Evan Savage

The Behavioral Economics of 23AndMe Results

Over the holidays, I received a 23andMe genetic testing kit as a gift. In this post, I'll take a look at my results through the lens of prospect theory, which aims to quantify our perception of risk. 23andMe results estimate your lifetime likelihood of various medical conditions, making them a great dataset for testing out these concepts in behavioral economics.

Prospect Theory: A Quick Example #

Suppose I offer you a bet. I flip a fair coin once. Heads, you gain \$1000; tails, you lose \$900. Do you take the bet? Probability dictates that you should, since you would expect to come out $ (1000 - 900) / 2 = 50 $ dollars ahead.

If you're like most people, though, you have a powerful aversion to losing \$900. This aversion is powerful enough that you'll decline the bet. This only makes sense if losing \$900 has a greater negative value than the positive value of gaining \$1000. In other words, your perception of value is non-linear. This perception underpins many real-world bets that make little sense from an expected utility standpoint:

Prospect theory creates a mathematical framework for understanding our perceptions of value and risk. It's an awesome paper with highly approachable mathematics. Definitely recommended reading for anyone interested in economics, game theory, and the like.

My Disease Risk #

Among other things, 23andMe can estimate your lifetime risk of various diseases. This information is divided into three categories according to whether your risk is highly elevated, highly decreased, or roughly typical:

Within each category, the diseases are ordered by decreasing confidence rating, then by decreasing absolute risk. The different confidence levels are as follows:

  1. Preliminary Research: fewer than 100 people studied
  2. Preliminary Research: fewer than 750 people studied
  3. Preliminary Research: a single study with 750+ participants
  4. Established Research: multiple studies with 750+ participants

The 23andMe dashboard doesn't show estimated risk for lower-confidence findings, but I can fetch that information through their API.

Armed with my raw risk data, I can now play around with a pair of alternative disease rankings. As an anchoring point, here's my disease ranking by absolute risk:

$ python risksort.py risk < risks.json
1 Obesity 0.5701
2 Coronary Heart Disease 0.5464
3 Atrial Fibrillation 0.3392
4 Prostate Cancer 0.2602
5 Age-related Macular Degeneration 0.2459
6 Type 2 Diabetes 0.1969
7 Venous Thromboembolism 0.1279
8 Lung Cancer 0.0823
9 Psoriasis 0.0708
10 Gallstones 0.0618
11 Alzheimer's Disease 0.0493
12 Colorectal Cancer 0.0417
13 Chronic Kidney Disease 0.0356
14 Rheumatoid Arthritis 0.0300
15 Restless Legs Syndrome 0.0245
16 Exfoliation Glaucoma 0.0217
17 Melanoma 0.0216
18 Type 1 Diabetes 0.0137
19 Parkinson'
s Disease 0.0109
20 Ulcerative Colitis 0.0066
21 Multiple Sclerosis 0.0047
22 Esophageal Squamous Cell Carcinoma (ESCC) 0.0043
23 Stomach Cancer (Gastric Cardia Adenocarcinoma) 0.0028
24 Crohn's Disease 0.0016
25 Bipolar Disorder 0.0015
26 Celiac Disease 0.0005
27 Scleroderma (Limited Cutaneous Type) 0.0005
28 Primary Biliary Cirrhosis 0.0004
29 Breast Cancer 0.0000
30 Lupus (Systemic Lupus Erythematosus) 0.0000

The alternative ranking metric code can be found here.

Relative-Risk Sorting #

An obvious ranking metric is relative risk, which is already provided in the disease listing.

$ python risksort.py relative_risk < risks.json
1 Age-related Macular Degeneration 3.7542
2 Exfoliation Glaucoma 2.8933
3 Bipolar Disorder 1.5000
4 Prostate Cancer 1.4593
5 Multiple Sclerosis 1.3824
6 Type 1 Diabetes 1.3431
7 Rheumatoid Arthritis 1.2605
8 Restless Legs Syndrome 1.2500
9 Atrial Fibrillation 1.2494
10 Stomach Cancer (Gastric Cardia Adenocarcinoma) 1.2174
11 Esophageal Squamous Cell Carcinoma (ESCC) 1.1944
12 Coronary Heart Disease 1.1665
13 Venous Thromboembolism 1.0365
14 Chronic Kidney Disease 1.0349
15 Lung Cancer 0.9728
16 Obesity 0.8926
17 Gallstones 0.8766
18 Ulcerative Colitis 0.8571
19 Type 2 Diabetes 0.7656
20 Melanoma 0.7552
21 Colorectal Cancer 0.7500
22 Scleroderma (Limited Cutaneous Type) 0.7143
23 Alzheimer's Disease 0.6885
24 Parkinson'
s Disease 0.6770
25 Psoriasis 0.6238
26 Primary Biliary Cirrhosis 0.5000
27 Celiac Disease 0.4167
28 Crohn's Disease 0.3019
29 Breast Cancer 0.0000
30 Lupus (Systemic Lupus Erythematosus) 0.0000

