MF Manual

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Package ‘MF’
November 9, 2018
Type Package
Title Mitigated Fraction
Version 4.3.5
Date XX XXXX XXXX
Author David Siev
Maintainer Marie Vendettuoli 
Description Calculate MF (mitigated fraction) with clustering and bootstrap options. See http://goo.gl/pcXYVr for definition of MF. No endorsement, claim, or warranty is implied for this package. It is made available for investigational or pedagogical use only
License MIT + file LICENSE
LazyLoad yes
LazyData yes
Depends R (>= 3.4.4)
Imports methods, dplyr (>= 0.7.1), plyr, stringr, tidyr, forcats,
purrr
Collate 'aaa.r' 'classes.r' 'generic_methods.r' 'MF-package.r'
'HLBoot.r' 'MFBoot.r' 'MFClus.r' 'MFClusBoot.r' 'MFClusHier.R'
'MFmp.r' 'MFnestBoot.r' 'MFr.r' 'MFSubj.r' 'MFHier-wrappers.r'
RoxygenNote 6.0.1
NeedsCompilation no

R topics documented:
MF-package . . . .
calflung . . . . . .
HLBoot . . . . . .
mf-class . . . . . .
MFBoot . . . . . .
mfboot-class . . . .
mfbootcluster-class
MFClus . . . . . .
MFClusBoot . . .
MFClusBootHier .
MFClusHier . . . .
mfcluster-class . .

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2
3
3
5
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12
13
15

2

MF-package
mfcomponents-class
MFh . . . . . . . . .
MFhBoot . . . . . .
mfhierdata-class . . .
mfhlboot-class . . . .
MFmp . . . . . . . .
mfmp-class . . . . .
MFnest . . . . . . .
MFnestBoot . . . . .
MFr . . . . . . . . .
MFSubj . . . . . . .
mlesions . . . . . . .
piglung . . . . . . .

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Index

MF-package

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15
16
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19
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22
24
26
27
28
29
30

MF Package

Description
Includes functions related to mitigated fraction.
For internal use only at the USDA Center for Veterinary Biologics.

Details
Package:
Type:
Version:
Date:
License:
LazyLoad:

MF-package
Package
4.3.5
XXXX-XX-XX
MIT
yes

Author(s)
David Siev 
Examples
#--------------------------------------------# Checking MF package
#--------------------------------------------example(MFr)
#--------------------------------------------# End examples
#--------------------------------------------invisible()

calflung

calflung

3

calflung dataset

Description
Post-mortem examination of the lungs of groups of calves.
Format
a data frame with 50 observations of the following 2 variables, no NAs
group Treatment group. One of con = control or vac = vaccinate
lesion Fraction of lungs with gross lesions.

HLBoot

Bootstrap CI for MF, HL, and Qdif

Description
Estimates bootstrap confidence intervals for MF, HL, and Qdif.
Usage
HLBoot(formula, data, compare = c("con", "vac"), b = 100, B = 100,
alpha = 0.05, hpd = TRUE, bca = FALSE, return.boot = FALSE,
trace.it = FALSE, seed = sample(1:1e+05, 1))
Arguments
formula

Formula of the form y ~ x + cluster(w), where y is a continuous response, x
is a factor with two levels of treatment, and w is a factor indicating the clusters.

data

Data frame

compare

Text vector stating the factor levels - compare[1] is the control or reference
group to which compare[2] is compared

b

Number of bootstrap samples to take with each cycle

B

Number of cycles, giving the total number of samples = B * b

alpha

Complement of the confidence level

hpd

Boolean whether to estimate highest density intervals for MF and HL.

bca

Boolean whether to estimate BCa intervals for MF.

return.boot

Boolean whether to save the bootstrap samples of the statistics.

trace.it

Boolean whether to display verbose tracking of the cycles.

seed

to initialize random number generator for reproducibility. Passed to set.seed.

4

HLBoot

Details
Estimates bootstrap confidence intervals for the mitigated fraction (MF), Hodge-Lehmann estimator
(HL), and the difference of medians and quartiles (Qdif). Equal tailed intervals are provided for
all three, highest density intervals are optionally provided for MF and HL, and BCa intervals are
optionally provided for MF. The Hodges-Lehmann estimator is the median difference; it assumes
that the two distributions have the same shape and differ by a constant shift. Assumes data is single
pool (no nesting).
Value
a mfhlboot-class data object
Author(s)
David Siev 
References
Hodges JL, Lehmann EL, (1963). Estimates of location based on rank tests. Annals of Mathematical Statistics. 34:598–611.
Siev D, (2005). An estimator of intervention effect on disease severity. Journal of Modern Applied Statistical Methods. 4:500–508.
Efron B, Tibshirani RJ. An Introduction to the Bootstrap. Chapman and Hall, New York, 1993.
See Also
mfhlboot-class
Examples
HLBoot(lesion~group, calflung, seed = 12345)
#
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#

