# MSstatsSampleSize : A package for optimal design of high-dimensional MS-based proteomics experiment

#### 2019-10-29

library(MSstatsSampleSize)

This vignette introduces all the functionalities and summarizes their options in MSstatsSampleSize. MSstatsSampleSize requires protein abundances quantified in mass spectrometry runs as a matrix (columns for biological replicates (samples) and rows for proteins) and annotation including biological replicates (samples) and their condition (such as a disease and time points). MSstatsSampleSize includes the following functionalities:

1. estimateVar: estimates the variance across biological replicates and MS run for each protein.
2. simulateDataset: simulates data with the given number(s) of biological replicates based on the variance estimation.
3. designSampleSizeClassification : fit the classification model (five classifier are provided) on each simulation and reports the mean predictive accuracy of the classifier and mean protein importance over multiple iterations of the simulation. The sample size per condition, which generates the largest predictive accuracy, is estimated, while varying the number of biological replicates to simulate. Also, the proteins, which can classify the conditions best, are reported. The reported sample size per condition can be used to design future experiments.

In addition, MSstatsTMT includes the following visualization plots for sample size estimation:

1. meanSDplot: draw the plot for the mean protein abundance vs standard deviation in each condition for the input preliminary dataset. It can exhibit the quality of input data.
2. designSampleSizePCAplot: make PCA plots for the simulated data with certain sample size.
3. designSampleSizeClassificationPlots: visualize sample size calculation in classification, including predictive accuracy plot and protein importance plot for different sample sizes.

## 1. Estimate mean protein abundance and variance per condition

### 1.1 estimateVar()

The function fits intensity-based linear model on the prelimiary data (Input, here is data). This function outputs variance components and mean abundance for each protein.

#### Arguments

• data : Data matrix with protein abundance. Rows are proteins and columns are Biological replicates or samples.
• annotation : annotation Group information for samples in data. BioReplicate for sample ID and Condition for group information are required. BioReplicate information should be the same with the column of data.

#### Example

# # read in protein abundance sheet
# # The CSV sheet has 173 columns from control and cancer groups.
# # Each row is protein and each column (except the first column) is biological replicate.
# # The first column 'Protein' contains the protein names.

