This package was developed to help prepare some samples to be send to a facility. It assumes that you have collected the samples and the information but you still need to do the experiment in several batches due to technical or practical limitations. The question that tries to answer is:
Which samples go with each batch?
Of all the possible combinations of samples, it looks for the combination which minimizes the differences between each subgroup according to the following rules:
NA (not available values) it looks to
distribute them randomly.Even with this measures you might end up with some batch effect due to: - Confounding variables not provided for their randomization on the batches Sometimes due to being unknown, impossible to measure. - Lack of replicates(samples with the same conditions) If you can’t provide new replicates, aim to provide more technical replicates. Technical replicates mean reanalyzing the same sample twice or more, the more samples with technical replicates the more accurate your measures will be and easier to avoid or detect batch effects. - Processing If there is a change on the methodology, or you pause and resume later the sample collection there might be changes on the outcome due to external factors.
Before building this package I would like to give credit to those that made also efforts in this direction:
The CRAN task View of Experimental Design includes many packages relevant for designing an experiment before collecting data, but none of them provides how to manage them once the samples are already collected.
Two packages allow to distribute the samples on batches:
The OSAT package handles categorical variables but not numeric data. It doesn’t work with our data.
The minDiff package reported in Stats.SE, handles both numeric and categorical data. But it can only optimize for two nominal criteria. It doesn’t work for our data.
The Omixer package handles both numeric and categorical data (converting categorical variables to numeric). But both the same way either Pearson’s Chi-squared Test if there are few samples or Kendall’s correlation. It does allow to protect some spots from being used.
If you are still designing the experiment and do not have collected any data DeclareDesign might be relevant for you.
Question in Bioinformatics.SE I made before developing the package.
Imagine you have some samples already collected and you want to distributed them in batches:
library("experDesign")
metadata <- expand.grid(height = seq(60, 80, 5),
weight = seq(100, 300, 50),
sex = c("Male","Female"))
head(metadata, 15)
## height weight sex
## 1 60 100 Male
## 2 65 100 Male
## 3 70 100 Male
## 4 75 100 Male
## 5 80 100 Male
## 6 60 150 Male
## 7 65 150 Male
## 8 70 150 Male
## 9 75 150 Male
## 10 80 150 Male
## 11 60 200 Male
## 12 65 200 Male
## 13 70 200 Male
## 14 75 200 Male
## 15 80 200 MaleFirst we can check the data to see if there are any concerns regarding the categories:
check_data(metadata)
## [1] TRUEThere are none confounding variables in this artificial dataset (see the examples, and you’ll find some). However, if you block incorrectly and end up with a group in a single batch we will end up with batch effect.
In order to avoid this design() helps you assign each
sample to a batch (in this case each batch has 24 samples at most).
First we can explore the number of samples and the number of
batches:
size_data <- nrow(metadata)
size_batch <- 24
(batches <- optimum_batches(size_data, size_batch))
## [1] 3
# So now the best number of samples for each batch is less than the available
(size <- optimum_subset(size_data, batches))
## [1] 17
# The distribution of samples per batch
sizes_batches(size_data, size, batches)
## [1] 17 17 16Note that instead of using a whole batch and then leave a single sample on the third distributes all the samples in the three batches that will be needed.
We can directly look for the distribution of the samples given our max number of samples per batch:
desi <- design(metadata, size_batch)
# It is a list but we can convert it to a vector with:
batch_names(desi)
## [1] "SubSet2" "SubSet2" "SubSet1" "SubSet2" "SubSet1" "SubSet1" "SubSet1"
## [8] "SubSet1" "SubSet3" "SubSet3" "SubSet3" "SubSet2" "SubSet1" "SubSet3"
## [15] "SubSet2" "SubSet3" "SubSet2" "SubSet2" "SubSet2" "SubSet2" "SubSet1"
## [22] "SubSet3" "SubSet3" "SubSet1" "SubSet2" "SubSet3" "SubSet3" "SubSet2"
## [29] "SubSet3" "SubSet2" "SubSet1" "SubSet1" "SubSet1" "SubSet1" "SubSet3"
## [36] "SubSet1" "SubSet1" "SubSet3" "SubSet3" "SubSet2" "SubSet2" "SubSet2"
## [43] "SubSet3" "SubSet3" "SubSet2" "SubSet3" "SubSet2" "SubSet1" "SubSet1"
## [50] "SubSet1"Naively one would either fill some batches fully or distribute them not evenly (the first 17 packages together, the next 17 and so on). This solution ensures that the data is randomized. For more random distribution you can increase the number of iterations performed to calculate this distribution.
