## The meme

The mathematical abilities of medical doctors is a classic meme. It is not totally unfounded. This classic study "Statistical Literacy of Obstetrics Gynecology Residents" is often summarized by the catchy phrase "significantly less than 50% of doctors can answer a true false question about statistics". Indeed, if one reads the abstract, it appears that only 42% of the respondents in a large sample of MDs (n=4173) were able to recognize the definition of what a P Value is. Some abstained, some - just a bit less - got it right, the study can't be generalized...

The question was ‘‘True or False: The P value is the probability that the null hypothesis is correct.’’

The correct answer is false. Assuming some null hypothesis is true, the P value is the probability of obtaining a test result at least as extreme as the one obtained. Say you want to test a placebo and your study produces a P Value of 0.01 basically means that your data had a 1% chance to occur if the if the null hypothesis was true (see here for an explanation with charts). It means nothing more. Likewise, a P value of 0.95 means the result you obtained had a 95% chance to be observed if the the null hypothesis was true.

Some important things to note:

• by definition, the math is based on a starting point where the null hypothesis is considered to be true. Therefore, you are NOT calculating a probability that it is valid or invalid. The probability is applied to the data, not the null hypothesis. (some will even argue that the data has no probability since it is there already, but that part is for the larger B vs F debate I will mention a bit later)
• if your data has comes up with a low P value, you can't really tell distinguish between "the null hypothesis is false"  and "my sample is biased by something else"
• the confidence value to which the P value is compared is a bit arbitrary and depends on the field. Medicine is often quite happy with 0.05, fundamental physics wants "5 sigmas" or a P Value of 0.0000003.

Let's stop for a minute to think about the first and last point: why such a discrepancy?  What is the chance of incorrectly rejecting a true null hypothesis? Well, it depends on several factors, selection bias (in the above case, only gynecologists for example), population size, prevalence of the observed effect, etc... Physicists can afford to characterize their testing environment, run as many tests as our taxes allow. Physicians are limited by who they enroll in their studies, vague null hypothesis based on previous studies, small sample sizes, different prevalences of what they test, etc... One of the main issue is the initial probability of the true null. It is assumed to be 100% in the calculations of the P value but, particularly in Medicine, it is almost always not the case! Addressing that question leads to another set of calculations that provide, you guessed it, another probability. What is the chance of incorrectly rejecting the null hypothesis? It turns out that a P value of 0.05 has at least a 23% chance of incorrectly rejecting a true null hypothesis. In practice, the probability is around 50%! (start here for a recursive exploration in the issue) but it can also simply be 100% if the null hypothesis is poorly chosen.

But there is more: even if an experiment has been set up and reported properly, it has a significant chance of being understood or reported incorrectly, even in the specialized press. In this case, a now famous Higgs Boson announcement was reported by both the Daily Telegraph and Nature. Nature got it wrong... Maybe both writers tossed a coin and one got lucky?  (medical analogy: after some procedure, you are either alive or dead, there is only one direction of interest. You can't be more alive or more dead. But you can be taller or smaller than average, or produce more or less TNF, etc...)

## Does ignorance matter?

Going back to our gynecologists study, generalizing it as "MD's don't know shit about maths and stats" could be a mistake. But, even if it is not, does it matter? Is it actually a bad thing not to know about P values? Let's see what Nature (again) has to say on the issue and let's hope that, this time, the coin they tossed fell, by chance, on the correct side: Scientific method: Statistical Errors. But is there a consensus on the issue? The comments are priceless and quickly turn into an argument.

Assume a study reports a P value 0.05, does it really matter if 50% of the MDs who read it get it wrong when the study itself has a true error rate of 50% ? A question worth asking I believe.

In the subset of MDs answering the question correctly, how many will go down one level deeper and understand all the parameters that intervened in the generation of that P value? If they don't understand them, what is the chance that they falsely convince themselves that a result is likely true or a null hypothesis is false? Now, that is getting a bit hairy... But we are not done yet.

Assume they are of the rare breed that gets it fully (I certainly would not claim that I do myself even if I spent more time than the average MD looking at the issue), is that beneficial? They could, of course, start teaching and improve the statistical literacy of other MDs by helping them understand the correct definition and interpretation of P values. If they are particularly gifted, they could even start disagreeing with other particularly gifted statisticians who happen to fundamentally disagree with them. Or they could decide to jump in the big arena and join the never ending Bayesian vs Frequentist debate...

A typical Bayesian vs Frequentist fundamental debate could be summarized as follow

Bob to Fred: "The probability that you are wrong is extremely high"
Fred to Bob: "Don't bother, I observe that you are wrong"

or the other way round... who cares.

## Meanwhile in the real world...

But that's not where the glory and money is... The main career path of statistically competent MD is in the industry, where his only goal will be tweak studies to achieve a nice P value for whatever drug or device study his employer wants to push on his statistically illiterate colleagues.

That's something he will achieve by slightly tweaking the null hypothesis, excluding some data, cherry picking the prevalence rate of the issue that he addressed... "We need P : 0.01 to push this through, get it."
More statistically competent MDs means more tweaked studies if they are on the dark side. Unfortunately, the dark side usually pays better.

