From 08cfb4b420e2e734017a253b3b69203ff3d9adbd Mon Sep 17 00:00:00 2001 From: Louis Lacoste Date: Wed, 20 Mar 2024 19:28:37 +0100 Subject: [PATCH] Ajout commentaire simus et analyse --- Rnw/simulations-methodes.Rnw | 101 ++++++++++++++++++++++++++++++----- rapport.Rnw | 29 +++++----- rapport.pdf | Bin 1964946 -> 1988588 bytes 3 files changed, 101 insertions(+), 29 deletions(-) diff --git a/Rnw/simulations-methodes.Rnw b/Rnw/simulations-methodes.Rnw index 506d008..3e67f2d 100644 --- a/Rnw/simulations-methodes.Rnw +++ b/Rnw/simulations-methodes.Rnw @@ -15,8 +15,6 @@ knitr::opts_knit$set(fig.pos = "HT", fig.width = 6, fig.height = 6, % \item soit partir sur regarder l'impact de la taille de l'arbre etc. % \end{itemize} -\subsection{Erreur de type I et puissance} - Dans cette partie nous souhaitons comparer les résultats de l'ANOVA et de l'ANOVA phylogénétique classique, avec approximation de Satterthwaite et avec le \emph{Likelihood ratio test}. @@ -32,7 +30,8 @@ l'\emph{erreur de première espèce} et la \emph{puissance} obtenue. En sélectionnant des espèces de manière aléatoire, nous cassons la structure induite par la phylogénie. Nous nous attendons donc à ce que l'ANOVA réalise de -meilleurs résultats en ne prenant pas en compte l'information phylogénétique. +meilleurs résultats que l'ANOVA Phylogénétique en ne prenant pas en compte +l'information phylogénétique. Pour les simulations avec des groupes respectant la structure de l'arbre phylogénétique, nous nous attendons à ce que l'ANOVA phylogénétique @@ -204,21 +203,97 @@ Sur toutes les sous-figures de la figure~\ref{fig:simus-results}, les étiquette A présentent les erreurs de type I commises par les méthodes et les étiquettes B présentent les puissances des mêmes méthodes. +\subsubsection*{Analyse pour les groupes respectant la phylogénie} +% Analyses des erreurs de type I + +\paragraph*{Analyse des erreurs de type I} L'erreur de type I est particulièrement importante à contrôler, en effet elle indique le nombre de faux positifs et l'on veut pouvoir en déterminer le seuil $\alpha$ avec comme seuil classique $0.05$. -TODO Insister sur pourquoi trop de faux-positifs pour l'ANOVA classique, du fait -de la structure Brownienne, deux clades peuvent être éloignés au niveau temporel -beaucoup de génération. En oubliant la structure, on peut vouloir mettre un saut -alors que l'écart est simplement dû à de la dérive. -L'ANOVA suppose des données iid ce qui n'est pas le cas ici. +% DONE Insister sur pourquoi trop de faux-positifs pour l'ANOVA classique, du fait +% de la structure Brownienne, deux clades peuvent être éloignés au niveau temporel +% beaucoup de génération. En oubliant la structure, on peut vouloir mettre un saut +% alors que l'écart est simplement dû à de la dérive. +% L'ANOVA suppose des données iid ce qui n'est pas le cas ici. +Nous constatons que dans le cas des groupes respectant la phylogénie, l'ANOVA +a une erreur de type I très