OmicsBraid: Cross-Omics Effect Inference
Why OmicsBraid?
Multi-omics studies frequently summarize each layer independently and then describe RNA/protein/metabolite agreement qualitatively. OmicsBraid makes that comparison explicit by estimating standardized effects with uncertainty, accounting for matched-subject dependence, testing joint multi-omic evidence, quantifying cross-layer heterogeneity, testing practical equivalence, and evaluating ordered effect trajectories.
Version 0.2.2 retains the hierarchical inference introduced in v0.1.9, deliberately distinguishes absence of detected evidence from evidence of practical equivalence, and separates confirmed braid patterns from suggestive effect geometry.
Simulate known biology
Run the full workflow
For a quick vignette we use fewer bootstrap and Monte Carlo replicates than are recommended for final analyses. Both the equivalence margin and the trajectory margin are scientific SESOIs and should be justified in a real study.
fit <- run_omics_braid(
sim$data,
group = "group",
reference = "Control",
comparison = "Disease",
omic_order = c("RNA", "Protein", "Metabolite"),
bootstrap_B = 150,
ci_method = "percentile",
integrated_ci_method = "percentile",
ci_min_boot = 75,
pattern_draws = 500,
equivalence_margin = 0.30,
trajectory_margin = 0.15,
seed = 42
)
fit
#> <omics_braid_result>
#> Analysis level: feature
#> Entities with integrated estimates: 7
#> Omic order: RNA -> Protein -> Metabolite
#> Pattern counts:
#>
#> uncertain amplification attenuation
#> 2 1 1
#> concordant_increase inversion no_detectable_effect
#> 1 1 1Layer-specific and integrated inference
fit$effects
#> entity omic effect se var conf_low
#> 1 concordant_up RNA 1.00144509 0.1936803 0.03751205 0.69605800
#> 2 attenuation RNA 1.25169392 0.1996532 0.03986141 0.89963986
#> 3 amplification RNA 0.46226988 0.1849965 0.03422372 0.07910780
#> 4 inversion RNA 0.89279590 0.1914537 0.03665452 0.52818957
#> 5 buffering RNA 1.00878168 0.1938389 0.03757350 0.65713148
#> 6 emergence RNA -0.09098272 0.1826686 0.03336782 -0.40556523
#> 7 null RNA 0.12827860 0.1827619 0.03340190 -0.16089932
#> 8 concordant_up Protein 0.97462689 0.1931094 0.03729124 0.66781544
#> 9 attenuation Protein 1.05459113 0.1948521 0.03796734 0.68234571
#> 10 amplification Protein 1.05270385 0.1948096 0.03795077 0.68844788
#> 11 inversion Protein 0.88871683 0.1913746 0.03662424 0.45590412
#> 12 buffering Protein 0.09028704 0.1826672 0.03336730 -0.28788651
#> 13 emergence Protein -0.14057652 0.1827995 0.03341567 -0.50590192
#> 14 null Protein 0.19565005 0.1830105 0.03349283 -0.08057614
#> 15 concordant_up Metabolite 0.98128400 0.1932498 0.03734549 0.65009450
#> 16 attenuation Metabolite 0.45993038 0.1849722 0.03421473 0.17618409
#> 17 amplification Metabolite 1.20804235 0.1985297 0.03941403 0.88497435
#> 18 inversion Metabolite -1.05471770 0.1948550 0.03796846 -1.40648236
#> 19 buffering Metabolite -0.09932691 0.1826867 0.03337444 -0.47128460
#> 20 emergence Metabolite 1.21540797 0.1987169 0.03948840 0.89655624
#> 21 null Metabolite -0.12112608 0.1827415 0.03339446 -0.45480952
#> conf_high p_value n_reference n_comparison df reference comparison
#> 1 1.4073756 2.333318e-07 60 60 118 Control Disease
#> 2 1.5982158 3.625814e-10 60 60 118 Control Disease
#> 3 0.7580930 1.246137e-02 60 60 118 Control Disease
#> 4 1.2118146 3.112587e-06 60 60 118 Control Disease