# OV_SRM_train <- read.csv(file = "OV_SRM_train.csv")
# # assign the column 'Protein' as row names
# rownames(OV_SRM_train) <- OV_SRM_train$Protein # # remove the column 'Protein # OV_SRM_train <- OV_SRM_train[, colnames(OV_SRM_train)!="Protein"] head(OV_SRM_train) #> 111_data2 112_data2 114_data2 115_data2 117_data2 118_data2 119_data2 #> AFM 18.125305 18.64349 17.786586 18.62598 18.097136 18.535312 18.840662 #> AHSG 19.128721 19.11689 19.286422 19.55758 19.344060 19.639931 19.959407 #> AIAG 14.622719 14.67904 14.573159 14.63815 14.721183 14.680685 14.689130 #> AOC3 9.632189 10.11125 9.206763 10.16800 9.684437 9.231637 9.119823 #> APOH 17.426479 17.43132 17.075589 17.56990 17.487654 17.387798 16.742562 #> ATRN 15.686383 15.87728 15.363577 15.94339 15.797377 15.895453 15.656975 #> 120_data2 121_data2 122_data2 124_data2 125_data2 126_data2 127_data2 #> AFM 18.03126 18.30078 18.174929 17.96232 17.689686 18.901496 18.575908 #> AHSG 19.15174 19.60217 19.874469 19.04089 19.501971 19.731607 19.584103 #> AIAG 14.68560 14.66908 14.698554 14.65223 14.665577 14.780582 14.619267 #> AOC3 9.81001 9.76118 9.601232 10.43671 8.985737 9.875627 9.334184 #> APOH 17.51288 17.79438 17.232558 17.65325 17.224110 17.785863 17.659559 #> ATRN 15.36520 15.95020 15.625773 15.68939 15.753342 16.270773 15.831303 #> 128_data2 129_data2 130_data2 131_data2 132_data2 133_data2 134_data2 #> AFM 17.947816 18.147868 18.51270 18.65929 18.47320 17.88667 18.507657 #> AHSG 18.841300 19.523012 18.84247 19.63918 19.42743 19.57734 19.659681 #> AIAG 14.644087 14.667445 14.63945 14.64111 14.56605 14.61757 14.618578 #> AOC3 9.223909 9.437629 10.33851 10.09512 10.42163 9.98921 9.644337 #> APOH 16.273186 17.621464 17.51718 17.70859 17.60183 17.39107 17.716885 #> ATRN 15.373676 15.687543 15.80440 16.15178 16.03244 15.22396 15.908807 #> 135_data2 136_data2 137_data2 138_data2 139_data2 141_data2 142_data2 #> AFM 18.056045 18.217216 18.190407 17.93129 18.190767 18.71189 18.697504 #> AHSG 18.684113 19.778128 19.072510 19.64681 19.144389 19.09215 19.173120 #> AIAG 14.788843 14.700861 14.690739 14.70032 14.557284 14.49786 14.527640 #> AOC3 9.883479 9.956687 9.923819 10.19981 9.584612 10.08803 9.856426 #> APOH 17.486721 17.634729 17.326886 17.87975 17.269722 17.51544 17.439385 #> ATRN 15.550850 15.945612 15.683677 15.46693 15.755415 15.83076 15.837718 #> 143_data2 144_data2 145_data2 148_data2 150_data2 152_data2 153_data2 #> AFM 18.333930 18.74509 18.883271 18.42733 18.238043 18.95043 17.924042 #> AHSG 19.205627 19.23469 19.437665 19.37992 18.847405 19.59803 19.252497 #> AIAG 14.726276 14.52811 14.667486 14.62488 14.649104 13.97571 14.585755 #> AOC3 9.671116 10.25606 9.428427 10.15433 9.718192 10.50247 9.860558 #> APOH 17.458798 18.01638 17.547977 17.69565 17.230260 18.20250 17.184654 #> ATRN 15.393106 15.89522 15.496752 15.65677 15.526452 16.08452 15.257093 #> 156_data2 158_data2 160_data2 161_data2 164_data2 165_data2 168_data2 #> AFM 18.483946 18.010669 18.385003 17.879145 17.903197 17.888331 17.004817 #> AHSG 19.276230 18.915663 18.973446 19.072742 19.088324 18.880597 19.117856 #> AIAG 14.569342 14.682799 14.622459 14.584713 14.688668 14.512316 14.559322 #> AOC3 9.492098 9.735485 9.662316 9.864964 9.193436 9.925697 8.993866 #> APOH 17.462395 17.565055 17.530551 17.132638 17.077047 17.430339 17.456123 #> ATRN 15.715309 15.578068 15.692108 15.352683 15.710086 15.541809 15.683521 #> 169_data2 170_data2 171_data2 173_data2 174_data2 175_data2 176_data2 #> AFM 18.632285 18.085689 18.051762 17.85643 17.836256 18.041862 18.40570 #> AHSG 19.400598 19.363621 18.747689 18.73413 19.685220 19.087447 19.39215 #> AIAG 14.739893 14.531010 14.744388 14.59457 14.683617 14.640865 14.65400 #> AOC3 9.947192 9.186059 9.831393 10.00113 9.766951 9.274928 10.28776 #> APOH 16.529038 17.424281 17.542339 16.10105 17.178624 16.936601 17.52544 #> ATRN 15.769345 15.898010 15.856918 15.43720 15.340032 15.533356 15.53440 #> 178_data2 179_data2 180_data2 182_data2 183_data2 184_data2 186_data2 #> AFM 18.75573 18.27063 18.52774 18.297518 17.582758 17.930931 17.904111 #> AHSG 19.29950 18.94489 19.08033 19.113432 18.691674 18.662868 18.530972 #> AIAG 14.65713 14.64914 14.72467 14.850340 14.827924 14.689922 14.669593 #> AOC3 10.02276 10.47037 9.59893 9.795267 9.370154 9.981769 9.794802 #> APOH 17.86451 17.48350 17.30439 17.544530 17.155819 17.169970 16.660848 #> ATRN 15.77620 15.58480 15.60318 15.697109 14.605720 15.260143 15.403576 #> 187_data2 188_data2 190_data2 192_data2 194_data2 195_data2 196_data2 #> AFM 18.396673 17.894678 17.707195 17.809669 18.34009 18.179624 18.596355 #> AHSG 19.080693 19.278260 18.558606 18.662771 19.21291 18.730319 18.834565 #> AIAG 14.620739 14.787837 14.720343 14.652637 14.68076 