diff --git a/docs/Testing.fsx b/docs/Testing.fsx index cbf5161c..b9243c58 100644 --- a/docs/Testing.fsx +++ b/docs/Testing.fsx @@ -12,18 +12,24 @@ categoryindex: 0 (*** condition: prepare ***) #I "../src/FSharp.Stats/bin/Release/netstandard2.0/" #r "FSharp.Stats.dll" -#r "nuget: Plotly.NET, 2.0.0-preview.16" +#r "nuget: Plotly.NET, 3.0.1" +#r "nuget: FSharpAux, 1.1.0" +#r "nuget: Deedle, 3.0.0" (*** condition: ipynb ***) #if IPYNB -#r "nuget: Plotly.NET, 2.0.0-preview.16" -#r "nuget: Plotly.NET.Interactive, 2.0.0-preview.16" +#r "nuget: Plotly.NET, 3.0.1" +#r "nuget: Plotly.NET.Interactive, 3.0.2" #r "nuget: FSharp.Stats" +#r "nuget: FSharpAux, 1.1.0" +#r "nuget: Deedle, 3.0.0" #endif // IPYNB open Plotly.NET open Plotly.NET.StyleParam open Plotly.NET.LayoutObjects +open FSharpAux +open Deedle //some axis styling module Chart = @@ -34,6 +40,8 @@ module Chart = |> Chart.withTemplate ChartTemplates.lightMirrored |> Chart.withXAxis (myAxis x) |> Chart.withYAxis (myAxis y) + + (** @@ -49,7 +57,7 @@ _Summary:_ this tutorial explains how to perform various statistical tests with - [T-Test](#T-Test) - [Anova](#Anova) - [F-Test](#F-Test) - - [H Test](#H-Test) + - [H-Test](#H-Test) - [Friedman-Test](#Friedman-Test) - [Wilcoxon signed-rank Test](#Wilcoxon-Test) - [Chi-Squared Test](#Chi-Squared-Test) @@ -63,6 +71,7 @@ _Summary:_ this tutorial explains how to perform various statistical tests with - [Multiple testing](#Multiple-testing) - [Benjamini-Hochberg](#Benjamini-Hochberg) - [Q Value](#Q-Value) + - [SAM](#SAM) FSharp.Stats provides hypothesis tests for different applications. A hypothesis test is a statistical test that is used to determine whether there is enough evidence @@ -368,16 +377,16 @@ let fTestFromParameters = FTest.testVariancesFromVarAndDof sampleF1 sampleF2 (** Using a significance level of 0.05 the sample variances do differ significantly. -### H Test +### H-Test -The H test is also known as Kruskal-Wallis one-way analysis-of-variance-by-ranks and is the non-parametric equivalent of one-way ANOVA. +The H-test is also known as Kruskal-Wallis one-way analysis-of-variance-by-ranks and is the non-parametric equivalent of one-way ANOVA. It is a non-parametric test for comparing the means of more than two independent samples (equal or different sample size), and therefore is an extension of Wilcoxon-Mann-Whitney two sample test. Testing with H test gives information whether the samples are from the same distribution. -A benefit of the H test is that it does not require normal distribution of the samples. +A benefit of the H-test is that it does not require normal distribution of the samples. The downside is that there is no information which samples are different from each other, or how many differences occur. For further investigation a post hoc test is recommended. -The distribution of the H test statistic is approximated by chi-square distribution with degrees of freedom = sample count - 1. +The distribution of the H-test statistic is approximated by chi-square distribution with degrees of freedom = sample count - 1. The implemented H-test is testing for duplicate values in the data. Duplicates lead to ties in the ranking, and are corrected by using a correction factor. @@ -403,7 +412,7 @@ let groupB = [70.;77.;48.;64.;71.;75.] let groupC = [80.;76.;34.;80.;73.;80.] let samples = [groupA;groupB;groupC] -// calculation of the H test +// calculation of the H-test let hResult = HTest.createHTest samples (*** include-value:hResult ***) @@ -411,7 +420,7 @@ let hResult = HTest.createHTest samples (** _PValueRight is significant at a alpha level of 0.05_ -A suitable post hoc test for H tests is Dunn's test. +A suitable post hoc test for H-tests is Dunn's test. *) (** @@ -458,6 +467,7 @@ ID | pre | month 1| month 2| month 3| month 4 + Ranking the results - average if values appear multiple times in one ID @@ -824,8 +834,8 @@ let aErrorAcc = [1. .. 100.] |> List.map (fun x -> x,(1. - 0.95**x)) |> Chart.Line - |> Chart.withAxisTitles "number of tests (k)" "probability of at least one false positive test" - + |> Chart.withXAxisStyle ( "number of tests (k)" ) + |> Chart.withYAxisStyle ( "probability of at least one false positive test") (*** condition: ipynb ***) #if IPYNB aErrorAcc @@ -865,7 +875,8 @@ let bhValues = Chart.Line(pValsAdj,Name="adj") ] |> Chart.combine - |> Chart.withAxisTitles "pValue" "BH corrected pValue" + |> Chart.withXAxisStyle "pValue" + |> Chart.withYAxisStyle "BH corrected pValue" (*** condition: ipynb ***) #if IPYNB @@ -929,8 +940,8 @@ let qHisto = Chart.Line([(0.,pi0);(1.,pi0)],Name="pi0",LineDash=StyleParam.DrawingStyle.Dash) ] |> Chart.combine - |> Chart.withAxisTitles "p value" "density" - + |> Chart.withXAxisStyle "p value" + |> Chart.withYAxisStyle"density" (*** condition: ipynb ***) #if IPYNB qChart @@ -947,4 +958,175 @@ qHisto (***hide***) qHisto |> GenericChart.toChartHTML -(***include-it-raw***) \ No newline at end of file +(***include-it-raw***) + + +(** +###SAM +SAM (Significance Analysis of Microarrays) is a method developed to overcome multiple testing problems, for example in microarray experiments. +SAM, short for Significance Analysis of Microarrays, is a statistical analysis created, but not restricted for, microarray analysis. +It serves as a blue print for any permutation test. +Therefore, high throughput experiments can be analysed using a combined permutation-bootstrap-method. For more in depth information see the [SAM BlogPost](https://csbiology.github.io/CSBlog/posts/7_SAM.html). +*) + +(** +Data: +To use SAM, data need to be in the format (string*float[])[]), with string being the name and float array being the replicates. One way of achieving this is the following data preparation: +
+*) +(** +Columns are samples, here 1 and 2, representing control and factor. Rows are transcript counts (here indicated with gene identifier). +Rows are indicated by the sample name, here 1 and 2, representing control and factor. Columns are indicated with the rowkey(A1), here the gene id. This can be saved as .txt. +The next step is to read in the data, e.g. via deedle, and to create a dataframe. The rows are indexed by the sample name and the rowkeys are extracted. +*) + +let df:Frame = + Frame.ReadCsv(@"data/TestDataSAM.txt",hasHeaders=true,separators = "\t") + // here, the name of A1 is needed. + |> Frame.indexRows "gene" + +// get Rowkeys as Array +let rowheader :string[] = df.RowKeys |> Seq.toArray + +// to separate control and factor sets (sample1 and sample2, respectively), +// the datasets are chunked by the number of replicates (here: triplicates -> chunkBySize 3). +let (preData1,preData2) :float[][] * float [][]= + df + |> Frame.getRows + |> Series.values + |> Seq.map (Series.values >> Seq.toArray >> Array.chunkBySize 3 >> fun x -> x.[0],x.