If you need space for replicates to control for batch effect you can use:
repli <- replicates(metadata, size_batch, 5)
lengths(repli)
## SubSet1 SubSet2 SubSet3
## 21 21 18
repli
## $SubSet1
## [1] 3 9 10 16 17 20 27 28 30 31 32 33 34 35 40 41 42 44 45 48 49
##
## $SubSet2
## [1] 4 5 7 8 9 10 13 15 18 21 22 25 26 32 33 34 36 37 38 39 47
##
## $SubSet3
## [1] 1 2 6 9 10 11 12 14 19 23 24 29 32 33 34 43 46 50Which seeks as controls the most diverse values and adds them to the samples distribution. Note that if the sample is already present on that batch is not added again, that’s why the number of samples per batch is different from the design without replicates.
We can analyze how these samples would be distributed in a layout of 6x4:
spati <- spatial(repli, metadata, rows = LETTERS[1:6], columns = 1:4)
head(spati)
## $A1
## [1] 33 48 24
##
## $B1
## [1] 15 22 39
##
## $C1
## [1] 40 5 32
##
## $D1
## [1] 3 9 41
##
## $E1
## [1] 28 10 50
##
## $F1
## [1] 4 13 29We can add the batches to the initial data with
inspect():
report <- inspect(repli, metadata)
report2 <- inspect(spati, report, index_name = "position")
head(report2)
## height weight sex batch position
## 1 60 100 Male SubSet3 C2
## 2 65 100 Male SubSet3 D2
## 3 70 100 Male SubSet1 D1
## 4 75 100 Male SubSet2 F1
## 5 80 100 Male SubSet2 C1
## 6 60 150 Male SubSet3 C4And now we can see the batch and position of each sample
If you have two indices you can also compare them:
desi2 <- create_subset(nrow(metadata), size_batch)
compare_index(metadata, desi, desi2)
## subgroups
## SubSet1 SubSet2 SubSet3
## height 0.05700647 0.4783996 -0.3486057
## weight -6.30024403 -6.3986631 -13.4486992
## sex 0.12670092 0.1267009 0.1267009As many of the variables for multiple subsets are negative it shows
that desi is better.
In the previous case the data was mostly balanced (check it out in
the orig object) but let’s create an unbalanced dataset to
check it.
n <- 99
samples <- 100
unbalanced <- data.frame(Classroom = rep(c("A", "B"), each = samples/2),
Sex = c(rep("M", n), rep("F", samples-n)),
Age = rnorm(samples, mean = 25, sd = 3))
table(unbalanced[, 1:2])
## Sex
## Classroom F M
## A 0 50
## B 1 49In this dataset there is only one female, resulting in a classroom full of males. Age is independent of the sex or classroom.
i <- design(unbalanced, 15)
## Warning: There might be some problems with the data use check_data().
evaluation <- evaluate_index(i, unbalanced)
## Warning: There might be some problems with the data use check_data().
# Mean entropy en each subset
rowMeans(evaluation["entropy", , ])
## Classroom Sex Age mix_cat
## 0.98906095 0.05047991 0.00000000 0.96130358
# Original entropy on the dataset
evaluate_orig(unbalanced)["entropy", ]
## Warning in evaluate_orig(unbalanced): There might be some problems with the
## data use check_data().
## Classroom Sex Age mix_cat
## 1.00000000 0.08079314 0.00000000 0.67554928
# Dispersion of the entropy
apply(evaluation["entropy", , ], 1, sd)
## Classroom Sex Age mix_cat
## 0.01057627 0.13355727 0.00000000 0.08171973We can see that in this simple case where a single variable has all the other cases we approximately reached the same entropy levels.
