Why use the Weibull model

1. Why use the Weibull model?

In this video, we will discuss why we want to use models to analyze survival or other time-to-event outcomes. In the previous exercises, we looked at the survival of breast cancer patients. The survival of patients may be interesting in general, but often we want to know how a treatment or the severity of an illness affects the survival of the patients.

2. What the Weibull model can do

In this image, you see several survival curves that were estimated by a Weibull model. In this analysis, we were interested if patients live longer if they receive hormonal therapy and if the tumor size plays a role. horTh here stands for hormonal therapy and tsize for tumor size. As we can immediately see, patients with a small tumor (20 mm) and who get hormonal therapy survive longest, because the red dashed line is the highest. Also, we can see that patients live longer if they get hormonal therapy. The dashed lines are always above the solid lines for each tumor grade.

3. Computing a Weibull model in R

To compute this model we use the survreg function again. The only difference from before is that instead of the value 1, we write down the covariates behind the tilde. In this case hormonal therapy (horTh) and tumor size (tsize). We can look at the model coefficients using the coef() function, such as for most other models in R. A positive effect suggests an increased time until the event - in this case, death - happens. Receiving hormonal therapy leads to a prolonged survival. Larger tumor sizes are associated with decreased survival. In this course, we will not go into the details of what the exact numbers mean but will focus on visualizing the results of the model. Visualizing effects of categorical variables such as hormonal therapy is easy. You can plot one survival curve per treatment option. For metric variables, it gets a bit more tricky. You need to choose certain values which to visualize. For the tumor size, I chose the 25-, 50-, and 75-% quantiles and plotted the three values 20, 25 and 35 mm. Instead of using quantiles you could choose values that are of particular interest to you, such as the tumor size of a certain patient. Visualizing 3 tumor sizes and 2 treatment options leads to 6 survival curves, which can be easily interpreted. How to create this pretty plot will be the topic of our next video.

4. Let's practice!

But first, let's practice what we've learned so far!

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