forte dans toutes les simulations. +Pour l'expliquer nous avons deux interprétations principales. +Tout d'abord, l'ANOVA suppose des observations indépendantes et identiquement +distribuées et les en accord avec la phylogénie ne respectent pas cette +hypothèse. +De plus, n'ayant pas l'information de la dérive génétique +sous-jacente, elle ne peut pas différencier ce qui est dû à la dérive et à de +vraies différences entre les groupes. +C'est la raison de son fort de taux de faux-positifs pour les +groupes qui respectent la structure phylogénétique. -TODO Important de préciser qu'il faut contrôler l'erreur de type I car les -manips coûtent très cher. +Par exemple, deux clades peuvent être éloignés à cause de leur éloignement +temporel. L'oubli de la structure peut suggérer de mettre un saut alors que cet +éloignement est seulement dû à la dérive. -TODO Ajouter les commentaires sur les simulations +Pour les autres méthodes, elles ont toutes tendances à avoir de forts taux de +faux-positifs, exceptée l'ANOVA phylogénétique REML avec approximation de +Satterthwaite qui respectent le seuil de 5\% dans toutes nos conditions. -\paragraph*{REML vs Maximum Likelihood (ML)} D'après nos simulations, les méthodes utilisant le REML contrôle toujours mieux +Nous remarquons qu'en général, plus l'héritabilité augmente et plus les méthodes incluant +l'information phylogénétique contrôle l'erreur de première espèce. + +% DONE Important de préciser qu'il faut contrôler l'erreur de type I car les +% manips coûtent très cher. + +\paragraph*{Importance de l'erreur de type I} Nous insistons particulièrement +sur le contrôle de l'erreur de type I, car dans +le cadre des analyses de données transcriptomiques cette phase d'analyse +statistique permet d'identifier des gènes différentiellement exprimés et pouvant +donc potentiellement intervenir dans des réseaux de gènes d'intérêt. + +Une fois les gènes identifiés il faut faire des expériences qui sont +particulièrement onéreuses et donc on ne souhaite pas faire des expériences +"pour rien". + +\paragraph*{Analyse des puissances} Le revers de la médaille se fait sentir sur +les puissances. La méthode d'ANOVA phylogénétique REML avec approximation de +Sattertwhaite, a les puissances les plus faibles de toutes les méthodes, ce qui +fait sens, étant plus conservatrice elle sélectionne moins. +Et nous observons donc que les méthodes avec les puissances les plus fortes sont +le LRT et l'ANOVA. + +\paragraph*{REML vs Maximum Likelihood (ML)} D'après nos simulations, les +méthodes utilisant le REML contrôle toujours mieux l'erreur de première espèce que les méthodes utilisant le maximum de -vraisemblance. \ No newline at end of file +vraisemblance. Les paramètres de variance étant mieux estimés dans ce cas, ce +résultat est cohérent avec les résultats classiques sur le REML. +Mais à cause de ce meilleur contrôle, les méthodes REML ont donc des puissances +plus faible, comme