If you need a subset with the samples that are more diverse you can use the following function:
data(survey, package = "MASS")
head(survey)
## Sex Wr.Hnd NW.Hnd W.Hnd Fold Pulse Clap Exer Smoke Height M.I
## 1 Female 18.5 18.0 Right R on L 92 Left Some Never 173.00 Metric
## 2 Male 19.5 20.5 Left R on L 104 Left None Regul 177.80 Imperial
## 3 Male 18.0 13.3 Right L on R 87 Neither None Occas NA <NA>
## 4 Male 18.8 18.9 Right R on L NA Neither None Never 160.00 Metric
## 5 Male 20.0 20.0 Right Neither 35 Right Some Never 165.00 Metric
## 6 Female 18.0 17.7 Right L on R 64 Right Some Never 172.72 Imperial
## Age
## 1 18.250
## 2 17.583
## 3 16.917
## 4 20.333
## 5 23.667
## 6 21.000
samples <- extreme_cases(survey, size = 10)
survey[samples, ]
## Sex Wr.Hnd NW.Hnd W.Hnd Fold Pulse Clap Exer Smoke Height M.I
## 5 Male 20.0 20.0 Right Neither 35 Right Some Never 165.00 Metric
## 48 Male 22.5 23.0 Right R on L 96 Right None Never 170.00 Metric
## 60 Male 20.6 21.0 Left L on R NA Left Freq Occas 175.26 Imperial
## 66 Male 19.5 19.8 Right Neither NA Right Freq Never 183.00 Metric
## 80 Male 20.0 20.5 Right L on R NA Right Freq Never 185.42 Imperial
## 83 Female 17.5 17.5 Right R on L 98 Left Freq Never NA <NA>
## 121 Male 20.0 20.0 Right R on L 80 Neither Freq Occas NA <NA>
## 154 Male 21.5 21.6 Right R on L 69 Right Freq Never 172.72 Imperial
## 170 Male 19.0 18.5 Right R on L 72 Right Freq Never 180.34 Imperial
## 225 Female 17.6 17.2 Right L on R NA Right Some Never NA <NA>
## Age
## 5 23.667
## 48 19.417
## 60 18.417
## 66 18.000
## 80 18.750
## 83 17.667
## 121 17.500
## 154 70.417
## 170 17.333
## 225 19.917You can also test a given index with check_index():
check_index(unbalanced, i)
## Warning in check_index(unbalanced, i): There might be some problems with the
## data use check_data().
## subgroups
## SubSet1 SubSet2 SubSet3 SubSet4 SubSet5 SubSet6
## Classroom 0.02244529 0.03105896 0.02629978 0.02137583 0.02137583 0.02629978
## Sex 0.16047517 0.22439953 0.16047517 0.16047517 0.16047517 0.16047517
## Age 0.17747553 0.17946189 0.17356821 0.26801527 0.16922656 0.22344403
## mix_cat 0.08031059 0.02527493 0.07741971 0.08111268 0.08111268 0.07741971
## subgroups
## SubSet7
## Classroom 0.02629978
## Sex 0.16047517
## Age 0.27062936
## mix_cat 0.07741971Each row has information about how accurate is a given variable to
the samples available (on this case unbalanced). Some
variables are distributed more randomly than others on this index.
If we are not satisfied we could design() a new index
increasing the iterations to obtain a potentially better distribution.
If you want a good stratified randomization you should increase the
iterations used 10 fold.
We could check all the combinations to select those that allow us to
do this comparison. But as this would be too long with
experDesign we can try to find the combination with the
best design by comparing each combination with the original according to
multiple statistics.
