1 / 14

Logistic regression , survival analysis , model II regres sion

Logistic regression , survival analysis , model II regres sion. Logist ic regres sion. Response ( dependent ) variable is either yes / no ( alive/ dead , flowering/sterile )

jenaya
Download Presentation

Logistic regression , survival analysis , model II regres sion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Logistic regression, survival analysis,model II regression

  2. Logistic regression • Response (dependent) variable is either • yes/no (alive/ dead, flowering/sterile) • Number of positive cases out of total (seed germination, number of flowering individuals out of total no of individuals) – assuming binomial distribution • Regression model predicts probability, i.e.value between 0 and 1

  3. Logistic regression 2 • Logit transformation: log( p / (1-p) )= log (odds ratio) • Can not be applied directly to 0/1, applied on predicted probabilities: p in(0, 1) • Special case of Generalized linear models (GLM)

  4. Logistická regrese a Statistica • Example – survival of winter depending on flowering and rhizome size • Advanced Linear /Nonlinear Models • Generalized ... Models • Logit model • Or non-linear estimation...

  5. Possible application • Example – how is the probability of survival over the winter affected by flowering in previous summer, storage of sugars, and length of the winter? • Surmalog.xls, list ReprEff

  6. Survival analysis • Survival analysis, mainly in medicine • Useful for data (usually about time) with censoring • Most often right censoring: I have finished the experiment, but some individuals are still alive (or did not germinate yet etc.] • Left censoring • For data without censoring are probably simpler methods available - mostlygeneralized linear models)

  7. Survival curve • Kaplan-Meier method:

  8. Míra rizika • Hazard rate, l: pravděpodobnost, že jedinec přežije časový úsek t, pokud se jej již dožil • Kumulativní funkce míry rizika L(t): ve vztahu ke křivce přežívání platí:L(t) = - log S(t) • Využití lu složitějších modelů analýzy přežívání (Coxův model relativního rizika, Cox proportional hazard rate):l(t) = l0(t)*eb0+b1x1+b2x2+…

  9. Use of survival analysis? • Comparison of survival curves among groups • Estimate “halftime” (of life, survival time, time to germination) with confidence interval • Testing effects of both quantitative and qualitative predictors

  10. Survival analysis - exercises • Germination dynamics affected by chilling, fileSurmalog.xls, sheetGermination,methodComparing two samples • Effect of radio-collars on survival of antilops -obojků na úmrtnost antilop,fileSurmalog.xls, sheetRadioCollars,methodRegression / Proportional hazard (Cox) regression

  11. Regression model typ II • In ordinary Least Squares, in dependence of Y on X, vertical differences are minimized (i.e. (Y-Ypredicted)2 • Similarly, if we study X ~ Y, (X-Xpredicted)2is minimized. • The angel among the two lines decreases with increasing (r) • Major axis (MA) regression – symmetric – what is perpendicular depends on units – various standardizations

  12. MA regression: motivation • Zkoumáme vztah mezi délkou (L)a hmotností (M) jedinců určitého druhu • Pokud se tvar těla s růstem nemění (isometrický růst), lze vztah popsat takto:M = c*L3 a po logaritmování:log(M) = b0 + 3*log(L), kde b0 = log(c) • Při užití „normální“ regrese bude ale odhadnutý koeficient b1< 3

  13. Alometricbiomass partitioning • Allometric biomass partitioning theory (APT): : Mleaves=b1*Mroots3/4 B.J. Enquist & K.J. Nikolas (2002): Global allocation rules for patterns of biomass partitioning in seed plants. Science295, 1517-1520.

  14. MA regression: example • Vztah biomasy listů a stonků: Mleaves=b1*Mroots3/4 • After log transformation, slope should be 0.75 • Various herb species • RMA program : • http://www.bio.sdsu.edu/pub/andy/rma.html

More Related