Bootstrapping
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
10000 bootstrap samples
95% confidence intervals
Comparing vac to con
Mitigated Fraction
observed median lower upper
Equal Tailed
0.44 0.4496 0.152 0.7088
Highest Density
0.44 0.4496 0.152 0.7088
Hodges-Lehmann
observed
median
lower
upper
Equal Tailed
-0.07335 -0.07615 -0.17220 -0.01565000

mf-class
#
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5

Highest Density -0.07335 -0.07615 -0.15635 -0.00850065
Quartile Differences (quartiles of vac - quartiles of con)
observed
median
lower
upper
Q25 -0.041500 -0.041500 -0.10340 -0.000905
Q50 -0.112525 -0.111175 -0.28115 0.019350
Q75 -0.168000 -0.170425 -0.38890 0.005300
Quartiles of con
observed
median
lower
upper
Q25 0.054000 0.054000 0.021005 0.11275
Q50 0.139275 0.139275 0.061400 0.31000
Q75 0.315000 0.315000 0.173000 0.44625
Quartiles of vac
observed median
lower
upper
Q25 0.01250 0.01250 0.00125 0.026000
Q50 0.02675 0.02675 0.01665 0.144575
Q75 0.14700 0.14700 0.02810 0.219250

mf-class

Class mf

Description
Parent class for package MF data objects.
Usage
mf$new(nboot, alpha, seed, compare, rng)
Fields
• nboot: numeric value specifying number of samples
• alpha: numeric value specifying complement of confidence interval
• seed: vector of integers specifying seed for pseudo-random number generator used
• compare: vector of character strings naming groups compared
• rng: character string naming type of random number generator
Author(s)
Marie Vendettuoli 
See Also
Other mf: mfboot-class, mfbootcluster-class, mfhlboot-class

6

MFBoot

MFBoot

Bootstrap MF CI

Description
Estimates bootstrap confidence intervals for the mitigated fraction.
Usage
MFBoot(formula, data, compare = c("con", "vac"), b = 100, B = 100,
alpha = 0.05, hpd = TRUE, bca = FALSE, return.boot = FALSE, trace.it = FALSE,
seed = sample(1:100000, 1))
Arguments
formula

Formula of the form y ~ x, where y is a continuous response and x is a factor
with two levels.

data

Data frame

compare

Text vector stating the factor levels - compare[1] is the control or reference
group to which compare[2] is compared

b

Number of bootstrap samples to take with each cycle

B

Number of cycles, giving the total number of samples = B * b

alpha

Complement of the confidence level

hpd

Estimate highest density intervals?

bca

Estimate BCa intervals?

return.boot

Save the bootstrap sample of the MF statistic?

trace.it

Verbose tracking of the cycles?

seed

to initialize random number generator for reproducibility. Passed to set.seed.

Details
Resamples the data and produces bootstrap confidence intervals. Equal tailed intervals are estimated
by the percentile method. Highest density intervals are estimated by selecting the shortest of all
possible intervals. For BCa intervals, see Efron and Tibshirani section 14.3.
Value
a mfboot-class data object
Author(s)
David Siev 
References
Siev D. (2005). An estimator of intervention effect on disease severity. Journal of Modern Applied
Statistical Methods. 4:500–508
Efron B, Tibshirani RJ. An Introduction to the Bootstrap. Chapman and Hall, New York, 1993.

mfboot-class

7

See Also
mfboot-class
Examples
MFBoot(lesion~group, calflung, seed = 12345)
#
#
#
#
#
#
#
#

10000 bootstrap samples
95% confidence interval
Seed = 12345
Comparing vac to con
observed median lower upper
Equal Tailed
0.44 0.4496 0.152 0.7088
Highest Density
0.44 0.4496 0.152 0.7088

mfboot-class

Class mfboot

Description
class for data objects produced by MFBoot, contains class mf with the two additional fields stat and
stuff.
Usage
mfboot$new(nboot, alpha, seed, compare, rng, sample, stat, stuff)
Fields
•
•
•
•
•
•
•

nboot: numeric value specifying number of samples
alpha: numeric value specifying complement of confidence interval
seed: vector of integers specifying seed for pseudo-random number generator used
compare: vector of character strings naming groups compared
rng: character string naming type of random number generator
sample: what is this?
stat: matrix of estimates

Contains
mf-class
Author(s)
Marie Vendettuoli 
See Also
MFBoot
Other mf: mf-class, mfbootcluster-class, mfhlboot-class

8

mfbootcluster-class

mfbootcluster-class

Class mfbootcluster

Description
Class mfbootcluster is created from output of function MFClusBoot
Usage
mfbootcluster$new(nboot, alpha, seed, compare, rng, stat, what, excludedClusters,
call, sample)
Fields
• nboot: numeric value specifying number of samples
• alpha: numeric value specifying complement of confidence interval
• seed: vector of integers specifying seed for pseudo-random number generator used
• compare: vector of character strings naming groups compared
• rng: character string naming type of random number generator
• stat: matrix matrix with columns observed, median, lower, upper for estimates
• what: character vector naming what was resampled: clusters, units, both
• excludedClusters: character vector naming clusters excluded because of missing treatment(s)
• call: the call to MFClusBoot
• sample: what is this?
• All: Field "All" from MFClus call.
Contains
mf-class
Author(s)
Marie Vendettuoli 
See Also
MFClusBoot
Other mf: mf-class, mfboot-class, mfhlboot-class

MFClus

MFClus

9

Clustered mitigated fraction

Description
Estimates mitigated fraction from clustered or stratified data.
Usage
MFClus(formula, data, compare = c("con", "vac"), trace.it = FALSE)
Arguments
formula

Formula of the form y ~ x + cluster(w), where y is a continuous response, x
is a factor with two levels of treatment, and w is a factor indicating the clusters.

data

Data frame. See Note for handling of input data with more than two levels.

compare

Text vector stating the factor levels - compare[1] is the control or reference
group to which compare[2] is compared

trace.it

Verbose tracking of the cycles? Default FALSE.