14.634261 14.678035 #> AOC3 9.702123 9.681856 9.736804 9.401154 9.33778 9.897792 9.822549 #> APOH 17.321073 17.005514 17.087448 17.047272 17.03732 17.227674 15.927422 #> ATRN 15.621545 14.806060 14.983297 15.092230 15.42662 15.727192 15.855226 #> 197_data2 198_data2 199_data2 205_data2 206_data2 207_data2 208_data2 #> AFM 18.00268 18.27635 18.331772 18.077828 17.452173 18.05501 18.235103 #> AHSG 18.25441 18.71128 18.792804 18.912961 18.840506 18.62855 18.553961 #> AIAG 14.63728 14.52884 14.778585 14.633616 14.814071 14.76750 14.690582 #> AOC3 10.00159 10.02890 9.634046 9.938078 9.831058 10.20700 9.498681 #> APOH 17.04321 17.17218 17.459782 16.547486 16.958609 16.02782 16.905076 #> ATRN 15.34257 15.24551 14.835897 15.954050 14.513800 15.21354 16.874498 #> 209_data2 210_data2 211_data2 212_data2 213_data2 214_data2 215_data2 #> AFM 18.132287 18.375079 17.770032 17.724905 17.657647 18.38242 17.921772 #> AHSG 18.949066 18.702423 18.877115 18.269341 19.118199 18.71252 19.296103 #> AIAG 14.909930 14.706238 14.684011 14.823715 14.893650 14.75854 14.343939 #> AOC3 9.579414 9.678326 9.495482 9.469346 8.824347 10.35025 9.412162 #> APOH 17.464916 17.128459 17.186659 17.072809 16.864841 16.59375 17.417278 #> ATRN 16.064397 16.378393 14.989205 15.140738 14.477049 15.09208 15.186785 #> 216_data2 218_data2 219_data2 221_data2 223_data2 225_data2 226_data2 #> AFM 18.632524 18.51812 18.917493 17.185341 19.13733 17.39628 17.668124 #> AHSG 19.355160 19.53827 19.493397 19.298672 19.89682 18.29875 19.171998 #> AIAG 14.913842 14.73214 14.965833 14.728767 14.68477 14.77646 14.697848 #> AOC3 9.406908 10.27621 9.351153 9.455133 10.01626 10.04424 8.795441 #> APOH 17.499664 17.51376 16.706372 17.315701 16.56589 16.23679 17.200088 #> ATRN 16.374801 15.95412 16.348563 15.242930 15.61262 14.92587 14.939998 #> 227_data2 228_data2 229_data2 230_data2 232_data2 233_data2 234_data2 #> AFM 18.219490 18.34502 18.276027 17.932387 17.929591 18.429553 18.436277 #> AHSG 19.010487 19.86036 18.969241 19.183166 19.269394 19.837211 19.301828 #> AIAG 14.702392 14.60841 14.678561 14.739957 14.701693 14.549578 14.723665 #> AOC3 9.592725 10.32214 9.734937 9.855735 9.760736 9.830378 9.021658 #> APOH 17.853825 16.86624 17.276985 17.590303 17.704829 17.666456 17.173970 #> ATRN 15.955115 16.02096 15.670380 15.186790 15.693796 15.597309 15.563141 #> 238_data2 239_data2 240_data2 241_data2 243_data2 245_data2 247_data2 #> AFM 18.96869 17.293384 17.875729 18.330708 18.483318 18.51463 17.869515 #> AHSG 19.63254 18.752183 18.986113 19.199029 19.283156 19.47072 18.885268 #> AIAG 14.66505 14.841246 14.864199 14.744263 14.824436 14.81997 14.755289 #> AOC3 10.06522 9.142904 8.526826 9.954245 9.788555 10.44169 9.398166 #> APOH 17.94275 17.553791 16.451953 17.468578 17.693520 17.39168 16.492304 #> ATRN 16.13144 15.405926 14.980693 15.970609 15.744037 15.58433 15.330940 #> 249_data2 250_data2 251_data2 252_data2 253_data2 256_data2 260_data2 #> AFM 18.379942 17.75743 18.061166 18.032662 18.031620 18.014187 18.334035 #> AHSG 19.140557 18.71993 18.881908 19.174453 19.121928 19.489746 18.722563 #> AIAG 14.675358 14.70208 14.726250 14.740409 14.687525 14.767787 14.637014 #> AOC3 9.526241 9.00285 9.482894 8.653987 9.523596 9.218346 8.802496 #> APOH 17.227454 17.24986 16.242826 17.319249 17.762734 17.863327 17.505322 #> ATRN 15.175162 14.95746 15.369109 14.607609 14.955496 15.418160 14.746083 #> 261_data2 262_data2 263_data2 264_data2 266_data2 268_data2 269_data2 #> AFM 17.340848 17.434467 18.26882 18.39991 18.228878 16.763601 18.31052 #> AHSG 18.410148 18.410194 18.97058 19.61394 18.955525 17.848421 19.72981 #> AIAG 14.665203 14.704354 14.61000 14.32172 14.573768 14.771025 14.64845 #> AOC3 9.191827 9.278675 10.24927 10.25673 9.106905 8.641794 9.13996 #> APOH 17.600706 17.315108 17.25575 18.16690 17.536522 16.615284 17.70658 #> ATRN 15.157038 14.906791 15.53208 16.16453 15.332228 14.757124 15.56021 #> 272_data2 273_data2 274_data2 276_data2 277_data2 278_data2 280_data2 #> AFM 18.097901 18.24783 17.930339 17.747268 18.180041 18.28853 18.43702 #> AHSG 18.979989 19.01244 18.668717 19.460339 19.246000 19.66590 19.50469 #> AIAG 14.658132 14.57915 14.525636 14.669980 14.633661 14.70032 14.76518 #> AOC3 9.709677 10.23607 8.901961 9.353579 9.874482 10.54489 10.01856 #> APOH 17.302029 16.60388 17.510074 17.271007 17.522941 17.75978 18.01372 #> ATRN 15.579564 15.98848 15.273826 14.715780 15.864879 15.94246 15.46217 #> 281_data2 283_data2 285_data2 287_data2 289_data2 291_data2 292_data2 #> AFM 18.442966 18.39470 17.469177 17.593275 17.319943 18.27916 18.040612 #> AHSG 19.468956 19.52308 18.395481 19.223018 18.488503 19.30705 18.852932 #> AIAG 14.600466 14.78339 14.735214 14.759663 14.690441 14.69510 