#> 5 1.3822497 1.948043e-07 60 60 118 Control Disease
#> 6 0.2624031 6.184310e-01 60 60 118 Control Disease
#> 7 0.4586201 4.827482e-01 60 60 118 Control Disease
#> 8 1.3301872 4.487557e-07 60 60 118 Control Disease
#> 9 1.4192255 6.223270e-08 60 60 118 Control Disease
#> 10 1.3630042 6.525893e-08 60 60 118 Control Disease
#> 11 1.2175392 3.419598e-06 60 60 118 Control Disease
#> 12 0.4719160 6.211150e-01 60 60 118 Control Disease
#> 13 0.2399769 4.418814e-01 60 60 118 Control Disease
#> 14 0.5828418 2.850404e-01 60 60 118 Control Disease
#> 15 1.3694721 3.818296e-07 60 60 118 Control Disease
#> 16 0.8478675 1.290127e-02 60 60 118 Control Disease
#> 17 1.6688926 1.165303e-09 60 60 118 Control Disease
#> 18 -0.7608886 6.203475e-08 60 60 118 Control Disease
#> 19 0.2098740 5.866474e-01 60 60 118 Control Disease
#> 20 1.6815974 9.578548e-10 60 60 118 Control Disease
#> 21 0.1814331 5.074412e-01 60 60 118 Control Disease
#> p_adj conf_low_analytic conf_high_analytic conf_low_bootstrap
#> 1 5.444408e-07 0.62183872 1.3810515 0.69605800
#> 2 2.538070e-09 0.86038080 1.6430070 0.89963986
#> 3 1.744591e-02 0.09968331 0.8248564 0.07910780
#> 4 5.447027e-06 0.51755354 1.2680383 0.52818957
#> 5 5.444408e-07 0.62886451 1.3886989 0.65713148
#> 6 6.184310e-01 -0.44900664 0.2670412 -0.40556523
#> 7 5.632062e-01 -0.22992807 0.4864853 -0.16089932
#> 8 1.047097e-06 0.59613942 1.3531144 0.66781544
#> 9 2.284063e-07 0.67268801 1.4364942 0.68234571
#> 10 2.284063e-07 0.67088409 1.4345236 0.68844788
#> 11 5.984296e-06 0.51362949 1.2638042 0.45590412
#> 12 6.211150e-01 -0.26773406 0.4483081 -0.28788651
#> 13 5.155283e-01 -0.49885705 0.2177040 -0.50590192
#> 14 3.990566e-01 -0.16304386 0.5543440 -0.08057614
#> 15 6.682018e-07 0.60252132 1.3600467 0.65009450
#> 16 1.806178e-02 0.09739143 0.8224693 0.17618409
#> 17 4.078560e-09 0.81893136 1.5971533 0.88497435
#> 18 1.447477e-07 -1.43662641 -0.6728090 -1.40648236
#> 19 5.866474e-01 -0.45738632 0.2587325 -0.47128460
#> 20 4.078560e-09 0.82593002 1.6048859 0.89655624
#> 21 5.866474e-01 -0.47929288 0.2370407 -0.45480952
#> conf_high_bootstrap ci_boot_n ci_method
#> 1 1.4073756 150 percentile
#> 2 1.5982158 150 percentile
#> 3 0.7580930 150 percentile
#> 4 1.2118146 150 percentile
#> 5 1.3822497 150 percentile
#> 6 0.2624031 150 percentile
#> 7 0.4586201 150 percentile
#> 8 1.3301872 150 percentile
#> 9 1.4192255 150 percentile
#> 10 1.3630042 150 percentile
#> 11 1.2175392 150 percentile
#> 12 0.4719160 150 percentile
#> 13 0.2399769 150 percentile
#> 14 0.5828418 150 percentile
#> 15 1.3694721 150 percentile
#> 16 0.8478675 150 percentile
#> 17 1.6688926 150 percentile
#> 18 -0.7608886 150 percentile
#> 19 0.2098740 150 percentile
#> 20 1.6815974 150 percentile
#> 21 0.1814331 150 percentile
fit$integrated
#> entity n_omics omics integrated_effect integrated_se
#> 1 concordant_up 3 RNA;Protein;Metabolite 0.9864109 0.1559653
#> 2 attenuation 3 RNA;Protein;Metabolite 0.8639380 0.1520348
#> 3 amplification 3 RNA;Protein;Metabolite 0.8900575 0.1401822
#> 4 inversion 3 RNA;Protein;Metabolite 0.2367999 0.1494312
#> 5 buffering 3 RNA;Protein;Metabolite 0.2017760 0.1492364
#> 6 emergence 3 RNA;Protein;Metabolite 0.2548307 0.1494271
#> 7 null 3 RNA;Protein;Metabolite 0.0725554 0.1505732
#> conf_low conf_high z_value p_value W_omnibus df_omnibus
#> 1 0.76202816 1.3108755 6.3245541 2.539649e-10 40.018617 3