[1]) + |> Array.ofSeq + |> Array.unzip + +// After chunking, the datasets are separated by factor and the rowkey is added to the data for later identification. +let data1 = Array.zip rowheader preData1 +let data2 = Array.zip rowheader preData2 +(** +Optional: Data can be normalised by median centering using the following function: +*) +open SAM +let corrected1 = + let medCorrect = + medianCentering data1 + Array.zip rowheader medCorrect +let corrected2 = + let medCorrect = + medianCentering data2 + Array.zip rowheader medCorrect + +(** +This calculates the median of a column and subtracts it from each value in this column. +The median centering is performed for each column (all samples) separately. +With data1 and data2 , or corrected1 and corrected2, SAM can be performed. +*) +let res = FSharp.Stats.Testing.SAM.twoClassUnpaired 100 0.05 data1 data2 (System.Random(1234)) +(** +The parameters are number of permutations, desired FDR, the datasets and a seed. For balanced permutations as in SAM, it seems to be sufficient to use ~ 100 permutations (also default in samR). The seed is used for randomization of the permutations (System.Random()), or can be fixed to achieve the same results multiple times (e.g. System.Random(1234)). +Result contains now the following information: s0, pi0, delta, upper Cut, lower Cut, positive significant bioitems, negative significant bioitems, non significant bioitems, False Discovery Rate (FDR), and median False Positives. +The following code will help to achieve the typical SAM plot. +*) + +let SAMChart = + + let observed = [| res.NegSigBioitem; res.NonSigBioitem; res.PosSigBioitem|] |> Array.concat + let obs = observed |> Array.map (fun x -> x.Statistics) + let expected = res.AveragePermutations |> Array.map (fun x -> x.Statistics) + let minDi = Seq.min obs + let maxDi = Seq.max obs + + + // positive significant changes + let posExpected = expected.[res.NegSigBioitem.Length + res.NonSigBioitem.Length .. res.NegSigBioitem.Length + res.NonSigBioitem.Length + res.PosSigBioitem.Length-1] + let posChart = + Chart.Point(posExpected,res.PosSigBioitem |> Array.map (fun x -> x.Statistics)) + |> Chart.withLineStyle(Color=Color.fromKeyword Green) + |> Chart.withTraceInfo("positive change",Visible = Visible.True ) + + + // no significant changes + let nonex = expected.[res.NegSigBioitem.Length .. res.NegSigBioitem.Length + res.NonSigBioitem.Length-1] + let nonchart = + Chart.Point(nonex,res.NonSigBioitem |> Array.map (fun x -> x.Statistics)) + |> Chart.withLineStyle(Color=Color.fromKeyword Gray) + |> Chart.withTraceInfo("no change",Visible = Visible.True) + + // negative significant changes + let negex = expected.[0 .. res.NegSigBioitem.Length-1] + let negchart = + Chart.Point(negex,res.NegSigBioitem |> Array.map (fun x -> x.Statistics)) + |> Chart.withLineStyle(Color=Color.fromKeyword Red) + |> Chart.withTraceInfo("negative change",Visible = Visible.True) + + let samValues = + [ + negchart + nonchart + posChart + ] + |> Chart.combine + + let chartConfig = + let svdConfig = + ConfigObjects.ToImageButtonOptions.init( + Format = StyleParam.ImageFormat.SVG) + Config.init ( + ToImageButtonOptions = svdConfig, + ModeBarButtonsToAdd=[ModeBarButton.HoverCompareCartesian] + + ) + + let cutLineUp = [(minDi + res.Delta) ; (maxDi + res.Delta)] + let cutsUp = + Chart.Line(cutLineUp,[minDi;maxDi]) + |> Chart.withLineStyle(Color=Color.fromKeyword Purple,Dash = StyleParam.DrawingStyle.Dash, Width = 0.5) + |> Chart.withTraceInfo("delta",Visible = Visible.True) + let cutLineLow = [(minDi - res.Delta) ; (maxDi - res.Delta)] + let cutsLow = + Chart.Line(cutLineLow,[minDi;maxDi]) + |> Chart.withLineStyle(Color=Color.fromKeyword Purple,Dash = StyleParam.DrawingStyle.Dash, Width = 0.5) + |> Chart.withTraceInfo("delta",Visible = Visible.True) + let linechart = + Chart.Line([minDi;maxDi], [minDi;maxDi]) + |> Chart.withTraceInfo("bisecting angle",Visible = Visible.True) + |> Chart.withLineStyle(Color=Color.fromKeyword Black, Width = 1) + + let uppercut = + let xAnchorUppercut = [minDi .. 5. .. maxDi] + Chart.Line (xAnchorUppercut, List.init xAnchorUppercut.Length (fun x -> res.UpperCut)) + + |> Chart.withTraceInfo("upper cut",Visible = Visible.True) + |> Chart.withLineStyle(Color=Color.fromKeyword Black,Dash = StyleParam.DrawingStyle.Dash, Width = 0.3) + + let lowercut = + Chart.Line([minDi;maxDi],[res.LowerCut;res.LowerCut]) + |> Chart.withTraceInfo("lower cut",Visible = Visible.True) + |> Chart.withLineStyle(Color=Color.fromKeyword Black,Dash = StyleParam.DrawingStyle.Dash,Width = 0.3) + //|> Chart.withXAxisStyle(MinMax = (-15,20)) + + |> Chart.withTraceInfo("lower cut",Visible = Visible.True) + let plot = + [linechart; + samValues; + cutsUp; + cutsLow; + uppercut; + lowercut] + |> Chart.combine + |> Chart.withTitle(title = "SAM results") + |> Chart.withXAxisStyle("expected Score") + |> Chart.withYAxisStyle ("observed Score") + |> Chart.withConfig(chartConfig) + |> Chart.withTemplate(ChartTemplates.lightMirrored) + plot + + + + +(*** condition: ipynb ***) +#if IPYNB +SAMChart +#endif // IPYNB + +(***hide***) +System.IO.File.ReadAllText (__SOURCE_DIRECTORY__ + "/img/SAM005.html") +(*** include-it-raw ***) diff --git a/docs/img/DataStructureSAM.jpeg b/docs/img/DataStructureSAM.jpeg new file mode 100644 index 00000000..cd6eb31f Binary files /dev/null and b/docs/img/DataStructureSAM.jpeg differ diff --git a/docs/img/SAM005.html b/docs/img/SAM005.html new file mode 100644 index 00000000..eee68ce3 --- /dev/null +++ b/docs/img/SAM005.html @@ -0,0 +1,62 @@ + + + + + + + + + + + +
+ + + + + \ No newline at end of file diff --git a/src/FSharp.Stats/Testing/SAM.fs b/src/FSharp.Stats/Testing/SAM.fs index 2a0e86a8..06d526c8 100644 --- a/src/FSharp.Stats/Testing/SAM.fs +++ b/src/FSharp.Stats/Testing/SAM.fs @@ -1,452 +1,662 @@ namespace FSharp.Stats.Testing -(** The module SAM as well as the module s0 were implemented as part of the master thesis Controlling false discovery ratio for differential pull down experiments by Esther Wieczorek submitted in July 2018. -**) + open FSharp.Stats +open FSharpAux + +module SAM = +////////////////////////////////////// Read in data ///////////////////////////////////////////////////////////////////////////////////////////////// +/// read Data via deedle and create 2 samples (control/factor) + +//let df:Frame = +// Frame.ReadCsv(@"C:\..\TestDataSAM.txt",hasHeaders=true,separators = "\t") +// |> Frame.indexRows "gene" + + +//df.Print() + +//let rowheader :string[] = df.RowKeys |> Seq.toArray + + +////////////////////// CHUNKING //////////////////// +//let (sample1,sample2) :float[][] * float [][]= +// df +// |> Frame.getRows +// |> Series.values +// ------------------------ Change the replicate amount ---------------- +// //|> Seq.map (Series.values >> Seq.toArray >> Array.chunkBySize 4 >> fun x -> x.[0],x.[1]) +// |> Seq.map (Series.values >> Seq.toArray >> Array.chunkBySize 3 >> fun x -> x.[0],x.