Alone Survival Analysis

May 8, 2023 Daniel Oehm 0 Comments

In 9 seasons there is yet to be a female winner on Alone, even though on quick inspection it seems that on average women survive more days than men. So, here I’ll run a survival analysis and compare the survival rates of men and women and test if there’s truly a difference.

All data used here is available in the {Alone} R package and all code is maintained in Github – Alone – Survival Analysis.

TL;DR

Is there a difference in the survival rates of men and women on Alone?

Potentially. There is some evidence that women survive longer on average in the short term, but with the small sample, it’s difficult to say conclusively. However, there is effectively the same chance of winning for both men and women in a balanced season.

In summary:

The average number of days survived is 37 and 49 days for men and women respectively.
Women have a higher average number of days survived before tapping out due to personal reasons, health reasons, and medical evacuations, but there’s not enough evidence to conclude there’s a true difference.
There is a difference in medical evacuations with 53% of women and 18% of men having been medically evacuated.
The P-value of the log-rank test on the survival curves is 0.2 so there’s some evidence the survival rates are different between men and women. One to watch for future seasons.
In a balanced season, there is a 52% chance a female will win the season.

Data setup and considerations

There are a few considerations for preparing the data for analysis:

Censoring:
- Winners are censored in the data since there is no way to know how long they may have survived. Once they are the last they are announced as the winner and get to go home.
- In season 5 Nicole Apelian experienced an MS attack and had to call for medical assistance. As a result, she was pulled from the competition. Nicole is also censored in the data since she left due to a condition she has been living with rather than the influences of isolation and surviving the elements.
- One way to check if censoring impacts the results is to test for a difference between the censored and uncensored participants. Since they’re all winners but one they are definitely different. We just need to keep this in mind.
Season 1:
- There were no women in the first season. Season 1 will still be used for the analysis but important to keep in mind that all contestants went into the game never seeing the show before and ultimately went in with less information and perhaps a different mindset. There were a few early taps in the first season which may introduce a bias for men in the analysis.
Season 4:
- This season featured teams that began separated from each other. One member started at the campsite to prepare shelter, food, etc, while the other had to trek across the dense forest to find them with only a compass. They both had 10 items shared between them. This season was different enough from the other seasons I am removing it from the analysis.
Season 7:
- The goal was to last 100 days. The winner is awarded $1M prize money. This differs from the other seasons such that the competition is not stopped when there is only 1 contestant left, but rather when day 100 is reached. This season is similar enough to the others that it is included in the analysis.
Medical evacuations and check-ins:
- In situations where a contestant is pulled from the competition due to injury or other medical concerns, they are still considered in the survival analysis since their condition was influenced by isolation and the environment.
Location:
- The location is not factored into the analysis. Mostly due to there not being enough data to account for the effect. While Patagonia may have been easier to survive than North Vancouver Island due to the better food sources it’s difficult to account for. This will be present as variation in the data and a random effect.

Analysis

The first two sections of the analysis are going to explore the results and reasons for tapping out to provide an overview and build an understanding of the data. The 3rd section goes into the survival analysis.

This table details the result for every season of Alone. Columns can be sorted by clicking the header and are also filterable. Useful for a quick inspection of the key data items and a useful tool for the analysis.

For a better view open the table in a new window.

1. Contestant breakdown

1.1 Overview

There have been 61 men and 19 women who have competed in 8 seasons. Nicole Apelian, Carleigh Fairchild, and Brooke Whipple have played twice. Brooke first played in season 4 with her husband.

Over the 8 seasons included in the analysis, the average number of days lasted is higher for women.

This does not account for the censored participants at the moment, it’s just a raw average to get an understanding. The mean is quite a bit higher for women with a 95% CI for the difference being [-5, 24] and 80% CI [0, 20] days is enough for me to say it appears women tend to survive longer, at least in the short term. The next couple of seasons will be interesting where the results may shift the means.

For more perspective, the winners would need to have lasted 2.2x longer in order to balance the mean days lasted for both men and women. That means 220 days for Roland Welker! So even accounting for the winners it’s a significant gap in the mean.