#> 2 0.59632557 1.1344355 5.6825020 1.327384e-08 48.655091 3
#> 3 0.64760674 1.1528350 6.3492910 2.163095e-10 53.211244 3
#> 4 -0.06483514 0.4822842 1.5846744 1.130403e-01 109.174080 3
#> 5 -0.11416166 0.4720860 1.3520562 1.763573e-01 45.726238 3
#> 6 -0.00114991 0.5668491 1.7053849 8.812267e-02 56.750954 3
#> 7 -0.18947378 0.3501312 0.4818613 6.299045e-01 3.737902 3
#> p_omnibus Q_omics df_heterogeneity p_heterogeneity I2_omics
#> 1 1.055871e-08 0.01863237 2 9.907271e-01 0.00000
#> 2 1.544725e-10 16.36426276 2 2.796054e-04 87.77825
#> 3 1.652761e-11 12.89774767 2 1.582303e-03 84.49342
#> 4 1.652244e-23 106.66288721 2 6.893636e-24 98.12493
#> 5 6.484857e-10 43.89818218 2 2.935154e-10 95.44400
#> 6 2.904514e-12 53.84261679 2 2.033407e-12 96.28547
#> 7 2.911922e-01 3.50571193 2 1.732784e-01 42.95025
#> direction_agreement min_gls_weight max_gls_weight has_negative_gls_weight
#> 1 1.0000000 0.3157307 0.3585517 FALSE
#> 2 1.0000000 0.2648280 0.4083866 FALSE
#> 3 1.0000000 0.3158030 0.3585545 FALSE
#> 4 0.6745374 0.3308672 0.3361403 FALSE
#> 5 0.6537945 0.2028120 0.4027403 FALSE
#> 6 0.2971626 0.2789258 0.3744956 FALSE
#> 7 0.6663153 0.3122066 0.3656074 FALSE
#> covariance_condition_number covariance_mode p_adj p_omnibus_adj
#> 1 4.123371 matched_bootstrap 8.888771e-10 1.231850e-08
#> 2 3.464132 matched_bootstrap 3.097229e-08 2.703268e-10
#> 3 2.515495 matched_bootstrap 8.888771e-10 3.856442e-11
#> 4 3.252030 matched_bootstrap 1.582564e-01 1.156571e-22
#> 5 4.379049 matched_bootstrap 2.057502e-01 9.078800e-10
#> 6 4.013146 matched_bootstrap 1.542147e-01 1.016580e-11
#> 7 4.780129 matched_bootstrap 6.299045e-01 2.911922e-01
#> p_heterogeneity_adj heterogeneity_test_flag has_omnibus_evidence_local
#> 1 9.907271e-01 FALSE TRUE
#> 2 4.893094e-04 TRUE TRUE
#> 3 2.215224e-03 TRUE TRUE
#> 4 4.825545e-23 TRUE TRUE
#> 5 6.848692e-10 TRUE TRUE
#> 6 7.116925e-12 TRUE TRUE
#> 7 2.021581e-01 FALSE FALSE
#> has_omnibus_evidence evidence_qualified_direction_agreement conf_low_analytic
#> 1 TRUE 1.0000000 0.68072458
#> 2 TRUE 1.0000000 0.56595528
#> 3 TRUE 1.0000000 0.61530545
#> 4 TRUE 0.6745374 -0.05607998
#> 5 TRUE 0.6537945 -0.09072196
#> 6 TRUE 0.2971626 -0.03804102
#> 7 FALSE NA -0.22256265
#> conf_high_analytic conf_low_bootstrap conf_high_bootstrap ci_boot_n
#> 1 1.2920973 0.76202816 1.3108755 150
#> 2 1.1619207 0.59632557 1.1344355 150
#> 3 1.1648095 0.64760674 1.1528350 150
#> 4 0.5296797 -0.06483514 0.4822842 150
#> 5 0.4942740 -0.11416166 0.4720860 150
#> 6 0.5477024 -0.00114991 0.5668491 150
#> 7 0.3676735 -0.18947378 0.3501312 150
#> ci_method
#> 1 percentile
#> 2 percentile
#> 3 percentile
#> 4 percentile
#> 5 percentile
#> 6 percentile
#> 7 percentile
fit$equivalence
#> entity omic effect se var conf_low
#> 1 concordant_up RNA 1.00144509 0.1936803 0.03751205 0.69605800
#> 2 attenuation RNA 1.25169392 0.1996532 0.03986141 0.89963986
#> 3 amplification RNA 0.46226988 0.1849965 0.03422372 0.07910780
#> 4 inversion RNA 0.89279590 0.1914537 0.03665452 0.52818957
#> 5 buffering RNA 1.00878168 0.1938389 0.03757350 0.65713148
#> 6 emergence RNA -0.09098272 0.1826686 0.03336782 -0.40556523
#> 7 null RNA 0.12827860 0.1827619 0.03340190 -0.16089932
#> 8 concordant_up Protein 0.97462689 0.1931094 0.03729124 0.66781544
#> 9 attenuation Protein 1.05459113 0.1948521 0.03796734 0.68234571
#> 10 amplification Protein 1.05270385 0.1948096 0.03795077 0.68844788
