Example 5: Multi-arm | Fixed design | Single continuous endpoint | Dunnett test + MCP-Mod
example-5.Rmd
# Core simulation framework (Timer, Population, Trial, gen_timepoints, add_timepoints, ...)
library(rxsim)
# Analyses
library(multcomp) # Dunnett
#> Loading required package: mvtnorm
#> Loading required package: survival
#> Loading required package: TH.data
#> Loading required package: MASS
#>
#> Attaching package: 'TH.data'
#> The following object is masked from 'package:MASS':
#>
#> geyser
library(DoseFinding) # MCP-Mod
# Helpers
library(dplyr)
#>
#> Attaching package: 'dplyr'
#> The following object is masked from 'package:MASS':
#>
#> select
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
set.seed(4566)Dose-finding trials aim to identify the dose-response relationship and establish an effective dose level. This example simulates a multi-arm fixed design across a placebo and four active doses, with the endpoint generated from an Emax dose-response model. At the final analysis, two methods are applied: a Dunnett test (comparing each active dose against placebo while controlling family-wise error rate) and MCP-Mod (a model-based contrast approach that selects the best-fitting dose-response shape from a candidate set).
Scenario
A multi-arm, fixed design (placebo + 4 active doses) with a single continuous endpoint. At the final analysis, we perform:
- Dunnett test: all active doses vs placebo using a normal-theory linear model.
- MCP-Mod: model-based multiple contrast test + model fitting on a candidate set of dose–response shapes.
The Emax model generates mean responses via
E(d) = e0 + emax × d / (ed50 + d), where
e0 = 0 (placebo baseline), emax = 1 (maximum
achievable effect), and ed50 = 20 (dose at half-maximum
effect). arm_names = paste0("d", doses) creates
human-readable labels (d0, d5,
d10, d20, d50) that propagate
through trial data and analysis results. delta = 0.1 is the
minimum effect size of clinical relevance used by MCP-Mod, and
alpha = 0.05 controls the family-wise Type I error rate for
both testing procedures.
# Dose levels (placebo + 4 actives)
doses <- c(0, 5, 10, 20, 50)
# Total N and allocation (balanced across arms)
sample_size <- 150
allocation <- rep(1, length(doses))
arm_names <- paste0("d", doses) # e.g., d0, d5, ... used as arm labels
# Enrollment & dropout profile (piece-wise constant)
enrollment <- list(
end_time = c(4, 8, 12, 16),
rate = c(6, 12, 18, 24)
)
dropout <- list(
end_time = c(4, 8, 12, 16),
rate = c(0, 1, 2, 3)
)
# Data-generating model: Emax with homoscedastic noise
e0 <- 0.0
emax <- 1.0
ed50 <- 20.0
sigma <- 1.0
mean_fun <- function(d) e0 + emax * d / (ed50 + d)
# operating characteristics
alpha <- 0.05
delta <- 0.1
scenario <- tidyr::expand_grid(
sample_size = sample_size,
allocation = list(allocation),
n_arms = length(doses),
alpha = alpha,
delta = delta
)Time points
gen_timepoints() generates a piecewise-constant
enrollment schedule with rates that increase in steps (6, 12, 18, 24
subjects per unit time), reflecting a realistic ramp-up in site
activation. tr_timer$get_end_timepoint() returns the
earliest calendar time at which all sample_size subjects
are expected to be enrolled — this value is used as the trigger time for
the final analysis.
timepoints <- gen_timepoints(
sample_size = sample_size,
arms = arm_names,
allocation = allocation,
enrollment = enrollment,
dropout = dropout
)
# Timer
tr_timer <- Timer$new(name = "timer_multiarm")
add_timepoints(tr_timer, timepoints)
final_time <- tr_timer$get_end_timepoint()
final_time
#> [1] 14Populations
mk_pop_gen is a closure factory: it captures the dose
value d and returns a generator function that, when called
with n, draws n responses from N(E(d), σ²).
Each arm’s generator stores dose as a numeric column
because MCP-Mod requires actual dose values — not just arm labels — to
fit dose-response models and evaluate contrasts at analysis time.
Trial Parameters
enrollment_fn and dropout_fn supply the
inter-arrival and time-to-dropout distributions for individual subjects.
These are passed to replicate_trial(), which uses them
internally when building each replicate’s enrollment schedule.
Triggers & Analyses
At the final time, run:
Dunnett test (active vs placebo) using
multcomp::glhtonlm(y ~ arm).MCP-Mod using
DoseFinding::MCPModwith a candidate model set (Mods).
The Dunnett test (multcomp::glht with
mcp(arm = "Dunnett")) simultaneously compares each active
dose against placebo while controlling the family-wise error rate at
alpha. MCP-Mod is run with five candidate dose-response
shapes; selModel = "aveAIC" selects the best model by
AIC-weighted averaging, and Delta = delta sets the minimum
effect size of clinical relevance for the contrast step.
mct_min_p extracts the minimum p-value across all candidate
model contrast tests — a small value indicates that at least one
candidate model detects a dose-response signal.