Details
Averages the U statistic over the clusters and computes MF from it. Clusters are excluded if they
do not include both treatments.
Value
a mfcluster-class data object
Note
If input data contains more than two levels of treatment, rows associated with unused treatment
levels will be removed.
Factor levels for treatments not present in the input data will be ignored.
Clusters with missing treatments will be excluded. See mfbootcluster-class or use trace.it to
identify excluded clusters.
Author(s)
David Siev 
References
Siev D. (2005). An estimator of intervention effect on disease severity. Journal of Modern Applied
Statistical Methods. 4:500–508
See Also
mfcluster-class

10

MFClusBoot

Examples
## Not run:
MFClus(lesion ~ group + cluster(litter), piglung)
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Comparing vac to con
MF = 0.3533835
By Cluster
w u
r
U 25 10 0.4000000
K 12 2 0.2500000
Z 16 10 0.8333333
D 3 2 1.0000000
N 1 0 0.0000000
T 8 5 0.8333333
P 4 1 0.5000000
L 3 2 0.6666667
G 15 9 0.7500000
J 15 9 1.0000000
W 6 3 0.7500000
A 9 3 0.3333333
X 12 6 1.0000000
F 13 7 0.7777778
S 21 11 0.9166667
H 14 8 0.8888889
Y 2 1 1.0000000
E 2 1 1.0000000

n1
5
4
3
1
1
2
2
1
3
3
2
3
3
3
4
3
1
1

n2
5
2
4
2
3
3
1
3
4
3
2
3
2
3
3
3
1
1

mf
-0.2000000
-0.5000000
0.6666667
1.0000000
-1.0000000
0.6666667
0.0000000
0.3333333
0.5000000
1.0000000
0.5000000
-0.3333333
1.0000000
0.5555556
0.8333333
0.7777778
1.0000000
1.0000000

All

w u
r n1 n2
mf
All 181 90 0.6766917 50 52 0.3533835
Excluded Clusters
[1] M, Q, R, B, O, V, I, C

## End(Not run)

MFClusBoot

Bootstrap MF CI from clustered data

Description
Estimates bootstrap confidence intervals for the mitigated fraction from clustered or stratified data.
Usage
MFClusBoot(formula, data, compare = c("con", "vac"), boot.cluster = TRUE,
boot.unit = TRUE, b = 100, B = 100, alpha = 0.05, hpd = TRUE,
return.boot = FALSE, trace.it = FALSE, seed = sample(1:1e+05, 1))

MFClusBoot

11

Arguments
formula

Formula of the form y ~ x + cluster(w), where y is a continuous response, x
is a factor with two levels of treatment, and w is a factor indicating the clusters.

data

Data frame. See Note for handling of input data with more than two levels.

compare

Text vector stating the factor levels - compare[1] is the control or reference
group to which compare[2] is compared

boot.cluster

Boolean whether to resample the clusters.

boot.unit

Boolean whether to resample the units within cluster.

b

Number of bootstrap samples to take with each cycle

B

Number of cycles, giving the total number of samples = B * b

alpha

Complement of the confidence level

hpd

Boolean whether to estimate highest density intervals.

return.boot

Boolean whether to save the bootstrap sample of the MF statistic.

trace.it

Boolean whether to display verbose tracking of the cycles.

seed

to initialize random number generator for reproducibility. Passed to set.seed.

Details
Resamples the data and produces bootstrap confidence intervals. Equal tailed intervals are estimated
by the percentile method. Highest density intervals are estimated by selecting the shortest of all
possible intervals.
Value
a mfbootcluster-class data object
Note
If input data contains more than two levels of treatment, rows associated with unused treatment
levels will be removed.
Factor levels for treatments not present in the input data will be ignored.
Clusters with missing treatments will be excluded. See mfbootcluster-class or use trace.it to
identify excluded clusters.
Author(s)
David Siev 
References
Siev D. (2005). An estimator of intervention effect on disease severity. Journal of Modern Applied
Statistical Methods. 4:500–508
Efron B, Tibshirani RJ. An Introduction to the Bootstrap. Chapman and Hall, New York, 1993.

12

MFClusBootHier

Examples
## Not run:
MFClusBoot(lesion ~ group + cluster(litter), piglung, seed = 12345)
Bootstrapping clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bootstrapping units. . . . . . . . . . . . . . . . . .
10000 bootstrap samples of clusters and units in treatment in cluster
Comparing vac to con
95% confidence interval
observed
median
lower
upper
Equal Tailed
0.3533835 0.3648649 -0.01409471 0.7109966
Highest Density 0.3533835 0.3648649 0.00000000 0.7236842
Excluded Clusters
M, Q, R, B, O, V, I, C
## End(Not run)

MFClusBootHier

MFClusBootHier

Description
Combines MFhBoot and MFnestBoot into a single function.
Usage
MFClusBootHier(formula, data, compare = c("con", "vac"), nboot = 10000,
boot.unit = TRUE, boot.cluster = TRUE, which.factor = "All",
alpha = 0.05)
Arguments
formula

data
compare
nboot
boot.unit
boot.cluster
which.factor
alpha

formula Formula of the form y ~ x + a/b/c, where y is a continuous response,
x is a factor with two levels of treatment, and a/b/c are variables corresponding
to the clusters. It is expected that levels of "c" are nested within levels of "b".
Nesting is assumed to be in order, left to right, highest to lowest.
a data.frame or tibble with the variables specified in formula. Additional variables will be ignored.
Text vector stating the factor levels - compare[1] is the control or reference group
to which compare[2] is compared.
number of bootstrapping events
Boolean whether to sample observations from within those of the same core.
Boolean whether to sample which cores are present. If TRUE, some trees have
all the cores while others only have a subset.
Which variables to include in the mitigated fraction summation. Default is
âC™AllâC™, to sum over entire tree.
Passed to emp.hpd to calculate high tailed upper and high tailed lower of mitigated fraction.

