Sunday, September 15, 2024

# Risks & Odds: Matter of Life or Death (Analytics)

Risks & Odds ratios are heavily used in medical fields mainly to track survivability of patients or effectiveness of some treatment on patients. You’re not a surgeon, nor a doctor. But you’re in charge to deliver information that’ll be used to determine the future of all patients! (e.g. Whether to administer a particular treatment, to abandon it, to promote it [or not] and if so, which how much weight to put behind it?)

You have an important job on hand! Your analysis is, in a way, a matter of life or death. What will you do?

First, you’ll get the most reliable data possible. Then you’ll look at it from both Risks perspective and Odds perspectives. For this example, we’ll keep the dataset really, really small (e.g. 100 patients), but the same approach applies to millions of samples.

DISCLAIMER: I’m not a statistician, so I will not delve into arguments about which method is better, and spend years on figuring this out. I’m  an analyst in a fast-paced real-world, so I work with the data to best deliver a story in the most efficient way (may not be most exhaustive)…besides, people are waiting on my findings!

Let’s start with the data on hand (or, let’s say we conducted experiments ourselves to collect the data, doesn’t matter! We have it)…Two groups were studied. One that we’ll call Treatment Group is a group of 100 patients who were treated. The group, we’ll call it Control Group, also consisted of 100 patients who were not treated. We have the numbers for each group as to how many survived (or did not survive. That’s all we need because the other required fields can be easily discovered).

So, the table we have to work with is as follows:

So, logically the next step is to quantify some risks and odds of survivability with or without the treatment.

Using Risk: We need to find the probability of death for patients who are treated vs not treated. So, let’s calculate a Risk Ratio using simple arithmetic:

The Risk % values are painfully obvious above. Now, if we divide the Risk % of Treatment Group by the Risk % of Control Group, we get the Risk Ratio of 67%.

You can now summarize this as follows:

Risk that a patient will NOT survive without treatment is 15% while the risk of survival with treatment is 10%
So, the risk of death when treated is about 2/3rd (67%) of those when NOT treated.

You can now take another angle, by approaching it NOT from probability but from odds. Using the same dataset, we can tabulate it as follows:

The Odds column shows as the odds for each group. e.g. 90 out of 100 survived in Treatment Group, the odds are 90% to 10% or, simply the odds are 9 to 1 (in favor of survival in Treatment group).

In the Control group, we see 85 of 100 survived, or odds are 85 to 15, or 5.67 to 1 (in favor or survival).

Now, you can tie the two groups together and be able to say, Now, we see the Odds Ratio is 1.59 (in favor of treatment, because:= 9/5.67).

### In other words, odds of survival, if treated, are about 1.6 times the odds of survival if un-treated.

Congratulations! These “small” findings by you may have changed the world…or a country, or a village, or a school, or maybe your reputation 🙂

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