| Title: | Prediction and Accuracy Measures for Nonlinear Models and for Right-Censored Time-to-Event Data |
|---|---|
| Description: | We propose a pair of summary measures for the predictive power of a prediction function based on a regression model. The regression model can be linear or nonlinear, parametric, semi-parametric, or nonparametric, and correctly specified or mis-specified. The first measure, R-squared, is an extension of the classical R-squared statistic for a linear model, quantifying the prediction function's ability to capture the variability of the response. The second measure, L-squared, quantifies the prediction function's bias for predicting the mean regression function. When used together, they give a complete summary of the predictive power of a prediction function. Please refer to Gang Li and Xiaoyan Wang (2016) <arXiv:1611.03063> for more details. |
| Authors: | Xiaoyan Wang, Gang Li |
| Maintainer: | Xiaoyan Wang<[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.0 |
| Built: | 2024-12-09 06:38:21 UTC |
| Source: | CRAN |
A dataset containing the number of transistors and the corresponding #' years. The Moore's Law #'states that the number of transistors in a dense integrated circuit doubles approximately every two #'years. moore.
mooremoore
A data frame with 48 rows and 3 variables:
year, from 1973 to 2011
time starting from 1973
number of transistors
This function calculates a pair of measures, R-Squared and L-Squared, for any regression models of right-censored data. R-squared is an extension of the classical R2 statistic for a linear model, quantifying the amount of variability in the response that is explained by a corrected prediction based on the original prediction function. L-squared is the proportion of the prediction error of the original prediction function that is explained by the corrected prediction function, quantifying the distance between the corrected and uncorrected predictions. When used together, they give a complete summary of the predictive power of a prediction function.
pam.censor(y, y.predict, delta)pam.censor(y, y.predict, delta)
y |
A numeric vector containing the response values. |
y.predict |
A numeric vector containing the predicted response values from a fitted model. |
delta |
A numeric vector indicating the status of the event, normally 0=alive, 1=dead. |
A list containing two components: R-squared and L-squared
library(survival) library(PAmeasures) # Use Mayo Clinic Primary Biliary Cirrhosis Data data(pbc) # Fit an exponential model with bilirubin fit1 <- survreg(Surv(time, status==2) ~ bili, data = pbc,dist="exponential" ) # Obtain predicted response from the fitted exponential model predict.time<-predict(fit1,type="response") # Recode status at endpoint, 0 for censored, 1 for dead delta.pbc<- as.numeric(pbc$status == 2) # R.squared and L.squared of log-linear model pam.censor(pbc$time, predict.time, delta.pbc)library(survival) library(PAmeasures) # Use Mayo Clinic Primary Biliary Cirrhosis Data data(pbc) # Fit an exponential model with bilirubin fit1 <- survreg(Surv(time, status==2) ~ bili, data = pbc,dist="exponential" ) # Obtain predicted response from the fitted exponential model predict.time<-predict(fit1,type="response") # Recode status at endpoint, 0 for censored, 1 for dead delta.pbc<- as.numeric(pbc$status == 2) # R.squared and L.squared of log-linear model pam.censor(pbc$time, predict.time, delta.pbc)
This function calculates a pair of measures, R-Squared and L-Squared, for Cox proportional hazards model. R-squared is an extension of the classical R2 statistic for a linear model, quantifying the amount of variability in the response that is explained by a corrected prediction based on the original prediction function. L-squared is the proportion of the prediction error of the original prediction function that is explained by the corrected prediction function, quantifying the distance between the corrected and uncorrected predictions. When used together, they give a complete summary of the predictive power of a prediction function.
pam.coxph(fit.cox)pam.coxph(fit.cox)
fit.cox |
object inheriting from class coxph representing a fitted Cox proportional hazards regression model. Specifying x = TRUE and y=TRUE are required in the call to coxph( ) to include the design matrix and the response vector in the object fit. |
A list containing two components: R-squared and L-squared
library(survival) library(PAmeasures) # Use Mayo Clinic Primary Biliary Cirrhosis Data data(pbc) head(pbc) # Fit a univariate Cox PH model with standardised blood clotting time fit1 <- coxph(Surv(time, status==2) ~ protime, data = pbc,x=TRUE,y=TRUE) # R.squared and L.squared of Cox PH model pam.coxph(fit1) # Fit a multiple Cox PH model with bilirubin and standardised blood clotting time fit2 <- coxph(Surv(time, status==2) ~ bili + protime, data = pbc,x=TRUE,y=TRUE) # R.squared and L.squared of Cox PH model pam.coxph(fit2)library(survival) library(PAmeasures) # Use Mayo Clinic Primary Biliary Cirrhosis Data data(pbc) head(pbc) # Fit a univariate Cox PH model with standardised blood clotting time fit1 <- coxph(Surv(time, status==2) ~ protime, data = pbc,x=TRUE,y=TRUE) # R.squared and L.squared of Cox PH model pam.coxph(fit1) # Fit a multiple Cox PH model with bilirubin and standardised blood clotting time fit2 <- coxph(Surv(time, status==2) ~ bili + protime, data = pbc,x=TRUE,y=TRUE) # R.squared and L.squared of Cox PH model pam.coxph(fit2)
This function calculates a pair of measures, R-Squared and L-Squared, for any nonlinear regression model. R-squared is an extension of the classical R2 statistic for a linear model, quantifying the amount of variability in the response that is explained by a corrected prediction based on the original prediction function. L-squared is the proportion of the prediction error of the original prediction function that is explained by the corrected prediction function, quantifying the distance between the corrected and uncorrected predictions. When used together, they give a complete summary of the predictive power of a prediction function.