MFClusHier

13

Value
A list with the following elements:

• MFhBoot as output from MFhBoot.
• MFnestBoot as output from MFnestBoot.
Note
Core variable is the variable corresponding to the lowest nodes of the hierarchical tree. Nest variables are those above the core. All refers to a summary of the entire tree.
See Also
MFhBoot, MFnestBoot.
Examples
a <- data.frame(
room = paste('Room',rep(c('W','Z'),each=24)),
pen = paste('Pen',rep(LETTERS[1:6],each=8)),
litter = paste('Litter',rep(11:22,each=4)),
tx = rep(rep(c('vac','con'),each=2),12),
stringsAsFactors = FALSE
)
set.seed(76153)
a$lung[a$tx=='vac'] <- rnorm(24,5,1.3)
a$lung[a$tx=='con'] <- rnorm(24,7,1.3)
set.seed(12345)
thismf1 <- MFClusBootHier(lung ~ tx + room/pen/litter, a, nboot = 10000,
boot.cluster = TRUE, boot.unit = TRUE)
thismfhboot <- thismf1$MFhBoot
thismfhboot$bootmfh
thismf1$MFnestBoot

MFClusHier

MFClusHier

Description
Combines MFh and MFnest into a single function.
Usage
MFClusHier(formula, data, compare = c("con", "vac"), which.factor = "All")

14

MFClusHier

Arguments
formula

Formula of the form y ~ x + a/b/c, where y is a continuous response, x is a
factor with two levels of treatment, and a/b/c are variables corresponding to the
clusters. It is expected that levels of "c" are nested within levels of "b". Nesting
is assumed to be in order, left to right, highest to lowest.

data

a data.frame or tibble with the variables specified in formula. Additional variables will be ignored.

compare

Text vector stating the factor levels - compare[1] is the control or reference group
to which compare[2] is compared.

which.factor

one or more variable(s) of interest. This can be any of the core or nest variables
from the data set. If none or NULL is specified, MF will be calculated for the
whole tree.

Value
A list with the following elements:

• MFh as output from MFh.
• MFnest as output from MFnest.
Note
Core variable is the variable corresponding to the lowest nodes of the hierarchical tree. Nest variables are those above the core. All refers to a summary of the entire tree.
See Also
MFh, MFnest
Examples
a <- data.frame(
room = paste('Room',rep(c('W','Z'),each=24)),
pen = paste('Pen',rep(LETTERS[1:6],each=8)),
litter = paste('Litter',rep(11:22,each=4)),
tx = rep(rep(c('vac','con'),each=2),12),
stringsAsFactors = FALSE
)
set.seed(76153)
a$lung[a$tx=='vac'] <- rnorm(24,5,1.3)
a$lung[a$tx=='con'] <- rnorm(24,7,1.3)
thismf <- MFClusHier(lung ~ tx + room/pen/litter,a)
thismf$MFnest
aCore <- thismf$MFh
aCore
aCore$data
aCore$formula
aCore$compare

mfcluster-class

mfcluster-class

15

Class mfcluster

Description
Class mfcluster is created from output of function MFClus
Usage
mfcluster$new(All, bycluster, excludedClusters, call, compare)
Fields
• All: vector with elements:
–
–
–
–
–
–

w Wilcoxon statistic
u Mann-Whitney statistic
r mean ridit
n1 size of group 1
n2 size of group 2
mf mitigated fraction

• byCluster: As for All, by clusters
• excludedClusters: character vector naming clusters excluded because of missing treatment
• call: the call to MFClus
• compare: character vector naming groups compared
Author(s)
Marie Vendettuoli 
See Also
MFClus

mfcomponents-class

Class mfcomponents

Description
Class mfcomponents is created from output of function MFSubj
Usage
mfcomponents$new(mf, x, y, subj, compare)

16

MFh

Fields
• mf: numeric estimator for mitigated fraction
• x: numeric vector containing responses of group 1
• y: numeric vector containing responses of group 2
• subj: matrix where mf.j are the subject components
• compare: character vector naming groups being compared
Author(s)
Marie Vendettuoli 
See Also
MFSubj

MFh

Identify ranks for use when evaluating MF for nested hierarchy.

Usage
MFh(formula, data, compare = c("con", "vac"))
Arguments
formula

Formula of the form y ~ x + a/b/c, where y is a continuous response, x is a
factor with two levels of treatment, and a/b/c are variables corresponding to the
clusters. It is expected that levels of "c" are nested within levels of "b". Nesting
is assumed to be in order, left to right, highest to lowest.

data

a data.frame or tibble with the variables specified in formula. Additional variables will be ignored.

compare

Text vector stating the factor levels - compare[1] is the control or reference group
to which compare[2] is compared.

Value
A mfhierdata object, which is a list of three items.
coreTbl A tibble with one row for each unique core level showing values for:
• con_n & vac_n - counts of observations for each treatment level in the core level.
• con_medResp & vac_medResp - median of the y continuous response for each treatment
level.
• n1n2 - product of the counts, con_n * vac_n.
• w - Wilcoxon statistic
• u - Mann-Whitney statistic
data A tibble of the restructured input data used for calculations.
compare The compare variables as input by user.
formula The formula as input by user.