1.2 Results

While there hasn’t been a female winner, 4 women have come very close and finished second.

During a routine check, Carleigh and Callie were medically evacuated. Woniya and Karie Lee tapped due to health reasons.

2. Reasons for tapping out

There are 2 main reasons for tapping out, personal reasons and health reasons. Sometimes players are medically evacuated and pulled from the game by the crew. I’ll compare the differences here.

2.1 Personal

There have been 4 women (21%) and 24 men (39%) that have tapped out due to personal reasons such as missing their family. Women have a higher average number of days survived before tapping for personal reasons at 41 days whereas men are at 27 days. A difference of 14 days.

The dotted lines are the posterior mean with prior N(39, 14). The prior was chosen to be simply the overall average number of dayes survived with a deviation of 2 weeks. Seemed reasonable. It doesn’t do a lot for the mean but given there are only 4 data points for women it’s an important specification.

Tests:

Days lasted
- Difference in means
  - 95% CI [-11, 35]
  - 80% CI [-4, 27]
- Not a hugely convincing difference in the mean days survived with 4 data points.
Proportion
- 95% CI: [-0.42, 0.05]
- P-value: 0.12
- There are potentially more men than women that tap out for personal reasons. It will be interesting to watch this stat for the next few seasons.

2.2 Health

There have been 5 women (26%) and 15 men (25%) that have tapped due to health concerns. Of the 5 women, 4 survived at least 73 days which is a huge feat. Women have a higher average number of days survived before tapping out due to health reasons at 65 days whereas men are at 39 days.

Similarly, with only 5 data points it’s difficult to draw conclusions but you can see the importance of the prior here. It is interesting that 4 observations occur from day 73 and only 1 male contestant achieved the same.

Tests:

Days lasted:
- Difference in means
  - 95% CI [-16, 37]
  - 80% CI [-4, 29]
- On first inspection, it looks like women survive longer before tapping out for health reasons, but the calibrated mean pulls it back into perspective. The credible interval of the difference easily contains 0 so not as convincing as it may seem at first. Interesting to watch this one over the next couple of seasons.
Proportion:
- 95% CI: [-0.22, 0.26]
- P-value: 0.88
- Effectively the same proportion of health-related taps for men and women.

2.3 Medical evacuations

In some situations, an injury or illness pulls people from the game and sometimes they have pushed themselves to the brink that they can’t be allowed to continue as it’s too much of a risk – when the mind is stronger than the body. There have been 11 men (18%) and 10 women (53%) that have been medically evacuated from the competition. Women have a higher number of days survived before being medically evacuated from the game, 45 days vs 32 days from the raw data.

Tests:

Days lasted
- Difference in means
  - 95% CI [-13, 31]
  - 80% CI [-6, 23]
- No clear difference but the mean is again higher for women.
Proportions
- 95% CI: [0.08, 0.61]
- P-value: 0.01
- Proportionally more women get medically evacuated either by injury, illness, or losing too much weight and it is too risky for them to continue.

2.4 Summary

In each category for the reasons behind tapping out women have a higher average number of days survived. The statistical tests aren’t particularly strong for each reason category however, it looks like there could be a difference between men and women but can’t say conclusively. There are proportionally more women medically evacuated than men and there are potentially more men that tap for personal reasons.

3. Survival Analysis

The analysis so far definitely indicates that women survive longer on average. We’ll dive deeper using survival analysis. This is important since the analysis so far hasn’t taken into account the censored survivalists. I’ve quantified how much longer they would have needed to survive to balance the average days survived, but need to account for them in the analysis itself.

3.1 Kaplan-Meier survival curves

There are some clear differences between the men and women survival curves. Two key observations:

Between days 10-65, the chart suggests that women could have a higher rate of survival, although since there are only 19 data points there is high variance, and may be hard to confirm this statistically.
The rate of tap-outs increases a lot at around day 65. This may be due to routine medical checks that happen more frequently at this point of the game (from my understanding) and therefore more likely to be pulled from the game. Because of the increased rate, it makes it tricky to answer the question if there is a difference in the survival rate between men and women. The increased rate could also be due to random variation.