14.608408 #> AOC3 9.636045 9.93667 9.407982 9.441949 9.188727 9.96577 9.208321 #> APOH 17.441397 17.62818 17.624138 16.631229 17.037041 17.31336 17.497227 #> ATRN 15.990297 15.21573 14.818069 15.639320 14.802373 15.67334 15.660417 #> 293_data2 294_data2 296_data2 297_data2 298_data2 299_data2 300_data2 #> AFM 17.53997 18.106933 17.863355 18.291169 17.886804 18.009294 17.820316 #> AHSG 18.85753 18.996350 18.907338 18.986280 18.944631 19.651977 19.306948 #> AIAG 14.69265 14.654902 14.740586 14.597331 14.774619 14.647562 14.667379 #> AOC3 10.01976 9.674252 8.782559 9.194235 9.032765 9.806832 9.451533 #> APOH 17.22411 17.386070 16.016076 17.244806 16.078584 16.409889 17.134223 #> ATRN 15.39936 15.765481 14.876109 15.528891 14.970902 14.890409 15.277566 #> 304_data2 305_data2 306_data2 307_data2 309_data2 310_data2 312_data2 #> AFM 17.780377 18.088523 17.543665 18.684386 17.421003 17.215059 17.514548 #> AHSG 18.621389 18.451854 18.124493 18.938180 18.037526 18.754185 19.572883 #> AIAG 14.680430 14.606103 14.683937 14.659891 14.857323 14.936426 14.667030 #> AOC3 9.912006 9.107903 8.757357 9.851319 8.624146 9.627355 9.314186 #> APOH 17.013894 17.343102 16.489484 17.055566 16.948763 15.753452 17.233069 #> ATRN 15.677189 15.235679 14.577096 15.037739 14.522558 14.543692 14.308494 #> 313_data2 314_data2 316_data2 317_data2 318_data2 319_data2 320_data2 #> AFM 17.155426 17.928557 17.577918 18.170263 18.162079 17.34586 17.400453 #> AHSG 18.436080 19.262887 17.863462 19.205413 18.730273 18.74122 18.958450 #> AIAG 14.759980 14.658502 14.773180 14.863401 14.722524 14.83162 14.755337 #> AOC3 8.630082 9.672823 8.892625 9.862696 8.795811 9.22160 9.706257 #> APOH 15.700634 17.793827 16.037153 17.414298 17.243269 16.32879 16.123737 #> ATRN 14.112309 15.067181 14.852712 13.845938 14.927448 15.32303 14.881399 #> 321_data2 322_data2 324_data2 325_data2 326_data2 327_data2 17_data1 #> AFM 18.591053 18.308186 18.137755 18.347084 18.252126 17.802494 18.319153 #> AHSG 19.205644 18.744856 18.167016 18.446565 18.901464 18.673620 19.449831 #> AIAG 14.915479 14.970198 14.778891 14.626631 14.828018 14.593578 14.550948 #> AOC3 9.806904 9.859974 9.540925 9.186197 9.941376 9.406369 9.504025 #> APOH 16.170522 16.321222 16.819747 17.227516 17.375660 17.298652 17.518350 #> ATRN 15.581586 15.941980 15.420064 15.432483 15.548218 15.525004 15.905615 #> 18_data1 19_data1 20_data1 22_data1 23_data1 24_data1 25_data1 #> AFM 18.530057 18.096524 17.863494 17.772719 17.906108 18.153054 16.878912 #> AHSG 19.644695 19.666677 19.060631 19.082822 19.179822 19.356952 19.239355 #> AIAG 14.478457 14.574919 14.708477 14.693666 14.688290 14.610936 14.656453 #> AOC3 9.212143 9.140614 8.650803 9.381733 9.690872 9.293172 9.225986 #> APOH 18.010057 12.511891 17.572180 17.591682 17.723092 18.158306 18.011159 #> ATRN 16.165473 15.186984 15.277472 15.088876 15.522584 15.026051 15.112880 #> 27_data1 29_data1 30_data1 31_data1 32_data1 34_data1 35_data1 #> AFM 18.044725 17.916760 18.46724 17.476939 18.259068 17.626156 17.076560 #> AHSG 19.328346 18.329613 18.99762 18.669560 19.470021 18.946247 17.613020 #> AIAG 15.135554 14.642973 14.50106 14.587588 14.392651 14.878944 14.763767 #> AOC3 8.830496 9.607988 10.22964 8.666865 9.197119 8.429024 8.745846 #> APOH 17.688508 17.622580 18.09545 16.932939 18.020715 17.465965 16.136053 #> ATRN 15.356655 15.083532 15.44032 15.050747 15.764067 15.134377 14.673516 #> 38_data1 39_data1 43_data1 44_data1 45_data1 #> AFM 17.819313 17.303960 17.640026 17.274972 18.47362 #> AHSG 18.717438 19.077383 18.607056 18.795921 19.40802 #> AIAG 15.125151 14.911137 14.625692 14.318688 14.54279 #> AOC3 9.241095 9.321773 9.080731 8.895516 10.11394 #> APOH 17.522211 16.976758 16.843956 17.486311 18.01415 #> ATRN 15.402824 15.192443 15.204575 15.563628 15.63803 # Read in annotation including condition and biological replicates. # Users should make this annotation file. # OV_SRM_train_annotation <- read.csv(file="OV_SRM_train_annotation.csv", header=TRUE) head(OV_SRM_train_annotation) #> BioReplicate Condition #> 88 111_data2 control #> 89 112_data2 control #> 90 114_data2 control #> 91 115_data2 control #> 92 117_data2 control #> 93 118_data2 control # estimate the mean protein abunadnce and variance in each condition variance_estimation <- estimateVar(data = OV_SRM_train, annotation = OV_SRM_train_annotation) #> Preparing variance analysis... #> Variance analysis completed. # the mean protein abundance in each condition head(variance_estimation$mu)
#>        control ovarian cancer
#> AFM  18.213066      17.956584
#> AHSG 19.137513      19.004551
#> AIAG 14.665297      14.699719
#> AOC3  9.749418       9.434263
#> APOH 17.274931      17.161911
#> ATRN 15.604271      15.297676