# Candidate model set for MCP-Mod
mods <- Mods(
linear = NULL,
emax = 20,
exponential= 50,
sigEmax = c(20, 3),
quadratic = -0.2,
doses = doses
)
analysis_generators <- list(
final = list(
trigger = rlang::exprs(
sum(!is.na(enroll_time)) >= !!sample_size
),
analysis = function(df, timer){
df_e <- df |>
dplyr::filter(!is.na(enroll_time)) |>
dplyr::mutate(
arm = factor(arm, levels = paste0("d", doses)),
dose = as.numeric(dose)
)
# 1) Dunnett (active vs placebo)
fit <- lm(y ~ arm, data = df_e)
dun <- multcomp::glht(fit, linfct = multcomp::mcp(arm = "Dunnett"))
summ <- summary(dun)
# 2) MCP-Mod (one-step)
mm <- DoseFinding::MCPMod(
dose = df_e$dose,
resp = df_e$y,
models = mods,
type = "normal",
Delta = delta,
alpha = alpha,
selModel = "aveAIC"
)
mct_min_p <- min(attr(mm$MCTtest$tStat, "pVal"), na.rm = TRUE)
data.frame(
scenario,
n_total = nrow(df_e),
dunn_min_p = summ$test$pvalues |> as.numeric() |> min(),
mcpmod_min_p = mct_min_p,
stringsAsFactors = FALSE
)
}
)
)Trial
trials <- replicate_trial(
trial_name = "multiarm_dunnett_mcpmod",
sample_size = sample_size,
arms = arm_names,
allocation = allocation,
enrollment = enrollment_fn,
dropout = dropout_fn,
analysis_generators = analysis_generators,
population_generators = population_generators,
n = 3
)Simulate
run_trials(trials)
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> Warning in MCTpval(contMat, corMat, df, tStat, alternative, mvtcontrol):
#> Warning from mvtnorm::pmvt: Completion with error > abseps.
#> [[1]]
#> <Trial>
#> Public:
#> clone: function (deep = FALSE)
#> initialize: function (name, seed = NULL, timer = NULL, population = list(),
#> locked_data: list
#> name: multiarm_dunnett_mcpmod_1
#> population: list
#> results: list
#> run: function ()
#> seed: NULL
#> timer: Timer, R6
#>
#> [[2]]
#> <Trial>
#> Public:
#> clone: function (deep = FALSE)
#> initialize: function (name, seed = NULL, timer = NULL, population = list(),
#> locked_data: list
#> name: multiarm_dunnett_mcpmod_2
#> population: list
#> results: list
#> run: function ()
#> seed: NULL
#> timer: Timer, R6
#>
#> [[3]]
#> <Trial>
#> Public:
#> clone: function (deep = FALSE)
#> initialize: function (name, seed = NULL, timer = NULL, population = list(),
#> locked_data: list
#> name: multiarm_dunnett_mcpmod_3
#> population: list
#> results: list
#> run: function ()
#> seed: NULL
#> timer: Timer, R6Results
collect_results() row-binds analysis outputs across all
replicates and prepends three bookkeeping columns:
replicate (integer index), timepoint (calendar
time at which the analysis fired), and analysis (the
analysis name, here "final"). dunn_min_p is
the smallest Dunnett-adjusted p-value across the four active-dose
comparisons — a value below alpha indicates that at least
one dose is significantly different from placebo after multiplicity
correction. mcpmod_min_p is the minimum MCP-Mod contrast
test p-value across candidate models; both metrics test for the presence
of a dose-response signal, but MCP-Mod is generally more powerful when
the true dose-response shape is well-captured by one of the candidate
models. See Core Concepts for background on
trial parameters.
One row per replicate, row-bound across all replicates:
replicate_results <- collect_results(trials)
replicate_results
#> replicate timepoint analysis sample_size allocation n_arms alpha delta
#> 1 1 143.0045 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 2 1 339.9395 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 3 1 360.7831 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 4 1 588.7844 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 5 1 670.0388 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 6 1 772.1356 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 7 1 775.1476 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 8 1 787.1425 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 9 1 798.6437 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 10 1 1028.4725 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 11 1 1080.1645 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 12 1 1253.6509 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 13 1 1317.8008 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 14 1 1397.0989 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 15 1 1492.6022 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 16 1 1775.4050 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 17 1 1887.0859 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 18 1 1915.6536 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 19 1 1930.4359 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 20 1 2106.0079 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 21 1 2153.1301 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 22 1 2154.5230 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 23 1 2159.6204 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 24 1 2246.0420 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 25 1 2284.4002 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 26 1 2394.9954 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 27 1 2437.6287 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 28 1 2988.2379 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 29 1 3058.7220 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 30 1 3073.4531 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 31 1 3108.8572 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 32 1 3318.4561 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 33 1 3331.7474 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 34 1 3449.3426 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 35 1 3541.0817 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 36 1 3710.8414 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 37 1 3892.1890 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 38 1 3965.8668 