#> 11 inversion Protein 0.88871683 0.1913746 0.03662424 0.45590412
#> 12 buffering Protein 0.09028704 0.1826672 0.03336730 -0.28788651
#> 13 emergence Protein -0.14057652 0.1827995 0.03341567 -0.50590192
#> 14 null Protein 0.19565005 0.1830105 0.03349283 -0.08057614
#> 15 concordant_up Metabolite 0.98128400 0.1932498 0.03734549 0.65009450
#> 16 attenuation Metabolite 0.45993038 0.1849722 0.03421473 0.17618409
#> 17 amplification Metabolite 1.20804235 0.1985297 0.03941403 0.88497435
#> 18 inversion Metabolite -1.05471770 0.1948550 0.03796846 -1.40648236
#> 19 buffering Metabolite -0.09932691 0.1826867 0.03337444 -0.47128460
#> 20 emergence Metabolite 1.21540797 0.1987169 0.03948840 0.89655624
#> 21 null Metabolite -0.12112608 0.1827415 0.03339446 -0.45480952
#> conf_high p_value n_reference n_comparison df reference comparison
#> 1 1.4073756 2.333318e-07 60 60 118 Control Disease
#> 2 1.5982158 3.625814e-10 60 60 118 Control Disease
#> 3 0.7580930 1.246137e-02 60 60 118 Control Disease
#> 4 1.2118146 3.112587e-06 60 60 118 Control Disease
#> 5 1.3822497 1.948043e-07 60 60 118 Control Disease
#> 6 0.2624031 6.184310e-01 60 60 118 Control Disease
#> 7 0.4586201 4.827482e-01 60 60 118 Control Disease
#> 8 1.3301872 4.487557e-07 60 60 118 Control Disease
#> 9 1.4192255 6.223270e-08 60 60 118 Control Disease
#> 10 1.3630042 6.525893e-08 60 60 118 Control Disease
#> 11 1.2175392 3.419598e-06 60 60 118 Control Disease
#> 12 0.4719160 6.211150e-01 60 60 118 Control Disease
#> 13 0.2399769 4.418814e-01 60 60 118 Control Disease
#> 14 0.5828418 2.850404e-01 60 60 118 Control Disease
#> 15 1.3694721 3.818296e-07 60 60 118 Control Disease
#> 16 0.8478675 1.290127e-02 60 60 118 Control Disease
#> 17 1.6688926 1.165303e-09 60 60 118 Control Disease
#> 18 -0.7608886 6.203475e-08 60 60 118 Control Disease
#> 19 0.2098740 5.866474e-01 60 60 118 Control Disease
#> 20 1.6815974 9.578548e-10 60 60 118 Control Disease
#> 21 0.1814331 5.074412e-01 60 60 118 Control Disease
#> p_adj conf_low_analytic conf_high_analytic conf_low_bootstrap
#> 1 5.444408e-07 0.62183872 1.3810515 0.69605800
#> 2 2.538070e-09 0.86038080 1.6430070 0.89963986
#> 3 1.744591e-02 0.09968331 0.8248564 0.07910780
#> 4 5.447027e-06 0.51755354 1.2680383 0.52818957
#> 5 5.444408e-07 0.62886451 1.3886989 0.65713148
#> 6 6.184310e-01 -0.44900664 0.2670412 -0.40556523
#> 7 5.632062e-01 -0.22992807 0.4864853 -0.16089932
#> 8 1.047097e-06 0.59613942 1.3531144 0.66781544
#> 9 2.284063e-07 0.67268801 1.4364942 0.68234571
#> 10 2.284063e-07 0.67088409 1.4345236 0.68844788
#> 11 5.984296e-06 0.51362949 1.2638042 0.45590412
#> 12 6.211150e-01 -0.26773406 0.4483081 -0.28788651
#> 13 5.155283e-01 -0.49885705 0.2177040 -0.50590192
#> 14 3.990566e-01 -0.16304386 0.5543440 -0.08057614
#> 15 6.682018e-07 0.60252132 1.3600467 0.65009450
#> 16 1.806178e-02 0.09739143 0.8224693 0.17618409
#> 17 4.078560e-09 0.81893136 1.5971533 0.88497435
#> 18 1.447477e-07 -1.43662641 -0.6728090 -1.40648236
#> 19 5.866474e-01 -0.45738632 0.2587325 -0.47128460
#> 20 4.078560e-09 0.82593002 1.6048859 0.89655624
#> 21 5.866474e-01 -0.47929288 0.2370407 -0.45480952
#> conf_high_bootstrap ci_boot_n ci_method equiv_margin p_tost_lower
#> 1 1.4073756 150 percentile 0.3 9.114086e-12
#> 2 1.5982158 150 percentile 0.3 3.864486e-15
#> 3 0.7580930 150 percentile 0.3 1.890628e-05
