> severity 0.122704339 1.6015608 0.07661547 0.938929449 hessian
#> followup_months -0.007964814 0.1008835 -0.07895058 0.937071935 hessian
#>
#> Fit Statistics:
#> model_type heterogeneity n_treatments n_edges estimator QE QE_df QE_p logLik
#> <NA> <NA> 0 NA <NA> NA NA NA 3.609517
#> Dev AIC BIC AICc
#> 16.78097 6.780967 10.17531 -133.219
#>
#> Node-Splitting Assessment:
#> Q_node_split df p_value
#> 9.934809 6 0.1274243
#>
#> treatment_1 treatment_2 direct indirect direct_indirect_diff
#> A B 0.233333333 -0.034949478 0.2682828
#> A C 0.010410142 0.377994985 -0.3675848
#> A D 0.016375839 0.579724980 -0.5633491
#> B C 0.186666667 0.003354605 0.1833121
#> B D 0.002802677 0.394914287 -0.3921116
#> C D 0.020418327 0.187277366 -0.1668590
#> diff_se z p_value ci_lower ci_upper
#> 0.4318174 0.6212876 0.5344104 -0.5780638 1.11462940
#> 0.3107142 -1.1830320 0.2367965 -0.9765735 0.24140380
#> 0.3546417 -1.5885022 0.1121728 -1.2584341 0.13173582
#> 0.4221084 0.4342773 0.6640871 -0.6440051 1.01062924
#> 0.2060007 -1.9034481 0.0569821 -0.7958655 0.01164232
#> 0.1238819 -1.3469207 0.1780058 -0.4096630 0.07594494
#>
#> Treatment Ranking:
#> treatment mean_effect std_error mean_rank median_rank sucra sucr_a
#> D 0.5961008 0.3545198 1.10650 1 96.45000 96.45000
#> C 0.3884051 0.3106627 2.18450 2 60.51667 60.51667
#> B 0.1983839 0.1938489 3.00675 3 33.10833 33.10833
#> A 0.0000000 0.0000000 3.70225 4 9.92500 9.92500
#> p_best
#> 0.92600
#> 0.02600
#> 0.00675
#> 0.04125
#>
#> Contribution Decomposition (top rows):
#> Fixed-Effect Design Diagnostics:
#> $rank
#> [1] NA
#>
#> $ncol
#> [1] 3
#>
#> $condition_number
#> [1] 43.11314
#>
#> $info_condition_number
#> [1] NA
#>
#> $singular
#> [1] TRUE
#>
#> $near_singular
#> [1] FALSE
#>
#> $recommendation
#> [1] "Fixed-effect information matrix is rank-deficient/ill-conditioned; consider simplifying contrasts, merging sparse levels, or adding regularization."
#>
#>
#> Treatment Order:
#> rank treatment effect_vs_reference
#> 1 D 0.5961
#> 2 C 0.3884
#> 3 B 0.1984
#> 4 A 0.0000
#>
#> Direct / Indirect / Total Effects:
#> treatment_1 treatment_2 direct direct_se direct_n_studies direct_n_effects
#> A B 0.2333 0.2728 3 3
#> A C 0.0104 0.0040 2 2
#> A D 0.0164 0.0066 1 1
#> B C 0.1867 0.2749 2 2
#> B D 0.0028 0.0011 2 2
#> C D 0.0204 0.0157 2 2
#> direct_observed direct_observed_se indirect indirect_se indirect_n_paths
#> 0.2100 0.1095 -0.0349 0.3347 2
#> 0.3878 0.1491 0.3780 0.3107 2
#> 0.6100 0.2449 0.5797 0.3546 2
#> 0.1950 0.1414 0.0034 0.3203 2
#> 0.4082 0.1651 0.3949 0.2060 2
#> 0.2050 0.1581 0.1873 0.1229 2
#> indirect_n_studies indirect_n_effects total total_se total_n_studies
#> 7 7 0.1984 0.1938 9
#> 8 8 0.3884 0.3107 9
#> 8 9 0.5961 0.3545 9
#> 8 9 0.1900 0.1645 10
#> 8 8 0.3977 0.2060 10
#> 7 7 0.2077 0.1219 9
#> total_n_effects direct_ci_lower direct_ci_upper direct_observed_ci_lower
#> 10 -0.3014 0.7681 -0.0047
#> 10 0.0026 0.0183 0.0956
#> 10 0.0035 0.0293 0.1299
#> 11 -0.3521 0.7254 -0.0822
#> 10 0.0006 0.0050 0.0845
#> 9 -0.0104 0.0513 -0.1049
#> direct_observed_ci_upper indirect_ci_lower indirect_ci_upper total_ci_lower
#> 0.4247 -0.6909 0.6210 -0.1816
#> 0.6800 -0.2309 0.9869 -0.2205
#> 1.0901 -0.1152 1.2747 -0.0987
#> 0.4722 -0.6245 0.6312 -0.1324
#> 0.7319 -0.0088 0.7987 -0.0060
#> 0.5149 -0.0536 0.4281 -0.0312
#> total_ci_upper
#> 0.5783
#> 0.9973
#> 1.2909
#> 0.5125
#> 0.8015
#> 0.4465
#>
#> Indirect SE note:
#> Indirect SEs are approximate; for mixed direct+indirect comparisons, var(indirect) is computed as var(total) + var(direct) assuming zero covariance.