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 39 1 4212.2229 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 40 1 4374.7451 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 41 1 4443.1475 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 42 1 4654.6850 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 43 1 4750.0769 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 44 1 4778.3686 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 45 1 4786.5390 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 46 1 4786.6340 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 47 1 5027.6661 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 48 1 5052.1873 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 49 1 5371.1915 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 50 1 5435.0975 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 51 1 5540.2019 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 52 1 5567.7204 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 53 1 5663.2639 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 54 1 5722.4476 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 55 1 5767.2693 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 56 1 5900.9525 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 57 1 6228.5340 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 58 1 6328.1474 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 59 1 6361.2112 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 60 1 6450.6320 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 61 1 6499.9763 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 62 1 6519.2181 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 63 1 6572.0482 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 64 1 6847.9736 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 65 1 6854.6817 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 66 1 6999.4844 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 67 1 7048.1833 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 68 1 7143.2179 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 69 1 7156.0925 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 70 1 7323.9579 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 71 1 7542.9430 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 72 1 7647.3063 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 73 1 7710.8601 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 74 1 7857.1631 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 75 1 7892.4612 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 76 1 7989.6922 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 77 1 8021.6614 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 78 1 8066.3794 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 79 1 8093.6099 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 80 1 8315.4158 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 81 1 8359.9900 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 82 1 8456.6798 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 83 1 8691.9279 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 84 1 8700.0742 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 85 1 8715.5817 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 86 1 8739.9677 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 87 1 9030.9311 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 88 1 9070.9733 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 89 1 9229.1156 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 90 1 9236.6338 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 91 1 9287.9738 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 92 1 9296.3791 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 93 1 9319.3655 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 94 1 9327.6958 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 95 1 9404.7676 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 96 1 9458.4023 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 97 1 9498.5916 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 98 1 9523.2242 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 99 1 9543.2741 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 100 1 9627.7292 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 101 1 9777.8174 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 102 1 9798.5206 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 103 1 10006.4467 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 104 1 10007.1916 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 105 1 10020.3462 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 106 1 10033.1938 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 107 1 10129.7089 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 108 1 10132.8448 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 109 1 10183.4848 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 110 1 10262.3121 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 111 1 10298.2363 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 112 1 10381.1510 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 113 1 10449.3668 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 114 1 10595.6510 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 115 1 10599.5382 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 116 1 10994.7581 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 117 1 11156.1662 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 118 1 11245.4584 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 119 1 11370.0855 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 120 1 11464.1854 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 121 1 11489.9480 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 122 1 11615.6723 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 123 1 11818.7085 