(25 pts) A laboratory scientist is examining the age at death of three genetic lines of mice, all bred to develop a certain type of cancer. He is interested in determining if certain characteristics of the mice are associated with the risk of death due to cancer. For a cohort of mice, he has measured the following:
Variable Description
id Mouse ID
age.death Age of death (weeks)
death Indicator of death (1 = death, 0 = right censored)
age.tumor Age at development of first tumor (weeks)
size Tumor surface area (mm2)
line Genetic line (X24, J33, F19)
wt Weight at time of tumor development (g)
treat Indicator of prenatal vitamins given to mother(1 = Treated)
gest.age Gestational age at birth (days)
sex Biological sex
These data are available in the data frame mouse in the file MouseCancer.Rdata posted to Blackboard. As the study statistician, your job is to build a model containing only those covariates that are related to the risk of death. A couple of notes about the analysis:
1. This data set is left truncated by the age of tumor development, as the cancer can’t develop until the tumor is present. Mice for which a tumor never developed are not included in this data set.
2. Build your model based on AIC selection (not p-value selection). Do not examine interactions in building your model.
3. Do not forget to evaluate proportional hazards! After selecting covariates through the AIC procedure, if a categorical covariate is significantly related to the risk of death but violates the proportional hazards, consider using it as a stratifying variable. If an included quantitative covariate violates the proportional hazards assumption, consider stratifying by discretizing it at some cut-point and use the discretized variable as a stratifying variable.
From your final model, produce the following for the included covariates:
1. Hazard ratios, 95% confidence intervals, and p-values from coefficient tests
2. Qualitative interpretations of the hazard ratios
3. Graphs of estimated survival functions for different cohorts defined by different variables included as covariates in the final model. There should be 1 graph for each included covariate. This will require creation of multiple new data frames to feed to survfit() (1 for each covariate).
a. For any categorical covariates in your final model, plot the estimated survival functions for each group defined by the covariate.
b. For any quantitative covariates in your final model, plot estimated survival functions at the three quartiles of the covariate (Q1, median, Q3).
c. When creating the data frames to feed to survfit() and create your survival graphs for a given covariate, set the value of all other quantitative covariates to their mean value and all other categorical covariates at their reference level.
4. For any variable defined to be a stratifying variable in your model, plot the baseline hazard function for the strata.
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