# the standard deviation in each condition
head(variance_estimation$sigma) #> control ovarian cancer #> AFM 0.4212154 0.4212154 #> AHSG 0.4295371 0.4295371 #> AIAG 0.1299203 0.1299203 #> AOC3 0.4432402 0.4432402 #> APOH 0.6306461 0.6306461 #> ATRN 0.4412322 0.4412322 # the mean protein abundance across all the conditions head(variance_estimation$promean)
#>      AFM     AHSG     AIAG     AOC3     APOH     ATRN
#> 18.07519 19.06604 14.68380  9.58000 17.21417 15.43945

### 1.2 meanSDplot()

This function draws the plot for the mean protein abundance (X-axis) vs standard deviation (Y-axis) in each condition. The lowess function is used to fit the LOWESS smoother between meann protein abundance and standard deviation (square root of variance). This function generates one pdf file with mean-SD plot.

#### Arguments

• data : A list with mean protein abundance matrix and standard deviation matrix. It should be the output of estimateVar function.
• x.axis.size : Size of x-axis labeling in Mean-SD Plot. Default is 10.
• y.axis.size : Size of y-axis labels. Default is 10.
• smoother_size : Size of lowess smoother. Default is 1.
• width : Width of the saved pdf file. Default is 4.
• height : Height of the saved pdf file. Default is 4.
• xlimUp : The upper limit of x-axis for mean-SD plot. Default is 30.
• ylimUp : The upper limit of y-axis for mean-SD plot. Default is 3.
• address : The name of folder that will store the results. Default folder is the current working directory. The other assigned folder has to be existed under the current working directory. An output pdf file is automatically created with the default name of MeanSDPlot.pdf. The command address can help to specify where to store the file as well as how to modify the beginning of the file name. If address=FALSE, plot will be not saved as pdf file but showed in window.

#### Example

#  output a pdf file with mean-SD plot
meanSDplot(variance_estimation)

## 2. Simulates data with the given numbers of biological replicates and proteins based on the variance estimation

### 2.1 simulateDataset()

This function simulate datasets with the given numbers of biological replicates and proteins based on the preliminary dataset (input for this function). The function fits intensity-based linear model on the input data data in order to get variance and mean abundance, using estimateVar function. Then it uses variance components and mean abundance to simulate new training data with the given sample size and protein number. It outputs the number of simulated proteins, a vector with the number of simulated samples in each condition, the list of simulated training datasets, the input dataset and the (simulated) validation dataset.

#### Arguments

• data : Protein abundance data matrix. Rows are proteins and columns are biological replicates(samples).
• annotation : Group information for samples in data. BioReplicate for sample ID and Condition for group information are required. BioReplicate information should match with column names of data.
• num_simulations : Number of times to repeat simulation experiments (Number of simulated datasets). Default is 10.
• expected_FC : Expected fold change of proteins. The first option (Default) is “data”, indicating the fold changes are directly estimated from the input data. The second option is a vector with predefined fold changes of listed proteins. The vector names must match with the unique information of Condition in annotation. One group must be selected as a baseline and has fold change 1 in the vector. The user should provide list_diff_proteins, which users expect to have the fold changes greater than 1. Other proteins that are not available in list_diff_proteins will be expected to have fold change = 1.
• list_diff_proteins : Vector of proteins names which are set to have fold changes greater than 1 between conditions. If user selected expected_FC= "data", this should be NULL.
• select_simulated_proteins : The standard to select the simulated proteins among data. It can be 1) “proportion” of total number of proteins in the input data or 2) “number” to specify the number of proteins. “proportion” indicates that user should provide the value for protein_proportion option. “number” indicates that user should provide the value for protein_number option.
• protein_proportion : Proportion of total number of proteins in the input data to simulate. For example, input data has 1,000 proteins and user selects protein_proportion=0.1. Proteins are ranked in decreasing order based on their mean abundance across all the samples. Then, 1,000 * 0.1 = 100 proteins will be selected from the top list to simulate. Default is 1.0, which meaans that all the proteins will be used.
• protein_number : Number of proteins to simulate. For example, protein_number=1000. Proteins are ranked in decreasing order based on their mean abundance across all the samples and top protein_number proteins will be selected to simulate. Default is 1000.
• samples_per_group : Number of samples per group to simulate. Default is 50.
• simulate_validation : Default is FALSE. If TRUE, simulate the validation set; otherwise, the input data will be used as the validation set.
• valid_samples_per_group : Number of validation samples per group to simulate. This option works only when user selects simulate_validation=TRUE. Default is 50.

#### Example

# expected_FC = "data": fold change estimated from OV_SRM_train
# select_simulated_proteins = "proportion": select the simulated proteins based on the proportion of total proteins
# simulate_valid = FALSE: use input OV_SRM_train as validation set
simulated_datasets <- simulateDataset(data = OV_SRM_train,
annotation = OV_SRM_train_annotation,
num_simulations = 10, # simulate 10 times
expected_FC = "data",
list_diff_proteins =  NULL,
select_simulated_proteins = "proportion",
protein_proportion = 1.0,
protein_number = 1000,
samples_per_group = 50, # 50 samples per condition
simulate_validation = FALSE,
valid_samples_per_group = 50)

Explore the output from simulateDataset function

# the number of simulated proteins
simulated_datasets$num_proteins #> [1] 67 # a vector with the number of simulated samples in each condition simulated_datasets$num_samples
#>        control ovarian cancer
#>             50             50