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 124 1 11896.2410 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 125 1 12035.7341 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 126 1 12155.2739 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 127 1 12171.0963 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 128 1 12435.5286 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 129 1 12721.4746 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 130 1 12785.5565 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 131 1 12991.3102 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 132 1 13073.8836 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 133 1 13238.9815 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 134 1 13382.9275 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 135 1 13433.1607 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 136 1 13491.5979 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 137 1 13613.6308 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 138 1 13620.4157 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 139 1 13738.3349 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 140 1 13763.0853 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 141 1 13779.3080 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 142 1 13990.4016 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 143 1 14018.8871 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 144 1 14037.5864 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 145 1 14040.5193 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 147 1 14211.0777 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 148 1 14232.8339 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 149 1 14242.4501 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 150 1 14256.6441 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 151 1 14260.4322 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 152 2 148.2639 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 157 2 591.6585 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 158 2 653.8085 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 159 2 693.7968 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 160 2 696.8845 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 161 2 796.6384 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 162 2 815.3134 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 163 2 943.4248 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 164 2 988.3653 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 165 2 1041.9727 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 168 2 1680.2417 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 170 2 1923.6892 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 171 2 2185.3293 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 172 2 2309.3059 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 173 2 2516.3584 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 174 2 2579.2572 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 175 2 2658.6346 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 176 2 2672.1026 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 177 2 2852.5090 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 178 2 3227.3399 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 179 2 3267.4390 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 180 2 3346.3101 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 181 2 3354.5941 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 182 2 3377.7399 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 183 2 3411.9433 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 184 2 3467.1993 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 185 2 3471.0882 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 186 2 3501.8996 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 187 2 3658.3615 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 188 2 3767.1029 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 189 2 4328.9796 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 190 2 4427.8640 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 191 2 4443.4503 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 192 2 4592.3509 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 193 2 4631.3513 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 194 2 4703.2820 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 195 2 4778.0570 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 196 2 4807.1763 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 197 2 4940.0382 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 198 2 5096.0842 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 199 2 5365.4437 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 200 2 5372.2570 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 201 2 5432.5425 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 202 2 5577.3849 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 203 2 5682.7839 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 204 2 5688.0523 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 205 2 5718.7936 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 206 2 5910.7442 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 207 2 6048.7189 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 208 2 6130.4166 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 209 2 6349.9997 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 210 2 6425.3210 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 211 2 6506.7830 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 212 2 6572.6640 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 213 2 6586.1021 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 214 2 6784.9064 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 215 2 6800.7430 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 