#> 4 1.2118146 150 percentile 0.3 2.329118e-10
#> 5 1.3822497 150 percentile 0.3 7.295784e-12
#> 6 0.2624031 150 percentile 0.3 1.262615e-01
#> 7 0.4586201 150 percentile 0.3 9.555219e-03
#> 8 1.3301872 150 percentile 0.3 2.048273e-11
#> 9 1.4192255 150 percentile 0.3 1.802075e-12
#> 10 1.3630042 150 percentile 0.3 1.909489e-12
#> 11 1.2175392 150 percentile 0.3 2.624630e-10
#> 12 0.4719160 150 percentile 0.3 1.631519e-02
#> 13 0.2399769 150 percentile 0.3 1.915710e-01
#> 14 0.5828418 150 percentile 0.3 3.381286e-03
#> 15 1.3694721 150 percentile 0.3 1.676218e-11
#> 16 0.8478675 150 percentile 0.3 1.992496e-05
#> 17 1.6688926 150 percentile 0.3 1.526467e-14
#> 18 -0.7608886 150 percentile 0.3 9.999463e-01
#> 19 0.2098740 150 percentile 0.3 1.360030e-01
#> 20 1.6815974 150 percentile 0.3 1.211081e-14
#> 21 0.1814331 150 percentile 0.3 1.638306e-01
#> p_tost_upper p_tost p_tost_adj p_difference p_difference_adj
#> 1 9.998536e-01 0.9998536 0.9999991 2.333318e-07 5.444408e-07
#> 2 9.999991e-01 0.9999991 0.9999991 3.625814e-10 2.538070e-09
#> 3 8.097976e-01 0.8097976 0.9999991 1.246137e-02 1.744591e-02
#> 4 9.990202e-01 0.9990202 0.9999991 3.112587e-06 5.447027e-06
#> 5 9.998722e-01 0.9998722 0.9999991 1.948043e-07 5.444408e-07
#> 6 1.616149e-02 0.1262615 0.6079979 6.184310e-01 6.184310e-01
#> 7 1.737137e-01 0.1737137 0.6079979 4.827482e-01 5.632062e-01
#> 8 9.997616e-01 0.9997616 0.9999462 4.487557e-07 1.047097e-06
#> 9 9.999462e-01 0.9999462 0.9999462 6.223270e-08 2.284063e-07
#> 10 9.999442e-01 0.9999442 0.9999462 6.525893e-08 2.284063e-07
#> 11 9.989519e-01 0.9989519 0.9999462 3.419598e-06 5.984296e-06
#> 12 1.254718e-01 0.1254718 0.6633104 6.211150e-01 6.211150e-01
#> 13 7.972719e-03 0.1915710 0.6633104 4.418814e-01 5.155283e-01
#> 14 2.842759e-01 0.2842759 0.6633104 2.850404e-01 3.990566e-01
#> 15 9.997886e-01 0.9997886 0.9999980 3.818296e-07 6.682018e-07
#> 16 8.063758e-01 0.8063758 0.9999980 1.290127e-02 1.806178e-02
#> 17 9.999976e-01 0.9999976 0.9999980 1.165303e-09 4.078560e-09
#> 18 1.795090e-12 0.9999463 0.9999980 6.203475e-08 1.447477e-07
#> 19 1.441307e-02 0.1360030 0.5734071 5.866474e-01 5.866474e-01
#> 20 9.999980e-01 0.9999980 0.9999980 9.578548e-10 4.078560e-09
#> 21 1.059757e-02 0.1638306 0.5734071 5.074412e-01 5.866474e-01
#> equivalent_local equivalent_adjusted state_local state_adjusted equivalent
#> 1 FALSE FALSE positive positive FALSE
#> 2 FALSE FALSE positive positive FALSE
#> 3 FALSE FALSE positive positive FALSE
#> 4 FALSE FALSE positive positive FALSE
#> 5 FALSE FALSE positive positive FALSE
#> 6 FALSE FALSE uncertain uncertain FALSE
#> 7 FALSE FALSE uncertain uncertain FALSE
#> 8 FALSE FALSE positive positive FALSE
#> 9 FALSE FALSE positive positive FALSE
#> 10 FALSE FALSE positive positive FALSE
#> 11 FALSE FALSE positive positive FALSE
#> 12 FALSE FALSE uncertain uncertain FALSE
#> 13 FALSE FALSE uncertain uncertain FALSE
#> 14 FALSE FALSE uncertain uncertain FALSE
#> 15 FALSE FALSE positive positive FALSE
#> 16 FALSE FALSE positive positive FALSE
#> 17 FALSE FALSE positive positive FALSE
#> 18 FALSE FALSE negative negative FALSE
#> 19 FALSE FALSE uncertain uncertain FALSE
#> 20 FALSE FALSE positive positive FALSE
#> 21 FALSE FALSE uncertain uncertain FALSE
#> state state_basis
#> 1 positive local
#> 2 positive local
#> 3 positive local
#> 4 positive local
#> 5 positive local
#> 6 uncertain local