[1]) +// |> Array.ofSeq +// |> Array.unzip + +//Array.map3 (fun id s1 s2 -> sprintf "%s\t%A\t%A" id s1 s2) rowheader sample1 sample2 + +// create tupel from sample name and data for better identification later -module SAM = +//let tupel a b = (a,b) +//let data1 = Array.zip rowheader sample1 +//let data2 = Array.zip rowheader sample2 - /// Represents the relative difference, the pooled standard error and the test statistics +////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// + + /// Type that contains all info regarding SAM for each sample type SAM = { + /// identification of bioitem + ID : string /// relative diffence of mean Ri : float /// pooled standard error Si : float /// test statistics Statistics : float - } + /// local FDR of bioitem + QValue : float + /// foldchange from condition to control + Foldchange : float + } with static member Create id ri si stats qv fc= {ID=id; Ri=ri; Si=si; Statistics=stats; QValue = qv;Foldchange = fc} + + + // Result after calculating SAM + /// SAM Result containing all information + type SAMResult = { + /// small positive constant for independent variance of statistic + S0 : float + /// coefficient to avoid overestimation of FDR + Pi0 : float + /// treshold, absolute difference between observed and expected statistics + Delta : float + /// first Statistic where the difference of observed and expected is greater than delta + UpperCut : float + /// first Statistic where the difference of observed and expected is greater than delta + LowerCut : float + /// Array of all positively regulated bioitems at given FDR + PosSigBioitem : SAM [] + /// Array of all negatively regulated bioitems at given FDR + NegSigBioitem : SAM [] + /// Array of nonsignificant/unchanged bioitems at given FDR + NonSigBioitem : SAM [] + /// Array of the expected values using the average of permutations + AveragePermutations : SAM [] + /// False Discovery Rate + FDR : float + /// Amount of bioitems called significant (positive and negative) in the dataset at given FDR + SigCalledCount : int + /// Amount of "random" significant bioitems in the permutations (false positives) + MedianFalsePositivesCount : float + } with static member Create s0 pi0 delta uc lc psg nesg nosg perms fdr scg mfp = { + S0 = s0 + Pi0 = pi0 + Delta = delta + UpperCut = uc + LowerCut = lc + PosSigBioitem = psg + NegSigBioitem = nesg + NonSigBioitem = nosg + AveragePermutations = perms + FDR = fdr + SigCalledCount = scg + MedianFalsePositivesCount = mfp + } - /// Creates the type SAM - let createSAM ri si stats = - {Ri=ri; Si=si; Statistics=stats} + /// median centering of the data + let medianCentering data = + let calculateMedian:float[] = + data + |> Array.map snd + |> JaggedArray.transpose + |> Array.map Array.median + //printf "medians are %A" calculateMedian + let medianCorrectedData = + data + |> Array.map snd + |> JaggedArray.mapi (fun i x -> x - calculateMedian.[i]) + medianCorrectedData + + /// t-test statistic for observed statistics, used as default. + let getObservedStats (s0:float) (dataA:(string*float[])[]) (dataB:(string*float[])[])= + + let calcStats (a:string*float[]) (b:string*float[]) = + // test is arrays are same length + if (fst a) <> (fst b) then failwithf "row identifier do not match" + // get name of observed sample + let idOfBioitem = fst a + // get datapoints + let dataA = snd a + let dataB = snd b + + // get average of one sample + let ma,mb = Array.average dataA,Array.average dataB + let fc = mb/ma + let ri = (fun x y -> x - y) mb ma + let si = + // length of arrays + let n1 = dataA |> Array.length |> float + let n2 = dataB |> Array.length |> float + // denominator of equation + let denominator = (fun x y -> ((x + y)-2.)) n1 n2 + + let sums = + ((dataA |> Array.sumBy (fun v -> (v - ma) * (v - ma))) + (dataB |> Array.sumBy (fun v -> (v - mb) * (v - mb)))) + + let firstPart = + (fun x y -> 1./x + 1./y) n1 n2 + let final = (((firstPart)*(sums/denominator))**0.5) + final - // small positive constant chosen to minimize the coefficient of variation of the test statistics - // samples with treatment A - // samples with treatment U + let statistic = ri / (si + s0) - /// Calculates SAM test statistics for two class unpaired data - let calculateTwoClassUnpaired s0 (dataA:float array array) (dataU:float array array) = - - let calcStats s0 (a:float[]) (u:float[]) = - let ma,mu = Array.average a,Array.average u - let ri = mu - ma - let si = - let n = ((1.0/ float a.Length) + (1.0/ float u.Length)) / float (a.Length+u.Length-2 ) - n * ((a |> Array.sumBy (fun v -> (v - ma) * (v - ma))) + (u |> Array.sumBy (fun v -> (v - mu) * (v - mu)))) - |> sqrt + + SAM.Create idOfBioitem ri si statistic nan fc - createSAM ri si (ri/(si+s0)) + Array.map2 (fun a b -> calcStats a b) dataA dataB - Array.map2 (fun a u -> calcStats s0 a u) dataA dataU - let expectedValue (dibs:SAM[][]) = - let iterations = dibs.Length - let dei = - dibs - |> JaggedArray.transpose - |> Array.map (fun tt -> - let (ri',si',di') = tt |> Array.fold (fun (ri,si,di) t -> ri+t.Ri,si+t.Si,di + t.Statistics) (0.,0.,0.) - createSAM (ri' / float iterations) (si' / float iterations) (di' / float iterations) - ) - - dei - - ///Permutes all the samples. Different treatments are NOT mixed. Then the statistics for the permuatations is calculated. - let permutationWithin calculate iterations s0 (dataA:float array array) (dataU:float array array) = - let dataA' = JaggedArray.copy dataA - let dataU' = JaggedArray.copy dataU - let dibs= - [|0..iterations-1|] - |> Array.map (fun _ -> - let rndDataA = JaggedArray.shuffleColumnWiseInPlace dataA' - let rndDataU = JaggedArray.shuffleColumnWiseInPlace dataU' - let tmp = calculate s0 rndDataA rndDataU - tmp |> Array.sortInPlaceBy (fun t -> t.Statistics) - tmp - ) - dibs - // for each di count dib > di - - - // TODO - /// Permutes all the samples. Different treatments are mixed. - let permutationBalanced calculate iterations s0 (dataA':float array array) (dataU':float array array) = - let half=int (float dataA'.[0].Length/ 2.) - let amount= dataA'.Length - let reps= dataA'.[0].Length - - let shuffleFisherYates (random:FSharp.Stats.Random.IRandom) (arr : _[]) = - let arr' = Array.copy arr - for i = arr.Length downto 1 do - let j = random.NextInt(i) - let tmp = arr'.[j] - arr'.[j] <- arr'.[i - 1] - arr'.[i - 1] <- tmp - arr' - - let dib= - let rec balanced index (dataA:float[][]) (dataU:float[][]) temp1= - if index < iterations then - let rndDataA0,rndDataU0 = Array.unzip ([|0..amount-1|]|>Array.map (fun x -> ([|dataA.[x].[0..half-1];dataU.[x].[half..reps-1]|]|> Array.concat),([|dataU.[x].[0..half-1];dataA.[x].[half..reps-1]|]|> Array.concat))) - let rndDataA = rndDataA0|> Array.map (fun x -> shuffleFisherYates Random.rndgen x) - let rndDataU = rndDataU0|> Array.map (fun x -> shuffleFisherYates Random.rndgen x) - let temp= calculate s0 rndDataA rndDataU - temp|> Array.sortInPlaceBy ( fun x -> x.Statistics) - balanced (index+1) rndDataA rndDataU (temp::temp1) - else temp1|> List.toArray - balanced 0 dataA' dataU' [] - dib - - - /// Permutes all the samples. Different treatments are mixed. - let permutationImbalanced calculate iterations s0 (dataA:float array array) (dataU:float array array) = - let dataA' = JaggedArray.copy dataA - let dataU' = JaggedArray.copy dataU - let data = Array.zip dataA' dataU' - - - // Case specific FisherYates shuffling - let shuffleInPlace' (random:FSharp.Stats.Random.IRandom) (arr : array<('a[]*'a[])>) = - let rowCount = arr.Length - let colCountFst,colCountSnd = - if rowCount < 1 then 0,0 else Array.length ( fst(arr.[0]) ), Array.length ( snd(arr.[0]) ) - let colCount = colCountFst + colCountSnd + + + module S0 = + /// S0 estimation + // the s0 percentiles used in R! are [|0. .. 0.05 .. 1.