Video Tutorial – Useful Relationships Between Any Pair of h(t), f(t) and S(t)

I first started my video tutorial series on survival analysis by defining the hazard function.  I then explained how this definition leads to the elegant relationship of

$h(t) = f(t) \div S(t)$.

In my new video, I derive 6 useful mathematical relationships that exist between any 2 of the 3 quantities in the above equation.  Each relationship allows one quantity to be written as a function of the other.

I am excited to continue adding to my Youtube channel‘s collection of video tutorials.  Please stay tuned for more!

Video Tutorial – The Hazard Function is the Probability Density Function Divided by the Survival Function

In an earlier video, I introduced the definition of the hazard function and broke it down into its mathematical components.  Recall that the definition of the hazard function for events defined on a continuous time scale is

$h(t) = \lim_{\Delta t \rightarrow 0} [P(t < X \leq t + \Delta t \ | \ X > t) \ \div \ \Delta t]$.

Did you know that the hazard function can be expressed as the probability density function (PDF) divided by the survival function?

$h(t) = f(t) \div S(t)$

In my new Youtube video, I prove how this relationship can be obtained from the definition of the hazard function!  I am very excited to post this second video in my new Youtube channel.

Video Tutorial: Breaking Down the Definition of the Hazard Function

The hazard function is a fundamental quantity in survival analysis.  For an event occurring at some time on a continuous time scale, the hazard function, $h(t)$, for that event is defined as

$h(t) = \lim_{\Delta t \rightarrow 0} [P(t < X \leq t + \Delta t \ | \ X > t) \ \div \ \Delta t]$,

where

• $t$ is the time,
• $X$ is the time of the occurrence of the event.

However, what does this actually mean?  In this Youtube video, I break down the mathematics of this definition into its individual components and explain the intuition behind each component.

I am very excited about the release of this first video in my new Youtube channel!  This is yet another mode of expansion of The Chemical Statistician since the beginning of 2014.  As always, your comments are most appreciated!