#>
#> Heterogeneity Summary:
#> Overall Q:
#> $value
#> [,1]
#> [1,] 0.106132
#>
#> $df
#> [1] 7
#>
#> $p
#> [,1]
#> [1,] 0.9999972
#>
#>
#> Q by random effect level:
#> level Q df p_value n_groups
#> study_id 0.001859865 1 0.965601 1
#> component_id 0.000000000 0 NA 0
#>
#> Level-specific I2 / Tau2:
#> component tau2 Q df p_value n_groups I2
#> component_id 1e-06 0.000000000 0 NA 0 0.003080906
#> study_id 1e-06 0.001859865 1 0.965601 1 0.003080906
#>
#> Total I^2:
#> [1] 0.0008802783
#>
#> Within I^2:
#> [1] 0.003080906 0.003080906
#>
#> Between-study variance (tau^2):
#> component tau2
#> study_id 1e-06
#> component_id 1e-06
nma_ml_mod$moderators
#> [1] "severity" "followup_months"You can optionally add deeper nested random-effect levels using
nested_levels:
nma_dat$site <- rep(c("north", "south", "west"), length.out = nrow(nma_dat))
nma_dat$cohort <- rep(c("c1", "c2"), length.out = nrow(nma_dat))
nma_ml_nested <- network_meta(
data = nma_dat,
study_id = "study",
treatment_1 = "trt1",
treatment_2 = "trt2",
effect = "yi",
variance = "vi",
reference = "A",
model_type = "multilevel",
tau_components = "comparison",
nested_levels = c("site", "cohort"),
estimation_method = "MLE"
)
#> Warning in return_estimates(q_f = q_f, q_r = q_r, estimated_pars =
#> optim_values[["par"]], : Hessian inversion fallback: used eigen-based
#> pseudo-inverse; hessian may be singular/indefinite
summary(nma_ml_nested)
#> Network Meta-analysis (MARS)
#> Model Type: multilevel
#> Heterogeneity: flexible
#> Tau components: comparison
#> Additional nested levels: site, cohort
#> Reference: A
#> Treatments: A, B, C, D
#>
#> Evidence Summary:
#> $n_comparisons_total
#> [1] 6
#>
#> $n_comparisons_with_direct
#> [1] 6
#>
#> $n_comparisons_with_indirect
#> [1] 6
#>
#> $n_comparisons_indirect_only
#> [1] 0
#>
#> $n_direct_effects
#> [1] 12
#>
#> $n_indirect_effects
#> [1] 48
#>
#>
#> Incoherence-Factor Assessment:
#> Global test:
#> Q_incoherence df p_value
#> 10.7598 6 0.09608975
#>
#> Per-comparison incoherence factors:
#> treatment_1 treatment_2 incoherence_factor if_se z p_value
#> A B 0.2143952 0.1826027 1.1741073 0.24035206
#> A C 0.3762058 0.2368249 1.5885401 0.11216426
#> A D 0.6124294 0.3638222 1.6833206 0.09231305
#> B C 0.1962550 0.2255831 0.8699900 0.38430588
#> B D 0.4143978 0.2564015 1.6162064 0.10604969
#> C D 0.2017791 0.2492729 0.8094707 0.41824442
#> ci_lower ci_upper
#> -0.14349959 0.5722900
#> -0.08796241 0.8403740
#> -0.10064901 1.3255078
#> -0.24587973 0.6383898
#> -0.08813997 0.9169356
#> -0.28678678 0.6903450
#>
#> Contribution Matrix (% information from direct comparisons):
#> A vs B A vs C A vs D B vs C B vs D C vs D
#> A vs B 90.37 4.42 0.29 3.82 1.04 0.06
#> A vs C 41.34 36.50 0.66 16.71 0.59 4.21
#> A vs D 50.86 12.36 3.52 0.64 16.35 16.26
#> B vs C 29.11 13.62 0.03 46.64 4.49 6.11
#> B vs D 24.22 1.45 2.15 13.68 38.74 19.76
#> C vs D 1.08 8.82 1.80 15.68 16.64 55.98
#>
#> Model Fixed Effects (SE fallback applied when needed):
#> term estimate std_error z_value p_value se_source
#> d_B 0.2056048 0.06488447 3.168783 1.530789e-03 hessian
#> d_C 0.3993497 0.07558430 5.283501 1.267379e-07 hessian
#> d_D 0.6075706 0.08148260 7.456446 8.888728e-14 hessian
#>
#> Fit Statistics:
#> model_type heterogeneity n_treatments n_edges estimator QE QE_df QE_p logLik
#> <NA> <NA> 0 NA <NA> NA NA NA 3.204852
#> Dev AIC BIC AICc
#> 13.5903 7.590296 10.98464 -304.4097
#>
#> Node-Splitting Assessment:
#> Q_node_split df p_value
#> 10.7598 6 0.09608975
#>
#> treatment_1 treatment_2 direct indirect direct_indirect_diff diff_se
#> A B 0.2100000 -0.004395213 0.2143952 0.1826027
#> A C 0.3877778 0.011571964 0.3762058 0.2368249
#> A D 0.6100000 -0.002429373 0.6124294 0.3638222
#> B C 0.1950000 -0.001255046 0.1962550 0.2255831
#> B D 0.4081818 -0.006215978 0.4143978 0.2564015
#> C D 0.2050000 0.003220886 0.2017791 0.2492729
#> z p_value ci_lower ci_upper
#> 1.1741073 0.24035206 -0.14349959 0.5722900
#> 1.5885401 0.11216426 -0.08796241 0.8403740
#> 1.6833206 0.09231305 -0.10064901 1.3255078
#> 0.8699900 0.38430588 -0.24587973 0.6383898
#> 1.6162064 0.10604969 -0.08813997 0.9169356
#> 0.8094707 0.41824442 -0.28678678 0.6903450
#>
#> Treatment Ranking:
#> treatment mean_effect std_error mean_rank median_rank sucra sucr_a
#> D 0.6075706 0.11120514 1.02900 1 99.0333333 99.0333333
#> C 0.3993497 0.10789614 2.00275 2 66.5750000 66.5750000
#> B 0.2056048 0.09666314 2.98375 3 33.8750000 33.8750000
#> A 0.0000000 0.00000000 3.98450 4 0.5166667 0.5166667
#> p_best
#> 0.971
#> 0.029
#> 0.000
#> 0.000
#>
#> Contribution Decomposition (top rows):
#> Fixed-Effect Design Diagnostics:
#> $rank
#> [1] NA
#>
#> $ncol
#> [1] 3
#>
#> $condition_number
#> [1] 4.27001
#>
#> $info_condition_number
#> [1] NA
#>
#> $singular
#> [1] TRUE
#>
#> $near_singular
#> [1] FALSE
#>
#> $recommendation
#> [1] "Fixed-effect information matrix is rank-deficient/ill-conditioned; consider simplifying contrasts, merging sparse levels, or adding regularization."
