13 Questions
What was the p-value for the Likelihood ratio test?
0.002
How many events were included in the sample?
152
What was the hazard ratio for sex?
.5939
What was the 95% confidence interval for sex?
(.422, .836)
What was the concordance reported for the initial Cox model?
0.612
What was used to model time-varying coefficients?
$tt()$ function
What test was repeated for the time-varying model?
Wald test
What does the Cox model equation with multiple predictors look like?
$h(t|X_1, X_2, ..., X_p) = h_0(t)exp(b_1X_1 + b_2X_2 + ... + b_pX_p)$
How can each coefficient $b_i$ in the Cox model equation be used to calculate a hazard ratio?
By exponentiating each coefficient $b_i$
What does the formula for fitting a Cox model in R typically look like?
Surv(time, event) ~ x1 + x2 + ...
What does the output 'exp(coef)' represent in the context of Cox modeling?
The exponentiated coefficients representing hazard ratios
What does a concordance value of 0.612 indicate in Cox modeling?
Moderate predictive accuracy
What does the 'status' variable represent in the lung cancer survival data set used for Cox modeling?
'status' indicates whether an event occurred or not (censored or dead)
Study Notes
Cox Proportional Hazards Model Analysis in Medical Research
- Likelihood ratio, Wald, and Score tests were conducted, resulting in p-values of 0.002, 0.003, and 0.003 respectively, on 3 degrees of freedom.
- The sample size was 214, with 152 events and some observations dropped due to missingness.
- Hazard ratios were calculated for age (1.0203), sex (.5939), and weight loss (1.008), with corresponding interpretations for each.
- Standard errors for log hazard ratios were provided.
- The 95% confidence interval for sex was between .422 and .836, indicating a decrease in hazard for females compared to males.
- A concordance of 0.612 was reported.
- Stratified Cox model was used to control for the effects of a variable, despite violating the proportional hazards assumption.
- The stratified Cox model provided new parameter estimates and a concordance of 0.561.
- Time-varying coefficients were modeled using interaction terms with time, with a recommendation to use the function tt() to avoid mistakes.
- An interaction of sex with time was specified, allowing the effect of sex to change linearly with time.
- The likelihood ratio, Wald, and Score tests were repeated for the time-varying model, resulting in p-values of 0.002, 0.003, and 0.002 respectively.
- The log-hazard-ratio for sex at day t = 0 was estimated as -0.942, corresponding to a hazard ratio of exp(-0.942) = 0.389, and the change in the log-hazard-ratio for each additional day was also estimated.
Test your knowledge of Cox model with multiple predictors, hazard ratios, and fitting the Cox model with the survival package. This quiz also covers using new data sets for Cox modeling.
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