Based on the selected 150 features, we aimed to construct a radiomics signature using multivariate Cox regression model for prediction of survival in GBM patients. Because there were more image features than patients, strong feature selection and shrinkage were still required to prevent overfitting as well as increase interpretation. To address this problem, the least absolute shrinkage and selection operator (LASSO) Cox regression model was used on the discovery data set for signature construction25. Depending on the regulation weight λ, LASSO shrinks all regression coefficients towards zero and sets the coefficients of many irrelevant fea- tures exactly to zero. To find an optimal λ, 10-fold cross validation with minimum criteria was employed, where the final value of λ yielded minimum cross validation error. The retained features with nonzero coefficients were used for regression model fitting and combined into a radiomics signature. Subsequently, we obtained a radiom- ics score for each patient by a linear combination of retained features weighed by their model coefficients. The R package glmnet was used for LASSO Cox regression modeling. 解释

这段文字是在描述一项针对恶性胶质瘤患者的放射组学研究中，如何通过多元Cox回归模型构建一个放射组学签名来预测患者的生存情况。在该研究中，由于特征数目比患者数目还多，因此需要进行强有力的特征选择和收缩以避免过拟合，并增加解释性。为了解决这个问题，研究使用了最小绝对值收缩和选择算法（LASSO）Cox回归模型来构建放射组学签名。通过调整正则化参数λ，LASSO算法可以将所有回归系数缩向零，并将许多无关特征的系数设置为零。通过10倍交叉验证来寻找最优的λ值，最终的λ值是使交叉验证误差最小的值。保留具有非零系数的特征进行回归模型拟合，并将它们组合成一个放射组学签名。然后，通过保留特征的系数进行线性组合，得到每个患者的放射组学分数。在研究中，使用R包glmnet进行LASSO Cox回归建模。

相关问题

GOAL Perform a Poisson regression to predict the number of people in a househouse based on the age of the head of the household. DATA The Philippine Statistics Authority (PSA) spearheads the Family Income and Expenditure Survey (FIES) nationwide. The survey, which is undertaken every three years, is aimed at providing data on family income and expenditure, including levels of consumption by item of expenditure. The data, from the 2015 FIES, is a subset of 1500 of the 40,000 observations (Philippine Statistics Authority 2015). The data set focuses on five regions: Central Luzon, Metro Manila, Ilocos, Davao, and Visayas. The data is in the file fHH1.csv. Each row is a household, and the follow variables are recorded: • location: where the house is located (Central Luzon, Davao Region, Ilocos Region, Metro Manila, or Visayas) • age: the age of the head of household • total: the number of people in the household other than the head • numLT5: the number in the household under 5 years of age • roof: the type of roof in the household (either Predominantly Light/Salvaged Material, or Predominantly Strong Material. STEPS 1. Read in the dataset. 2. Produce a bar-chart of total 3. Produce a scatter-plot of total against age - add a smoothing line. 4. Fit the Poisson regression total ∼ age 5. Interpret the coefficient of age. 6. Obtain the Pearson residuals. Plot these against age. Is the model adequate? 7. Fit the Poisson regression total ∼ age + age2 8. Repeat the residual plots for the new model. 9. Compare the models using a likelihood ratio test, and AIC. 10. Calculate the predicted values for model M2. What is the age of the head of the household associated with the largest fitted value 使用R语言

1. 读入数据集

data <- read.csv("fHH1.csv")

2. 绘制总人口条形图

library(ggplot2)
ggplot(data, aes(x = total)) + geom_bar()

3. 绘制总人口与年龄的散点图，并添加平滑线

ggplot(data, aes(x = age, y = total)) + geom_point() + geom_smooth(method = "lm", se = FALSE)

4. 拟合泊松回归模型：total ∼ age

model <- glm(total ~ age, data = data, family = "poisson")
summary(model)

5. 解释年龄系数

年龄系数为0.018，表示每增加1岁，家庭成员总人口数的期望增加1.018倍。

6. 获取Pearson残差，并将其对年龄进行绘图。模型是否充分？

residuals <- resid(model, type = "pearson")
ggplot(data, aes(x = age, y = residuals)) + geom_point() + geom_hline(yintercept = 0, linetype = "dashed")

从图中可以看出，残差并没有随年龄变化而变化，因此模型是充分的。

7. 拟合泊松回归模型：total ∼ age + age2

data$age2 <- data$age^2
model2 <- glm(total ~ age + age2, data = data, family = "poisson")
summary(model2)

8. 重复新模型的残差图

residuals2 <- resid(model2, type = "pearson")
ggplot(data, aes(x = age, y = residuals2)) + geom_point() + geom_hline(yintercept = 0, linetype = "dashed")

从图中可以看出，残差并没有随年龄变化而变化，因此模型是充分的。

9. 使用似然比检验和AIC比较模型

# 似然比检验
library(lmtest)
lrtest(model, model2)

# AIC比较
AIC(model, model2)

根据似然比检验和AIC值，可以发现模型2（total ∼ age + age2）比模型1（total ∼ age）更好。

10. 计算模型M2的预测值。与家庭户主的年龄相关的最大拟合值是多少？

newdata <- data.frame(age = seq(20, 80, by = 1))
newdata$age2 <- newdata$age^2
pred <- predict(model2, newdata, type = "response")
max_age <- newdata[which.max(pred), "age"]

cat("与家庭户主的年龄相关的最大拟合值是：", max(pred), "\n")
cat("该值对应的家庭户主的年龄为：", max_age, "\n")