décrit plus haut. + +\subsubsection*{Analyse pour les groupes choisis} + +Nous analysons ici les groupes sélectionnés pour ne pas respecter la phylogénie. +Ils correspondent aux barres de couleurs bleues sur la +figure~\ref{fig:simus-results} + +\paragraph*{Analyse des erreurs de type I} +Toutes les erreurs de types sont proches d'être sous la barre des 5\%. Les +méthodes qui ne sont pas sous les 5\% sont l'ANOVA et le LRT\footnote{Ainsi que +pour les valeurs d'héritabilité de $h = 0.7$ et $h=0.9$ l'ANOVA phylogénétique +et l'ANOVA phylogénétique avec approximation de Satterthwaite, qui sont +légèrement au-dessus. Un point intéressant à remarquer est que leurs +contreparties utilisant le REML ne présentent pas ces problèmes.}. +Cela indique peut-être que malgré notre sélection que nous avons souhaité +la plus aléatoire possible\footnote{Cela en respectant la contrainte de ne pas +séparer les individus d'une même espèce.}, nous n'avons peut-être pas +cassé toute la structure phylogénétique existante. Il faudrait investiguer avec +d'autres simulations. + +\paragraph*{Analyse des puissances} +Comme l'on pouvait s'y attendre cette fois-ci toutes les puissances sont +relativement élevées. Nous remarquons que la méthode la plus puissante est +l'ANOVA phylogénétique REML avec approximation de Satterthwaite. +Aux vues du doute émis au paragraphe précédent cela pourrait être dû à la +persistance d'une structure phylogénétique. + +\paragraph*{REML vs Maximum Likelihood (ML)} +Ici aussi les méthodes REML contrôlent mieux l'erreur de type I mais fait +intéressant elles obtiennent aussi de meilleures puissances. Cela pourrait être +dû au fait que leur estimation de la variance est meilleure. \ No newline at end of file diff --git a/rapport.Rnw b/rapport.Rnw index da11cb7..db7e13e 100644 --- a/rapport.Rnw +++ b/rapport.Rnw @@ -117,12 +117,11 @@ On cherche alors d'abord à trouver quels gènes pourraient être différentiels En considérant l'arbre precédent \ref{fig:arbre-chen2019}, on pourra chercher les gènes qui sont différents entre les groupes des \textit{mus} et \textit{rat} par rapport aux autres espèces. \newline Le modèle le plus couramment utilisé est actuellement l'Expression Variance and Evolution modèle (EVE) présenté dans \cite{rohlfsPhylogeneticANOVAExpression2015}. -L'EVE modèle est basé sur un LIkelihood Ratio Test (LRT), une méthode statistique classique. +L'EVE modèle est basé sur un Likelihood Ratio Test (LRT), une méthode statistique classique. Ce projet s'inscrit alors dans un questionnement plus large qui cherche à se demander si d'autres modèles classiques comme l'ANOVA, en les adaptant, pourrait produire des résultats similaires voire meilleurs que l'EVE modèle. -E effet, avoir un bon modèle qui, en particulier, donne peu de faux positifs est important. +En effet, avoir un bon modèle qui, en particulier, donne peu de faux positifs est important. On peut ensuite étudier les gènes