# To reduce the variables used:
omit <- c("Wr.Hnd", "NW.Hnd", "Fold", "Pulse", "Clap", "Exer", "Height", "M.I")
(keep <- colnames(survey)[!colnames(survey) %in% omit])
## [1] "Sex" "W.Hnd" "Smoke" "Age"
head(survey[, keep])
## Sex W.Hnd Smoke Age
## 1 Female Right Never 18.250
## 2 Male Left Regul 17.583
## 3 Male Right Occas 16.917
## 4 Male Right Never 20.333
## 5 Male Right Never 23.667
## 6 Female Right Never 21.000
# Set a seed for reproducibility
# Looking for groups at most of 70 samples.
index <- create_subset(nrow(survey), size_subset = 70)
index
## $SubSet1
## [1] 2 4 5 8 10 12 16 21 23 24 26 35 37 41 46 47 51 58 61
## [20] 75 77 78 84 85 90 96 98 100 101 102 108 109 113 121 122 126 128 135
## [39] 139 141 146 147 148 157 165 167 168 176 181 182 192 193 207 210 212 223 229
## [58] 230 234 235
##
## $SubSet2
## [1] 9 15 17 30 31 42 43 56 59 60 62 63 69 79 80 91 93 94 107
## [20] 110 112 117 120 124 125 129 131 133 134 137 140 142 143 152 153 154 155 156
## [39] 160 163 166 175 183 184 186 188 194 196 205 208 216 217 218 219 222 225 228
## [58] 231 232
##
## $SubSet3
## [1] 3 6 18 19 20 25 29 33 36 38 45 53 54 64 67 73 76 81 82
## [20] 83 89 97 103 106 111 114 115 116 118 119 123 130 138 149 151 158 159 162
## [39] 169 171 174 178 179 185 187 189 200 201 202 203 206 209 211 213 220 226 227
## [58] 236 237
##
## $SubSet4
## [1] 1 7 11 13 14 22 27 28 32 34 39 40 44 48 49 50 52 55 57
## [20] 65 66 68 70 71 72 74 86 87 88 92 95 99 104 105 127 132 136 144
## [39] 145 150 161 164 170 172 173 177 180 190 191 195 197 198 199 204 214 215 221
## [58] 224 233We can measure how does this index does:
score_index1 <- check_index(survey[, keep], index)
## Warning in check_index(survey[, keep], index): There might be some problems
## with the data use check_data().
score_index1
## subgroups
## SubSet1 SubSet2 SubSet3 SubSet4
## Sex 0.29039360 0.453058819 0.2878351 0.28783513
## W.Hnd 0.41713852 0.419252156 0.6229796 0.46727445
## Smoke 0.13503168 0.145091225 0.1307635 0.29376264
## Age 0.82832190 0.630881628 0.7192229 0.83508648
## mix_cat 0.02839793 0.002034746 0.0245089 0.01467664These values come from calculating the difference between the
original data and the samples for each subset for the median, mean, mad,
NA, entropy and independence (chisq.test() p.value).
On themselves these values have no meaning, but internally they are used to compare with other possible index:
index2 <- create_subset(nrow(survey), size_subset = 70)Then it compares to the previous index
score_index2 <- check_index(survey[, keep], index2)
## Warning in check_index(survey[, keep], index2): There might be some problems
## with the data use check_data().
sum(rowMeans(abs(score_index2-score_index1)))
## [1] 0.9014104If this score is lower than the previous one the new index is kept.
This is done similarly for the spatial search, which adds two new categorical variables with the position of the samples before calculating any statistics.
sessionInfo()
## R version 4.2.2 (2022-10-31)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 22.04.2 LTS
##
## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=es_ES.UTF-8 LC_COLLATE=C
## [5] LC_MONETARY=es_ES.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=es_ES.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=es_ES.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] experDesign_0.2.0
##
## loaded via a namespace (and not attached):
## [1] digest_0.6.31 R6_2.5.1 jsonlite_1.8.4 evaluate_0.20
## [5] cachem_1.0.7 rlang_1.1.0 cli_3.6.0 rstudioapi_0.14
## [9] jquerylib_0.1.4 bslib_0.4.2 rmarkdown_2.20 tools_4.2.2
## [13] xfun_0.37 yaml_2.3.7 fastmap_1.1.1 compiler_4.2.2
## [17] htmltools_0.5.4 knitr_1.42 sass_0.4.5