pam.nlm(y, y.predict)pam.nlm(y, y.predict)
y |
A numeric vector containing the response values. |
y.predict |
A numeric vector containing the predicted response values from a fitted model. |
A list containing two components: R-squared and L-squared
library(PAmeasures) data(moore) head(moore) # Transistor count count <- moore$count time<-moore$time # Fit a log-linear model moore.glm= glm(log2(count) ~ time, family=gaussian(link = "identity") ) # Obtain predicted transistor count count.predict<-2^(predict(moore.glm,newdata = data.frame(X = time),type = "response" )) # R.squared and L.squared of log-linear model pam.nlm(count, count.predict)library(PAmeasures) data(moore) head(moore) # Transistor count count <- moore$count time<-moore$time # Fit a log-linear model moore.glm= glm(log2(count) ~ time, family=gaussian(link = "identity") ) # Obtain predicted transistor count count.predict<-2^(predict(moore.glm,newdata = data.frame(X = time),type = "response" )) # R.squared and L.squared of log-linear model pam.nlm(count, count.predict)
This function calculates a pair of measures, R-Squared and L-Squared, for parametric survival regression models. R-squared is an extension of the classical R2 statistic for a linear model, quantifying the amount of variability in the response that is explained by a corrected prediction based on the original prediction function. L-squared is the proportion of the prediction error of the original prediction function that is explained by the corrected prediction function, quantifying the distance between the corrected and uncorrected predictions. When used together, they give a complete summary of the predictive power of a prediction function.
pam.survreg(fit.survreg)pam.survreg(fit.survreg)
fit.survreg |
object inheriting from class survreg representing a fitted parametric survival regression model. Specifying x = TRUE and y=TRUE are required in the call to survreg( ) to include the design matrix and the response vector in the object fit. |
A list containing two components: R-squared and L-squared
library(survival) library(PAmeasures) # Use Mayo Clinic Primary Biliary Cirrhosis Data data(pbc) head(pbc) # Fit an exponential model with bilirubin fit1 <- survreg(Surv(time, status==2) ~ bili, data = pbc,dist="exponential",x=TRUE,y=TRUE) # R.squared and L.squared of exponential model pam.survreg(fit1) # Fit a lognormal model with standardised blood clotting time fit2 <- survreg(Surv(time, status==2) ~ protime, data = pbc,dist="lognormal",x=TRUE,y=TRUE) # R.squared and L.squared of lognormal model pam.survreg(fit2) # Fit a weibull model with bilirubin and standardised blood clotting time fit3 <- survreg(Surv(time, status==2) ~ bili + protime, data = pbc,dist="weibull",x=TRUE,y=TRUE) # R.squared and L.squared of weibull model pam.survreg(fit3)library(survival) library(PAmeasures) # Use Mayo Clinic Primary Biliary Cirrhosis Data data(pbc) head(pbc) # Fit an exponential model with bilirubin fit1 <- survreg(Surv(time, status==2) ~ bili, data = pbc,dist="exponential",x=TRUE,y=TRUE) # R.squared and L.squared of exponential model pam.survreg(fit1) # Fit a lognormal model with standardised blood clotting time fit2 <- survreg(Surv(time, status==2) ~ protime, data = pbc,dist="lognormal",x=TRUE,y=TRUE) # R.squared and L.squared of lognormal model pam.survreg(fit2) # Fit a weibull model with bilirubin and standardised blood clotting time fit3 <- survreg(Surv(time, status==2) ~ bili + protime, data = pbc,dist="weibull",x=TRUE,y=TRUE) # R.squared and L.squared of weibull model pam.survreg(fit3)