R for biostatistics in just 5 minutes (!)                 gilles.hunault "at" univ-angers.fr   Attention:         this is the continuation of  R15          so read first the page R15   There is a French version available here.   Clickable table of contents   1. Why R for biostatistics?   2. References limited and biostatistics oriented   3. Short demo via Datajoy   4. Short demoS via RStudio   1. Why R for biostatistics? All that have been written in favor of R for bioinformatics is also adapted to R for biostatistics: R is free and exhaustively complete for everything that refers to biostatistics. Moreover, because R has been created for statistics in general, all recent and new statistical methods are available in R, as opposed to the classical statistical software such as SAS, SPSS or Statistica. 2. References limited and biostatistics oriented In opposition to books dedicated to bioinformatics with R, there is a plethora of books dedicated to biostatistics with R (click on the image):            If you look on the Web expressions such as biostatistics, "with R", "using R" and books or filetype:pdf you will find thousands (yes, thousands) of books, sometimes published by notorious editors, othertimes only stored on the Web, as you can check below.             3. Short demo via Datajoy Here is a short easy to read R text to show the difference between Pearson's correlation, the classical linear correlation and Spearman's correlation, that is to say, the monotonous rank correlation (all that begins with # is a comment, ignored by R): cat("Calculs de coeficients de corrélation\n") # x et exp(x*x) sont liés mais pas linéairement xCor <- 1:10 yCor <- exp(xCor*xCor) # donc la corrélation au sens de Pearson est faible corp <- cor(xCor,yCor,method="pearson") corpf <- sprintf("%0.3f",corp) pvcp <- cor.test(xCor,yCor,method="pearson")$p.value cat(" pearson : ",corpf) cat(" ; p-value = " ,sprintf("%0.3f",pvcp),"\n",sep="") # alors que celle de Spearman est au maximum cors <- cor(xCor,yCor,method="spearman") corsf <- sprintf("%0.3f",cors) pvcs <- cor.test(xCor,yCor,method="spearman")$p.value cat(" spearman : ",corsf) cat(" ; p-value = ",sprintf("%0.3f",pvcs),"\n",sep="") cat("\n") # vérifications par le tracé titre <- "Tracé direct de y = exp(x*x)" plot(xCor,yCor,main=titre,pch=19,col="red") text(x=1.0,y=2.6*10**43,pos=4,adj=4,labels="Corrélations") text(x=1.5,y=2.5*10**43,pos=4,adj=4,labels=paste("pearson : ",corpf)) text(x=1.5,y=2.4*10**43,pos=4,adj=4,labels=paste("spearman :",corsf,"***")) # données utilisées cat("Voici les valeurs de x et de y\n") print(cbind(xCor,yCor),row.names=FALSE) The result of the execution is: Calculs de coeficients de corrélation pearson : 0.522 ; p-value = 0.122 spearman : 1.000 ; p-value = 0.000 Voici les valeurs de x et de y xCor yCor [1,] 1 2.718282e+00 [2,] 2 5.459815e+01 [3,] 3 8.103084e+03 [4,] 4 8.886111e+06 [5,] 5 7.200490e+10 [6,] 6 4.311232e+15 [7,] 7 1.907347e+21 [8,] 8 6.235149e+27 [9,] 9 1.506097e+35 [10,] 10 2.688117e+43 And the clickable curve is (please note the values on the Y-axis):          A simple cut-and-paste of the above R code in the site Datajoy allows youto check all this by yourself without installating R. 4. Short demoS via RStudio A very strong and important feature of R is its reactivity. For instance, there is in R a package named survivalROC for time depending AUROCS, which are recent computations, that neither SAS, SPSS or Statistica are able to compute. A look at  this link  every day will suffice to check which package is updated ou newly avaliable. That shows that R is evolving very quickly, when SAS, SPSS and Statistica release an update of their software at most once a year, and even, without a lot of new changes. Moreover, to install a new package in R takes a few seconds (in the worst case a few dozen of de seconds) with Rstudio so everything in available in R as soon as you need it. Another noticeable point today (2016) is its ability to deliver reproductible research with the least costs for every user. For example, the following text, that uses the Markdown format, leads to the production, thanks to these two easy to modify instructions output: pdf_document and nbp <- 10, of the parametrized document demor5Biostats.pdf. --- title: "Corrélations de Pearson et de Spearman" output: pdf_document --- # Notion de corrélation La chose la plus importante à se rappeler en [bio]statistiques au niveau des corrélations, c'est que **corrélation n'est pas causalité**, soit, en d'autres termes, ce n'est pas parce que _x_ et _y_ sont liés que _y_ est la cause de _x_. La corrélation au sens de Pearson calcule la force de la relation **linéaire** et linéaire seulement entre _x_ et _y_ alors que la corrélation au sens de Spearman calcule la force de la liaison **monotone** (au sens des fonctions monotones, donc croissantes ou décroissantes). Il est donc correct de dire que la corrélation de Pearson est une corrélation paramétrique et celle de Spearman une corrélation non paramétrique parce que la corrélation de Spearman est basée sur les rangs des valeurs. De façon plus précise, la corrélation de Spearman de $x$ et $y$ est exactement la corrélation de Pearson appliquée aux rangs de $x$ et de $y$. # Exemple numérique ```{r,eval=TRUE,echo=FALSE} nbp <- 10 # paramètre modifiable xCor <- 1:nbp yCor <- exp(xCor*xCor) corp <- cor(xCor,yCor, method="pearson") corpf <- sprintf("%0.3f",corp) pvcp <- cor.test(xCor,yCor, method="pearson")$p.value pvcpf <- sprintf("%0.4f",pvcp) cors <- cor(xCor,yCor, method="spearman") corsf <- sprintf("%0.3f",cors) pvcs <- cor.test(xCor,yCor, method="spearman")$p.value pvcsf <- sprintf("%0.4f",pvcs) ``` Pour bien illuster la différence entre ces deux types de corrélation, il suffit de regarder la corrélation entre $x$ et $y = e^{x^2}$. Il s'agit d'une corrélation "exponentielle du carré" donc non linéaire mais strictement croissante donc monotone. Il n'est donc pas étonnant que pour les valeurs $x=1,2,3..`r nbp`$, on trouve une coefficient de corrélation de Pearson d'environ `r corpf` et pour Spearman `r corsf` exactement, avec comme p-values respectives `r pvcpf` et `r pvcsf`. La courbe suivante qui n'est pas facile à lire (regarder les valeurs sur l'axe $Y$) résume ce phénomène : ```{r,eval=TRUE,echo=FALSE} titre <- "Tracé direct de y = exp(x*x)" plot(xCor,yCor, main=titre,pch=19,col="red") if (nbp==10) { text(x=1.0,y=2.6*10**43, pos=4,adj=4,labels="Corrélations") text(x=1.5,y=2.5*10**43, pos=4,adj=4,labels=paste("pearson : ",corpf)) text(x=1.5,y=2.4*10**43, pos=4,adj=4,labels=paste("spearman :",corsf,"***")) } # fin si ``` If you change the two instructions into output: word_document and nbp <- 8, then R produces, instead of a PDF file, the following Word file demor5Biostats.docx. At last, if you change them to output: html_document et nbp <- 20, then R gives you the following Web page demor5Biostats.html. So, in less that 10 seconds (the time you need to change output: and nbp and to re-run the code) R is able to deliver different external documents with the required parametrization. You can imagine how easy it is to automate a report analyses of date in Excel files for an article or a publication without having to cut/paste results... What a saving of time! Who is against not having any more to transfer results from a statistical software to one's favorite word processing system and to use its time to more "clever"activities?

 

 

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