Perceived Relative-Risk Sorting #

In prospect theory, a probability $ p $ has perceived weight $ w(p) $. In Advances in Prospect Theory: Cumulative Representation of Uncertainty, Tversky and Kahneman fit $ w $ to observed results for subjects evaluating bets similar to the one listed above:

The corresponding equations are

$$
w^+(p) = \frac{p^{0.61}}{(p^{0.61} + (1-p)^{0.61})^{\frac{1}{0.61}}}
$$

for positive prospects and

$$
w^-(p) = \frac{p^{0.69}}{(p^{0.69} + (1-p)^{0.69})^{\frac{1}{0.69}}}
$$

for negative prospects. If my risk is $ p_0 $ and the general risk is $ p $, I can define my perceived relative risk as

$$
r = \frac{w^+(p_0)}{w^+(p)}
$$

if $ p_0 < p $ (I consider decreased risk as a positive prospect!) and

$$
r = \frac{w^-(p_0)}{w^-(p)}
$$

otherwise. The resulting rankings are pretty close to ordinary relative risk, but not identical:

$ diff <(python risksort.py relative_risk < risks.json \
| cut -c-53) <(python risksort.py perceived_relative_risk < risks.json | cut -c-53)
13,14c13,14
< 13 Venous Thromboembolism
< 14 Chronic Kidney Disease
---
> 13 Chronic Kidney Disease
> 14 Venous Thromboembolism
16,17c16,17
< 16 Obesity
< 17 Gallstones
---
> 16 Gallstones
> 17 Obesity
20,23c20,23
< 20 Melanoma
< 21 Colorectal Cancer
< 22 Scleroderma (Limited Cutaneous Type)
< 23 Alzheimer's Disease
---
> 20 Colorectal Cancer
> 21 Melanoma
> 22 Alzheimer'
s Disease
> 23 Scleroderma (Limited Cutaneous Type)

The difference is due to distortion of small probabilities.

Further Ideas #

So far, I've only used the probability weighting functions from prospect theory. I could also assign values to each disease:

This is definitely morbid, but it's also potentially worthwhile. After all, insurance companies make very detailed estimates of our risk. They will certainly incorporate genetic data into their models as soon as it's legal to do so. If we want to make more informed decisions in situations involving risk, from medical insurance to lottery tickets, it helps to understand how we value different outcomes.

Appendix: How To Use The 23andMe API #

The 23andMe API is actually quite easy to use, and their documentation is excellent. Nevertheless, I'll list the flow I went through to get my genetic disease risk data. If you're unfamiliar with OAuth 2.0, the Google API docs include this primer complete with cute stick figure diagrams.

First, I log into the API console and create an app. This gives me the client_id and client_secret parameters I need to initiate the flow. Looking at the 23andMe API reference, I see that I need permissions under the analyses scope, so I request that by visiting

https://api.23andme.com/authorize/?redirect_uri=http://localhost:5000/receive_code/&response_type=code&client_id=<client_id>&scope=analyses

in the browser. I'm redirected to

http://localhost:5000/receive_code/?code=<code>

which gives me the auth code I need to request a token:

$ curl https://api.23andme.com/token/ \
-d client_id=<client_id> \
-d client_secret=<client_secret> \
-d code=<code> \
-d grant_type=authorization_code \
-d "redirect_uri=http://localhost:5000/receive_code/" \
-d scope=analyses > token.json
$ jsonpp token.json
{
"access_token": "<access_token>"
"token_type": "bearer",
"expires_in": 86400,
"refresh_token": "<refresh_token>"
"scope": "analyses"
}

Finally, I use my shiny new access_token to get my genetic risk data:

$ curl https://api.23andme.com/1/risks/ \
-H "Authorization: Bearer <access_token>" > risks.json
$ jsonpp risks.json | head
[
{
"id": "6d2de403675a0d07",
"risks": [
{
"description": "Atrial Fibrillation",
"risk": 0.3392,
"population_risk": 0.2715,
"report_id": "atrialfib"
},