216 2 6872.1424 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 217 2 6930.0081 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 218 2 7141.8191 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 219 2 7243.3190 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 220 2 7352.9040 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 221 2 7354.0977 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 222 2 7398.4770 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 223 2 7496.9767 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 224 2 7572.9416 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 225 2 7635.8752 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 226 2 7729.2110 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 227 2 7748.9087 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 228 2 7807.0321 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 229 2 7821.2778 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 230 2 7855.2292 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 231 2 8049.9707 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 232 2 8111.1810 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 233 2 8165.1570 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 234 2 8289.7631 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 235 2 8320.9267 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 236 2 8432.9956 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 237 2 8483.3301 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 238 2 8680.5709 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 239 2 8882.3747 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 240 2 9181.1285 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 241 2 9186.0610 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 242 2 9263.9555 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 243 2 9269.8875 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 244 2 9281.1404 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 245 2 9310.2995 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 246 2 9321.7835 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 247 2 9351.1467 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 248 2 9364.9909 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 249 2 9415.6142 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 250 2 9530.2165 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 251 2 9556.7782 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 252 2 9666.0535 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 253 2 9704.6674 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 254 2 9773.5464 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 255 2 9848.4262 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 256 2 10056.3384 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 257 2 10285.2922 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 258 2 10294.8585 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 259 2 10330.9952 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 260 2 10398.9500 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 263 2 10461.3726 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 264 2 10515.8574 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 268 2 10835.3669 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 269 2 10837.6253 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 270 2 10893.6843 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 272 2 11006.8909 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 278 2 11486.5331 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 280 2 11675.1681 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 281 2 11691.3073 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 282 2 11780.5489 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 283 2 11792.4402 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 284 2 11793.7679 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 285 2 11855.7885 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 289 2 12022.3184 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 290 2 12150.9301 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 294 2 12358.7083 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 296 2 12397.8754 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 300 2 12661.4331 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 415 3 11177.7385 final 150 1, 1, 1, 1, 1 5 0.05 0.1
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#> 417 3 11425.8466 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 418 3 11573.3197 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 419 3 11597.4206 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 420 3 11781.5131 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 421 3 11804.2088 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 422 3 11875.9285 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 423 3 11951.4247 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 424 3 11999.7391 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 425 3 12029.2570 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 426 3 12037.5722 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 427 3 12418.5675 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 428 3 12444.1163 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 429 3 12464.3175 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 430 3 12482.7694 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 431 3 12597.8750 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 432 3 12718.4910 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 433 3 13169.1349 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 434 3 13330.4794 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 435 3 13339.2446 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 