#>
#>
#> Treatment Order:
#> rank treatment effect_vs_reference
#> 1 D 0.6076
#> 2 C 0.3993
#> 3 B 0.2056
#> 4 A 0.0000
#>
#> Direct / Indirect / Total Effects:
#> treatment_1 treatment_2 direct direct_se direct_n_studies direct_n_effects
#> A B 0.2100 0.1095 3 3
#> A C 0.3878 0.1491 2 2
#> A D 0.6100 0.2449 1 1
#> B C 0.1950 0.1414 2 2
#> B D 0.4082 0.1651 2 2
#> C D 0.2050 0.1581 2 2
#> direct_observed direct_observed_se indirect indirect_se indirect_n_paths
#> 0.2100 0.1095 -0.0044 0.1461 2
#> 0.3878 0.1491 0.0116 0.1840 2
#> 0.6100 0.2449 -0.0024 0.2690 2
#> 0.1950 0.1414 -0.0013 0.1757 2
#> 0.4082 0.1651 -0.0062 0.1961 2
#> 0.2050 0.1581 0.0032 0.1927 2
#> indirect_n_studies indirect_n_effects total total_se total_n_studies
#> 7 7 0.2056 0.0967 9
#> 8 8 0.3993 0.1079 9
#> 8 9 0.6076 0.1112 9
#> 8 9 0.1937 0.1043 10
#> 8 8 0.4020 0.1058 10
#> 7 7 0.2082 0.1102 9
#> total_n_effects direct_ci_lower direct_ci_upper direct_observed_ci_lower
#> 10 -0.0047 0.4247 -0.0047
#> 10 0.0956 0.6800 0.0956
#> 10 0.1299 1.0901 0.1299
#> 11 -0.0822 0.4722 -0.0822
#> 10 0.0845 0.7319 0.0845
#> 9 -0.1049 0.5149 -0.1049
#> direct_observed_ci_upper indirect_ci_lower indirect_ci_upper total_ci_lower
#> 0.4247 -0.2907 0.2819 0.0161
#> 0.6800 -0.3491 0.3722 0.1879
#> 1.0901 -0.5297 0.5248 0.3896
#> 0.4722 -0.3457 0.3432 -0.0108
#> 0.7319 -0.3906 0.3782 0.1946
#> 0.5149 -0.3745 0.3809 -0.0077
#> total_ci_upper
#> 0.3951
#> 0.6108
#> 0.8255
#> 0.3983
#> 0.6094
#> 0.4241
#>
#> Indirect SE note:
#> Indirect SEs are approximate; for mixed direct+indirect comparisons, var(indirect) is computed as var(total) + var(direct) assuming zero covariance.
#>
#> Heterogeneity Summary:
#> Overall Q:
#> $value
#> [,1]
#> [1,] 0.1092282
#>
#> $df
#> [1] 9
#>
#> $p
#> [,1]
#> [1,] 1
#>
#>
#> Q by random effect level:
#> level Q df p_value n_groups
#> study_id 0.000155816 1 0.9900406 1
#> component_id 0.000000000 0 NA 0
#> .nma_nested_1 0.000000000 0 NA 0
#> .nma_nested_2 0.000000000 0 NA 0
#>
#> Level-specific I2 / Tau2:
#> component tau2 Q df p_value n_groups I2
#> .nma_nested_1 1e-06 0.000000000 0 NA 0 0.004014865
#> .nma_nested_2 1e-06 0.000000000 0 NA 0 0.004014865
#> component_id 1e-06 0.000000000 0 NA 0 0.004014865
#> study_id 1e-06 0.000155816 1 0.9900406 1 0.004014865
#>
#> Total I^2:
#> [1] 0.002294248
#>
#> Within I^2:
#> [1] 0.004014865 0.004014865 0.004014865 0.004014865
#>
#> Between-study variance (tau^2):
#> component tau2
#> study_id 1e-06
#> component_id 1e-06
#> .nma_nested_1 1e-06
#> .nma_nested_2 1e-06Example: Outcomes Within Study, Comparisons Within Outcome
The example below uses two explicit nested levels for multilevel NMA:
-
outcomewithinstudy -
comparison_within_outcomewithinoutcome
nma_nested_dat <- nma_dat
nma_nested_dat$outcome <- rep(c("pain", "function"), length.out = nrow(nma_nested_dat))
nma_nested_dat$comparison_within_outcome <- ave(
seq_len(nrow(nma_nested_dat)),
nma_nested_dat$study,
nma_nested_dat$outcome,
FUN = seq_along
)
nma_ml_outcome_nested <- network_meta(
data = nma_nested_dat,
study_id = "study",
treatment_1 = "trt1",
treatment_2 = "trt2",
effect = "yi",
variance = "vi",
reference = "A",
model_type = "multilevel",
tau_components = "comparison",
nested_levels = c("outcome", "comparison_within_outcome"),
estimation_method = "MLE"
)
#> Warning in return_estimates(q_f = q_f, q_r = q_r, estimated_pars =
#> optim_values[["par"]], : Hessian inversion fallback: used eigen-based
#> pseudo-inverse; hessian may be singular/indefinite
nma_ml_outcome_nested$fit$formula
#> effect ~ -1 + d_B + d_C + d_D + (1 | study_id/component_id/.nma_nested_1/.nma_nested_2)
#> <environment: 0x558c4d4e44d8>
nma_ml_outcome_nested$heterogeneity_summary$Q_by_level
#> level Q df p_value n_groups
#> 1 study_id 0.000155816 1 0.9900406 1
#> 2 component_id 0.000000000 0 NA 0
#> 3 .nma_nested_1 0.000000000 0 NA 0
#> 4 .nma_nested_2 0.000000000 0 NA 0
nma_ml_outcome_nested$heterogeneity_summary$tau2
#> component tau2
#> 1 study_id 1e-06
#> 2 component_id 1e-06
#> 3 .nma_nested_1 1e-06
#> 4 .nma_nested_2 1e-06Multilevel and robustID
In network_meta(), robustID is restricted
to model_type = "multivariate". For multilevel models,
clustering is handled through random effects (study_id,
tau_components, nested_levels), so
robustID now returns a clear error.
Forest Plots for Network Effects
network_forest_plot() provides a standard forest plot
for one selected effect type ("direct",
"indirect", or "total").
network_forest_plot(
nma_ml_flexible,
effect_type = "total",
order_by = "effect",
right_digits = 2,
main = "Network Forest Plot: Total Effects"
)
network_forest_overlay_plot() draws direct, total, and
indirect effects for each comparison using nearly overlapping lines for
fast visual comparison.
network_forest_overlay_plot(
nma_ml_flexible,
order_by = "total",
right_label = "all",
right_digits = 2,
main = "Overlay Forest Plot: Direct vs Indirect vs Total"
)
Contribution Heatmap (Base R)
network_contribution_heatmap() visualizes the percentage
information contributed by each direct comparison estimate to each
network comparison.
network_contribution_heatmap(
nma_ml_flexible,
main = "Contribution Matrix Heatmap",
show_values = FALSE
)
Speed Controls
For larger networks, control can enable sparse matrix
algebra, reuse cached intermediate matrices, and parallelize selected
post-fit computations.
nma_ml_fast <- network_meta(
data = nma_dat,
study_id = "study",
treatment_1 = "trt1",
treatment_2 = "trt2",
effect = "yi",
variance = "vi",
reference = "A",
model_type = "multilevel",
tau_components = "comparison",
estimation_method = "MLE",
control = list(
use_sparse = TRUE,
reuse_inverses = TRUE,
parallel = 2
)
)
nma_ml_fast$control
#> $use_sparse
#> [1] TRUE
#>
#> $reuse_inverses
#> [1] TRUE
#>
#> $parallel
#> [1] 2
#>
#> $singular_threshold
#> [1] 1e+08All Plots for All Fitted Models
The chunk below draws the three plot types (forest, overlay, contribution heatmap) for each model fit in this vignette.