MFhBoot

17

Note
Core variable is the variable corresponding to the lowest nodes of the hierarchial tree. Nest variables
are those above the core.
See Also
MFnest for calculation of MF for nest, core and all variables. mfhierdata for returned object.MFClusHier
for a wrapper.
Examples
a <- data.frame(
room = paste('Room',rep(c('W','Z'),each=24)),
pen = paste('Pen',rep(LETTERS[1:6],each=8)),
litter = paste('Litter',rep(11:22,each=4)),
tx = rep(rep(c('vac','con'),each=2),12),
stringsAsFactors = FALSE
)
set.seed(76153)
a$lung[a$tx=='vac'] <- rnorm(24,5,1.3)
a$lung[a$tx=='con'] <- rnorm(24,7,1.3)
aCore <- MFh(lung ~ tx + room/pen/litter,a)
aCore
# A tibble: 12 x 10
#
room
pen
litter
con_medResp con_n
w vac_medResp vac_n n1n2
u
#
  
  
   
#
1 Room W Pen A Litter 11
8.24
2
7
5.13
2
4
4
#
2 Room W Pen A Litter 12
4.91
2
5
3.81
2
4
2
#
3 Room W Pen B Litter 13
8.10
2
7
5.23
2
4
4
#
4 Room W Pen B Litter 14
8.11
2
7
5.59
2
4
4
#
5 Room W Pen C Litter 15
8.09
2
7
5.26
2
4
4
#
6 Room W Pen C Litter 16
6.77
2
7
4.50
2
4
4
#
7 Room Z Pen D Litter 17
5.58
2
7
4.26
2
4
4
#
8 Room Z Pen D Litter 18
7.44
2
6
6.33
2
4
3
#
9 Room Z Pen E Litter 19
7.98
2
7
4.58
2
4
4
# 10 Room Z Pen E Litter 20
6.78
2
7
4.86
2
4
4
# 11 Room Z Pen F Litter 21
6.82
2
7
5.36
2
4
4
# 12 Room Z Pen F Litter 22
7.27
2
7
5.13
2
4
4

MFhBoot

MFhBoot

Description
Calculate rank tables for MF using bootstrapping.
Usage
MFhBoot(formula, data, compare = c("con", "vac"), nboot = 10000,
boot.unit = TRUE, boot.cluster = TRUE, seed = sample(1:1e+05, 1))

18

MFhBoot

Arguments
formula

Formula of the form y ~ x + a/b/c, where y is a continuous response, x is a
factor with two levels of treatment, and a/b/c are variables corresponding to the
clusters. It is expected that levels of "c" are nested within levels of "b". Nesting
is assumed to be in order, left to right, highest to lowest.

data

a data.frame or tibble with the variables specified in formula. Additional variables will be ignored.

compare

Text vector stating the factor levels - compare[1] is the control or reference group
to which compare[2] is compared.

nboot

number of bootstrapping events

boot.unit

Boolean whether to sample observations from within those of the same core.

boot.cluster

Boolean whether to sample which cores are present. If TRUE, some trees have
all the cores while others only have a subset.

seed

to initialize random number generator for reproducibility. Passed to set.seed.

Value
A list with the following elements:

bootmfh Rank table for the bootstrapped values as output from MFh. Includes a new bootID variable to distinguish each bootstrapped incidence.
clusters Table of unique nodes with an ID.
compare Compare vector as specified by user.
mfh MFh run on original data input.
See Also
MFClusBootHier, MFnestBoot
Examples
set.seed(76153)
a <- data_frame(room = paste('Room', rep(c('W','Z'), each = 24)),
pen = paste('Pen', rep(LETTERS[1:6], each = 8)),
litter = paste('Litter', rep(11:22, each = 4)),
tx = rep(rep(c('vac', 'con'), each = 2), 12)) %>%
mutate(lung = ifelse(tx == 'vac', rnorm(24, 5, 1.3), rnorm(24, 7, 1.3)))
a
formula <- lung ~ tx + room/pen/litter
nboot <- 10000
boot.cluster <- TRUE
boot.unit <- TRUE
which.factors <- c('All', 'room', 'pen', 'litter')
system.time(test1 <- MFhBoot(formula, a,
nboot = 10000,
boot.cluster = TRUE, boot.unit = TRUE, seed = 12345))
test1$bootmfh

mfhierdata-class

mfhierdata-class

19

Class mfhierdata

Description
Class mfhierdata is created from output of function MFh
Usage
mfhierdata$new(coreTbl, data)
Fields
• coreTbl: data.frame with one row for each unique core level showing values for nx, ny, N,
w, u, and median observed response.
• data: data.frame is the restructured input data used for calculations in MFh and MFnest.
• compare: character vector naming groups being compared.
• formula: formula that was called by user.
Author(s)
Marie Vendettuoli 
See Also
MFh

mfhlboot-class

Class mfhlboot

Description
class for data objects produced by HLBoot, contains class mf with additional fields MFstat, HLstat,
QDIFstat, QXstat, QYstat
Usage
mfhlboot$new(nboot, alpha, seed, compare, rng, sample, MFstat, HLstat,
QDIFstat, QXstat, QYstat)
Fields
• nboot: Numeric value specifying number of samples.
• alpha: Numeric value specifying complement of confidence interval.
• seed: Vector of integers specifying seed for pseudo-random number generator used.
• compare: Vector of character strings naming groups compared.
• rng: Character string naming type of random number generator.
• sample: The bootstrapped values.

20

MFmp
• MFstatMatrix with columns observed, median, lower, upper for Equal Tailed and Highest
Density estimates of mitigated fraction (MF).
• HLstatMatrix with columns observed, median, lower, upper for Equal Tailed and Highest
Density estimates of Hodge-Lehmann estimator (HL).
• QDIFstatMatrix with columns observed, median, lower, upper for estimates of Quartile Differences.
• QXstatMatrix with columns observed, median, lower, upper for quartiles of treatments, equal
tailed.
• QYstatMatrix with columns observed, median, lower, upper for quartiles of response, equal
tailed.