436 3 13532.5844 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 437 3 13591.1442 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 438 3 13601.6034 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 439 3 13659.2478 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 440 3 13891.0138 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 441 3 13935.3991 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 442 3 14349.8417 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 443 3 14545.6029 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 444 3 14627.2554 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 445 3 14636.8145 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 446 3 14639.2416 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 447 3 14665.9031 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 448 3 14718.3569 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 449 3 14874.7654 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 450 3 15081.0408 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> 451 3 15189.6279 final 150 1, 1, 1, 1, 1 5 0.05 0.1
#> n_total dunn_min_p mcpmod_min_p
#> 1 150 2.614327e-01 9.360871e-02
#> 2 150 2.614396e-01 9.275725e-02
#> 3 150 2.613955e-01 9.319514e-02
#> 4 150 2.614196e-01 9.270148e-02
#> 5 150 2.614895e-01 9.276225e-02
#> 6 150 2.614892e-01 9.345740e-02
#> 7 150 2.614015e-01 9.306070e-02
#> 8 150 2.615511e-01 9.272428e-02
#> 9 150 2.614361e-01 9.244525e-02
#> 10 150 2.614332e-01 9.290695e-02
#> 11 150 2.614584e-01 9.308355e-02
#> 12 150 2.614969e-01 9.253591e-02
#> 13 150 2.614508e-01 9.292989e-02
#> 14 150 2.614040e-01 9.363291e-02
#> 15 150 2.614044e-01 9.262052e-02
#> 16 150 2.615193e-01 9.286933e-02
#> 17 150 2.614002e-01 9.284280e-02
#> 18 150 2.614238e-01 9.340432e-02
#> 19 150 2.614416e-01 9.290941e-02
#> 20 150 2.616167e-01 9.323894e-02
#> 21 150 2.614347e-01 9.300686e-02
#> 22 150 2.613603e-01 9.293349e-02
#> 23 150 2.614027e-01 9.298311e-02
#> 24 150 2.614211e-01 9.312740e-02
#> 25 150 2.613984e-01 9.349511e-02
#> 26 150 2.614601e-01 9.277710e-02
#> 27 150 2.614322e-01 9.265344e-02
#> 28 150 2.615036e-01 9.326216e-02
#> 29 150 2.613462e-01 9.300571e-02
#> 30 150 2.614575e-01 9.273741e-02
#> 31 150 2.614319e-01 9.316567e-02
#> 32 150 2.613480e-01 9.312085e-02
#> 33 150 2.614617e-01 9.343095e-02
#> 34 150 2.614056e-01 9.312477e-02
#> 35 150 2.615702e-01 9.300466e-02
#> 36 150 2.614963e-01 9.327955e-02
#> 37 150 2.614518e-01 9.329042e-02
#> 38 150 2.614567e-01 9.273575e-02
#> 39 150 2.615624e-01 9.326930e-02
#> 40 150 2.613972e-01 9.303780e-02
#> 41 150 2.614363e-01 9.299402e-02
#> 42 150 2.614751e-01 9.284153e-02
#> 43 150 2.614512e-01 9.295286e-02
#> 44 150 2.614149e-01 9.237586e-02
#> 45 150 2.614151e-01 9.278536e-02
#> 46 150 2.614348e-01 9.250590e-02
#> 47 150 2.614754e-01 9.298851e-02
#> 48 150 2.613954e-01 9.314493e-02
#> 49 150 2.615101e-01 9.309354e-02
#> 50 150 2.615213e-01 9.347243e-02
#> 51 150 2.614228e-01 9.281253e-02
#> 52 150 2.614546e-01 9.329139e-02
#> 53 150 2.615069e-01 9.290822e-02
#> 54 150 2.614887e-01 9.343875e-02
#> 55 150 2.614446e-01 9.310967e-02
#> 56 150 2.614339e-01 9.302447e-02
#> 57 150 2.615390e-01 9.288955e-02
#> 58 150 2.614182e-01 9.292151e-02
#> 59 150 2.614378e-01 9.322694e-02
#> 60 150 2.614630e-01 9.310439e-02
#> 61 150 2.614645e-01 9.317999e-02
#> 62 150 2.614052e-01 9.274885e-02
#> 63 150 2.614066e-01 9.316136e-02
#> 64 150 2.613996e-01 9.305733e-02
#> 65 150 2.615829e-01 9.311495e-02
#> 66 150 2.613643e-01 9.326818e-02
#> 67 150 2.613852e-01 9.333006e-02
#> 68 150 2.615034e-01 9.350892e-02
#> 69 150 2.614114e-01 9.306649e-02
#> 70 150 2.613583e-01 9.301616e-02
#> 71 150 2.613885e-01 9.298870e-02
#> 72 150 2.614391e-01 9.286583e-02
#> 73 150 2.614707e-01 9.323755e-02
#> 74 150 2.615086e-01 9.326162e-02
#> 75 150 2.614686e-01 9.281220e-02
#> 76 150 2.613521e-01 9.321166e-02
#> 77 150 2.614946e-01 9.328788e-02
#> 78 150 2.614557e-01 9.268851e-02
#> 79 150 2.614772e-01 9.309326e-02
#> 80 150 2.614987e-01 9.313837e-02
#> 81 150 2.614306e-01 9.313236e-02
#> 82 150 2.614124e-01 9.361133e-02
#> 83 150 2.615002e-01 9.320870e-02
#> 84 150 2.614384e-01 9.335957e-02
#> 85 150 2.613176e-01 9.335430e-02
#> 86 150 2.614249e-01 9.288760e-02
#> 87 150 2.615418e-01 9.320970e-02
#> 88 150 2.614237e-01 9.285773e-02
#> 89 150 2.614312e-01 9.320397e-02
#> 90 150 2.614070e-01 9.296978e-02
#> 91 150 2.614820e-01 9.337207e-02
#> 92 150 2.614042e-01 9.321349e-02
#> 93 150 2.614723e-01 9.309716e-02
#> 94 150 2.614290e-01 9.382504e-02
#> 95 150 2.613988e-01 9.268601e-02
#> 96 150 2.615152e-01 9.282868e-02
#> 97 150 2.614500e-01 9.241847e-02
#> 98 150 2.614159e-01 9.328178e-02
#> 99 150 2.614869e-01 9.309507e-02
#> 100 150 2.614638e-01 9.291479e-02
#> 101 150 2.615125e-01 9.244476e-02
#> 102 150 2.614196e-01 9.135931e-02
#> 103 150 2.613786e-01 9.295149e-02
#> 104 150 2.614485e-01 9.297123e-02
#> 105 150 2.614764e-01 9.345298e-02
#> 106 150 2.613265e-01 9.319463e-02
#> 107 150 2.615018e-01 9.310204e-02
#> 108 150 2.614128e-01 9.269482e-02
#> 109 150 2.614334e-01 9.318676e-02
#> 110 150 2.613965e-01 9.323312e-02
#> 111 150 2.614217e-01 9.297889e-02
#> 112 150 2.613930e-01 9.354575e-02
#> 113 150 2.614780e-01 9.297310e-02
#> 114 150 2.614366e-01 9.295070e-02
#> 115 150 2.613386e-01 9.309881e-02
#> 116 150 2.614538e-01 9.306822e-02
#> 117 150 2.614093e-01 9.320874e-02
#> 118 150 2.613804e-01 9.338952e-02
#> 119 150 2.614565e-01 9.331719e-02
#> 120 150 2.614653e-01 9.296052e-02
#> 121 150 2.613838e-01 9.416520e-02
#> 122 150 2.613849e-01 9.308690e-02
#> 123 150 2.615031e-01 9.303579e-02
#> 124 150 2.615844e-01 9.244391e-02
#> 125 150 2.614941e-01 9.304041e-02
#> 126 150 2.615478e-01 9.272218e-02
#> 127 150 2.615309e-01 9.294953e-02
#> 128 150 2.614171e-01 9.315036e-02
#> 129 150 2.614899e-01 9.329863e-02
#> 130 150 2.613846e-01 9.289970e-02
#> 131 150 2.614287e-01 9.300815e-02