potentiellement intéressants selon une problématique et des groupes d'espèces données. -TODO Présenter les 4 modèles. C'est quoi les 4 ? -\newline + Au vu de la forme des données étudiées, le projet s'est tourné vers une méthode d'ANOVA phylogénétique. Celle-ci sera d'abord décrite ainsi que d'autres outils mathématiques utilisés pour affiner la fiabilité du test dans une première partie. Certains auront fait l'objet de calculs explicites en vue de leur implémentation. @@ -135,10 +134,19 @@ Au cours de ce projet nous avons donc eu une partie d'étude théoriques et math A partir de la formulation mathématiques des modèles \newline \newline +Tout le code produit est disponible sur le dépôt GitHub suivant +\url{https://github.com/Polarolouis/anova-phylogenetique-projet-msv/}. +Ce dépôt contient le code pour implémenter la méthode, faire les +simulations et compiler le rapport. + +Nous avons au maximum indiqué le code qui n'a pas été écrit par nous, la plupart +du temps dans les commentaires du code. + Un gène, comparer les moyennes d'expression d'un gène On connait les groupes exemple individus malade/sain - +\newline +\newline Contrairement à une comparaison basée sur la santé des individus, cette approche se focalise sur les espèces. La non-indépendance et les relations complexes entre individus et groupes comparés nécessitent l'utilisation d'un modèle mixte, @@ -476,15 +484,4 @@ le tableau suivant. \label{tab:na-evemodel} \end{table} -\section*{Code du projet} - -Tout le code produit est disponible sur le dépôt GitHub suivant -\url{https://github.com/Polarolouis/anova-phylogenetique-projet-msv/}. -Ce dépôt contient le code pour implémenter la méthode, faire les -simulations et compiler le rapport. - - -Nous avons au maximum indiqué le code qui n'a pas été écrit par nous, la plupart -du temps dans les commentaires du code. - \end{document} \ No newline at end of file diff --git a/rapport.pdf b/rapport.pdf index 8c14ed0ddf990dad3938cb5faa7c617ccac2b325..6db94a47e994cbd5a55377c84e8bccfe512f378d 100644 GIT binary patch delta 140021 zcmZsiQ*@XOu(e~`wr$&X8Z~U}q_N)EP8vInZQHhO+wA|Hb9?@~S#v#W&7S@2Nqlj? ztnoyqRFRNkWM$%nqnuqFT7^s93ns*A#pIVh7%BgV^%P;w{Wo};o?jU zNF}5LuC(MG7FkfbU$kCBf6JWTZHxqBL7WFJN_Al%8FM!VTm}i`eR>bO&D(34VMCNk z9-+luc@O~XJFoEM*ue?d(6*Mj$IxLjMPx>7NOFmv;H(S{y6A;JhZ`y1va%KgoT9OA zF4$y4%v}tcEor2&CAGRRBRP3)nShXL4$x5`OKr2mgyM+r0IL97Ms0+{w@m?Jwpu42 zIq$)5S+l|{(b=L`W$z0CUbMY6ek4SF6Rv&2SpOBuXjv8a16#si&G`lh{na%x% zZ7DgrEBr=G?3ZjdFJug7h4ejt{WZ5aYyL{|D-Sn%V*Is9qQk{Bi3`pjiqY?y zV2%Bv?IMNYPYV_UKK{>*r|tD;Vt&5BQ(VEhqnzBGQC+~6K!dyZU#aj%khw8auV_C8 zpmNB^qM4UrvG>_D6E`mlYp;4srsCjSy;RzjQvqRt^-al#Y#93i0vzSkuINq6DNwI) zW1Wf+a=2IpRkbwh2RyUWJD*C!)4CMApvNW_H(Rx+{mPQ#nBg#v;6 zoH<)&vjc5`P?G2O19Z#=l7rAhYft`#_v%iV?vZdAD znIe?bFlKTneI-8dPb(cC8Ggx^U>z`2Ait2sZ$U z9vj#drAO1q(YkYxvcWfMm*|AW#1>^CU*sQ6ivwtLtti|F-GJH-{!O}r!2o4%(1$37 z0Od_$Hdjy5hUElhNv&fAm51aYVP)Y-LY-s)XJz4SK!me|0%dIgbqa$6XJzF|Kt%`R zW=|4HrUgQDS9z zA)0{J<&BCTBL#lyF5Y);g;^=|g>m|l+L2o=Jlscz@I|IrxU_X(js5DGQsri~2d&fH zPOsJD`B7ncBB)jMVPJPqaC=^kzI!I56f_*;hXDNWzh3q4PF1zK3F4s|udRZpdBiy~ z*!h88EsNrztd+k)6qZ`SsK|dz3HqY39wxp{bh{ODTm2{MsA-oQ(r_QPRs?Kw zi{qifcLo^@;aP%}zkXiPA$ReYnvk#NmqGCC;&eGP(C^JYg;rLz%o?q15C@^%*oZ%i ziyICTWBi++f9H7m);lZSTIbs8ZsOy3s=G?54A<<5d4SM5VP?HC(wkcJfvvd~QL$Su z8AsIveP#((w?