op <- par(mfrow = c(1, 3))
network_forest_plot(nma_ml_flexible, effect_type = "total", main = "ML Flexible: Total")
network_forest_overlay_plot(nma_ml_flexible, order_by = "total", right_label = "total",
main = "ML Flexible: Overlay")
network_contribution_heatmap(nma_ml_flexible, main = "ML Flexible: Contribution")
par(op)
op <- par(mfrow = c(1, 3))
network_forest_plot(nma_ml_nested, effect_type = "total", main = "ML Nested: Total")
network_forest_overlay_plot(nma_ml_nested, order_by = "total", right_label = "total",
main = "ML Nested: Overlay")
network_contribution_heatmap(nma_ml_nested, main = "ML Nested: Contribution")
par(op)
op <- par(mfrow = c(1, 3))
network_forest_plot(nma_ml_outcome_nested, effect_type = "total", main = "ML Outcome Nested: Total")
network_forest_overlay_plot(nma_ml_outcome_nested, order_by = "total", right_label = "total",
main = "ML Outcome Nested: Overlay")
network_contribution_heatmap(nma_ml_outcome_nested, main = "ML Outcome Nested: Contribution")
par(op)Multivariate Network Meta-analysis
You can also fit in multivariate mode using
model_type = "multivariate". Use
within_varcov_type to choose the within-study covariance
structure used by the multivariate engine (for example
"multilevel"/"univariate" or metric-based
options such as "log_or" or
"smd_shared_control" when those required fields are
available).
nma_mv <- suppressWarnings(network_meta(
data = nma_dat,
study_id = "study",
treatment_1 = "trt1",
treatment_2 = "trt2",
effect = "yi",
variance = "vi",
reference = "A",
model_type = "multivariate",
heterogeneity = "flexible",
estimation_method = "MLE",
within_varcov_type = "multilevel"
))
summary(nma_mv)
#> Network Meta-analysis (MARS)
#> Model Type: multivariate
#> Heterogeneity: flexible
#> Within-study covariance type: multilevel
#> Stored within-study covariance blocks: 11
#> Reference: A
#> Treatments: A, B, C, D
#>
#> Evidence Summary:
#> $n_comparisons_total
#> [1] 6
#>
#> $n_comparisons_with_direct
#> [1] 6
#>
#> $n_comparisons_with_indirect
#> [1] 6
#>
#> $n_comparisons_indirect_only
#> [1] 0
#>
#> $n_direct_effects
#> [1] 12
#>
#> $n_indirect_effects
#> [1] 48
#>
#>
#> Incoherence-Factor Assessment:
#> Global test:
#> Q_incoherence df p_value
#> 10.75994 6 0.09608507
#>
#> Per-comparison incoherence factors:
#> treatment_1 treatment_2 incoherence_factor if_se z p_value
#> A B 0.2143952 0.1826008 1.1741196 0.24034713
#> A C 0.3762057 0.2368231 1.5885514 0.11216170
#> A D 0.6124294 0.3638208 1.6833273 0.09231176
#> B C 0.1962549 0.2255816 0.8699954 0.38430291
#> B D 0.4143979 0.2564000 1.6162167 0.10604746
#> C D 0.2017793 0.2492712 0.8094771 0.41824078
#> ci_lower ci_upper
#> -0.14349582 0.5722862
#> -0.08795907 0.8403704
#> -0.10064619 1.3255051
#> -0.24587682 0.6383867
#> -0.08813678 0.9169326
#> -0.28678326 0.6903419
#>
#> Contribution Matrix (% information from direct comparisons):
#> A vs B A vs C A vs D B vs C B vs D C vs D
#> A vs B 90.37 4.42 0.29 3.82 1.04 0.06
#> A vs C 41.34 36.50 0.66 16.71 0.59 4.21
#> A vs D 50.86 12.36 3.52 0.64 16.35 16.26
#> B vs C 29.11 13.62 0.03 46.64 4.49 6.11
#> B vs D 24.22 1.45 2.15 13.68 38.74 19.76
#> C vs D 1.08 8.82 1.80 15.68 16.64 55.98
#>
#> Model Fixed Effects (SE fallback applied when needed):
#> term estimate std_error z_value p_value
#> factor(data[[effectID]])A vs B 0.2100001 0.08649398 2.427915 1.518588e-02
#> factor(data[[effectID]])A vs C 0.3900000 0.11168692 3.491904 4.795908e-04
#> factor(data[[effectID]])A vs D 0.6100000 0.12247653 4.980546 6.340508e-07
#> factor(data[[effectID]])B vs C 0.1944445 0.10540989 1.844651 6.508834e-02
#> factor(data[[effectID]])B vs D 0.4077778 0.10540821 3.868559 1.094806e-04
#> factor(data[[effectID]])C vs D 0.2000001 0.10934126 1.829137 6.737914e-02
#> se_source
#> hessian
#> hessian
#> hessian
#> hessian
#> hessian
#> hessian
#>
#> Fit Statistics:
#> model_type heterogeneity n_treatments n_edges estimator QE QE_df QE_p logLik
#> <NA> <NA> 0 NA <NA> NA NA NA 7.024345
#> Dev AIC BIC AICc
#> 9.95131 9.95131 15.77019 -130.0487
#>
#> Node-Splitting Assessment:
#> Q_node_split df p_value
#> 10.75994 6 0.09608507
#>
#> treatment_1 treatment_2 direct indirect direct_indirect_diff diff_se
#> A B 0.2100000 -0.004395181 0.2143952 0.1826008
#> A C 0.3877778 0.011572112 0.3762057 0.2368231
#> A D 0.6100000 -0.002429438 0.6124294 0.3638208
#> B C 0.1950000 -0.001254930 0.1962549 0.2255816
#> B D 0.4081818 -0.006216076 0.4143979 0.2564000
#> C D 0.2050000 0.003220672 0.2017793 0.2492712
#> z p_value ci_lower ci_upper
#> 1.1741196 0.24034713 -0.14349582 0.5722862
#> 1.5885514 0.11216170 -0.08795907 0.8403704
#> 1.6833273 0.09231176 -0.10064619 1.3255051
#> 0.8699954 0.38430291 -0.24587682 0.6383867
#> 1.6162167 0.10604746 -0.08813678 0.9169326
#> 0.8094771 0.41824078 -0.28678326 0.6903419
#>
#> Treatment Ranking:
#> treatment mean_effect std_error mean_rank median_rank sucra sucr_a
#> D 0.6075706 0.11120055 1.03425 1 98.85833 98.85833
#> C 0.3993499 0.10789224 2.00025 2 66.65833 66.65833
#> B 0.2056048 0.09665948 2.98125 3 33.95833 33.95833
#> A 0.0000000 0.00000000 3.98425 4 0.52500 0.52500
#> p_best
#> 0.96575
#> 0.03425
#> 0.00000
#> 0.00000
#>
#> Contribution Decomposition (top rows):
#> Fixed-Effect Design Diagnostics:
#> $rank
#> [1] NA
#>
#> $ncol
#> [1] 3
#>
#> $condition_number
#> [1] 4.269947
#>
#> $info_condition_number
#> [1] NA
#>
#> $singular
#> [1] TRUE
#>
#> $near_singular
#> [1] FALSE
#>
#> $recommendation
#> [1] "Fixed-effect information matrix is rank-deficient/ill-conditioned; consider simplifying contrasts, merging sparse levels, or adding regularization."