Contains
mf-class
Author(s)
Marie Vendettuoli 
See Also
HLBoot
Other mf: mf-class, mfboot-class, mfbootcluster-class

MFmp

Mitigated fraction from matched pairs

Description
Estimates mitigated fraction from matched pairs.
Usage
MFmp(formula=NULL, data=NULL, compare = c("con", "vac"), x=NULL, alpha=0.05, df=NULL, tdist=T)
Arguments
formula

Formula of the form y ~ x + cluster(w), where y is a continuous response, x
is a factor with two levels of treatment, and w is a factor indicating the clusters.

data

Data frame

compare

Text vector stating the factor levels - compare[1] is the control or reference
group to which compare[2] is compared

x

Trinomial vector {ΣI(x < y), ΣI(x = y), ΣI(x > y)}

alpha

Complement of the confidence level.

df

Degrees of freedom. Default N-2

tdist

Use quantiles of t or Gaussian distribution for confidence interval? Default t
distribution.

mfmp-class

21

Details
Estimates MF from matched pairs by the difference of multinomial fractions (ΣI(x < y)−ΣI(x >
y))/N . The trinomial vector is {ΣI(x < y), ΣI(x = y), ΣI(x > y)}
Value
a mfmp-class data object
Note
upper confidence interval is truncated to 1; lower confidence interval is truncated to -1. Point
estimate of 1.0 indicates complete separation.
Author(s)
David Siev 
References
Siev D. (2005). An estimator of intervention effect on disease severity. Journal of Modern Applied
Statistical Methods. 4:500–508
See Also
mfmp-class
Examples
MFmp(les ~ tx + cluster(cage), mlesions, compare = c('con', 'vac'))
MFmp(x = c(12, 12, 2))

mfmp-class

Class mfmp

Description
Class mfmp is created from output of function MFmp
Usage
mfmp$new(ci, x, what, alpha, tdist, df)
Fields
• ci: numeric vector of point and interval estimates
• x: numeric vector of length three holding data
• what: text string describing interval type
• alpha: numeric value specifying complement of confidence interval
• tdist: Logical indicating if t distribution(TRUE) or gaussian (FALSE)
• df: numeric value indicating degrees freedom

22

MFnest

Author(s)
Marie Vendettuoli 
See Also
MFmp

MFnest

Summations to calculate the MF for nested data from a rank table.

Usage
MFnest(Y, which.factor = "All")
Arguments
Y

rank table (tibble or data.frame), structured as $coreTbl output from MFh or
output list from MFh.

which.factor

one or more variable(s) of interest. This can be any of the core or nest variables
from the data set. If none or All is specified, MF will be calculated for the
whole tree.

Value
A tibble with each unique level of a variable as a row. Other values include:
MF Mitigated fraction for the particular level of the variable in this row.
N1N2 Sum of the n1n2 variable in $coreTbl field of mfhierdata object output by MFh for this
particular variable-level combination.
U Sum of u variable in $coreTbl field of mfhierdata object output by MFh for this particular
variable-level combination.
_N Sum of the _n variable in $coreTbl field of mfhierdata object output by MFh for this particular
variable-level combination.
_medResp Median of responses for each comparison group for this particular variable-level combination.
Note
Core variable is the variable corresponding to the lowest nodes of the hierarchial tree. Nest variables
are those above the core. All refers to a summary of the entire tree.
See Also
MFh

MFnest
Examples
a <- data.frame(
room = paste('Room',rep(c('W','Z'),each=24)),
pen = paste('Pen',rep(LETTERS[1:6],each=8)),
litter = paste('Litter',rep(11:22,each=4)),
tx = rep(rep(c('vac','con'),each=2),12),
stringsAsFactors = FALSE
)
set.seed(76153)
a$lung[a$tx=='vac'] <- rnorm(24,5,1.3)
a$lung[a$tx=='con'] <- rnorm(24,7,1.3)
aCore <- MFh(lung ~ tx + room/pen/litter,a)
MFnest(aCore)
# # A tibble: 1 x 9
#
variable level
MF N1N2
U con_N vac_N con_medResp vac_medResp
#

     


# 1 All
All
0.875
48
45
24
24
7.24
4.91
MFnest(aCore$coreTbl)
# Skipping median summary, no response data provided.
# # A tibble: 1 x 7
#
variable level
MF N1N2
U con_N vac_N
#

     
# 1 All
All
0.875
48
45
24
24
MFnest(aCore, 'room')
# # A tibble: 2 x 9
#
variable level
MF N1N2
U con_N vac_N con_medResp vac_medResp
#

     


# 1 room
Room W 0.833
24
22
12
12
7.79
4.85
# 2 room
Room Z 0.917
24
23
12
12
6.71
4.98
MFnest(aCore, 'pen')
# Complete separation observed for variable(s): pen
# # A tibble: 6 x 9
#
variable level
MF N1N2
U con_N vac_N con_medResp vac_medResp
#

     


# 1 pen
Pen A 0.5
8
6
4
4
6.79
4.24
# 2 pen
Pen B 1
8
8
4
4
8.11
5.59
# 3 pen
Pen C 1
8
8
4
4
7.69
4.85
# 4 pen
Pen D 0.75
8
7
4
4
6.10
4.98
# 5 pen
Pen E 1
8
8
4
4
6.86
4.86
# 6 pen
Pen F 1
8
8
4
4
6.88
5.13
MFnest(aCore, c('All', 'litter'))
# Complete separation observed for variable(s): litter
# # A tibble: 13 x 9
#
variable level
MF N1N2
U con_N vac_N con_medResp vac_medResp
#


    


