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Survival Analysis and Zombies

Reliability and survival analysis is used most frequently in manufacturing. Companies use these methods to estimate the proportion of units that will fail within, or survive beyond, a given period of time. But could these reliability and survival analysis techniques prove useful in a zombie apocalypse, too? Today's blog post explores that chilling scenario. 

Think. This is what Zachary is telling himself as he helps his nephew Liam across a creek located somewhere in the woods of Wayne County, Pennsylvania. Liam has just been bitten in the lower leg by a fallen zombie, hidden underneath some dense brush a few miles back.

Zachary knows his nephew doesn’t have a lot of time left. But how much? That question, consuming all other thoughts at the moment, has quietly invoked a core tenet of this new era's code of conduct: When you have the unfortunate luck of running into someone who has just been bitten, then certain...actions must be taken quickly. It gets easier to carry out the more you do it—unless it involves your nephew. 

After reaching the other side of the creek, Zachary glances at his nephew. Liam gives a familiar nod to keep going, and they do. They slowly march up the small hill in front of them, reaching the top to discover a pleasant surprise. A camp. They don’t make it within 15 feet of the tents and campfires before a small group of 8 approach them with guns. Zachary hears one person tell another that “one of them” has been bitten. He knows he has to talk fast.

“We don’t want trouble. I hear a clinic close by has developed a vaccine. I am taking my nephew there. Do you know what direction the clinic is in?”

“It's about nine hours to the east. We’re heading to the clinic tomorrow if you’d like join us. He won’t make it. 

“We’ll be on our way then. Thank you for your help”

“Wait!” Someone emerges from the circle of people surrounding Zachary and Liam. “My name is Claire. I am the group's doctor. When was he bitten?” 

“Just a few hours ago, so he may have a chance. But I would have a better idea if I had actual data on time to transformation.”

“We do, actually," Claire replies. "This group has stuck together for a quite a while, and we have had access to enough medical supplies to start testing if we can prolong the period between virus exposure and transformation into a zombie. Wait here."

Claire steps into her tent and comes back out holding a notepad. “Here are the transformation times for the 65 people we’ve lost in our group. Each value represents the elapsed time from being bitten to waking up as a zombie."

Zachary removes a laptop from his backpack and turns it on. So...the clinic is 9 hours away. With your data, we might be able to find out the likelihood of Liam surviving after 9 hours.”

 Zachary opens Minitab 17 and quickly enters Claire's data in the worksheet. Here is an excerpt of the data set (in hours):

He then goes to Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Distribution ID Plot... to figure out what distribution the data follows prior to running a survival analysis. Minitab quickly returns the following results:

Zach is looking for the distribution with the smallest A-D value, and in this case it is Weibull. Zachary goes to Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Parametric Distribution Analysis… to perform his survival analysis.

Now he clicks on the Estimate... button in the dialog box. He wants to estimate the odds of surviving 9 hours after a zombie bite. Since this dialog window only accepts numeric values, Zachary enters 9:0:0 in a blank column. The colons separate the hours, minutes and seconds. He then right-clicks on the column and chooses Format Column > Automatic Numeric. Minitab calculates that 0.375 is the numerical equivalent of 9:0:0, or 9 hours of elapsed time, and Zach enters that into the dialog:

Here is the table of survival probabilities after pressing OK:

Things are not looking good for Liam. He has an estimated 0.3% chance of making it to the clinic alive after 9 hours have passed. Using the confidence interval, the upper bound is at around 2 percent. Pretty low. Liam re-runs the analysis quickly, using 0.354167(equivalent to 8 hours and 30 minutes), knowing that time is ticking and they should be leaving now.

It’s still poor odds, but not impossible. If they pick up the pace, they might make it there in time. Zachary leaves his laptop with the camp. The less weight he carries, the better. He thanks the group for the data they provided, informing them that if all goes well, he will see them again in a few days. He hoists his nephew onto his shoulders, and hastily makes his way towards the clinic.

 

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