#>
#>
#> Treatment Order:
#> rank treatment effect_vs_reference
#> 1 D 0.6076
#> 2 C 0.3993
#> 3 B 0.2056
#> 4 A 0.0000
#>
#> Direct / Indirect / Total Effects:
#> treatment_1 treatment_2 direct direct_se direct_n_studies direct_n_effects
#> A B 0.2100 0.1095 3 3
#> A C 0.3878 0.1491 2 2
#> A D 0.6100 0.2449 1 1
#> B C 0.1950 0.1414 2 2
#> B D 0.4082 0.1651 2 2
#> C D 0.2050 0.1581 2 2
#> direct_observed direct_observed_se indirect indirect_se indirect_n_paths
#> 0.2100 0.1095 -0.0044 0.1461 2
#> 0.3878 0.1491 0.0116 0.1840 2
#> 0.6100 0.2449 -0.0024 0.2690 2
#> 0.1950 0.1414 -0.0013 0.1757 2
#> 0.4082 0.1651 -0.0062 0.1961 2
#> 0.2050 0.1581 0.0032 0.1927 2
#> indirect_n_studies indirect_n_effects total total_se total_n_studies
#> 7 7 0.2056 0.0967 9
#> 8 8 0.3993 0.1079 9
#> 8 9 0.6076 0.1112 9
#> 8 9 0.1937 0.1043 10
#> 8 8 0.4020 0.1058 10
#> 7 7 0.2082 0.1102 9
#> total_n_effects direct_ci_lower direct_ci_upper direct_observed_ci_lower
#> 10 -0.0047 0.4247 -0.0047
#> 10 0.0956 0.6800 0.0956
#> 10 0.1299 1.0901 0.1299
#> 11 -0.0822 0.4722 -0.0822
#> 10 0.0845 0.7319 0.0845
#> 9 -0.1049 0.5149 -0.1049
#> direct_observed_ci_upper indirect_ci_lower indirect_ci_upper total_ci_lower
#> 0.4247 -0.2907 0.2819 0.0162
#> 0.6800 -0.3491 0.3722 0.1879
#> 1.0901 -0.5297 0.5248 0.3896
#> 0.4722 -0.3457 0.3432 -0.0108
#> 0.7319 -0.3906 0.3782 0.1946
#> 0.5149 -0.3745 0.3809 -0.0077
#> total_ci_upper
#> 0.3951
#> 0.6108
#> 0.8255
#> 0.3982
#> 0.6093
#> 0.4241
#>
#> Indirect SE note:
#> Indirect SEs are approximate; for mixed direct+indirect comparisons, var(indirect) is computed as var(total) + var(direct) assuming zero covariance.
#>
#> Heterogeneity Summary:
#> Overall Q:
#> $value
#> [,1]
#> [1,] 9.140389
#>
#> $df
#> [1] 6
#>
#> $p
#> [,1]
#> [1,] 0.1658353
#>
#>
#> Within-level Q:
#> $`A vs B`
#> QE_value QE_df QE_p
#> 0.0400000 2.0000000 0.9801987
#>
#> $`A vs C`
#> QE_value QE_df QE_p
#> 0.0160000 1.0000000 0.8993432
#>
#> $`A vs D`
#> [1] "only one effect size in this category"
#>
#> $`B vs C`
#> QE_value QE_df QE_p
#> 0.001111111 1.000000000 0.973408772
#>
#> $`B vs D`
#> QE_value QE_df QE_p
#> 0.01777778 1.00000000 0.89392977
#>
#> $`C vs D`
#> QE_value QE_df QE_p
#> 0.0250000 1.0000000 0.8743671
#>
#>
#> Total I^2:
#> [1] 93.43997
#>
#> Within I^2:
#> [1] 0.002136528 0.002136528 95.528876009 95.528876009 95.528876009
#> [6] 95.528876009
#>
#> Between-study variance (tau^2):
#> component tau2
#> A vs B 1e-06
#> A vs C 1e-06
#> A vs D 1e+00
#> B vs C 1e+00
#> B vs D 1e+00
#> C vs D 1e+00Multivariate with Cluster-Robust Standard Errors
For multivariate NMA where studies contribute multiple outcomes or
multiple contrasts, cluster-robust SEs can be requested by setting
robustID:
nma_mv_cluster <- suppressWarnings(network_meta(
data = nma_dat,
study_id = "study",
treatment_1 = "trt1",
treatment_2 = "trt2",
effect = "yi",
variance = "vi",
reference = "A",
model_type = "multivariate",
heterogeneity = "flexible",
estimation_method = "MLE",
within_varcov_type = "multilevel",
robustID = "study"
))
nma_mv_cluster$fit_coefficients
#> term estimate std_error z_value p_value
#> 1 factor(data[[effectID]])A vs B 0.2100001 0.01471607 14.270117 3.360139e-46
#> 2 factor(data[[effectID]])A vs C 0.3900000 0.00642259 60.723171 0.000000e+00
#> 3 factor(data[[effectID]])A vs D 0.6100000 0.12247653 4.980546 6.340508e-07
#> 4 factor(data[[effectID]])B vs C 0.1944445 0.10540989 1.844651 6.508834e-02
#> 5 factor(data[[effectID]])B vs D 0.4077778 0.10540821 3.868559 1.094806e-04
#> 6 factor(data[[effectID]])C vs D 0.2000001 0.10934126 1.829137 6.737914e-02
#> se_source
#> 1 cluster_robust
#> 2 cluster_robust
#> 3 hessian
#> 4 hessian
#> 5 hessian
#> 6 hessian
nma_mv_cluster$robust_cluster_id
#> [1] "study"Multivariate with Moderators
nma_mv_mod <- suppressWarnings(network_meta(
data = nma_dat,
study_id = "study",
treatment_1 = "trt1",
treatment_2 = "trt2",
effect = "yi",
variance = "vi",
reference = "A",
model_type = "multivariate",
heterogeneity = "flexible",
moderators = c("severity", "followup_months"),
estimation_method = "MLE"
))
summary(nma_mv_mod)