|] + // can be changed to users preference + let estS0 (values:SAM[]) (s0perc: float []) = + // tt is Statistics (Score) + // si is Si(Standard Deviation) + let tt = values |> Array.map (fun x -> x.Statistics) + let si = values |> Array.map (fun x -> x.Si) + + //separate the list of (tt,si) tuples into 100 percentiles + //The very first value is assigned to the first percentile + let percentilesOfSi = + Array.init 100 (fun percentile -> + let lower = Quantile.mode (float percentile / 100.) si + let upper = Quantile.mode ((float percentile + 1.) / 100.) si + Array.zip tt si + |> Array.filter (fun (t,s) -> + if percentile = 0 then + lower <= s && s <= upper + else + lower < s && s <= upper + ) + ) + + //for the given quantile, determine an estimate of s0 (as quantile of si) and calculate the statistics within the given percentiles + let getCVFromQuantile quantile = + //current s0 estimate based on sis + let w = + // if perc = 0 take correctionfactor s0 = 0, else calculate percentile + if quantile = 0. then + 0. + else Quantile.mode quantile si + + //With the given s0 calculate the median absolute deviation (mad) of every percentile. + //Determine the cv of the mad. + percentilesOfSi + |> Array.map (fun percentiles -> + let tt2 = + percentiles + |> Array.map (fun (tt,si) -> + let tnew = tt * si / (si + w) + tnew + ) + tt2 + |> Array.filter (fun t -> not (nan.Equals t) && not (infinity.Equals t)) + |> Seq.medianAbsoluteDev + ) + |> fun x -> + let cv = Seq.cv x + // this filter is implemented in R!, not completely sure of function because we didn't have that case + let siWOnull = si |> Array.filter (fun x -> x <> 0.) + let s0 = Quantile.mode quantile siWOnull + quantile,cv,s0 + + s0perc + |> Array.map getCVFromQuantile + + /// search s0 where coefficient of variation is minimal. + /// input is the result from estS0 function + let s0ForMinCV s0List= s0List |> Array.minBy (fun (x,y,z) -> y) |> fun (x,y,z) -> z + + + module Permutations = + + /// default permutation method. + /// create permutations using Fisher Yates Shuffling + let getPermutations iterations s0 (dataA:(string*float[])[]) (dataB:(string*float[])[]) rnd = + let dataset = + dataA + |> Array.mapi (fun i (id,data) -> + id,Array.append data (snd dataB.[i]) + ) + let replicateCount1 = (snd dataA.[0]).Length + let replicateCount2 = (snd dataB.[0]).Length - let getByIndex i (darr:'a[]*'a[]) = - if i > colCountFst-1 then (snd(darr)).[i-colCountFst] else (fst(darr)).[i] - - let setByIndexInPlace i value (darr:'a[]*'a[]) = - if i > colCountFst-1 then (snd(darr)).[i-colCountFst] <- value else (fst(darr)).[i] <- value - - - for colI = colCount downto 1 do - for rowI = rowCount downto 1 do - // Pick random element to swap. - let i = random.NextInt(rowI) // 0 <= i <= rowI-1 - let j = random.NextInt(colI) // 0 <= j <= colI-1 - // Swap. - let tmp = arr.[i] |> getByIndex j - arr.[i] |> setByIndexInPlace j (arr.[rowI - 1] |> getByIndex (colI - 1)) - arr.[rowI - 1] |> setByIndexInPlace (colI - 1) tmp - arr + Array.init iterations (fun _ -> + let shuffleTemplate = + Array.init (replicateCount1 + replicateCount2) id + |> FSharpAux.Array.shuffleFisherYates rnd + + let shuffledSampleA,shuffledSampleB = + dataset + |> Array.map (fun (id,row) -> + shuffleTemplate + |> Array.map (fun si -> row.[si]) + |> fun x -> + (id,x.[..replicateCount1-1]),(id,x.[replicateCount2..]) + ) + |> Array.unzip - [|0..iterations-1|] - |> Array.map (fun _ -> - let rndData = shuffleInPlace' Random.rndgen data - let rndDataA,rndDataU = Array.unzip rndData - let tmp = calculate s0 rndDataA rndDataU - tmp |> Array.sortInPlaceBy (fun t -> t.Statistics) - tmp - ) - - - // TODO: move to Array private - /// Iterates over elements of the input array and increase the counter if the function returens true - let private countIf f (arr : _[]) = - let mutable counter = 0 - for i=0 to arr.Length-1 do - if f arr.[i] then - counter <- counter + 1 - counter - - // TODO: move to Array private - let private binarySearchIndexBy compare (arr: 'a []) = - if arr.Length = 0 then ~~~(1) else - - let rec loop lower upper = - if lower > upper then ~~~ lower - else - let middle = lower + ((upper - lower) / 2) - let comparisonResult = compare arr.[middle] - if comparisonResult = 0 then - middle - elif comparisonResult > 0 then - loop lower (middle - 1) - else - loop (middle + 1) upper - loop 0 (arr.Length-1) - - // TODO: move to Array private - let private bindBy (objArr:float[]) (arr:float[]) = - let arr' = Array.copy arr - let objArr' = Array.copy objArr - let index = Array.init arr.Length id - System.Array.Sort(objArr',index) - for i=1 to arr'.Length-1 do - if arr'.[index.[i]] < arr'.[index.[i-1]] then - arr'.[index.[i]] <- arr'.[index.[i-1]] - arr' - - /// Estimates pi0. Chosen to minimize the coefficient of variation of the test statistics - let estimatePi0 (dis:SAM []) (dibs:SAM[][]) = - let perms = - dibs - |> Array.collect (fun x -> x |> Array.map (fun y -> y.Statistics)) - let q25 = Quantile.InPlace.modeInPLace 0.25 perms - let q75 = Quantile.InPlace.modeInPLace 0.75 perms - //let q0,q50=modeInPLace 0.0 perms , modeInPLace 0.5 perms - let notSig = - dis |> countIf (fun x -> q25 < x.Statistics && x.Statistics < q75) - - float notSig / (0.5 * float dis.Length) - - - ///Finds all pairs of asymmetric cutoffs according to the differences between di and dEi - let getAsymmetricCuts (di : SAM []) (dei : SAM []) = - let getDelta (_,_,delta) = delta - let getDi (di,_,_) = di - let replaceDeltaAbs (disA,deisA,deltaA) (disB,deisB,deltaB) = (disA,deisA,(abs deltaB)) - let di' = di |> Array.sortBy (fun x -> x.Statistics) - let dei' = dei |> Array.sortBy (fun x -> x.Statistics) - let ups,los = - Array.zip di' dei' - |> Array.map (fun (di,dei) -> di.Statistics,dei.Statistics, (di.Statistics - dei.Statistics)) - |> Array.partition (fun (dis,deis,delta) -> deis >= 0.) - //monoton increase ups (inplace) - for i=1 to ups.Length-1 do - if getDelta ups.[i] < getDelta ups.[i-1] then - ups.[i] <- replaceDeltaAbs ups.[i] ups.[i-1] - - // monoton increase los (inplace) - let los' = los |> Array.map (fun (a,b,c) -> a,b, abs c) - for i=1 to los'.Length-1 do - if getDelta los'.[i] > getDelta los'.[i-1] then - los'.[i] <- replaceDeltaAbs los'.[i] los'.[i-1] - // find the matching cutoffs - let cuts set1 set2= - set1 - |> Array.map (fun x -> - let cur = - set2 - |> Array.filter (fun (dis,deis,delta) -> delta >= (getDelta x) ) - let y = - if Array.isEmpty cur then - let (dis,deis,delta) = x - (dis,deis,(set1 |> Array.maxBy getDelta |> getDelta)) - else - cur |> Array.minBy (fun (dis,deis,delta)-> delta ) - x,y) - - let cutsFromUp = cuts ups los' |> Array.map (fun (a,b) -> getDi a, getDi b ) - let cutsFromLow = cuts los' ups |> Array.map (fun (a,b) -> getDi b, getDi a ) - - [|cutsFromUp;cutsFromLow|]|> Array.concat |> Array.distinct - + let stats = getObservedStats s0 shuffledSampleA shuffledSampleB |> Array.sortBy (fun x -> x.Statistics) + stats + ) - ///Finds all pairs of symmetric cutoffs - // an array conmtaining all the pairs of cuts, the higher cut is the first, the lower cut the second value - let getSymmetricCuts (di : SAM []) (dei : SAM [])= - let ups,los = - di - |> Array.map (fun b -> b.Statistics) - |> Array.sort - |> Array.map (fun x -> (x, -x)) - |> Array.partition (fun (a,b) -> a >= 0.) - [|ups;los|]|> Array.concat |> Array.distinct - + /// expected Stats are the scores/values obtained from the permutations via averaging + // ID stays unchanged + let getExpectedStats (expStats:SAM[][]) = + let iterations = expStats.Length + let expAvgStats = + expStats + |> Array.map (Array.sortBy (fun x -> x.Statistics)) + |> JaggedArray.transpose + |> Array.map (fun tt -> + let (id',ri',si',di') = tt |> Array.fold (fun (id,ri,si,di) t -> t.ID,ri+t.Ri,si+t.Si,di + t.Statistics) ("",0.,0.,0.) + SAM.Create id' (ri' / float iterations) (si' / float iterations) (di' / float iterations) nan nan + ) + expAvgStats - let qvalueByCut pi0 (dis: SAM []) (dibs: SAM[][]) (cut:(float*float)) = - // median amount of permutations above and below the cuts - let cut1,cut2 = cut - let gmed = - dibs - |> Array.map (fun arr -> arr |> countIf ( fun x -> x.Statistics >= cut1 || x.Statistics <= cut2) ) - |> Array.median + // default for Microarray Analysis : + // let permStats = getPermutations 100 s0 dataA dataB + // let expectedStats = getExpectedStats permStats + + module SAMHelper = + + /// function for counting + let private countIf f (arr : _[]) = + let mutable counter = 0 + for i=0 to arr.Length-1 do + if f arr.