# 1 All
All
0.875
48
45
24
24
7.24
4.91
# 2 litter
Litter 11 1
4
4
2
2
8.24
5.13
# 3 litter
Litter 12 0
4
2
2
2
4.91
3.81
# 4 litter
Litter 13 1
4
4
2
2
8.10
5.23
# 5 litter
Litter 14 1
4
4
2
2
8.11
5.59
# 6 litter
Litter 15 1
4
4
2
2
8.09
5.26

23

24

MFnestBoot
#
#
#
#
#
#
#

7
8
9
10
11
12
13

litter
litter
litter
litter
litter
litter
litter

Litter
Litter
Litter
Litter
Litter
Litter
Litter

16
17
18
19
20
21
22

1
1
0.5
1
1
1
1

4
4
4
4
4
4
4

4
4
3
4
4
4
4

2
2
2
2
2
2
2

2
2
2
2
2
2
2

6.77
5.58
7.44
7.98
6.78
6.82
7.27

4.50
4.26
6.33
4.58
4.86
5.36
5.13

MFnest(aCore, 'litter')
# Complete separation observed for variable(s): litter
# # A tibble: 12 x 9
#
variable level
MF N1N2
U con_N vac_N con_medResp vac_medResp
#


    


# 1 litter
Litter 11
1
4
4
2
2
8.24
5.13
# 2 litter
Litter 12
0
4
2
2
2
4.91
3.81
# 3 litter
Litter 13
1
4
4
2
2
8.10
5.23
# 4 litter
Litter 14
1
4
4
2
2
8.11
5.59
# 5 litter
Litter 15
1
4
4
2
2
8.09
5.26
# 6 litter
Litter 16
1
4
4
2
2
6.77
4.50
# 7 litter
Litter 17
1
4
4
2
2
5.58
4.26
# 8 litter
Litter 18
0.5
4
3
2
2
7.44
6.33
# 9 litter
Litter 19
1
4
4
2
2
7.98
4.58
# 10 litter
Litter 20
1
4
4
2
2
6.78
4.86
# 11 litter
Litter 21
1
4
4
2
2
6.82
5.36
# 12 litter
Litter 22
1
4
4
2
2
7.27
5.13
MFnest(aCore,
# # A tibble:
#
variable
#

# 1 room
# 2 room
# 3 pen
# 4 pen
# 5 pen
# 6 pen
# 7 pen
# 8 pen
# 9 litter
# 10 litter
# 11 litter
# 12 litter
# 13 litter
# 14 litter
# 15 litter
# 16 litter
# 17 litter
# 18 litter
# 19 litter
# 20 litter

MFnestBoot

c('room',
20 x 9
level

Room W
Room Z
Pen A
Pen B
Pen C
Pen D
Pen E
Pen F
Litter 11
Litter 12
Litter 13
Litter 14
Litter 15
Litter 16
Litter 17
Litter 18
Litter 19
Litter 20
Litter 21
Litter 22

'pen', 'litter'))
MF N1N2
U con_N vac_N con_medResp vac_medResp
    


0.833
24
22
12
12
7.79
4.85
0.917
24
23
12
12
6.71
4.98
0.5
8
6
4
4
6.79
4.24
1
8
8
4
4
8.11
5.59
1
8
8
4
4
7.69
4.85
0.75
8
7
4
4
6.10
4.98
1
8
8
4
4
6.86
4.86
1
8
8
4
4
6.88
5.13
1
4
4
2
2
8.24
5.13
0
4
2
2
2
4.91
3.81
1
4
4
2
2
8.10
5.23
1
4
4
2
2
8.11
5.59
1
4
4
2
2
8.09
5.26
1
4
4
2
2
6.77
4.50
1
4
4
2
2
5.58
4.26
0.5
4
3
2
2
7.44
6.33
1
4
4
2
2
7.98
4.58
1
4
4
2
2
6.78
4.86
1
4
4
2
2
6.82
5.36
1
4
4
2
2
7.27
5.13

MFnestBoot

MFnestBoot

25

Description
MFnest using bootstrapping
Usage
MFnestBoot(x, which.factor = "All", alpha = 0.05)
Arguments
x

output from MFhBoot

which.factor

Which variables to include in the mitigated fraction summation. Default is
âC™AllâC™, to sum over entire tree.

alpha

Passed to emp.hpd to calculate high tailed upper and high tailed lower of mitigated fraction

Value
A list with the following elements:

mfnest_details The MF and summary statistics as calculated for each bootstrap event. Variables
as in MFnest output.
mfnest_summary Statistical summary of bootstrapped MF with each unique level of a core or nest
variable passed to which.factor as a row. Other variables include:
•
•
•
•
•
•

median Median of MFs from all of the bootstrap events.
etlower Lower value of equal tailed range.
etupper Upper value of equal tailed range.
htlower Lower value of the high tailed range.
htupper Upper value of the high tailed range.
mf.obs MF calculated from data using MFh.

following variables for each
a table with one row for each level of the variable specified in which.factor and including the
following variables:

median median mitigated fraction across all bootstrapping instances.
etlower equal tailed lower of the mitigated fraction across all bootstrapping instances.
etupper equal tailed upper of the mitigated fraction across all bootstrapping instances.
htlower high tailed lower of the mitigated fraction across all bootstrapping instances.
htupper high tailed upper of the mitigated fraction across all bootstrapping instances.
mf.obs mitigated fraction using MFnest(x$mfh, which.factor), no bootstrapping.
See Also
MFClusBootHier, MFhBoot