#> Network Meta-analysis (MARS)
#> Model Type: multivariate
#> Heterogeneity: flexible
#> Moderators: severity, followup_months
#> Within-study covariance type: multilevel
#> Stored within-study covariance blocks: 11
#> Reference: A
#> Treatments: A, B, C, D
#>
#> Evidence Summary:
#> $n_comparisons_total
#> [1] 6
#>
#> $n_comparisons_with_direct
#> [1] 6
#>
#> $n_comparisons_with_indirect
#> [1] 6
#>
#> $n_comparisons_indirect_only
#> [1] 0
#>
#> $n_direct_effects
#> [1] 12
#>
#> $n_indirect_effects
#> [1] 48
#>
#>
#> Incoherence-Factor Assessment:
#> Global test:
#> Q_incoherence df p_value
#> 9.935036 6 0.1274146
#>
#> Per-comparison incoherence factors:
#> treatment_1 treatment_2 incoherence_factor if_se z p_value
#> A B 0.2682826 0.4318164 0.6212886 0.53440973
#> A C -0.3675853 0.3107103 -1.1830483 0.23679000
#> A D -0.5633495 0.3546375 -1.5885219 0.11216838
#> B C 0.1833119 0.4221076 0.4342776 0.66408688
#> B D -0.3921117 0.2059983 -1.9034708 0.05697914
#> C D -0.1668590 0.1238805 -1.3469346 0.17800131
#> ci_lower ci_upper
#> -0.5780619 1.11462711
#> -0.9765662 0.24139567
#> -1.2584263 0.13172731
#> -0.6440038 1.01062752
#> -0.7958610 0.01163749
#> -0.4096603 0.07594241
#>
#> Contribution Matrix (% information from direct comparisons):
#> A vs B A vs C A vs D B vs C B vs D C vs D
#> A vs B 0 0.16 2.14 0 97.69 0.01
#> A vs C 0 99.87 0.11 0 0.00 0.02
#> A vs D 0 6.76 92.80 0 0.00 0.43
#> B vs C 0 4.89 1.81 0 93.29 0.02
#> B vs D 0 0.00 0.00 0 100.00 0.00
#> C vs D 0 72.80 26.93 0 0.00 0.27
#>
#> Model Fixed Effects (SE fallback applied when needed):
#> term estimate std_error z_value p_value
#> factor(data[[effectID]])A vs B 0.21372546 0.1568131 1.3629310 0.17290426
#> factor(data[[effectID]])A vs C 0.36372546 0.2586715 1.4061290 0.15968583
#> factor(data[[effectID]])A vs D 0.58372546 0.2633918 2.2161870 0.02667870
#> factor(data[[effectID]])B vs C 0.20725491 0.1546595 1.3400723 0.18022184
#> factor(data[[effectID]])B vs D 0.42973857 0.2207945 1.9463285 0.05161529
#> factor(data[[effectID]])C vs D 0.20549028 0.1192613 1.7230258 0.08488385
#> severity 0.37254908 2.0109120 0.1852637 0.85302218
#> followup_months -0.02666667 0.1331013 -0.2003487 0.84120789
#> se_source
#> hessian
#> hessian
#> hessian
#> hessian
#> hessian
#> hessian
#> hessian
#> hessian
#>
#> Fit Statistics:
#> model_type heterogeneity n_treatments n_edges estimator QE QE_df QE_p logLik
#> <NA> <NA> 0 NA <NA> NA NA NA 7.234778
#> Dev AIC BIC AICc
#> 9.530444 13.53044 20.31914 -126.4696
#>
#> Node-Splitting Assessment:
#> Q_node_split df p_value
#> 9.935036 6 0.1274146
#>
#> treatment_1 treatment_2 direct indirect direct_indirect_diff
#> A B 0.233333333 -0.034949264 0.2682826
#> A C 0.010410142 0.377995400 -0.3675853
#> A D 0.016375839 0.579725324 -0.5633495
#> B C 0.186666667 0.003354805 0.1833119
#> B D 0.002802677 0.394914417 -0.3921117
#> C D 0.020418327 0.187277295 -0.1668590
#> diff_se z p_value ci_lower ci_upper
#> 0.4318164 0.6212886 0.53440973 -0.5780619 1.11462711
#> 0.3107103 -1.1830483 0.23679000 -0.9765662 0.24139567
#> 0.3546375 -1.5885219 0.11216838 -1.2584263 0.13172731
#> 0.4221076 0.4342776 0.66408688 -0.6440038 1.01062752
#> 0.2059983 -1.9034708 0.05697914 -0.7958610 0.01163749
#> 0.1238805 -1.3469346 0.17800131 -0.4096603 0.07594241
#>
#> Treatment Ranking:
#> treatment mean_effect std_error mean_rank median_rank sucra sucr_a
#> D 0.5961012 0.3545156 1.11775 1 96.07500 96.07500
#> C 0.3884055 0.3106587 2.18750 2 60.41667 60.41667
#> B 0.1983841 0.1938465 2.99750 3 33.41667 33.41667
#> A 0.0000000 0.0000000 3.69725 4 10.09167 10.09167
#> p_best
#> 0.91375
#> 0.03550
#> 0.01100
#> 0.03975
#>
#> Contribution Decomposition (top rows):
#> Fixed-Effect Design Diagnostics:
#> $rank
#> [1] NA
#>
#> $ncol
#> [1] 3
#>
#> $condition_number
#> [1] 43.11297
#>
#> $info_condition_number
#> [1] NA
#>
#> $singular
#> [1] TRUE
#>
#> $near_singular
#> [1] FALSE
#>
#> $recommendation
#> [1] "Fixed-effect information matrix is rank-deficient/ill-conditioned; consider simplifying contrasts, merging sparse levels, or adding regularization."
