--- title: "exprDesign" author: "LluĂ­s Revilla Sancho" date: "`r Sys.Date()`" output: html_document: fig_caption: true code_folding: show self_contained: yes toc: true toc_float: true toc_depth: 3 vignette: > %\VignetteIndexEntry{exprDesign} %\VignetteEncoding{UTF-8} %\VignetteEngine{knitr::rmarkdown} editor_options: chunk_output_type: console --- ```{r knitsetup, message=FALSE, warning=FALSE, include=FALSE} knitr::opts_knit$set(root.dir = ".") knitr::opts_chunk$set(collapse = TRUE, warning = TRUE) set.seed(445) library("experDesign") ``` # Introduction 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: - If the variable is categorical it tires to randomize the variable across the subgroups. - If the variable is numeric it tries to distribute evenly following the original distribution of values. - If there are `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](https://en.wikipedia.org/wiki/Replication_(statistics))(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. # Previous work 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](https://CRAN.R-project.org/view=ExperimentalDesign) 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](https://bioconductor.org/packages/release/bioc/html/OSAT.html) package handles categorical variables but not numeric data. It doesn't work with our data. - The [minDiff](https://github.com/m-Py/minDiff) package reported in [Stats.SE](https://stats.stackexchange.com/a/326015/105234), handles both numeric and categorical data. But it can only optimize for two nominal criteria. It doesn't work for our data. - The [Omixer](https://bioconductor.org/packages/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](https://cran.r-project.org/package=DeclareDesign) might be relevant for you. Question in [Bioinformatics.SE](https://bioinformatics.stackexchange.com/q/4765/48) I made before developing the package. # Design of Experiment {#DoE} Imagine you have some samples already collected and you want to distributed them in batches: ```{r experDesign_setup} library("experDesign") metadata <- expand.grid(height = seq(60, 80, 5), weight = seq(100, 300, 50), sex = c("Male","Female")) head(metadata, 15) ``` First we can check the data to see if there are any concerns regarding the categories: ```{r check_data} check_data(metadata) ``` There 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: ```{r size} size_data <- nrow(metadata) size_batch <- 24 (batches <- optimum_batches(size_data, size_batch)) # So now the best number of samples for each batch is less than the available (size <- optimum_subset(size_data, batches)) # The distribution of samples per batch sizes_batches(size_data, size, batches) ``` Note 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. # Randomization We can directly look for the distribution of the samples given our max number of samples per batch: ```{r design} desi <- design(metadata, size_batch) # It is a list but we can convert it to a vector with: batch_names(desi) ``` 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. # Randomization and replicates If you need space for replicates to control for batch effect you can use: ```{r replicates} repli <- replicates(metadata, size_batch, 5) lengths(repli) repli ``` Which 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. # Layout We can analyze how these samples would be distributed in a layout of 6x4: ```{r spatial} spati <- spatial(repli, metadata, rows = LETTERS[1:6], columns = 1:4) head(spati) ``` # Report for easy on field usage We can add the batches to the initial data with `inspect()`: ```{r report} report <- inspect(repli, metadata) report2 <- inspect(spati, report, index_name = "position") head(report2) ``` And now we can see the batch and position of each sample # Compare indices If you have two indices you can also compare them: ```{r compare_index} desi2 <- create_subset(nrow(metadata), size_batch) compare_index(metadata, desi, desi2) ``` As many of the variables for multiple subsets are negative it shows that `desi` is better. # Unbalanced setting 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. ```{r unbalanced} 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]) ``` In this dataset there is only one female, resulting in a classroom full of males. Age is independent of the sex or classroom. ```{r unbalanced_design} i <- design(unbalanced, 15) evaluation <- evaluate_index(i, unbalanced) # Mean entropy en each subset rowMeans(evaluation["entropy", , ]) # Original entropy on the dataset evaluate_orig(unbalanced)["entropy", ] # Dispersion of the entropy apply(evaluation["entropy", , ], 1, sd) ``` We can see that in this simple case where a single variable has all the other cases we approximately reached the same entropy levels. # Quality check If you need a subset with the samples that are more diverse you can use the following function: ```{r QC} data(survey, package = "MASS") head(survey) samples <- extreme_cases(survey, size = 10) survey[samples, ] ``` You can also test a given index with `check_index()`: ```{r check_index} check_index(unbalanced, i) ``` Each 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. # Internals 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. ```{r internal, fig.show='hold'} # 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]) head(survey[, keep]) # Set a seed for reproducibility # Looking for groups at most of 70 samples. index <- create_subset(nrow(survey), size_subset = 70) index ``` We can measure how does this index does: ```{r check_index1} score_index1 <- check_index(survey[, keep], index) score_index1 ``` These 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: ```{r design2, warning=FALSE} index2 <- create_subset(nrow(survey), size_subset = 70) ``` Then it compares to the previous index ```{r check_index2} score_index2 <- check_index(survey[, keep], index2) sum(rowMeans(abs(score_index2-score_index1))) ``` If 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 sessioninfo} sessionInfo() ```