Compute total effects as ACEs of variables X
on variables Y in a directed acyclic graph (DAG). The ACE will be estimated
as the path coefficient of X (i.e., theta) in the linear equation
Y ~ X + Z. The set Z is defined as the adjustment (or conditioning) set of
Y over X, applying various adjustement sets. Standard errors (SE),
for each ACE, are computed following the lm standard procedure
or a bootstrap-based procedure (see boot for details).
SEMace(
graph,
data,
group = NULL,
type = "parents",
effect = "all",
method = "BH",
alpha = 0.05,
boot = NULL,
...
)An igraph object.
A matrix or data.frame. Rows correspond to subjects, and columns to graph nodes (variables).
A binary vector. This vector must be as long as the
number of subjects. Each vector element must be 1 for cases and 0
for control subjects. If group = NULL (default), group influence
will not be considered.
character Conditioning set Z. If "parents" (default) the Pearl's back-door set (Pearl, 1998), "minimal" the dagitty minimal set (Perkovic et al, 2018), or "optimal" the O-set with the smallest asymptotic variance (Witte et al, 2020) are computed.
character X to Y effect. If "all" (default) all effects from X to Y, "source2sink" only effects from source X to sink Y, or "direct" only direct effects from X to Y are computed.
Multiple testing correction method. One of the values
available in p.adjust.
By default, method = "BH" (i.e., FDR multiple test correction).
Significance level for ACE selection (by default,
alpha = 0.05).
The number of bootstrap samplings enabling bootstrap
computation of ACE standard errors. If NULL (default), bootstrap
is disabled.
Currently ignored.
A data.frame of ACE estimates between network sources and sinks.
Pearl J (1998). Graphs, Causality, and Structural Equation Models. Sociological Methods & Research, 27(2):226-284. <https://doi.org/10.1177/0049124198027002004>
Perkovic E, Textor J, Kalisch M, Maathuis MH (2018). Complete graphical characterization and construction of adjustment sets in Markov equivalence classes of ancestral graphs. Journal of Machine Learning Research, 18:1-62. <http://jmlr.org/papers/v18/16-319.html>
Witte J, Henckel L, Maathuis MH, Didelez V (2020). On efficient adjustment in causal graphs. Journal of Machine Learning Research, 21:1-45. <http://jmlr.org/papers/v21/20-175.htm>
# ACE without group, O-set, all effects:
ace1 <- SEMace(graph = sachs$graph, data = log(sachs$pkc),
group = NULL, type = "optimal", effect = "all",
method = "BH", alpha = 0.05, boot = NULL)
#>
#> WARNING: input graph is not acyclic!
#> Applying graph -> DAG conversion.
#> DAG conversion : TRUE
#>
#> Frequency distribution of path length from X to Y :
#> 1 2 3 4
#> 18 11 6 1
#>
#>
ACE= 1 of 36
ACE= 2 of 36
ACE= 3 of 36
ACE= 4 of 36
ACE= 5 of 36
ACE= 6 of 36
ACE= 7 of 36
ACE= 8 of 36
ACE= 9 of 36
ACE= 10 of 36