#>
#>
#> Treatment Order:
#> rank treatment effect_vs_reference
#> 1 D 0.5961
#> 2 C 0.3884
#> 3 B 0.1984
#> 4 A 0.0000
#>
#> Direct / Indirect / Total Effects:
#> treatment_1 treatment_2 direct direct_se direct_n_studies direct_n_effects
#> A B 0.2333 0.2728 3 3
#> A C 0.0104 0.0040 2 2
#> A D 0.0164 0.0066 1 1
#> B C 0.1867 0.2749 2 2
#> B D 0.0028 0.0011 2 2
#> C D 0.0204 0.0157 2 2
#> direct_observed direct_observed_se indirect indirect_se indirect_n_paths
#> 0.2100 0.1095 -0.0349 0.3347 2
#> 0.3878 0.1491 0.3780 0.3107 2
#> 0.6100 0.2449 0.5797 0.3546 2
#> 0.1950 0.1414 0.0034 0.3203 2
#> 0.4082 0.1651 0.3949 0.2060 2
#> 0.2050 0.1581 0.1873 0.1229 2
#> indirect_n_studies indirect_n_effects total total_se total_n_studies
#> 7 7 0.1984 0.1938 9
#> 8 8 0.3884 0.3107 9
#> 8 9 0.5961 0.3545 9
#> 8 9 0.1900 0.1645 10
#> 8 8 0.3977 0.2060 10
#> 7 7 0.2077 0.1219 9
#> total_n_effects direct_ci_lower direct_ci_upper direct_observed_ci_lower
#> 10 -0.3014 0.7681 -0.0047
#> 10 0.0026 0.0183 0.0956
#> 10 0.0035 0.0293 0.1299
#> 11 -0.3521 0.7254 -0.0822
#> 10 0.0006 0.0050 0.0845
#> 9 -0.0104 0.0513 -0.1049
#> direct_observed_ci_upper indirect_ci_lower indirect_ci_upper total_ci_lower
#> 0.4247 -0.6909 0.6210 -0.1815
#> 0.6800 -0.2309 0.9869 -0.2205
#> 1.0901 -0.1152 1.2747 -0.0987
#> 0.4722 -0.6245 0.6312 -0.1324
#> 0.7319 -0.0088 0.7987 -0.0060
#> 0.5149 -0.0536 0.4281 -0.0311
#> total_ci_upper
#> 0.5783
#> 0.9973
#> 1.2909
#> 0.5125
#> 0.8015
#> 0.4465
#>
#> Indirect SE note:
#> Indirect SEs are approximate; for mixed direct+indirect comparisons, var(indirect) is computed as var(total) + var(direct) assuming zero covariance.
#>
#> Heterogeneity Summary:
#> Overall Q:
#> $value
#> [,1]
#> [1,] 9.140389
#>
#> $df
#> [1] 6
#>
#> $p
#> [,1]
#> [1,] 0.1658353
#>
#>
#> Within-level Q:
#> $`A vs B`
#> QE_value QE_df QE_p
#> 0.0400000 2.0000000 0.9801987
#>
#> $`A vs C`
#> QE_value QE_df QE_p
#> 0.0160000 1.0000000 0.8993432
#>
#> $`A vs D`
#> [1] "only one effect size in this category"
#>
#> $`B vs C`
#> QE_value QE_df QE_p
#> 0.001111111 1.000000000 0.973408772
#>
#> $`B vs D`
#> QE_value QE_df QE_p
#> 0.01777778 1.00000000 0.89392977
#>
#> $`C vs D`
#> QE_value QE_df QE_p
#> 0.0250000 1.0000000 0.8743671
#>
#>
#> Total I^2:
#> [1] 93.43997
#>
#> Within I^2:
#> [1] 0.002136528 0.002136528 95.528876009 95.528876009 95.528876009
#> [6] 95.528876009
#>
#> Between-study variance (tau^2):
#> component tau2
#> A vs B 1e-06
#> A vs C 1e-06
#> A vs D 1e+00
#> B vs C 1e+00
#> B vs D 1e+00
#> C vs D 1e+00
nma_mv_mod$moderators
#> [1] "severity" "followup_months"The output structure is the same, including effects, heterogeneity summaries, and treatment order:
nma_mv$effects
#> treatment_1 treatment_2 direct direct_se direct_n_studies direct_n_effects
#> 1 A B 0.2100000 0.1095445 3 3
#> 2 A C 0.3877778 0.1490712 2 2
#> 3 A D 0.6100000 0.2449490 1 1
#> 4 B C 0.1950000 0.1414214 2 2
#> 5 B D 0.4081818 0.1651446 2 2
#> 6 C D 0.2050000 0.1581139 2 2
#> direct_observed direct_observed_se indirect indirect_se indirect_n_paths
#> 1 0.2100000 0.1095445 -0.004395181 0.1460926 2
#> 2 0.3877778 0.1490712 0.011572112 0.1840189 2
#> 3 0.6100000 0.2449490 -0.002429438 0.2690085 2
#> 4 0.1950000 0.1414214 -0.001254930 0.1757471 2
#> 5 0.4081818 0.1651446 -0.006216076 0.1961331 2
#> 6 0.2050000 0.1581139 0.003220672 0.1927074 2
#> indirect_n_studies indirect_n_effects total total_se total_n_studies
#> 1 7 7 0.2056048 0.09665948 9
#> 2 8 8 0.3993499 0.10789224 9
#> 3 8 9 0.6075706 0.11120055 9
#> 4 8 9 0.1937451 0.10434100 10
#> 5 8 8 0.4019657 0.10580870 10
#> 6 7 7 0.2082207 0.11016412 9
#> total_n_effects direct_ci_lower direct_ci_upper direct_observed_ci_lower
#> 1 10 -0.004703297 0.4247033 -0.004703297
#> 2 10 0.095603598 0.6799520 0.095603598
#> 3 10 0.129908832 1.0900912 0.129908832
#> 4 11 -0.082180765 0.4721808 -0.082180765
#> 5 10 0.084504419 0.7318592 0.084504419
#> 6 9 -0.104897516 0.5148975 -0.104897516
#> direct_observed_ci_upper indirect_ci_lower indirect_ci_upper total_ci_lower
#> 1 0.4247033 -0.2907315 0.2819411 0.016155725
#> 2 0.6799520 -0.3490983 0.3722425 0.187884992
#> 3 1.0900912 -0.5296764 0.5248175 0.389621491
#> 4 0.4721808 -0.3457129 0.3432031 -0.010759522
#> 5 0.7318592 -0.3906300 0.3781978 0.194584506
#> 6 0.5148975 -0.3744789 0.3809202 -0.007697043
#> total_ci_upper
#> 1 0.3950539
#> 2 0.6108148
#> 3 0.8255196
#> 4 0.3982497
#> 5 0.6093470
#> 6 0.4241384
nma_mv$evidence_summary
#> $n_comparisons_total
#> [1] 6
#>
#> $n_comparisons_with_direct
#> [1] 6
#>
#> $n_comparisons_with_indirect
#> [1] 6
#>
#> $n_comparisons_indirect_only
#> [1] 0
#>
#> $n_direct_effects
#> [1] 12
#>
#> $n_indirect_effects
#> [1] 48
nma_mv$indirect_se_note
#> [1] "Indirect SEs are approximate; for mixed direct+indirect comparisons, var(indirect) is computed as var(total) + var(direct) assuming zero covariance."