#> 7 uncertain local
#> 8 positive local
#> 9 positive local
#> 10 positive local
#> 11 positive local
#> 12 uncertain local
#> 13 uncertain local
#> 14 uncertain local
#> 15 positive local
#> 16 positive local
#> 17 positive local
#> 18 negative local
#> 19 uncertain local
#> 20 positive local
#> 21 uncertain local
fit$trend
#> entity n_layers_trend trend_omics aligned_direction
#> 1 concordant_up 3 RNA;Protein;Metabolite 1
#> 2 attenuation 3 RNA;Protein;Metabolite 1
#> 3 amplification 3 RNA;Protein;Metabolite 1
#> 4 inversion 3 RNA;Protein;Metabolite 1
#> 5 buffering 3 RNA;Protein;Metabolite 1
#> 6 emergence 3 RNA;Protein;Metabolite 1
#> 7 null 3 RNA;Protein;Metabolite 1
#> same_sign_estimates trend_intercept trend_slope trend_slope_se
#> 1 TRUE 0.9954493 -0.009345233 0.10157657
#> 2 TRUE 1.3152377 -0.394645063 0.10143190
#> 3 TRUE 0.5212506 0.385278032 0.11249942
#> 4 FALSE 1.1802529 -0.938504303 0.10668915
#> 5 FALSE 0.8821600 -0.570966455 0.09098996
#> 6 FALSE -0.3017976 0.597018242 0.09862480
#> 7 FALSE 0.1971335 -0.123347212 0.08445347
#> trend_conf_low trend_conf_high p_trend_zero p_meaningful_amplification
#> 1 -0.2084317 0.18974119 9.266966e-01 9.416434e-01
#> 2 -0.5934479 -0.19584218 9.993941e-05 1.000000e+00
#> 3 0.1647832 0.60577285 6.154532e-04 1.824741e-02
#> 4 -1.1476112 -0.72939742 1.409938e-18 1.000000e+00
#> 5 -0.7493035 -0.39262941 3.495243e-10 1.000000e+00
#> 6 0.4037172 0.79031930 1.417946e-09 2.914298e-06
#> 7 -0.2888730 0.04217855 1.441432e-01 9.993953e-01
#> p_meaningful_attenuation p_flat_tost trajectory_margin covariance_mode_trend
#> 1 9.169304e-01 0.08306957 0.15 matched_bootstrap
#> 2 7.934505e-03 0.99206549 0.15 matched_bootstrap
#> 3 9.999990e-01 0.98175259 0.15 matched_bootstrap
#> 4 7.304525e-14 1.00000000 0.15 matched_bootstrap
#> 5 1.859346e-06 0.99999814 0.15 matched_bootstrap
#> 6 1.000000e+00 0.99999709 0.15 matched_bootstrap
#> 7 6.238437e-01 0.37615634 0.15 matched_bootstrap
#> trend_state_local p_meaningful_amplification_adj p_meaningful_attenuation_adj
#> 1 uncertain 1.000000e+00 1.000000e+00
#> 2 attenuation 1.000000e+00 1.851385e-02
#> 3 amplification 6.386593e-02 1.000000e+00
#> 4 not_applicable 1.000000e+00 5.113167e-13
#> 5 not_applicable 1.000000e+00 6.507711e-06
#> 6 not_applicable 2.040009e-05 1.000000e+00
#> 7 not_applicable 1.000000e+00 1.000000e+00
#> p_flat_tost_adj trend_state_adjusted
#> 1 0.581487 uncertain
#> 2 1.000000 attenuation
#> 3 1.000000 uncertain
#> 4 1.000000 not_applicable
#> 5 1.000000 not_applicable
#> 6 1.000000 not_applicable
#> 7 1.000000 not_applicable
fit$classification
#> entity pattern pattern_status suggestive_pattern
#> 1 concordant_up concordant_increase direction_confirmed concordant_increase
#> 2 attenuation attenuation confirmed attenuation
#> 3 amplification amplification confirmed amplification
#> 4 inversion inversion confirmed inversion
#> 5 buffering uncertain unresolved buffering
#> 6 emergence uncertain unresolved emergence
#> 7 null no_detectable_effect no_evidence null_equivalent
#> interpretation_label
#> 1 concordant_increase (trajectory unresolved; geometry: concordant_increase)
#> 2 attenuation
#> 3 amplification
#> 4 inversion
#> 5 suggestive_buffering
#> 6 suggestive_emergence
#> 7 no_detectable_effect (geometry: null_equivalent)
#> confirmatory_basis
#> 1 all observed layers support one direction; magnitude trajectory is unresolved