#> 132 150 2.613020e-01 9.335157e-02
#> 133 150 2.614981e-01 9.296093e-02
#> 134 150 2.615437e-01 9.284297e-02
#> 135 150 2.615497e-01 9.323686e-02
#> 136 150 2.613633e-01 9.267196e-02
#> 137 150 2.614964e-01 9.336882e-02
#> 138 150 2.614169e-01 9.309549e-02
#> 139 150 2.613611e-01 9.278984e-02
#> 140 150 2.613671e-01 9.266914e-02
#> 141 150 2.613687e-01 9.337392e-02
#> 142 150 2.614785e-01 9.289227e-02
#> 143 150 2.614767e-01 9.311363e-02
#> 144 150 2.615267e-01 9.311493e-02
#> 145 150 2.613882e-01 9.299885e-02
#> 146 150 2.614772e-01 9.313427e-02
#> 147 150 2.615392e-01 9.319678e-02
#> 148 150 2.614104e-01 9.313141e-02
#> 149 150 2.615117e-01 9.273186e-02
#> 150 150 2.615516e-01 9.237583e-02
#> 151 150 2.613845e-01 9.217027e-02
#> 152 150 8.981219e-05 1.123651e-05
#> 153 150 7.961448e-05 3.660842e-06
#> 154 150 7.860573e-05 3.293457e-06
#> 155 150 9.792402e-05 4.038984e-06
#> 156 150 9.217714e-05 3.253847e-06
#> 157 150 9.473143e-05 3.105401e-06
#> 158 150 9.080252e-05 3.706229e-06
#> 159 150 1.052573e-04 4.266154e-06
#> 160 150 8.708270e-05 4.546306e-06
#> 161 150 8.849276e-05 5.623681e-06
#> 162 150 8.256923e-05 4.426698e-06
#> 163 150 8.535531e-05 4.387355e-06
#> 164 150 9.959180e-05 3.542223e-06
#> 165 150 9.606843e-05 3.174445e-06
#> 166 150 8.546491e-05 3.907943e-06
#> 167 150 7.335827e-05 4.771371e-06
#> 168 150 7.789603e-05 3.058025e-06
#> 169 150 8.127999e-05 6.561985e-06
#> 170 150 7.613346e-05 7.149066e-06
#> 171 150 8.592316e-05 5.534546e-06
#> 172 150 8.550120e-05 3.156882e-06
#> 173 150 9.074101e-05 1.225210e-05
#> 174 150 7.406792e-05 3.494359e-06
#> 175 150 8.354890e-05 4.180008e-06
#> 176 150 8.195689e-05 3.841123e-06
#> 177 150 9.993704e-05 5.589129e-06
#> 178 150 9.753898e-05 2.961110e-06
#> 179 150 7.338543e-05 1.169763e-05
#> 180 150 8.659199e-05 3.351433e-06
#> 181 150 8.271319e-05 3.048907e-06
#> 182 150 9.544456e-05 4.022911e-06
#> 183 150 9.664125e-05 2.924540e-06
#> 184 150 9.100926e-05 3.382574e-06
#> 185 150 9.213875e-05 3.625582e-06
#> 186 150 8.541382e-05 3.410981e-06
#> 187 150 8.638013e-05 3.197464e-06
#> 188 150 7.753415e-05 3.212647e-06
#> 189 150 8.848871e-05 1.015368e-05
#> 190 150 9.241812e-05 3.391715e-06
#> 191 150 8.070419e-05 4.568120e-06
#> 192 150 8.982265e-05 4.710213e-06
#> 193 150 7.849511e-05 4.366608e-06
#> 194 150 9.924447e-05 9.715528e-06
#> 195 150 8.329449e-05 3.880861e-06
#> 196 150 8.000101e-05 3.295047e-06
#> 197 150 8.994803e-05 1.298347e-05
#> 198 150 8.038019e-05 3.136372e-06
#> 199 150 8.575402e-05 2.842082e-06
#> 200 150 1.034467e-04 3.987165e-06
#> 201 150 7.850827e-05 6.031850e-06
#> 202 150 8.247827e-05 1.061563e-05
#> 203 150 7.637356e-05 2.952576e-06
#> 204 150 9.407388e-05 3.127547e-06
#> 205 150 9.673583e-05 3.317754e-06
#> 206 150 8.014738e-05 5.329364e-06
#> 207 150 8.566631e-05 3.649790e-06
#> 208 150 8.196794e-05 5.677936e-06
#> 209 150 8.112970e-05 5.267769e-06
#> 210 150 8.375053e-05 3.101002e-06
#> 211 150 9.351520e-05 3.065850e-06
#> 212 150 7.845088e-05 4.538759e-06
#> 213 150 8.673866e-05 3.077422e-06
#> 214 150 8.343704e-05 3.406318e-06
#> 215 150 1.085818e-04 4.300808e-06
#> 216 150 8.687553e-05 5.950416e-06
#> 217 150 9.085260e-05 5.127386e-06
#> 218 150 8.159712e-05 3.848200e-06
#> 219 150 8.710774e-05 4.249256e-06
#> 220 150 9.324710e-05 3.163779e-06
#> 221 150 8.445660e-05 3.742343e-06
#> 222 150 9.823264e-05 5.100253e-06
#> 223 150 7.781721e-05 3.298102e-06
#> 224 150 8.093244e-05 3.623732e-06
#> 225 150 8.155167e-05 3.016929e-06
#> 226 150 9.046981e-05 3.523167e-06
#> 227 150 9.854356e-05 3.057922e-06
#> 228 150 7.610552e-05 4.073044e-06
#> 229 150 9.194991e-05 3.324073e-06
#> 230 150 8.039539e-05 3.238537e-06
#> 231 150 7.908109e-05 3.412122e-06
#> 232 150 7.865262e-05 3.049822e-06
#> 233 150 8.774424e-05 3.380072e-06
#> 234 150 9.936927e-05 4.110546e-06
#> 235 150 8.256012e-05 3.157050e-06
#> 236 150 9.565554e-05 4.699858e-06
#> 237 150 8.394185e-05 2.986234e-06
#> 238 150 8.053769e-05 4.120730e-06
#> 239 150 9.178960e-05 4.732087e-06
#> 240 150 8.146128e-05 4.419217e-06
#> 241 150 8.896865e-05 3.323733e-06
#> 242 150 8.324750e-05 3.573718e-06
#> 243 150 7.727374e-05 3.156861e-06
#> 244 150 8.597741e-05 3.333968e-06
#> 245 150 9.901049e-05 3.434634e-06
#> 246 150 8.585519e-05 3.768781e-06
#> 247 150 9.592965e-05 3.144893e-06
#> 248 150 8.946895e-05 5.456388e-06
#> 249 150 1.036129e-04 4.441485e-06
#> 250 150 8.639761e-05 3.125239e-06
#> 251 150 8.862373e-05 3.395543e-06
#> 252 150 8.100858e-05 5.381122e-06
#> 253 150 8.249337e-05 4.294650e-06
#> 254 150 9.258027e-05 3.218535e-06
#> 255 150 7.995027e-05 5.870885e-06
#> 256 150 8.035010e-05 1.063567e-05
#> 257 150 7.883884e-05 4.726642e-06
#> 258 150 1.335054e-04 3.415576e-06
#> 259 150 9.059259e-05 3.031212e-06
#> 260 150 9.759776e-05 3.513580e-06
#> 261 150 8.427311e-05 9.716059e-06
#> 262 150 1.050883e-04 1.429249e-05
#> 263 150 8.671316e-05 4.649378e-06
#> 264 150 8.030417e-05 3.155409e-06
#> 265 150 1.092399e-04 3.029741e-06
#> 266 150 1.044078e-04 3.376731e-06
#> 267 150 1.049721e-04 5.558451e-06
#> 268 150 1.149923e-04 3.884535e-06
#> 269 150 8.230897e-05 2.907439e-06
#> 270 150 8.922891e-05 4.698365e-06
#> 271 150 8.542828e-05 3.246686e-06
#> 272 150 8.528368e-05 3.627737e-06
#> 273 150 8.781407e-05 3.899593e-06
#> 274 150 7.956818e-05 3.145309e-06
#> 275 150 1.063663e-04 4.189047e-06
#> 276 150 8.127860e-05 5.753535e-06
#> 277 150 8.841512e-05 2.889243e-06
#> 278 150 1.071952e-04 3.230267e-06
#> 279 150 7.531926e-05 4.160609e-06
#> 280 150 8.166653e-05 3.250126e-06
#> 281 150 8.731245e-05 4.065649e-06
#> 282 150 7.861762e-05 3.086610e-06
#> 283 150 7.869225e-05 3.788437e-06
#> 284 150 7.903125e-05 4.672738e-06
#> 285 150 1.021289e-04 3.142116e-06
#> 286 150 8.853428e-05 4.476558e-06
#> 287 150 7.863446e-05 4.278731e-06
#> 288 150 7.751441e-05 4.601287e-06
#> 289 150 9.068121e-05 3.025168e-06
#> 290 150 8.383178e-05 6.816018e-06
#> 291 150 8.212471e-05 6.802007e-06