3.2 Log-rank test

The log-rank test will test if there is a difference between the survival curves for men and women. This is done in R with the survdiff function from the survival package.

library(survival)

survdiff(Surv(days_lasted, event = censored) ~ gender, df)

Call:
survdiff(formula = Surv(days_lasted, event = censored) ~ gender, 
    data = df)

               N Observed Expected (O-E)^2/E (O-E)^2/V
gender=Female 19       18       23     1.069      1.69
gender=Male   61       53       48     0.511      1.69

 Chisq= 1.7  on 1 degrees of freedom, p= 0.2

The output shows p = 0.2 which I interpret as some evidence that women on Alone tend to survive longer. The small sample and the semi-complicated survival function where the curves cross at day 80 make it difficult to call with certainty. If a few of the 4 women that finished second actually finished first it would become a bigger difference.

I haven’t used a Cox-PH model here because the assumption of proportional hazards doesn’t hold – indicated by how the curves cross at around day 80.

3.3 Log-normal survival curves

The K-M survival curves are a non-parametric approach that has its advantages such as easily showing the complex nature of survival over time. I’ll also fit a parametric version assuming a log-normal model. The parameters will be estimated using Stan.

Two initial observations:

The estimated survival curve for women is higher than the men’s which is in line with the analysis above.
The curves are an OK-ish fit for men but a bit janky for women largely due to the increased rate of tap-outs beyond day 65. It’s not too bad considering there’s only a small number of observations beyond that point. It’s interesting they intersect and cross on day 100.

The advantage of this approach is there is actually a chance for women to survive beyond day 88 whereas the K-M approach estimates the chance of survival to be 0. But it’s not 0, it’s something greater than 0. 0 is just a bad estimate. With that in mind, this may be a better estimate of the probability of survival.

The female survival curve looks like it could be a mixture of distributions influenced by the medical check-ins. I did look at fitting a more complex model to better fit the curve but was in two minds about it. Because there are only 19 data points the drop near the end could be due to chance rather some systematic process. I also think it’s reasonable to assume that the days survived for men and women are similarly distributed and should be modeled the same way. In this case, closely fitting the curve could be overfitting.

This is worth investigating further but for this analysis, I’m going to stick with the simpler model.

4. Probability of a female winner

So what are the chances of a female winner in future seasons? I’ll calculate the probability by taking the Bayesian approach and the following steps:

Fit a Bayesian regression model to estimate the distribution of days survived for both men and women.
Specify the number of men and women (10 in total) and draw the days survived for each.
Record who would have won by finding the maximum number of days survived.
Repeat 40,000 times.

In a season with 5 men and 5 women, there is a 52% chance there will be a female winner. Although, the most we’ve seen in a given season is 3, so in a season with a 7-3 split there is a 31% chance. Effectively the same chance for both men and women.

It’s interesting these are the results. Based on the curves and the average days lasted by women always being greater than men. But what we see is the tails of the distributions and the survival curves are very similar from day 90, with women having a slight edge. Since the game is the last one standing wins, the winner from the simulation the winner is usually from 80 days onwards. So, it makes sense that the probabilities start to even out.

For comparison I also ran a simulation based on the K-M estimated survival probabilities which came to 47% in a balanced season. This is again due to the drop off in survival past day 65. However, for the reasons discussed above, I think the Bayes model is better but we would come to the same conclusion that the chances of winning for men and women are effectively the same.

5. Final thoughts

On average women survive more days than men in the short term, but there is a high amount of uncertainty. While it looks to favour women there isn’t really enough evidence to conclusively say that women survive longer. The increased rate of tap-outs around day 65 makes it a more complicated question but also an interesting feature of the data.

In a balanced season, the simulation model suggests there is a 52% chance a female will win the season suggesting that the chances are essentially the same for men and women. In which case it’s wild there hasn’t been a female winner yet. I think there definitely will be in future seasons.

In a future post, I’ll be looking at age and location.