#> 2 same-direction layers plus meaningful negative GLS trajectory
#> 3 same-direction layers plus meaningful positive GLS trajectory
#> 4 statistically supported effects occur in opposite directions
#> 5 partial or transient layer pattern does not satisfy a confirmatory braid rule
#> 6 partial or transient layer pattern does not satisfy a confirmatory braid rule
#> 7 joint-null omnibus test not rejected; equivalence not established
#> n_layers_observed n_positive n_negative n_equivalent n_uncertain
#> 1 3 3 0 0 0
#> 2 3 3 0 0 0
#> 3 3 3 0 0 0
#> 4 3 2 1 0 0
#> 5 3 1 0 0 2
#> 6 3 1 0 0 2
#> 7 3 0 0 0 3
#> omnibus_p_local omnibus_evidence_local trend_slope trend_slope_se
#> 1 1.055871e-08 TRUE -0.009345233 0.10157657
#> 2 1.544725e-10 TRUE -0.394645063 0.10143190
#> 3 1.652761e-11 TRUE 0.385278032 0.11249942
#> 4 1.652244e-23 TRUE -0.938504303 0.10668915
#> 5 6.484857e-10 TRUE -0.570966455 0.09098996
#> 6 2.904514e-12 TRUE 0.597018242 0.09862480
#> 7 2.911922e-01 FALSE -0.123347212 0.08445347
#> trend_conf_low trend_conf_high p_trend_zero p_meaningful_amplification
#> 1 -0.2084317 0.18974119 9.266966e-01 9.416434e-01
#> 2 -0.5934479 -0.19584218 9.993941e-05 1.000000e+00
#> 3 0.1647832 0.60577285 6.154532e-04 1.824741e-02
#> 4 -1.1476112 -0.72939742 1.409938e-18 1.000000e+00
#> 5 -0.7493035 -0.39262941 3.495243e-10 1.000000e+00
#> 6 0.4037172 0.79031930 1.417946e-09 2.914298e-06
#> 7 -0.2888730 0.04217855 1.441432e-01 9.993953e-01
#> p_meaningful_attenuation p_flat_tost trajectory_margin trend_state_local
#> 1 9.169304e-01 0.08306957 0.15 uncertain
#> 2 7.934505e-03 0.99206549 0.15 attenuation
#> 3 9.999990e-01 0.98175259 0.15 amplification
#> 4 7.304525e-14 1.00000000 0.15 not_applicable
#> 5 1.859346e-06 0.99999814 0.15 not_applicable
#> 6 1.000000e+00 0.99999709 0.15 not_applicable
#> 7 6.238437e-01 0.37615634 0.15 not_applicable
#> p_meaningful_amplification_adj p_meaningful_attenuation_adj p_flat_tost_adj
#> 1 1.000000e+00 1.000000e+00 0.581487
#> 2 1.000000e+00 1.851385e-02 1.000000
#> 3 6.386593e-02 1.000000e+00 1.000000
#> 4 1.000000e+00 5.113167e-13 1.000000
#> 5 1.000000e+00 6.507711e-06 1.000000
#> 6 2.040009e-05 1.000000e+00 1.000000
#> 7 1.000000e+00 1.000000e+00 1.000000
#> trend_state_adjusted covariance_mode_trend uncertainty_mode_pattern
#> 1 uncertain matched_bootstrap concordant_increase
#> 2 attenuation matched_bootstrap attenuation
#> 3 uncertain matched_bootstrap amplification
#> 4 not_applicable matched_bootstrap inversion
#> 5 not_applicable matched_bootstrap buffering
#> 6 not_applicable matched_bootstrap emergence
#> 7 not_applicable matched_bootstrap null_equivalent
#> uncertainty_mode_support deterministic_pattern_support
#> 1 0.848 0.848
#> 2 0.800 0.800
#> 3 0.812 0.812
#> 4 1.000 1.000
#> 5 0.830 NA
#> 6 0.722 NA
#> 7 0.522 NA
#> suggestive_pattern_support pattern_entropy mode_agrees_with_deterministic
#> 1 0.848 0.4741966 TRUE
#> 2 0.800 0.7219281 TRUE
#> 3 0.812 0.4939400 TRUE
#> 4 1.000 0.0000000 TRUE
#> 5 0.830 0.4710142 NA
#> 6 0.722 0.6166020 NA
#> 7 0.522 0.5657668 NA
#> classification_stability
#> 1 direction_high
#> 2 high
#> 3 high
#> 4 high
#> 5 unresolved
#> 6 unresolved
#> 7 geometry_lowThe integrated table separates the multivariate all-zero omnibus test from the GLS consensus effect. This is important when opposite layer effects cancel in the consensus.