[i] then + counter <- counter + 1 + counter + + //let countIfCuts cutlow cuthigh (arr : SAM[]) = + // arr |> countIf (fun x -> x.Statistics > cuthigh || x.Statistics < cutlow) + + /// estimate pi0 using the quantile method. Helps to not overestimate the False Discovery Rate + let estimatePi0 (obsStats:SAM []) (expStats:SAM[][]) = + let perms = + expStats + |> Array.collect (fun x -> x |> Array.map (fun y -> y.Statistics)) + // obtain 25% and 75% + let q25 = Quantile.InPlace.modeInPLace 0.25 perms + let q75 = Quantile.InPlace.modeInPLace 0.75 perms + // non significant data are between the 25 and 75 quantile + let notSig = + obsStats |> countIf (fun x -> q25 < x.Statistics && x.Statistics < q75) + + float notSig / (0.5 * float obsStats.Length) + + /// ensures continuous increase of data. + let monotonizeIncreasing (accessionFun: 'a -> float) (replaceFun: 'a -> float -> 'a) (input : 'a []) = + let copy = Array.copy input + for i=1 to copy.Length-1 do + if accessionFun copy.[i] < accessionFun copy.[i-1] then + copy.[i] <- replaceFun copy.[i] (accessionFun copy.[i-1]) + copy + + /// ensures continuous decrease of data. + let monotonizeDecreasing (accessionFun: 'a -> float) (replaceFun: 'a -> float -> 'a) (input : 'a []) = + let copy = Array.copy input + for i=1 to copy.Length-1 do + if accessionFun copy.[i] > accessionFun copy.[i-1] then + copy.[i] <- replaceFun copy.[i] (accessionFun copy.[i-1]) + copy + + + /// default in R!. Calculates asymmetric cuts for each delta present. + // can be substituted with symmetric cuts (not implemented yet) + let getDeltaAndAsymmCuts (obsStats : SAM[]) (expAvgStats: SAM[]) = + let getDelta (_,_,delta) = delta + // di' are sorted Statistics from the observed (measured) values + let di' = obsStats |> Array.sortBy (fun x -> x.Statistics) + // dei' are the sorted Statistics from the averaged values (permutations) + let dei' = expAvgStats |> Array.sortBy (fun x -> x.Statistics) + // ups and los observed Statistics partitioned at 0. to sort them to positive and negative + let ups,los = + Array.zip di' dei' + |> Array.map (fun (di,dei) -> di.Statistics , dei.Statistics , (di.Statistics - dei.Statistics)) + |> Array.partition (fun (dis,deis,delta) -> dis >= 0.) - let fdis = dis |> countIf (fun v -> v.Statistics > cut1 || v.Statistics < cut2) + // obtaining cuts based on delta (difference between observed and averaged statistics) + // finding matching positive or negative statistic as cutoff + let getCuts set1 set2 = + set1 + |> Array.map (fun (currentDi, currentDei, currentDelta) -> + if currentDi > 0. then + set2 + |> Array.tryFindBack (fun (di,dei,delta) -> delta >= currentDelta) + |> fun x -> + match x with + | Some (di,dei,delta) -> (di,currentDi),currentDelta + | None -> (-infinity,currentDi),currentDelta + else + set2 + |> Array.tryFind (fun (di,dei,delta) -> delta >= currentDelta) + |> fun x -> + match x with + | Some (di,dei,delta) -> (currentDi,di),currentDelta + | None -> (currentDi,infinity),currentDelta + ) + let los' = los |> Array.map (fun (a,b,c) -> a,b, abs c ) + // increase of cutoffs by +1E-80 to include the statistic itself that is used as cutoff + let ups' = monotonizeIncreasing getDelta (fun (di,dei,delta) newDelta -> (di,dei,newDelta+1E-80)) ups + let los' = monotonizeDecreasing getDelta (fun (di,dei,delta) newDelta -> (di,dei,newDelta-1E-80)) los' + let resultingcuts = [|getCuts ups' los';getCuts los' ups'|] |> Array.concat |> Array.distinct - let medianfdr= (pi0 * float gmed)/( float fdis) - //medianfdr*100. - medianfdr - - - let qvalues pi0 (dis: SAM []) (dibs: SAM[][]) (cuts:(float*float)[]) = - let convertIndex (arr: _ []) (i:int) = - if i < 0 then - let i' = (~~~i)-1 - if i' < 0 then arr.[0] else arr.[i'] - else - if i >= arr.Length then arr.[arr.Length-1] else arr.[i] - - let convertIndex' (arr: _ []) (i:int) = - if i < 0 then - let i' = (~~~i) - if i' < 0 then arr.[0] else - if i' >= arr.Length then arr.[arr.Length-1] else arr.[i'] - else - if i >= arr.Length then arr.[arr.Length-1] else arr.[i] - - + resultingcuts + + /// median false positives are obtained by counting how many statistics (from permuted data) fall outside of the cuts by chance. + /// Permuted data should show no effect/change, therefor the ones that do are false positive + let getMedianFalsePositives cut expStats = + let cut1,cut2 = cut + expStats + |> Array.map (fun arr -> arr |> countIf ( fun x -> x.Statistics >= cut2 || x.Statistics <= cut1) ) + |> Array.map float + |> Array.median + + /// amount of Bioitems that are more extreme than the cuts and therefor are called significant + let getSignificantBioitem cut obsStats = + let cut1,cut2 = cut + obsStats |> countIf (fun v -> v.Statistics > cut2 || v.Statistics < cut1) + + /// calculate the median False Discovery Rate + let getMedianFdr pi0 medianFalsePos significantBioitems = + //if no permutation statistic is significant and no observed statistic is significant the fdr is 0 (not nan) + if significantBioitems = 0. then + if medianFalsePos = 0. then + 0. + else 1. + else (pi0 * float medianFalsePos)/( float significantBioitems) + - let cuToQ,clToQ = - cuts - |> Array.map (fun cut -> - let q = qvalueByCut pi0 dis dibs cut - (fst cut,q),(snd cut,q) ) - |> Array.unzip - // Ensure monotonicity within q values - let cuToQ = - let cu,q = cuToQ |> Array.unzip - let q' = bindBy (cu |> Array.map (fun x -> -x)) q - Array.zip cu q' - - let clToQ = - let cl,q = clToQ |> Array.unzip - let q' = bindBy cl q - Array.zip cl q' - - cuToQ |> Array.sortInPlaceBy fst - clToQ |> Array.sortInPlaceBy fst - dis - |> Array.map (fun s -> - let cuQ = binarySearchIndexBy (fun (cu,v) -> compare cu s.Statistics) cuToQ |> convertIndex cuToQ |> snd - let clQ = binarySearchIndexBy (fun (cl,v) -> compare cl s.Statistics) clToQ |> convertIndex' clToQ |> snd - min cuQ clQ - |> min 1.0 - ) - - - /// Module with different estimation methods computing s0 - module S0 = + + /// get the smallest cut and corresponding delta for chosen FDR + // Result has to be smallestCutForFDR,delta + let smallestCutAndDeltaForFDR cuts expStats obsStats fdr pi0 = + cuts + |> Array.filter (fun (cut,delta) -> + let tmpfdr = + let medianFalsePos = getMedianFalsePositives cut expStats + let significantBioitems = getSignificantBioitem cut obsStats - - /// Computes s0 using the nearest rank method - let nearestRank percentile (tt:array) = - if percentile < 0. || percentile > 100.0 then failwith "Percentile must be between 0.0 and 100.0" - let sortedTT= - tt - |> Array.sortBy (fun t -> t.Si) - let index = System.Math.Round( percentile / 100. * float tt.Length, 0) + getMedianFdr pi0 medianFalsePos ( significantBioitems |> float) + // "take the smallest delta such that FDR <= alpha " + // alpha as in significance - sortedTT.