ACE= 11 of 36
ACE= 12 of 36
ACE= 13 of 36
ACE= 14 of 36
ACE= 15 of 36
ACE= 16 of 36
ACE= 17 of 36
ACE= 18 of 36
ACE= 19 of 36
ACE= 20 of 36
ACE= 21 of 36
ACE= 22 of 36
ACE= 23 of 36
ACE= 24 of 36
ACE= 25 of 36
ACE= 26 of 36
ACE= 27 of 36
ACE= 28 of 36
ACE= 29 of 36
ACE= 30 of 36
ACE= 31 of 36
ACE= 32 of 36
ACE= 33 of 36
ACE= 34 of 36
ACE= 35 of 36
ACE= 36 of 36
print(ace1)
#> pathL sink op source est se z pvalue ci.lower ci.upper
#> PKA 1 Mek <- PKA -0.074 0.024 -3.119 0.002 -0.121 -0.028
#> PKA1 1 Raf <- PKA -0.124 0.024 -5.258 0.000 -0.171 -0.078
#> PKA2 1 Jnk <- PKA 0.093 0.024 3.938 0.000 0.047 0.139
#> PKA4 1 Akt <- PKA 0.546 0.020 27.439 0.000 0.507 0.585
#> PKA5 1 Erk <- PKA 0.458 0.021 21.582 0.000 0.416 0.499
#> PKC2 1 Jnk <- PKC 0.128 0.024 5.436 0.000 0.082 0.174
#> PKC3 1 P38 <- PKC 0.646 0.018 35.484 0.000 0.611 0.682
#> PIP3 3 Mek <- PIP3 0.085 0.024 3.560 0.000 0.038 0.131
#> PIP31 3 Raf <- PIP3 0.155 0.023 6.600 0.000 0.109 0.201
#> 11 1 PIP2 <- PIP3 0.536 0.020 26.687 0.000 0.497 0.576
#> 12 1 Plcg <- PIP3 0.207 0.023 8.892 0.000 0.161 0.253
#> PIP32 3 Jnk <- PIP3 -0.077 0.024 -3.250 0.001 -0.124 -0.031
#> PIP34 1 Akt <- PIP3 -0.065 0.020 -3.249 0.001 -0.104 -0.026
#> PIP35 4 Erk <- PIP3 -0.063 0.021 -2.988 0.003 -0.105 -0.022
#> Raf 1 Mek <- Raf 0.683 0.018 38.898 0.000 0.649 0.718
#> Raf1 2 Erk <- Raf -0.081 0.021 -3.784 0.000 -0.122 -0.039
#> Plcg1 2 Mek <- Plcg -0.059 0.024 -2.451 0.014 -0.107 -0.012
#> Plcg2 2 Raf <- Plcg -0.091 0.024 -3.822 0.000 -0.138 -0.044
#> Plcg3 1 PIP2 <- Plcg 0.227 0.020 11.435 0.000 0.188 0.265
#> Plcg4 2 Jnk <- Plcg 0.104 0.024 4.317 0.000 0.057 0.151
#> Plcg6 3 Erk <- Plcg 0.057 0.022 2.631 0.009 0.015 0.099
# ACE with group perturbation, Pa-set, direct effects:
ace2 <- SEMace(graph = sachs$graph, data = log(sachs$pkc),
group = sachs$group, type = "parents", effect = "direct",
method = "none", alpha = 0.05, boot = NULL)
#>
#> Frequency distribution of path length from X to Y :
#> 1
#> 20
#>
#>
ACE= 1 of 20
ACE= 2 of 20
ACE= 3 of 20
ACE= 4 of 20
ACE= 5 of 20
ACE= 6 of 20
ACE= 7 of 20
ACE= 8 of 20
ACE= 9 of 20
ACE= 10 of 20
ACE= 11 of 20
ACE= 12 of 20
ACE= 13 of 20
ACE= 14 of 20
ACE= 15 of 20
ACE= 16 of 20
ACE= 17 of 20
ACE= 18 of 20
ACE= 19 of 20
ACE= 20 of 20
print(ace2)
#> pathL sink op source d_est d_se d_z pvalue d_lower d_upper
#> PKA 1 PIP3 <- PKA 0.000 0.000 3.584 0.000 0.000 0.000
#> PKA5 1 Akt <- PKA 0.341 0.039 8.722 0.000 0.265 0.418
#> PKA6 1 Erk <- PKA 0.242 0.042 5.706 0.000 0.159 0.326
#> PKC2 1 Jnk <- PKC 0.643 0.044 14.506 0.000 0.556 0.730
#> PKC3 1 P38 <- PKC 0.345 0.036 9.684 0.000 0.275 0.415
#> PIP31 1 PIP2 <- PIP3 0.351 0.040 8.693 0.000 0.272 0.431
#> PIP32 1 Plcg <- PIP3 0.321 0.047 6.774 0.000 0.228 0.414
#> PIP33 1 Akt <- PIP3 0.079 0.040 1.994 0.046 0.001 0.158
#> Plcg1 1 PIP2 <- Plcg 0.375 0.039 9.715 0.000 0.299 0.450