# the list of simulated protein abundance matrices
# Each element of the list represents one simulation
head(simulated_datasets$simulation_train_Xs[[1]]) # first simulation #> IGHG2 HP CFH AHSG AFM CP ITIH4 SERPINA3 #> 1 22.59659 23.61310 20.45297 19.76987 17.53382 18.38388 18.22785 18.49212 #> 2 22.29766 22.80745 21.03452 19.21182 18.53479 18.10878 18.23473 18.22563 #> 3 24.60785 21.48131 20.44468 19.84705 17.57010 18.15945 17.47228 18.24914 #> 4 22.19199 22.14809 20.56187 18.85168 18.95446 18.65094 17.29665 19.38778 #> 5 23.72960 21.56996 20.24546 18.66037 18.61572 18.15219 18.18591 17.22042 #> 6 23.30008 21.95770 20.48012 18.70597 18.16304 18.12637 17.46481 18.77114 #> KNG1 ITIH2 APOH PON1 CLU SERPINA6 LRG1 LUM #> 1 17.63838 17.40602 17.04498 16.61857 17.56587 16.40191 16.58277 16.52259 #> 2 17.47225 17.52196 17.41582 16.35913 17.50879 16.49850 17.09485 15.57225 #> 3 18.27060 17.24895 16.74420 17.33801 17.26732 16.97234 16.68668 15.86130 #> 4 16.98372 17.49133 17.54469 17.26034 17.37128 16.41699 17.40288 16.18761 #> 5 17.51060 17.20679 17.24884 16.14819 16.98673 17.30253 16.32296 16.32521 #> 6 18.22917 17.27119 18.03720 17.36555 17.01825 16.32296 16.99780 16.04227 #> FETUA KLKB1 ATRN LGALS3BP AIAG ECM1 F5 HYOU1 #> 1 15.95452 15.62689 15.40058 16.18849 14.84157 14.65119 14.46747 14.45177 #> 2 16.05405 14.62790 15.49882 16.56062 14.71979 13.72386 14.68369 14.12957 #> 3 16.06321 16.18484 15.18025 14.87776 14.58943 14.83506 14.01891 13.67788 #> 4 16.07440 15.56702 14.92186 15.39529 14.72977 15.25406 14.48521 13.72637 #> 5 15.92098 16.22145 15.77697 14.61501 14.71189 15.15176 13.90561 13.45870 #> 6 16.00156 15.83644 15.43882 14.45750 14.72927 13.45626 14.33624 14.79700 #> COL6A6 SERPINA10 BTD VTN PLTP CD44 F11 CPE #> 1 14.34213 13.25311 13.02979 14.66667 13.41646 12.21864 12.51914 12.75768 #> 2 14.00887 13.84570 12.88985 13.36610 13.55567 13.21657 13.43009 12.08583 #> 3 13.60003 14.07621 13.00449 11.02750 13.06342 13.26017 13.86320 13.25067 #> 4 13.98855 14.30634 13.44635 14.97518 12.93689 12.92168 13.16972 13.06176 #> 5 14.22760 13.62330 13.87804 13.92167 13.18146 12.36522 12.87036 12.49490 #> 6 14.06656 13.39882 12.85717 14.46534 12.78776 13.83042 12.32279 14.40359 #> CTBS SERPINA7 ICAM1 NCAM1 LCN2 PRG4 FN1 CD163 #> 1 12.29038 12.63197 12.34202 11.99557 11.93267 12.46840 12.22268 12.17327 #> 2 12.04029 12.60315 12.06229 12.15032 12.25767 12.22054 11.72352 12.58633 #> 3 13.03964 13.05243 11.82843 11.74293 11.94744 11.67252 11.07286 10.56169 #> 4 11.89187 12.13271 12.15233 12.06535 11.56373 11.58041 12.54189 12.40203 #> 5 11.82958 12.57154 12.25305 12.24767 11.31129 12.14754 11.59391 11.87065 #> 6 12.79803 12.79577 12.01761 11.47303 12.82049 11.33375 11.93885 12.65017 #> CDH5 CADM1 C20orf3 CTSD PVRL1 CDH13 PCYOX1 DSG2 #> 1 11.59970 11.03070 12.12489 10.59656 10.58801 11.00610 10.94443 10.57940 #> 2 11.54183 11.23805 10.80295 11.50174 10.58845 10.49077 11.00312 11.59618 #> 3 11.85860 11.08182 10.41809 11.65552 11.19431 11.22972 11.02532 11.92557 #> 4 11.42852 11.67259 10.89458 11.84760 11.18421 11.00356 11.13933 10.98184 #> 5 12.29364 11.49053 11.20523 11.06934 11.55876 11.35629 10.48010 11.01524 #> 6 11.75315 11.42171 11.25833 11.41904 10.95493 11.14574 11.07524 11.05781 #> TIMP1 MFAP4 IGFBP3 SLC3A2 ICAM2 GOLM1 LAMP1 #> 1 11.48455 11.96767 11.47007 10.734645 10.115960 10.88351 11.513088 #> 2 10.25182 10.77873 10.85521 9.922367 10.038213 10.99150 10.721215 #> 3 10.93821 10.22429 11.85687 10.310946 10.077127 9.54100 9.663065 #> 4 10.86259 10.09285 10.43150 10.829273 10.933437 10.61162 10.504138 #> 5 10.92977 10.15983 11.24009 10.466815 10.222245 10.63751 10.808492 #> 6 11.67897 10.82060 9.92525 9.903867 9.935344 11.33938 11.019673 #> CHL1 L1CAM TNC MRC2 LAMC1 STAB1 DSC2 #> 1 10.195904 9.745880 10.444384 10.006330 9.945264 9.381339 8.852725 #> 2 9.668918 10.441291 9.459196 10.571839 10.745806 9.542865 10.036710 #> 3 10.453723 10.691794 9.318735 9.253278 8.913234 9.650561 9.147784 #> 4 9.214064 10.555759 9.914370 10.246849 9.498740 10.287718 9.275818 #> 5 9.538203 9.610108 9.726015 9.797533 9.719119 9.582401 9.264676 #> 6 10.297722 8.709777 9.469108 10.233242 10.144140 10.358758 9.887733 #> AOC3 SIRPA CFP PGCP THBS1 #> 1 9.566627 9.071811 8.678501 8.636989 10.140994 #> 2 9.341364 9.483340 10.042900 9.032855 9.515555 #> 3 10.053701 9.846041 9.076228 8.588469 6.242198 #> 4 9.677580 9.119826 8.972266 9.069656 7.487012 #> 5 9.813223 9.429512 9.884448 8.363273 8.032218 #> 6 10.019627 9.612489 8.964238 8.882023 6.674298 # the list of simulated condition vectors # Each element of the list represents one simulation head(simulated_datasets$simulation_train_Ys[[1]]) # first simulation
#> [1] ovarian cancer ovarian cancer control        ovarian cancer
#> [5] control        ovarian cancer
#> Levels: control ovarian cancer