[(int index)].Si + tmpfdr <= fdr + + ) + |> Array.minBy snd - /// Creates s0 by calulating the mean of si (pooled standard error ) - let median (tt:array) = - tt - |> Array.map (fun t -> t.Si) - |> Array.median + /// Calculate the FDR for each cut + let fdrsPerCut cuts expStats obsStats pi0 = + cuts + |> Array.map (fun (cut,delta) -> + let medianFalsePos = getMedianFalsePositives cut expStats + let significantBioitems = getSignificantBioitem cut obsStats + let localFDR = + getMedianFdr pi0 medianFalsePos ( significantBioitems |> float) + + (cut,localFDR) + ) + + + /// obtain negative cut for chosen FDR + let negCutToFDR fdrsPerCut = + fdrsPerCut + |> Array.map (fun ((lower,upper),fdr) -> lower,fdr) + |> Array.sortByDescending fst + |> monotonizeDecreasing snd (fun (origCut,fdr) newFdr -> origCut,newFdr) + //to elimiate same cuts with multiple fdrs, minimal fdr per cut are isolated + |> Array.sortBy snd + |> Array.distinctBy fst + //Array must be sorted by cut (descending because of negative values) + |> Array.sortByDescending fst + + /// obtain positive cut for chosen FDR + let posCutToFDR fdrsPerCut = + fdrsPerCut + |> Array.map (fun ((lower,upper),fdr) -> upper,fdr) + |> Array.sortBy fst + |> monotonizeDecreasing snd (fun (origCut,fdr) newFdr -> origCut,newFdr) + //to elimiate same cuts with multiple fdrs, minimal fdr per cut are isolated + |> Array.sortBy snd + |> Array.distinctBy fst + //Array must be sorted by cut + |> Array.sortBy fst - /// Estimates s0. Chosen to minimize the coefficient of variation of the test statistics - let estimate (tt:array) = //(sd:array) (tt:array) = - // Refactor to Care - let partition predicate source = - let map = - source - |> Seq.groupBy predicate - |> Map.ofSeq - let get flag = - map - |> Map.tryFind flag - |> Option.defaultValue Seq.empty - get true, get false - - - // Refactor to Care - let bind (predicate:'a -> 'b -> bool) (binder:seq<'a>) (source:seq<'b>) = - let en = binder.GetEnumerator() - let rec loop rest = - seq { - match en.MoveNext() with - | false -> () - | true -> - let a,rest' = partition (fun x -> predicate en.Current x) rest - yield a - yield! loop rest' - } - loop source - - - let si = tt |> Array.map (fun t -> t.Si) - let di = tt |> Array.map (fun t -> t.Statistics) - let si' = Array.copy si |> Array.sort - let s0percentile= [|0. .. 0.05 .. 1.|] - let br = [|0. .. 0.01 .. 1.|] |> Array.map (fun p -> Quantile.mode p si') - let cvSd = - let tmp = Seq.zip si di - s0percentile - |> Array.map (fun k -> - let w = if k = 0. then 0. else Quantile.mode k si' - let mads = - bind (fun a b -> fst b < a) br tmp - |> Seq.map (fun v -> - v - |> Seq.map (fun (t,s) -> t * s / (s + w)) - |> Seq.medianAbsoluteDev - //|> fun x -> x / 0.64 + + // >= and <= because of "The q-value of a gene is the FDR for the gene List that includes that gene and all genes that are more significant (SAM Manual) + // Storey Chapter : d(j) - de >= delta & de - d(j) <= delta + // Qvalue calculation is done as in R! + // Cuts corresponding to the chosen FDR are used. First data are parted at 0. for use of positive and negative cuts. + // Array.tryFind searches the statistic in observed statistics that is greater/less or equal than the cut. + // The nearest cut from observed statistics is matched with the FDR of that statistic (QValue = fdr) + + + // negative and positive cut are results from negCutToFDR and posCutToFDR + /// returns the value for each sample where it is firstly called significantly different. + let getQvalues obsStats negativeCut positiveCut = + obsStats + |> Array.map (fun currentBioitem -> + if currentBioitem.Statistics < 0. then + let firstLowerCut = + negativeCut + |> Array.tryFind (fun (lowerCut,fdr) -> + lowerCut <= currentBioitem.Statistics ) - |> Seq.toArray - |> Array.map (fun (x) ->if nan.Equals(x) then 100. else x) - printfn "s0Perc = %f, cv = %f" k (Seq.cv mads) - k, Seq.cv mads //Seq.stDev mads / Array.median mads - + match firstLowerCut with + | Some (cut,fdr) -> {currentBioitem with QValue = fdr} + | None -> {currentBioitem with QValue = 1.} + else + let firstGreaterCut = + positiveCut + |> Array.tryFind (fun (upperCut, fdr)-> + upperCut >= currentBioitem.Statistics + ) + match firstGreaterCut with + | Some (cut,fdr) -> {currentBioitem with QValue = fdr} + | None -> {currentBioitem with QValue = 1.} ) - - let pMinCvSd = cvSd |> Array.minBy snd |> fst - Quantile.mode pMinCvSd si' - /// Estimates s0 from given data set. Chosen to minimize the coefficient of variation of the test statistics - let estimateFrom calculate (dataA:float array array) (dataU:float array array) = - let tt = calculate 0.0 dataA dataU - estimate tt + /// default version of SAM. Two class unpaired calculation. Rnd can be either System.Random() or System.Random(seed). + let twoClassUnpaired iterations fdr data1 data2 rnd = + + let getMedianFalsePositives cut expStats = + let cut1,cut2 = cut + + // function for counting + let countIf' (arr : SAM[]) = + let mutable counter = 0 + for i=0 to arr.Length-1 do + if arr.[i].Statistics > cut2 || arr.[i].Statistics < cut1 then + counter <- counter + 1 + counter + expStats + |> Array.map (fun permutation -> + permutation + |> countIf' + ) + |> Array.map float + |> Array.median + + + let getSignificantBioitem cut obsStats = + let cut1,cut2 = cut + + let countIf' (arr : SAM[]) = + let mutable counter = 0 + for i=0 to arr.Length-1 do + if arr.[i].Statistics > cut2 || arr.[i].Statistics < cut1 then + counter <- counter + 1 + counter + + obsStats + |> countIf' + + let getMedianFdr pi0 medianFalsePos significantBioitems = + //if no permutation statistic is significant and no observed statistic is significant the fdr is 0 (not nan) + if significantBioitems = 0. then + if medianFalsePos = 0. then + 0. + else 1. + else (pi0 * float medianFalsePos)/( float significantBioitems) + + let priorStats = getObservedStats 0.0 data1 data2 + let s0prior = S0.estS0 priorStats [|0. .. 0.05 .. 1.|] + let s0 = s0prior |> Array.minBy (fun (x,y,z) -> y) |> fun (x,y,z) -> z + let obsStats = getObservedStats s0 data1 data2 |> Array.sortBy (fun x -> x.Statistics) + let expStats = Permutations.getPermutations iterations s0 data1 data2 rnd + let expAvgStats = Permutations.getExpectedStats(expStats) + let cuts = SAMHelper.getDeltaAndAsymmCuts obsStats expAvgStats + let pi0 = SAMHelper.estimatePi0 obsStats expStats + let fdrsPerCut = + cuts + |> Array.map (fun (cut,delta) -> + let medianFalsePos = getMedianFalsePositives cut expStats + let significantBioitem = getSignificantBioitem cut obsStats + let localFDR = + getMedianFdr pi0 medianFalsePos ( significantBioitem |> float) + (cut,localFDR,delta) + ) + + let smallestCutForFDR,delta = + let smallestCut = + fdrsPerCut + |> Array.filter (fun (cut,tmpfdr,delta) -> + tmpfdr <= fdr + ) + match smallestCut with + | [||] -> ((0.,0.),100000.) + | _ -> + smallestCut + |> Array.minBy (fun (a,b,c) -> c) + |> (fun (a,b,c) -> a,c) + + match smallestCutForFDR,delta with + | ((0.,0.),100000.) -> + let defaultIfNoSignificance:SAM[]= [||] + printfn "No significant results were found" + SAMResult.Create s0 pi0 delta 0. 0. defaultIfNoSignificance defaultIfNoSignificance obsStats expAvgStats 0. 