Deck 7: Time to Event Data

Question 1

The log-rank test CANNOT be used to

A) compare two survival curves
B) compare multiple survival curves
C) compare two survival curves while adjusting for continuous covariates
D) compare hazard ratios

Answer 1

compare two survival curves while adjusting for continuous covariates

Question 2

The survival function plot for time until hip fractures are healed is produced using the Kaplan-Meier method. Based on the plot, which gender has a better recovery experience? Describe the plot of each gender at time point 3.

Answer 2

As more time progresses, the curves in the graph decrease, but females decline at a faster rate. Thus, females have a better recovery. At time point 3, approximately 50% of the female subjects and 35% of the male subjects have healed.

Question 3

Can the log-rank test be used to compare survival curves at a specific time point? Why or why not?

Answer 3

No, the test is used to determine if the survival functions of the comparison groups are the same for all points in time. By rejecting the null hypothesis, it implies that the survival curves are different at some time t.

Question 4

Describe how an interaction with time in a proportional-hazards model can be used to check the proportional hazards assumption.

Question 5

Suppose the hazard ratio of cancer recurrence is 1.45 (95% CI: 1.32, 1.58) when comparing the hazard rates of male patients to female patients. Interpret this result.

Question 6

How does the Kaplan-Meier estimator of the survival function differ from the percentage of subjects with the event?

Question 7

Suppose a study is conducted to investigate the risk factors associated with the time to receive treatment after the start of stroke symptoms. The proportional-hazards model is fitted. Estimate the adjusted hazard ratio for every 5 units of body mass index (BMI) and interpret the result. Include the 95% confidence interval and interpret.

Question 8

Which of the following statements is NOT true about the survival function?

A) It describes the event rates.
B) A specific time point of the survival function is a probability.
C) It describes the proportion of event-free people at a particular point of time.
D) They are not constant over time.

Question 9

In the presence of tied event times (i.e., events that occur at the same time), what methods can be used to compute the likelihood? When would each method be preferred?

Question 10

Describe in what scenario you might observe this hazard function plot.

Question 11

Identify the following events as right-censored, left-censored, or interval-censored. Provide a justification for your choice.
a.A person without an event who drops out of the study because he/she is too busy to participate.
b.Suppose the event of interest is the presence of tumors in rats. A rat dies during the study period but the death was before a tumor is detected.
c.Suppose the event of interest is menarche. A female entered the study and the menarche had already occurred.
d.Suppose the event of interest is dental caries in children. A healthy child entered the study with no cavities but came back one year later with a cavity.

Question 12

What is the difference between a life table method and Kaplan-Meier method in estimating the survival probability? Provide an example when the life table method is preferred to the Kaplan-Meier method.

Question 13

Which of the following equations does NOT represent the proportional-hazards regression model?

A) h(t)= h0(t)(exp(b1x1+b2x2+ · · · +bKxK))
B) h(t)=a(t)+b1x1+b2x2+ · · · +bKxK
C) ln(h(t))=a(t)+b1x1+b2x2+ · · · +bKxK
D) ln(h(t)/h0(t))=b1x1+b2x2+ · · · +bKxK

Question 14

How does the Kaplan-Meier method estimate the survival probability in the presence of censoring?

Question 15

Describe the difference between a survival function and a hazard function?

Question 16

Describe the types of outcomes appropriate for time-to-event analyses. Provide a specific example.

Question 17

Which of the following methods is used to estimate the b's (coefficient of parameters) in a proportional hazards regression?

A) least squares method
B) maximum likelihood estimation
C) partial likelihood estimation
D) probability plotting method

Question 18

Suppose an investigator is interested to study the relationship between hormone therapy treatments (treatment A, treatment B, and no treatment) and time to recurrence of breast cancer. Age (years), postmenopause (yes/no), and tumor size (millimeter) are also considered as possible predictors.
a.Using proportional-hazards regression to investigate this research question, what is the statistical model?
b.Provide appropriate global null and research hypotheses for the model in (a). What would you conclude if the null hypothesis is rejected?
c.Provide appropriate null and research hypotheses for the specific effect of each hormone therapy. What does a rejected null hypothesis imply?
d.If the estimate HRT A is -0.70 (95% CI: -0.84, -0.56) and the control is used as the reference, provide an estimate of the hazard ratio and its 95% confidence interval and interpret.

Question 19

Which of the following statements is NOT true about hazard rates?

A) Two hazard rates at the same time can be compared.
B) They are probabilities.
C) Change in hazard rates can be described by a hazard function.
D) They are not constant over time.

Question 20

The major assumption of proportional-hazards regression is that the hazards are proportional. Explain what this means.