User can also specify the expected fold change of proteins they consider to be differentially abundant between conditions.

# expected_FC = expected_FC: user defined fold change
unique(OV_SRM_train_annotation$Condition) #> [1] control ovarian cancer #> Levels: benign ovarian cancer control expected_FC <- c(1, 1.5) names(expected_FC) <- c("control", "ovarian cancer") set.seed(1212) # Here I randomly select some proteins as differential to show how the function works # The user should prepare this list of differential proteins by themselves diff_proteins <- sample(rownames(OV_SRM_train), 20) simualted_datasets_predefined_FC <- simulateDataset(data = OV_SRM_train, annotation = OV_SRM_train_annotation, num_simulations = 10, # simulate 10 times expected_FC = expected_FC, list_diff_proteins = diff_proteins, select_simulated_proteins = "proportion", protein_proportion = 1.0, protein_number = 1000, samples_per_group = 50, # 50 samples per condition simulate_validation = FALSE, valid_samples_per_group = 50) ## 3. Sample size estimation for classification ### 3.1. designSampleSizeClassification() This function fits the classification model, in order to classify the subjects in the simulated training datasets (in the output of simulatedDataset). Then the fitted model is validated by the (simulated) validation set. Two performance are reported : (1) the mean predictive accuracy : The function trains classifier on each simulated training dataset and reports the predictive accuracy of the trained classifier on the validation data (output of SimulateDataset function). Then these predictive accuracies are averaged over all the simulation. (2) the mean protein importance : It represents the importance of a protein in separating different groups. It is estimated on each simulated training dataset using function varImp from package caret. Please refer to the help file of varImp about how each classifier calculates the protein importance. Then these importance values for each protein are averaged over all the simulation. The list of classification models trained on each simulated dataset, the predictive accuracy on the validation set predicted by the corresponding classification model and the importance value for all the proteins estimated by the corresponding classification model are also reported. ### Arguments • simulations : A list of simulated datasets It should be the name of the output of SimulateDataset function. • classifier : A string specifying which classfier to use. This function uses function train from package caret. The options are 1) rf (random forest calssifier, default option). 2) nnet (neural network), 3) svmLinear (support vector machines with linear kernel), 4) logreg(logistic regression), and 5) naive_bayes (naive_bayes). • parallel : Default is FALSE. If TRUE, parallel computation is performed. ### Example classification_results <- designSampleSizeClassification( simulations = simulated_datasets, parallel = FALSE) Explore the output of designSampleSizeClassification # the number of simulated proteins classification_results$num_proteins
#> [1] 67
# a vector with the number of simulated samples in each condition
classification_results$num_samples #> #> control ovarian cancer #> 50 50 # the mean predictive accuracy over all the simulated datasets, # which have same 'num_proteins' and 'num_samples' classification_results$mean_predictive_accuracy
#> [1] 0.7867052
# the mean protein importance vector over all the simulated datasets,
# the length of which is 'num_proteins'.
#> SERPINA3    GOLM1    TIMP1     LRG1    IGHG2 LGALS3BP
#> 82.81031 68.10258 67.02620 65.36341 52.06357 47.73045

In order to speed up the running time, the package also provides parallel computation for designSampleSizeClassification function.

## try parallel computation to speed up
## The parallel computation may cause error while allocating the core resource
## Then the users can try the abova function without parallel computation
classification_results_parallel <- designSampleSizeClassification(
simulations = simulated_datasets,
parallel = TRUE)

### 3.2 designSampleSizeClassificationPlots()

This function visualizes for sample size calculation in classification. Mean predictive accuracy and mean protein importance under each sample size is from the input data, which is the output from function designSampleSizeClassification. To illustrate the mean predictive accuracy and protein importance under different sample sizes, it generates two types of plots in pdf files as output :

1. The predictive accuracy plot shows the mean predictive accuracy under different sample sizes. The X-axis represents different sample sizes and y-axis represents the mean predictive accuracy.