0 0 + | _ -> + let negCutToFDR = + fdrsPerCut + |> Array.map (fun ((lower,upper),fdr,delta) -> lower,fdr) + |> Array.sortByDescending fst + |> SAMHelper.monotonizeDecreasing snd (fun (origCut,fdr) newFdr -> origCut,newFdr) + //to elimiate same cuts with multiple fdrs, minimal fdr per cut are isolated + |> Array.sortBy snd + |> Array.distinctBy fst + //Array must be sorted by cut (descending because of negative values) + |> Array.sortByDescending fst + + let posCutToFDR = + fdrsPerCut + |> Array.map (fun ((lower,upper),fdr,delta) -> upper,fdr) + |> Array.sortBy fst + |> SAMHelper.monotonizeDecreasing snd (fun (origCut,fdr) newFdr -> origCut,newFdr) + //to elimiate same cuts with multiple fdrs, minimal fdr per cut are isolated + |> Array.sortBy snd + |> Array.distinctBy fst + //Array must be sorted by cut + |> Array.sortBy fst + + // >= and <= because of "The q-value of a gene is the FDR for the gene List that includes that gene and all genes that are more significant (SAM Manual) + // Storey Chapter : d(j) - de >= delta & de - d(j) <= delta + let getQvalues obsStats = + obsStats + |> Array.map (fun currentBioitem -> + if currentBioitem.Statistics < 0. then + let firstLowerCut = + negCutToFDR + |> Array.tryFind (fun (lowerCut,fdr) -> + lowerCut <= currentBioitem.Statistics + ) + match firstLowerCut with + | Some (cut,fdr) -> {currentBioitem with QValue = fdr} + | None -> {currentBioitem with QValue = 1.} + else + let firstGreaterCut = + posCutToFDR + |> Array.tryFind (fun (upperCut, fdr)-> + upperCut >= currentBioitem.Statistics + ) + match firstGreaterCut with + | Some (cut,fdr) -> {currentBioitem with QValue = fdr} + | None -> {currentBioitem with QValue = 1.} + ) + let chosenDelta = delta + let upperCut = snd smallestCutForFDR + let lowerCut = fst smallestCutForFDR + let getQvals = getQvalues obsStats + let PosSigBioitem = getQvals |> Array.filter (fun x -> x.Statistics > upperCut) + let NegSigBioitem = getQvals |> Array.filter (fun x -> x.Statistics < lowerCut) + let NonSigBioitem = getQvals |> Array.filter (fun x -> x.Statistics >= lowerCut && x.Statistics <= upperCut) + let medianFalsePos = getMedianFalsePositives smallestCutForFDR expStats + let significantBioitems = getSignificantBioitem smallestCutForFDR getQvals + let medianFDR = getMedianFdr pi0 medianFalsePos ( significantBioitems |> float) + let delta = chosenDelta + SAMResult.Create s0 pi0 delta upperCut lowerCut PosSigBioitem NegSigBioitem NonSigBioitem expAvgStats medianFDR significantBioitems medianFalsePos +// Workflow of SAM (default mode) +//let priorStats = getObservedStats 0.0 data1 data2 +//let s0est = S0.estS0 priorStats [|0. .. 0.05 .. 1.|] +//let s0 = S0.s0ForMinCV s0est -//let n = 1000 -//let nRep = 3 +//let observedStats = teststatsSAM.getObservedStats s0 data1 data2 -//let dataA = -// [|0..n|] -// |> Array.map (fun i -> -// Array.init 3 (fun _ -> Distributions.Continuous.Normal.Sample 0. 1. )) +//let permStats = Permutations.getPermutations 100 s0 data1 data2 +//let expStats = Permutations.getExpectedStats permStats -//let dataB = -// [|0..n|] -// |> Array.map (fun i -> -// if i < 100 then -// Array.init 3 (fun _ -> Distributions.Continuous.Normal.Sample 5. 1. ) -// elif i > 100 && i < 200 then -// Array.init 3 (fun _ -> Distributions.Continuous.Normal.Sample -5. 1. ) -// else -// Array.init 3 (fun _ -> Distributions.Continuous.Normal.Sample 0. 1. )) +//let pi0 = SAMHelper.estimatePi0 observedStats permStats +//let cutsAndDelta = SAMHelper.getDeltaAndAsymmCuts observedStats expStats +//let smallestCutForFDR = SAMHelper.smallestCutAndDeltaForFDR cutsAndDelta permStats observedStats 0.05 pi0 -//let priorStats = SAM.calculateTwoClassUnpaired 0. dataA dataB -//let s0 = SAM.S0.estimate priorStats +//let fdrsPerCut = SAMHelper.fdrsPerCut cutsAndDelta permStats observedStats pi0 -//let samStats = SAM.calculateTwoClassUnpaired s0 dataA dataB -//let permStats = SAM.permutationWithin (SAM.calculateTwoClassUnpaired) 5 s0 dataA dataB +//let negCut = SAMHelper.negCutToFDR fdrsPerCut -//let pi0 = SAM.estimatePi0 samStats permStats +//let posCut = SAMHelper.posCutToFDR fdrsPerCut -//let cuts = SAM.getSymmetricCuts samStats (SAM.expectedValue permStats) +//let qValues = SAMHelper.getQvalues observedStats negCut posCut -//let qValues = SAM.qvalues pi0 samStats permStats cuts +//let delta = snd smallestCutForFDR +//let upperCut = snd (fst smallestCutForFDR) -//qValues |> Array.filter (fun q -> q <= 0.05) |> Array.length - +//let lowerCut = fst (fst smallestCutForFDR) -//Chart.Point(Seq.zip (samStats |> Seq.map (fun s -> s.Statistics)) qValues) -//|> Chart.Show +//let posSigGenes = qValues |> Array.filter (fun x -> x.Statistics > upperCut) +//let negSigGenes = qValues |> Array.filter (fun x -> x.Statistics < lowerCut) -//Chart.Histogram (samStats |> Seq.map (fun x -> x.Statistics)) -//|> Chart.Show +//let nonSigGenes = qValues |> Array.filter (fun x -> x.Statistics >= lowerCut && x.Statistics <= upperCut) +//let medianFalsePos = SAMHelper.getMedianFalsePositives (fst smallestCutForFDR) permStats +//let significantGenes = SAMHelper.getSignificantGenes (fst smallestCutForFDR) qValues - \ No newline at end of file +//let medianFDR = SAMHelper.getMedianFdr pi0 medianFalsePos ( significantGenes |> float) diff --git a/tests/FSharp.Stats.Tests/FSharp.Stats.Tests.fsproj b/tests/FSharp.Stats.Tests/FSharp.Stats.Tests.fsproj index 82b3c0cd..7c1f19a1 100644 --- a/tests/FSharp.Stats.Tests/FSharp.Stats.Tests.fsproj +++ b/tests/FSharp.Stats.Tests/FSharp.Stats.Tests.fsproj @@ -31,7 +31,7 @@ - + @@ -64,6 +64,7 @@ + diff --git a/tests/FSharp.Stats.Tests/Main.fs b/tests/FSharp.Stats.Tests/Main.fs index 4a1c84fc..37032cca 100644 --- a/tests/FSharp.Stats.Tests/Main.fs +++ b/tests/FSharp.Stats.Tests/Main.fs @@ -77,6 +77,7 @@ let main argv = Tests.runTestsWithCLIArgs [] argv TestingTests.friedmanTestTests |> ignore Tests.runTestsWithCLIArgs [] argv TestingTests.wilcoxonTestTests |> ignore Tests.runTestsWithCLIArgs [] argv TestingTests.tTestTests |> ignore + Tests.runTestsWithCLIArgs [] argv TestingTests.SAMTests |> ignore //================================== ML ================================================================= //SimilarityMetrics diff --git a/tests/FSharp.Stats.Tests/Testing.fs b/tests/FSharp.Stats.Tests/Testing.fs index fb9f51c4..04e2700f 100644 --- a/tests/FSharp.Stats.Tests/Testing.fs +++ b/tests/FSharp.Stats.Tests/Testing.fs @@ -4,7 +4,8 @@ open System open FSharp.Stats.Testing open FSharp.Stats open TestExtensions - +open FSharp.Stats.Testing.SAM +open Deedle [] let testPostHocTests = @@ -1024,4 +1025,80 @@ let comparisonMetricsTests = testCase "C: threshold 0-0" (fun _ -> TestExtensions.comparisonMetricsEqualRounded 3 (snd (actual["C"][10])) (snd (expectedMetricsMap["C"][10])) "Incorrect metrics for threshold 0.0") ] ] - +[] + let SAMTests = + // data preparation + let df:Frame = + Frame.ReadCsv(@"data/TestDataSAM.txt",hasHeaders=true,separators = "\t") + |> Frame.indexRows "gene" + // get Rowkeys as Array + let rowheader :string[] = df.RowKeys |> Seq.toArray + // chunk data into Arrays for sample1 and sample2 to compare them + let (sample1,sample2) :float[][] * float [][]= + df + |> Frame.getRows + |> Series.values + //|> Seq.map (Series.values >> Seq.toArray >> Array.chunkBySize 4 >> fun x -> x.[0],x.[1]) + |> Seq.map (Series.values >> Seq.toArray >> Array.chunkBySize 3 >> fun x -> x.[0],x.