#> 292 150 9.848770e-05 3.188885e-06
#> 293 150 9.288432e-05 5.531478e-06
#> 294 150 1.028726e-04 5.493731e-06
#> 295 150 9.532545e-05 3.416792e-06
#> 296 150 8.175583e-05 6.115948e-06
#> 297 150 9.853731e-05 4.144229e-06
#> 298 150 8.443076e-05 3.171534e-06
#> 299 150 8.534431e-05 3.931003e-06
#> 300 150 8.463621e-05 3.234322e-06
#> 301 150 8.525217e-05 5.311228e-06
#> 302 150 1.540937e-04 1.831518e-05
#> 303 150 1.486112e-04 2.105323e-05
#> 304 150 1.538273e-04 2.127895e-05
#> 305 150 1.422745e-04 1.702716e-05
#> 306 150 2.005675e-04 2.343646e-05
#> 307 150 1.485906e-04 3.806392e-05
#> 308 150 1.623462e-04 2.441022e-05
#> 309 150 1.503481e-04 3.733663e-05
#> 310 150 1.797116e-04 2.915798e-05
#> 311 150 1.614737e-04 2.068826e-05
#> 312 150 1.843080e-04 1.853905e-05
#> 313 150 1.907370e-04 2.714468e-05
#> 314 150 1.592947e-04 4.017872e-05
#> 315 150 1.531499e-04 2.694495e-05
#> 316 150 1.443367e-04 1.904073e-05
#> 317 150 1.509031e-04 1.738920e-05
#> 318 150 1.481064e-04 3.571296e-05
#> 319 150 1.653353e-04 2.341770e-05
#> 320 150 1.538056e-04 3.135866e-05
#> 321 150 1.553463e-04 2.817980e-05
#> 322 150 1.560652e-04 1.951457e-05
#> 323 150 1.438423e-04 2.858206e-05
#> 324 150 1.448520e-04 1.890106e-05
#> 325 150 1.483413e-04 2.692030e-05
#> 326 150 1.736704e-04 3.171798e-05
#> 327 150 1.797214e-04 1.754470e-05
#> 328 150 1.439721e-04 1.609126e-05
#> 329 150 1.620651e-04 1.818050e-05
#> 330 150 1.571943e-04 1.631641e-05
#> 331 150 1.542269e-04 1.734375e-05
#> 332 150 1.581470e-04 2.295099e-05
#> 333 150 1.666742e-04 2.268851e-05
#> 334 150 1.520787e-04 1.790566e-05
#> 335 150 1.704419e-04 3.194841e-05
#> 336 150 1.601266e-04 1.922853e-05
#> 337 150 1.539982e-04 1.182779e-04
#> 338 150 1.598785e-04 1.659750e-05
#> 339 150 1.424631e-04 1.545492e-05
#> 340 150 1.411589e-04 1.682579e-05
#> 341 150 1.677200e-04 1.570373e-05
#> 342 150 1.562820e-04 2.466652e-05
#> 343 150 1.720883e-04 2.126923e-05
#> 344 150 1.866546e-04 1.766676e-05
#> 345 150 1.551548e-04 1.730262e-05
#> 346 150 1.566000e-04 2.129428e-05
#> 347 150 1.640063e-04 2.122334e-05
#> 348 150 1.483623e-04 2.619601e-05
#> 349 150 1.458905e-04 1.893657e-05
#> 350 150 1.760133e-04 2.420377e-05
#> 351 150 1.739001e-04 1.656794e-05
#> 352 150 1.835615e-04 2.148656e-05
#> 353 150 1.453044e-04 3.058325e-05
#> 354 150 1.873121e-04 2.288007e-05
#> 355 150 1.620287e-04 2.044667e-05
#> 356 150 1.819241e-04 2.102506e-05
#> 357 150 1.591919e-04 1.656483e-05
#> 358 150 1.500343e-04 1.855311e-05
#> 359 150 1.701330e-04 2.657025e-05
#> 360 150 1.559658e-04 2.700287e-05
#> 361 150 1.470612e-04 2.069972e-05
#> 362 150 1.846304e-04 2.968998e-05
#> 363 150 2.044847e-04 1.750060e-05
#> 364 150 1.784955e-04 2.650080e-05
#> 365 150 1.927798e-04 2.904097e-05
#> 366 150 1.685548e-04 3.940434e-05
#> 367 150 1.466113e-04 2.428654e-05
#> 368 150 1.723505e-04 2.653453e-05
#> 369 150 1.463968e-04 1.725588e-05
#> 370 150 1.542035e-04 1.970338e-05
#> 371 150 1.540188e-04 2.063157e-05
#> 372 150 1.691332e-04 3.565796e-05
#> 373 150 1.865557e-04 1.797510e-05
#> 374 150 1.461914e-04 1.732894e-05
#> 375 150 1.867721e-04 1.958258e-05
#> 376 150 1.688553e-04 6.769882e-05
#> 377 150 1.934134e-04 1.666127e-05
#> 378 150 1.843593e-04 1.960807e-05
#> 379 150 1.669163e-04 2.291828e-05
#> 380 150 1.681233e-04 1.785072e-05
#> 381 150 1.646755e-04 1.905143e-05
#> 382 150 1.873625e-04 1.833666e-05
#> 383 150 1.584607e-04 1.909523e-05
#> 384 150 1.494487e-04 2.744092e-05
#> 385 150 1.539640e-04 1.900844e-05
#> 386 150 1.604525e-04 2.128285e-05
#> 387 150 1.571142e-04 2.582744e-05
#> 388 150 1.467875e-04 2.025071e-05
#> 389 150 1.817136e-04 2.586465e-05
#> 390 150 1.601060e-04 3.486711e-05
#> 391 150 1.527500e-04 2.630914e-05
#> 392 150 1.825167e-04 1.531044e-05
#> 393 150 1.505055e-04 1.991110e-05
#> 394 150 1.837598e-04 1.644515e-05
#> 395 150 1.614936e-04 4.544858e-05
#> 396 150 1.555598e-04 2.474531e-05
#> 397 150 1.751303e-04 1.776269e-05
#> 398 150 1.651111e-04 2.589872e-05
#> 399 150 1.637869e-04 3.064272e-05
#> 400 150 1.694460e-04 1.520250e-05
#> 401 150 1.738804e-04 1.685538e-05
#> 402 150 1.722240e-04 3.123791e-05
#> 403 150 1.471121e-04 1.658194e-05
#> 404 150 1.687523e-04 1.959535e-05
#> 405 150 2.945914e-04 2.241390e-05
#> 406 150 1.631506e-04 1.788922e-05
#> 407 150 1.674377e-04 2.819270e-05
#> 408 150 1.661221e-04 1.755670e-05
#> 409 150 1.504291e-04 1.841208e-05
#> 410 150 1.501874e-04 8.222209e-05
#> 411 150 1.514275e-04 1.984766e-05
#> 412 150 1.760528e-04 2.726822e-04
#> 413 150 1.593024e-04 2.251545e-05
#> 414 150 1.568605e-04 3.848548e-05
#> 415 150 1.500970e-04 2.020868e-05
#> 416 150 1.655930e-04 1.724270e-05
#> 417 150 1.579336e-04 2.109224e-05
#> 418 150 1.709845e-04 2.863219e-05
#> 419 150 1.592823e-04 1.923521e-05
#> 420 150 1.713582e-04 1.710489e-05
#> 421 150 1.427187e-04 1.657991e-05
#> 422 150 1.569930e-04 2.155653e-05
#> 423 150 1.501364e-04 1.433629e-05
#> 424 150 1.805139e-04 2.670733e-05
#> 425 150 1.535945e-04 1.788749e-05
#> 426 150 1.665864e-04 1.584645e-05
#> 427 150 1.753771e-04 2.525791e-05
#> 428 150 1.636859e-04 3.648080e-05
#> 429 150 1.621157e-04 2.506888e-05
#> 430 150 1.577081e-04 1.975706e-05
#> 431 150 1.904207e-04 1.974486e-05
#> 432 150 1.756263e-04 1.669109e-05
#> 433 150 1.425341e-04 1.946775e-05
#> 434 150 1.520832e-04 1.785669e-05
#> 435 150 1.495511e-04 3.419877e-05
#> 436 150 1.705446e-04 1.683549e-05
#> 437 150 1.612790e-04 1.598924e-05
#> 438 150 1.749557e-04 1.723506e-05
#> 439 150 1.420741e-04 2.662785e-05
#> 440 150 1.509071e-04 2.191179e-05
#> 441 150 1.645254e-04 1.650869e-05
#> 442 150 1.546173e-04 3.886625e-05
#> 443 150 1.710297e-04 1.777615e-05
#> 444 150 1.629038e-04 1.883680e-05
#> 445 150 1.629410e-04 3.222050e-05
#> 446 150 1.532248e-04 2.501029e-05
#> 447 150 1.405828e-04 1.555058e-05
#> 448 150 1.786101e-04 4.265987e-05
#> 449 150 1.475729e-04 1.816474e-05
#> 450 150 1.562633e-04 2.517472e-05
#> 451 150 1.546718e-04 2.178772e-05