2. The protein importance plot includes multiple subplots. The number of subplots is equal to list_samples_per_group. Each subplot shows the top num_important_proteins_show most important proteins under each sample size. The Y-axis of each subplot is the protein name and X-axis is the mean protein importance under the sample size.

While varying the number of biological replicates to simulate, the sample size per condition which generates the largest predictive accuracy can be found from the predictive accuracy plot, The optimal sample size per condition can be used to design future experiments. Also, the proteins, which can classify the conditions best, are reported by the protein importance plot.

#### Arguments

• data : A list of outputs from function designSampleSizeClassification. Each element represents the results under a specific sample size. The input should include at least two simulation results with different sample sizes.
• list_samples_per_group : A vector includes the different sample sizes simulated. This is required. The number of simulation in the input data should be equal to the length of list_samples_per_group
• num_important_proteins_show : The number of proteins to show in protein importance plot.
• protein_importance_plot : TRUE(default) draws protein importance plot.
• predictive_accuracy_plot : TRUE(default) draws predictive accuracy plot.
• x.axis.size : Size of x-axis labeling in predictive accuracy plot and protein importance plot. Default is 10.
• y.axis.size : Size of y-axis labels in predictive accuracy plot and protein importance plot. Default is 10.
• predictive_accuracy_plot_width : Width of the saved pdf file for predictive accuracy plot. Default is 4.
• predictive_accuracy_plot_height : Height of the saved pdf file for predictive accuracy plot. Default is 4.
• protein_importance_plot_width : Width of the saved pdf file for protein importance plot. Default is 3.
• protein_importance_plot_height : Height of the saved pdf file for protein importance plot. Default is 3.
• ylimUp_predictive_accuracy : The upper limit of y-axis for predictive accuracy plot. Default is 1. The range should be 0 to 1.
• ylimDown_predictive_accuracy : The lower limit of y-axis for predictive accuracy plot. Default is 0.0. The range should be 0 to 1.
• address : The name of folder that will store the results. Default folder is the current working directory. The other assigned folder has to be existed under the current working directory. An output pdf file is automatically created with the default name of PredictiveAccuracyPlot.pdf and ProteinImportancePlot.pdf. The command address can help to specify where to store the file as well as how to modify the beginning of the file name. If address=FALSE, plot will be not saved as pdf file but showed in window.

#### Example

#### sample size classification ####
# simulate different sample sizes
# 1) 10 biological replicats per group
# 1) 25 biological replicats per group
# 2) 50 biological replicats per group
# 3) 100 biological replicats per group
# 4) 200 biological replicats per group
list_samples_per_group <- c(10, 25, 50, 100, 200)

# save the simulation results under each sample size
multiple_sample_sizes <- list()

for(i in seq_along(list_samples_per_group)){
# run simulation for each sample size
simulated_datasets <- simulateDataset(data = OV_SRM_train,
annotation = OV_SRM_train_annotation,
num_simulations = 10, # simulate 10 times
expected_FC = "data",
list_diff_proteins =  NULL,
select_simulated_proteins = "proportion",
protein_proportion = 1.0,
protein_number = 1000,
samples_per_group = list_samples_per_group[i],
simulate_valid = FALSE,
valid_samples_per_group = 50)

# run classification performance estimation for each sample size
res <- designSampleSizeClassification(simulations = simualted_datasets,
parallel = TRUE)

# save results
multiple_sample_sizes[[i]] <- res
}

## make the plots
designSampleSizeClassificationPlots(multiple_sample_sizes,
list_samples_per_group,
ylimUp_predictive_accuracy = 0.8,
ylimDown_predictive_accuracy = 0.6)

## 4. Visualization for simulated datasets

### 4.1 designSampleSizePCAplot()

This function draws PCA plots for the preliminary dataset and each simulated dataset in simulations (input for this function). It outputs a pdf file where the number of page is equal to the number of simulations plus 1. The first page represents a PCA plot for the input data (OV_SRM_train). Each of the following pages presents a PCA plot under one simulation. X-axis of PCA plot is the first component and y-axis is the second component. This function can be used to validate whether the simulated dataset looks consistent with the input preliminary dataset.

#### Arguments

• simulations : A list of simulated datasets. It should be the output of simulateDataset function.
• which.PCA : Select one PCA plot to show. It can be “all”, “allonly”, or “simulationX”. X should be index of simulation, such as “simulation1” or “simulation5”. Default is “all”, which generates all the plots. “allonly” generates the PCA plot for the whole input dataset. “simulationX” generates the PCA plot for a specific simulated dataset (given by index).
• x.axis.size : Size of x-axis labeling in PCA Plot. Default is 10.
• y.axis.size : Size of y-axis labels. Default is 10.
• dot.size : Size of dots in PCA plot. Default is 3.
• legend.size : Size of legend above Profile plot. Default is 7.
• width : Width of the saved pdf file. Default is 6.
• height : Height of the saved pdf file. Default is 5.
• address : The name of folder that will store the results. Default folder is the current working directory. The other assigned folder has to be existed under the current working directory. An output pdf file is automatically created with the default name of PCAPlot.pdf. The command address can help to specify where to store the file as well as how to modify the beginning of the file name. If address=FALSE, plot will be not saved as pdf file but showed in window.

#### Example

#  output a pdf file with 11 PCA plots
designSampleSizePCAplot(simulated_datasets)