[1]) + |> Array.ofSeq + |> Array.unzip + // map rowheader to samples, so its (GeneName,[float;float;float]) + + let data1 = Array.zip rowheader sample1 + let data2 = Array.zip rowheader sample2 + let corrected1 = + let medCorrect = + medianCentering data1 + Array.zip rowheader medCorrect + let corrected2 = + let medCorrect = + medianCentering data2 + Array.zip rowheader medCorrect + + + let result1 = FSharp.Stats.Testing.SAM.twoClassUnpaired 100 0.05 data1 data2 (System.Random(27)) + let result2 = twoClassUnpaired 100 0.05 data1 data2 (System.Random(1337)) + let result3 = twoClassUnpaired 100 0.05 corrected1 corrected2 (System.Random(1337)) + let result4 = twoClassUnpaired 100 0.05 data1 data1 (System.Random(27)) + + testList "SAM Tests" [ + testCase "twoClassUnpaired Seed 27" <| fun () -> + Expect.floatClose Accuracy.low result1.S0 0.041419 "S0 should be equal." + Expect.floatClose Accuracy.low result1.Pi0 0.388060 "Pi0 should be equal." + Expect.floatClose Accuracy.low result1.Delta 0.986042 "Delta should be equal." + Expect.floatClose Accuracy.low result1.UpperCut 1.301745 "Upper Cut should be equal." + Expect.floatClose Accuracy.low result1.LowerCut -1.632438 "Lower Cut should be equal." + Expect.floatClose Accuracy.low (result1.PosSigBioitem |> Array.length |> float ) 80. "PosSigBioitems should be equal." + Expect.floatClose Accuracy.low (result1.NegSigBioitem |> Array.length |> float ) 61. "NegSigBioitems should be equal." + Expect.floatClose Accuracy.low (result1.MedianFalsePositivesCount |> float ) 14. "medFP should be equal." + + testCase "twoClassUnpaired Seed 1337" <| fun () -> + Expect.floatClose Accuracy.low result2.S0 0.041419 "S0 should be equal." + Expect.floatClose Accuracy.low result2.Pi0 0.388060 "Pi0 should be equal." + Expect.floatClose Accuracy.low result2.Delta 0.997591 "Delta should be equal." + Expect.floatClose Accuracy.low result2.UpperCut 1.301745 "Upper Cut should be equal." + Expect.floatClose Accuracy.low result2.LowerCut -1.632438 "Lower Cut should be equal." + Expect.floatClose Accuracy.low (result2.PosSigBioitem |> Array.length |> float ) 80. "PosSigBioitems should be equal." + Expect.floatClose Accuracy.low (result2.NegSigBioitem |> Array.length |> float ) 61. "NegSigBioitems should be equal." + Expect.floatClose Accuracy.low (result2.MedianFalsePositivesCount |> float ) 17. "medFP should be equal." + + testCase "twoClassUnpaired median centered Seed 1337" <| fun () -> + Expect.floatClose Accuracy.low result3.S0 0.026303 "S0 should be equal." + Expect.floatClose Accuracy.low result3.Pi0 0.407960 "Pi0 should be equal." + Expect.floatClose Accuracy.low result3.Delta 1.036888 "Delta should be equal." + Expect.floatClose Accuracy.low result3.UpperCut 1.381420 "Upper Cut should be equal." + Expect.floatClose Accuracy.low result3.LowerCut -1.740646 "Lower Cut should be equal." + Expect.floatClose Accuracy.low (result3.PosSigBioitem |> Array.length |> float ) 78. "PosSigBioitems should be equal." + Expect.floatClose Accuracy.low (result3.NegSigBioitem |> Array.length |> float ) 61. "NegSigBioitems should be equal." + Expect.floatClose Accuracy.low (result3.MedianFalsePositivesCount |> float ) 17. "medFP should be equal." + testCase "twoClassUnpaired Seed 27 data similar " <| fun () -> + Expect.floatClose Accuracy.low result4.S0 0.005275473477 "S0 should be equal." + Expect.floatClose Accuracy.low result4.Pi0 2.0 "Pi0 should be equal." + Expect.floatClose Accuracy.low result4.Delta 100000.0 "Delta should be equal." + Expect.floatClose Accuracy.low result4.UpperCut 0.0 "Upper Cut should be equal." + Expect.floatClose Accuracy.low result4.LowerCut 0.0 "Lower Cut should be equal." + Expect.floatClose Accuracy.low (result4.PosSigBioitem |> Array.length |> float ) 0. "PosSigBioitems should be equal." + Expect.floatClose Accuracy.low (result4.NegSigBioitem |> Array.length |> float ) 0. "NegSigBioitems should be equal." + Expect.floatClose Accuracy.low (result4.MedianFalsePositivesCount |> float ) 0. "medFP should be equal." + + ] diff --git a/tests/FSharp.Stats.Tests/data/SamInput.txt b/tests/FSharp.Stats.Tests/data/SamInput.txt deleted file mode 100644 index bcfae6dc..00000000 --- a/tests/FSharp.Stats.Tests/data/SamInput.txt +++ /dev/null @@ -1,14846 +0,0 @@ -gene 1 1 1 2 2 2 -G00001 0.384403738 0.707018443 0.481278354 4.269516345 4.07758637 3.643168637 -G00002 0.724079121 0.854058047 0.76708605 10.56715165 4.075089816 4.164782895 -G00003 1.320677577 1.336913436 1.193096056 1.850115196 1.803871467 1.569551759 -G00004 0.599147434 0.487877016 0.513936874 0.93808102 0.755788401 0.671501537 -G00005 7.683031263 7.880179756 7.415983865 10.33195447 9.568779434 9.064157461 -G00006 2.314254084 2.221602183 1.952955272 2.861109252 2.008856333 2.103510777 -G00007 8.590171065 8.99141731 8.321330307 9.10742892 8.914709756 8.870009451 -G00008 3.776026968 3.615560722 3.618937535 6.616759418 4.727432658 5.085908623 -G00009 22.76519948 26.15714523 20.91437555 29.19709214 28.61824439 30.46680669 -G00010 4.797293714 3.916382621 5.062300312 3.843000635 4.965330936 5.206896885 -G00011 4.230795957 3.446569831 4.01375617 4.58741083 4.480851086 5.481913527 -G00012 2.06605048 1.862775748 2.003626194 1.276579375 0.951167242 0.935181314 -G00013 0.122751646 0.065355111 0.114360924 0.530259248 0.200006586 0.264767659 -G00014 6.017865376 6.803446277 5.450345992 5.518552272 4.902346647 4.603520486 -G00015 0.294481433 0.125429628 0.180250638 5.52810761 2.345767989 2.917114313 -G00016 0.180462796 0.241983113 0.194930102 0.43746258 0.351300846 0.252289733 -G00017 1.554524208 1.693658413 1.507342382 2.514170292 1.545784979 1.882563008 -G00018 6.799851289 7.870345758 6.021971529 4.791512427 3.818187602 3.568023949 -G00019 61.28647133 60.24783669 62.9311939 82.15343776 52.64349387 55.97172056 -G00020 14.16927888 18.38732714 15.03423131 10.84486785 8.334101473 7.333354989 -G00021 0.342044364 0.225469977 0.329879741 0.973664742 0.522213695 0.505020035 -G00022 1.181777259 0.958779061 1.043502601 0 0.032864657 0.028097663 -G00023 14.84295718 14.72934948 13.89469606 11.69130276 9.376398865 8.204242617 -G00024 225.8057449 230.182878 206.3551721 191.0486578 338.6821198 319.2546365 -G00025 2.043045457 2.692457727 2.073001769 3.974810993 2.714685031 2.399700021 -G00026 0.348268252 0.318369634 0.335375287 0.404280563 0.259032679 0.295280243 -G00027 1.307636484 1.29003321 1.074928799 3.154944281 1.920379207 1.555417548 -G00028 0.994077997 1.075465279 1.121016972 0.929974359 1.22889013 1.000610031 -G00029 0.550879266 0.751908646 0.641022568 0.769187356 0.631728195 0.720128655 -G00030 1.060873293 1.129654771 1.017136455 0.467149013 0.542248252 0.358630518 -G00031 0.245284614 0.215479758 0.223550332 0.636814589 0.483455885 0.41333097 -G00032 11.66598975 12.52463989 11.34456257 15.46198488 12.17352746 11.83703568 -G00033 1.497385576 1.915306348 1.486751365 2.087597732 2.255500526 1.854490465 -G00034 0.092911794 0.098935709 0.086023139 0.231663988 0.069763471 0.107359797 -G00035 9.47922415 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9.764805745 10.7527991 15.90560429 14.95628036 17.34564596 -G02349 2.112937552 1.967236013 1.953334177 1.834400227 1.200398517 1.50346987 -G02350 0.550745719 0.600416364 0.600209381 0.474903821 0.551375042 0.530323316 -G02351 19.89736821 19.31004414 20.0982048 32.74994249 24.35800111 25.0125052 -G02352 19.74180428 18.65007395 17.05956908 31.89445314 21.6039688 26.84111883 -G02353 0.486948419 0.54106394 0.41735846 0.708251393 0.623158364 0.558139694 -G02354 2.444683679 2.333042432 2.363522954 4.347366822 3.394142849 2.984734243 -G02355 572.2983395 572.5415898 598.4363368 1000.199529 667.9646266 738.6560101 -G02356 1.246257776 1.136003484 1.025339661 1.988970508 1.539454913 1.595079052 -G02357 0.322982937 0.452195663 0.271347821 0.365375639 0.408681002 0.290272536 -G02358 9.165770215 15.17821618 10.47887419 1.173655309 2.03506788 1.39344596 -G02359 2.303486783 2.682459726 2.731673541 3.900663017 3.730024685 3.964210837 -G02360 0.258162056 0.239992006 0.225742466 0.271782307 0.245534199 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