Robust interval reporting
Version 0.2.2 can display matched subject-bootstrap intervals without
changing the analytic SE/p-value inferential machinery.
fit$effects and fit$integrated retain analytic
interval columns alongside the selected percentile bootstrap intervals,
while fit$effect_intervals and
fit$consensus_intervals contain bootstrap diagnostics. BCa
layer intervals are available for targeted/prefiltered analyses through
bootstrap_effect_intervals(..., method = "bca").
head(fit$effect_intervals)
#> entity omic ci_method conf_level boot_n boot_mean boot_sd
#> 1 concordant_up RNA percentile 0.95 150 1.04582890 0.1905216
#> 2 attenuation RNA percentile 0.95 150 1.26372747 0.1734969
#> 3 amplification RNA percentile 0.95 150 0.47158553 0.1754207
#> 4 inversion RNA percentile 0.95 150 0.84723275 0.1843416
#> 5 buffering RNA percentile 0.95 150 1.00721498 0.1946918
#> 6 emergence RNA percentile 0.95 150 -0.08981906 0.1894424
#> boot_bias conf_low_boot conf_high_boot bca_z0 bca_acceleration
#> 1 0.044383809 0.6960580 1.4073756 NA NA
#> 2 0.012033557 0.8996399 1.5982158 NA NA
#> 3 0.009315653 0.0791078 0.7580930 NA NA
#> 4 -0.045563150 0.5281896 1.2118146 NA NA
#> 5 -0.001566704 0.6571315 1.3822497 NA NA
#> 6 0.001163659 -0.4055652 0.2624031 NA NA
#> bca_prob_low bca_prob_high
#> 1 0.025 0.975
#> 2 0.025 0.975
#> 3 0.025 0.975
#> 4 0.025 0.975
#> 5 0.025 0.975
#> 6 0.025 0.975
head(fit$consensus_intervals)
#> entity ci_method conf_level boot_n boot_mean boot_sd boot_bias
#> 1 concordant_up percentile 0.95 150 1.0228558 0.1527612 0.036444855
#> 2 attenuation percentile 0.95 150 0.8790283 0.1442353 0.015090364
#> 3 amplification percentile 0.95 150 0.9095808 0.1315381 0.019523289
#> 4 inversion percentile 0.95 150 0.2083199 0.1455697 -0.028479919
#> 5 buffering percentile 0.95 150 0.2080203 0.1559036 0.006244268
#> 6 emergence percentile 0.95 150 0.2576351 0.1560624 0.002804395
#> conf_low_boot conf_high_boot
#> 1 0.76202816 1.3108755
#> 2 0.59632557 1.1344355
#> 3 0.64760674 1.1528350
#> 4 -0.06483514 0.4822842
#> 5 -0.11416166 0.4720860
#> 6 -0.00114991 0.5668491Ordered GLS trend test
fit$trend reports a covariance-aware slope over the
prespecified omic order. For same-direction layer effects, OmicsBraid
only calls attenuation or amplification when the slope exceeds the
user-specified practical trajectory margin with inferential support.
Otherwise the broader concordant direction can be retained with
pattern_status = "direction_confirmed".
Null-like outcomes
null_equivalent means all observed layers passed
practical-equivalence testing. no_detectable_effect means
the joint-null omnibus test was not rejected, but the data were not
precise enough to establish equivalence. These are different scientific
conclusions.
Interpretation
A significant Q_omics indicates that the effect vector
is poorly summarized by a single common effect after accounting for
estimated sampling covariance. The I2-like index is descriptive and has
no universal low/moderate/high cutoffs in this development version.
Braid order is descriptive/inferential, not causal. A pattern such as
inversion describes supported effects across a prespecified
layer order; it does not prove molecular propagation. Likewise,
suggestive_pattern describes effect geometry when
confirmatory precision is insufficient and must not be reported as a
confirmed result.