#kn&4K`PjijvrPX~Cygp6FB+K9eVrG7WjqG9KD1b7L_2Yqo+2@4Xe zCXhKdXEGZ)rQB#4$9r?*i)zKFEZaxWPRTnQ=E#xH9mw2UoY?4<213d{GFWEW*AiI6 zYVsNE>x*w?8n9*yuC8mh;nn#K2}xJ}R2j;z$6yb|3gBP!6y5}-i)If-#sRoQQdF)f z4&lG-$dfS9Btj-YY-$S!(Kg_$Rrsk*rqhL-XkH5U+@R~T1|Lg)Ku zSyF7%WVr|yDi6rSPM6lN7yxJH&GDRm>Vh`jB4ZwV&EGE6DuO=HnVzMhek_Ib7C9c) z#mC~N${EG(ITNNwUO5w|$#U=sL51=Td(+AbCVtcSqk_ntT0ZU}qq)OP2{#9IN6A#= zLQvr3Haf?quGTlCREBkz8mA zq)~Znh7utI4{nMKh6jV3fcL`T6q+)z?K*eSBpM-+fsL*|s#*y_=*eUVf~8Y`*r2sw zP$lW}SuixJ{0pRKvjVa6<7nXc(n(!~gZfN1)$~qljag_Z{YT*}QnOMmEl0~5ppFr& zEl~``sEz}EwEt8}J_1O7cbW19QVc#Yp|JjTs0a#CBn>qV&BnX$+ZC4-ve+VHZ#|$gVfbkMr-R5Sh;Or-9g>w#zq@}J6yh44_6J33nGpx z+9~6U{?>dKaxNwFig&fv{KuXbaVE2a~gA&~MgR_;w-qf5Dw z+;O<)WoNYw5#xTeW`jC$6|p%VL<=i04a^S9VBU^t=+du5mZpw{8)2ez8%>~~Y^LZJ zmu3Ut(r_9=P@g270>|Wgz}+4@*h`Xh%4*^MApA}r#ND%A4?CLV+0NoTm3Qp4Gy0yA z0xN)TmlCS=V+1Cx61j5+*KM15X;!&Vu)fK1hE*rGM5yzUZGz`-ba1iwlgKO+!*$$M z1H~`R>eZGr*i4?Jw@jUfsABkPiW08_9}!rK$M$^@Yv?Y0mb(3AX~Z61 zrdt)lzBkqc;hA_uQ)|^Mgq@Z{TY%IaeyFesMWC8DnBM#cm*7_84Bbmjg)W~1NkV5` z$tG`DXi<*2S)l=`k5}&W`ha1sDcAO&`>B~nJS(Pjjn-ed-{m%?=o98!K-L@Xlfb&M z;LDf%%LDNAlyvpq@VVxSjWj*)%JHf9^~5gX5L_G>b=VYePu=~Qbj(zd{6g5$LexPB zaY8FD*dXVH+nwcisac7-0q+<^9;n-Sqy&6-1)5#lC$BjT*XjV!=4DRww_iN+jW7>- zE1=`U4}s5YknxH<>=_X95XUiisR>G;!P6c*dBD+vO01j=yqJWgUfkr;j}m4wcvd;z zkEp>+mM$4%5yX4JH11Q-W6}{Gm~E~ib5h)g<;Sf!-|AP-(|4f^8~>m9ea=+ux<#Ss z^w=Nh@>So9k|Hbp_tz*i(9n*z6$MIjNy(yod$!}c^fhy+K_vy4O&!HT6A(nA z&?$YAOqA3eMz0-#L@tz_CF?Z3PwwubAqAv4KsM7**jLo7N<`S_vu2Y!KzpKWAzEtQ z4RjLXEO`ibNIk-a%J)@i5jD3ztuw408P#5BE{M?GOGYGezHJXT2r?N7$0SLUy^Dm7 zF*8V%C)H}Il#mSn+6r*eDu&U`{?N)zZgOT2umqnGW@~aP=KBF99+N z&%CDk55L75h-Xa_{h16P{Tmzve}b^U{er_cAI8Xt21EWTI@9Yg)bO|DjLy2C%Gb~k zncFJj|Jx`UwgdCygW3P5kdb6p4#(l?+xi_IwOgT1JOR{J`GvIlSl5Z{X&{GE4f6r+ zg?;ny!=!jX2tQvy^4gmDK??68|6(T1 zTEVn+>18A#xA&*T>|;LJK{bTCAi3WBq;F>wrtFsJs9)jTzhFk3oPb56mYy zr+ao3)MzrdQrc*7?N=K%DU+c|-){Z$(6BB34_>D+?W~@f1B9E<{g6bwuM7T=dgg_H zyWH?#)+=1OTahf;HmNi2t2~X3+tu@gdRMnK(~Ymub&e{!<9DpH@0TK=HSS6gI&-j! zE4o3uo|=yLav?YU#-~98hZ8_Hgn3&|+O^|0JM-Jc(Z|R1ho`|>_B!hsJV$_91bufT zlhi~PI@8_sm!vGsbfVK^^cSIU@@7R$$|3)!JC^#gvrzJ@PB}oLCMgF7AJqFXIZt{O z?@|!{_rbzIVuDR`T2(Mztpl1Lh*+6U$kxVe=C2wQ^W(lXbp3A=_#! zx!=eS#bcF8dz2WUEdPmGa9&p4B++CV;0SLmakKeO->|RcNP`2#3DxwcXD#J~nS4U| zPdPeT2clN?O?^57=OOWgZ=o$q{}q#Zdd=AS2NJ|pOO9Fh!a7+ObjmqoWwe)%tq$rL zgK>)etRvm1(=FFzGX+>e-0TL5sRH+r)6`ejwhj5dgN|xzq@^u;W`#=;=@&giz~{rf z<>YQ7dvss;#v^fPXI^0q8R@Cu(?v@w%$kP3Wt6#ke3+D*KTpub-o$ou_dw~Q^|X9{ zyylGsD_9S4NX2(^N}4Xr^KNJR3*)NISoh?%B26tr+ge&e?x4f#vch?=&|NSf#ak!7 zZ_2ty8H#{a-b0exwSX>s)O8~pki*M~%m=TY$cVMyuOt4FK8Hvf<|G0QZpAdhGnD%? 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