nma_mv$heterogeneity_summary
#> $Q_total
#> $Q_total$value
#> [,1]
#> [1,] 9.140389
#>
#> $Q_total$df
#> [1] 6
#>
#> $Q_total$p
#> [,1]
#> [1,] 0.1658353
#>
#>
#> $Q_within
#> $Q_within$`A vs B`
#> QE_value QE_df QE_p
#> 0.0400000 2.0000000 0.9801987
#>
#> $Q_within$`A vs C`
#> QE_value QE_df QE_p
#> 0.0160000 1.0000000 0.8993432
#>
#> $Q_within$`A vs D`
#> [1] "only one effect size in this category"
#>
#> $Q_within$`B vs C`
#> QE_value QE_df QE_p
#> 0.001111111 1.000000000 0.973408772
#>
#> $Q_within$`B vs D`
#> QE_value QE_df QE_p
#> 0.01777778 1.00000000 0.89392977
#>
#> $Q_within$`C vs D`
#> QE_value QE_df QE_p
#> 0.0250000 1.0000000 0.8743671
#>
#>
#> $Q_by_level
#> NULL
#>
#> $I2_total
#> [1] 93.43997
#>
#> $I2_within
#> [1] 0.002136528 0.002136528 95.528876009 95.528876009 95.528876009
#> [6] 95.528876009
#>
#> $level_heterogeneity
#> NULL
#>
#> $tau2
#> component tau2
#> 1 A vs B 1e-06
#> 2 A vs C 1e-06
#> 3 A vs D 1e+00
#> 4 B vs C 1e+00
#> 5 B vs D 1e+00
#> 6 C vs D 1e+00
nma_mv$heterogeneity_summary$tau2
#> component tau2
#> 1 A vs B 1e-06
#> 2 A vs C 1e-06
#> 3 A vs D 1e+00
#> 4 B vs C 1e+00
#> 5 B vs D 1e+00
#> 6 C vs D 1e+00
nma_mv$incoherence_assessment$global
#> Q_incoherence df p_value
#> 1 10.75994 6 0.09608507
nma_mv$incoherence_assessment$per_comparison
#> treatment_1 treatment_2 incoherence_factor if_se z p_value
#> 1 A B 0.2143952 0.1826008 1.1741196 0.24034713
#> 2 A C 0.3762057 0.2368231 1.5885514 0.11216170
#> 3 A D 0.6124294 0.3638208 1.6833273 0.09231176
#> 4 B C 0.1962549 0.2255816 0.8699954 0.38430291
#> 5 B D 0.4143979 0.2564000 1.6162167 0.10604746
#> 6 C D 0.2017793 0.2492712 0.8094771 0.41824078
#> ci_lower ci_upper
#> 1 -0.14349582 0.5722862
#> 2 -0.08795907 0.8403704
#> 3 -0.10064619 1.3255051
#> 4 -0.24587682 0.6383867
#> 5 -0.08813678 0.9169326
#> 6 -0.28678326 0.6903419
nma_mv$contribution_matrix
#> A vs B A vs C A vs D B vs C B vs D C vs D
#> A vs B 90.368175 4.423892 0.28859562 3.8207366 1.0435139 0.05508629
#> A vs C 41.342442 36.496433 0.65531482 16.7057362 0.5851147 4.21495961
#> A vs D 50.864110 12.358909 3.52304713 0.6445192 16.3481046 16.26130979
#> B vs C 29.107446 13.618556 0.02785936 46.6434337 4.4913978 6.11130750
#> B vs D 24.217443 1.453047 2.15266159 13.6821576 38.7374037 19.75728756
#> C vs D 1.076873 8.817042 1.80366089 15.6818831 16.6424910 55.97804929
nma_mv$treatment_order
#> rank treatment effect_vs_reference
#> 1 1 D 0.6075706
#> 2 2 C 0.3993499
#> 3 3 B 0.2056048
#> 4 4 A 0.0000000
nma_mv$node_splitting$global
#> Q_node_split df p_value
#> 1 10.75994 6 0.09608507
nma_mv$ranking$rankings
#> treatment mean_effect std_error mean_rank median_rank sucra sucr_a
#> D D 0.6075706 0.11120055 1.03425 1 98.85833 98.85833
#> C C 0.3993499 0.10789224 2.00025 2 66.65833 66.65833
#> B B 0.2056048 0.09665948 2.98125 3 33.95833 33.95833
#> A A 0.0000000 0.00000000 3.98425 4 0.52500 0.52500
#> p_best
#> D 0.96575
#> C 0.03425
#> B 0.00000
#> A 0.00000
nma_mv$fit_stats
#> model_type heterogeneity n_treatments n_edges estimator QE QE_df QE_p
#> 1 <NA> <NA> 0 NA <NA> NA NA NA
#> logLik Dev AIC BIC AICc
#> 1 7.024345 9.95131 9.95131 15.77019 -130.0487
nma_mv$level_heterogeneity_summary
#> NULL
nma_mv$heterogeneity_summary$level_heterogeneity
#> NULL
op <- par(mfrow = c(1, 3))
network_forest_plot(nma_mv, effect_type = "total", main = "Multivariate: Total")
network_forest_overlay_plot(nma_mv, order_by = "total", right_label = "total",
main = "Multivariate: Overlay")
network_contribution_heatmap(nma_mv, main = "Multivariate: Contribution")
par(op)Compare multilevel and multivariate model fit side-by-side on the same dataset
mars:::compare_nma_models(
multilevel = nma_ml_flexible,
multivariate = nma_mv,
nested = nma_ml_nested
)
#> model_type heterogeneity n_treatments n_edges estimator
#> multilevel multilevel flexible 4 6 MLE
#> multivariate multivariate flexible 4 6 MLE
#> nested multilevel flexible 4 6 MLE
#> QE QE_df QE_p logLik Dev AIC BIC
#> multilevel 0.1092282 9 1.0000000 3.204918 9.590164 3.590164 6.014697
#> multivariate 9.1403889 6 0.1658353 7.024345 9.951310 9.951310 15.770189
#> nested 0.1092282 9 1.0000000 3.204852 13.590296 7.590296 10.984642
#> AICc AIC_rank BIC_rank AICc_rank
#> multilevel 223.5902 1 1 3
#> multivariate -130.0487 3 3 2
#> nested -304.4097 2 2 1