26

MFr

Examples
set.seed(76153)
a <- data_frame(room = paste('Room', rep(c('W','Z'), each = 24)),
pen = paste('Pen', rep(LETTERS[1:6], each = 8)),
litter = paste('Litter', rep(11:22, each = 4)),
tx = rep(rep(c('vac', 'con'), each = 2), 12)) %>%
mutate(lung = ifelse(tx == 'vac', rnorm(24, 5, 1.3), rnorm(24, 7, 1.3)))
a
formula <- lung ~ tx + room/pen/litter
nboot <- 10000
boot.cluster <- TRUE
boot.unit <- TRUE
which.factors <- c('All', 'room', 'pen', 'litter')
#################
test1 <- MFhBoot(formula, a,
nboot = 10000,
boot.cluster = TRUE, boot.unit = TRUE, seed = 12345)
MFnestBoot(test1, c('All', 'litter'))
## Not run:
system.time(test2
test2
system.time(test3
test3
system.time(test4
test4
system.time(test5
test5
system.time(test6
test6

<- MFnestBoot(test1, which.factors))
<- MFnestBoot(test1, which.factors[1]))
<- MFnestBoot(test1, which.factors[2]))
<- MFnestBoot(test1, which.factors[2:3]))
<- MFnestBoot(test1, which.factors[2:4]))

## End(Not run)

MFr

Mitigated fraction

Description
Mitigated fraction comparing treatment to control.
Usage
MFr(formula, data, compare = c("con", "vac"))
Arguments
formula
data
compare

Formula of the form y ~ x, where y is a continuous response and x is a factor
with two levels
Data frame
Text vector stating the factor levels – compare[1] is the control or reference
group to which compare[2] is compared

MFSubj

27

Details
The mitigated fraction is an estimator that quantifies an intervention’s effect on reducing the severity
of a condition. Since its units are on the probability scale, it is often a good idea to accompany it
with an estimator on the original scale of measurement.
Value
The estimated mitigated fraction.
Author(s)
David Siev
References
Siev D, 2005. An estimator of intervention effect on disease severity. Journal of Modern Applied
Statistical Methods. 4:500-508
Examples
MFr(lesion~group,calflung)
# [1] 0.44

MFSubj

Subject components of mitigated fraction

Description
Estimates the subject components of the mitigated fraction.
Usage
MFSubj(formula, data, compare = c("con", "vac"))
Arguments
formula

Formula of the form y ~ x, where y is a continuous response and x is a factor
with two levels

data

Data frame

compare

Text vector stating the factor levels - compare[1] is the control or reference
group to which compare[2] is compared

Details
The mitigated fraction is an estimator that quantifies an intervention’s effect on reducing the severity of a condition. Since its units are on the probability scale, it is often a good idea to accompany
it with an estimator on the original scale of measurement.
The subject components are the individual contributions of the treated subjects to MF, which is
the average of the subject components.

28

mlesions

Value
a mfcomponents-class data object
Author(s)
David Siev 
References
Siev D. (2005). An estimator of intervention effect on disease severity. Journal of Modern Applied
Statistical Methods. 4:500–508
Examples
x <- MFSubj(lesion ~ group, calflung)
x
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#

MF = 0.44 comparing vac to con
MF Subject Components
mf.j freq
min.y
max.y
1.00
6 0.000030 0.00970
0.84
1 0.012500 0.01250
0.76
3 0.016650 0.02030
0.68
6 0.023250 0.03190
0.04
1 0.132100 0.13210
-0.04
3 0.144575 0.16325
-0.20
2 0.210000 0.21925
-0.36
1 0.292000 0.29200
-0.52
1 0.356500 0.35650
-0.84
1 0.461500 0.46150

mean(x$subj[,'mf.j'])
# [1] 0.44

mlesions

mlesions dataset

Description
Post-mortem examination of the lungs of dogs housed in cages by pairs.
Format
A data frame with 52 observations of the following 3 variables, no NAs.
cage Cage ID. 1 - 26.
tx Treatment. One of ’con’ or ’vac’.
les Percent gross lung lesions.

piglung

piglung

29

piglung dataset

Description
Post-mortem examination of the lungs of pigs in litters.
Format
A data frame with 102 observations of the following 3 variables, no NAs.
lesion Percent gross lung lesions.
group Treatment group. One of ’con’ or ’vac’.
litter Litter ID.

Index
∗Topic datasets
calflung, 3
mlesions, 28
piglung, 29
∗Topic documentation
mf-class, 5
mfboot-class, 7
mfbootcluster-class, 8
mfcluster-class, 15
mfcomponents-class, 15
mfhierdata-class, 19
mfhlboot-class, 19
mfmp-class, 21

mfhlboot-class, 19
MFmp, 20, 22
mfmp (mfmp-class), 21
mfmp-class, 21
MFnest, 13, 14, 17, 22, 25
MFnestBoot, 12, 13, 18, 24
MFr, 26
MFSubj, 16, 27
mlesions, 28
mlesions-data (mlesions), 28

calflung, 3
calflung-data (calflung), 3

tibble, 16

piglung, 29
piglung-data (piglung), 29

emp.hpd, 12, 25
HLBoot, 3, 20
MF (MF-package), 2
mf (mf-class), 5
mf-class, 5
MF-package, 2
MFBoot, 6, 7
mfboot (mfboot-class), 7
mfboot-class, 7
mfbootcluster (mfbootcluster-class), 8
mfbootcluster-class, 8
MFClus, 9, 15
MFClusBoot, 8, 10
MFClusBootHier, 12, 18, 25
MFClusHier, 13, 17
mfcluster (mfcluster-class), 15
mfcluster-class, 15
mfcomponents (mfcomponents-class), 15
mfcomponents-class, 15
MFh, 13, 14, 16, 18, 19, 22, 25
MFhBoot, 12, 13, 17, 25
mfhierdata, 16, 17, 22
mfhierdata (mfhierdata-class), 19
mfhierdata-class, 19
mfhlboot (mfhlboot-class), 19
30



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