Clearly, increasing the number of statistically competent MDs is NOT  good thing. Quite the opposite.

Disclaimer: since I am expressing a single opinion about a binary choice, there's a 50% chance that I am wrong. A priori. If my hypotheses are true. And I understood the issue. Got my prior right...

## Wednesday, December 16, 2015

### Accessing the NightScout Mongo database in Python.

I've already mentioned the NighScout and xDrip projects many times on these pages. Unless you have been living under a rock for the last 18 months, you probably know that these free and open source projects have had a major impact on the quality of life of many Type 1 diabetics and caregivers.

In late 2015, MongoLab upgraded their database system and subsequently their Mongo-db as a service web site to a new version (version 3.x). The NightScout developers and support team, once again, delivered: thanks to an upgrade, their users were able to continue to use the system with minimal inconvenience.

Unfortunately, for a non standard user such as your servitor, the new system had several drawbacks:
• data could not be posted directly to the database anymore, it had to be sent to the web site, then to the database.
• the web site itself had started to evolve into something much bigger than a simple remote viewer.
• for most users, this meant that setting up the full new portal on Azure was the only practical solution.
My own requirements were
• the database is all that matters.
• simpler architecture that I can fire up in VMs, local computers, Raspberry PI, any hosting service.
• no need for the current additional features but the necessity to be compatible with my analytical interests.
• no desire to depend on the availability of chained elements (uploaders, azure, database, azure again, github for updates)
This is why I decided to leave the NightScout paradise for a while and revert to my private purgatory which includes, I shamefully admit, SQL and SQLITE databases...

### Born again?

But then, right in time for the Holiday season, good news showed up. xDrip will support direct database uploads. Thank you guys, you made my day! And that brings me to the point of this short post: if MongoDB was again a viable option, how hard was it to access it outside the normal setup? I've always been a bit suspicious of MongoDB, as a memory and resource hog... Plus, if I had had the final say on product naming, I would have called it LISCB (lots of insane stupid curly braces). I was a bit reluctant and I was WRONG!. It turns out that, in Python at least, the task was extremely easy and took a few minutes!

Assuming you are running Python 3.4+, here's how to do it.

Start by installing the pymongo package

python -m pip install pymongo

and here is some simple sample code, with no error checking included, I just want the smallest demo possible. The prints aren't needed, they are just there to show the output. If you want to test it on your own installation, replace the user, password, 00000s db and collections with your own identifiers of course.

```# import the required package
from pymongo import MongoClient
# database connection setup
client = MongoClient(uri)
print(client)
# set the db we need, we could of course query what's available
db = client['testdb']
# get the list of available collections, call them tables for fun
tables = db.collection_names(include_system_collections=False)
print(tables)
# set the collection we need
testcoll = db['testcoll']
# see if we can get a record
result = testcoll.find_one()
print('Result\n______\n', result)
# find out how many record we have
count = testcoll.count()
print('Number of Documents in collection :', count)
# let's look for values above 270 mg/dl
cursor = db.testcoll.find({"sgv": {"\$gt": 270}})
# and display some information about them
for value in cursor:
print(value['sgv'], 'provided by', value['device'], 'on', ['dateString'] )
```

And here is the output

/mongodb/minimal.py

getting there

MongoClient(host=['ds000000.mongolab.com:00000'], document_class=dict, tz_aware=False, connect=True, authmechanism='SCRAM-SHA-1')

collections

['devicestatus', 'objectlabs-system', 'objectlabs-system.admin.collections', 'profile', 'testcoll', 'treatments']

first record in that test db

Result
______
{'dateString': 'Fri Oct 24 14:14:00 CEST 2014', 'direction': 'SingleUp', 'date': 1414152840000, 'device': 'dexcom', '_id': ObjectId('544c6816a885b50eecc2571e'), 'sgv': 101}

number of records in the testcoll collection

Number of Documents in collection : 37192

result of the conditional query

271 provided by dexcom
271 provided by dexcom
271 provided by dexcom
271 provided by dexcom
271 provided by xDrip-BluetoothWixel
271 provided by xDrip-BluetoothWixel
271 provided by xDrip-BluetoothWixel
271 provided by xDrip-BluetoothWixel
271 provided by xDrip-BluetoothWixel
273 provided by xDrip-BluetoothWixel
275 provided by dexcom
276 provided by xDrip-BluetoothWixel
277 provided by dexcom
277 provided by xDrip-BluetoothWixel
277 provided by xDrip-BluetoothWixel
278 provided by dexcom
278 provided by xDrip-BluetoothWixel
278 provided by xDrip-BluetoothWixel
278 provided by xDrip-BluetoothWixel
279 provided by dexcom
279 provided by xDrip-BluetoothWixel
279 provided by xDrip-BluetoothWixel
280 provided by xDrip-BluetoothWixel
281 provided by dexcom
282 provided by xDrip-BluetoothWixel
282 provided by xDrip-BluetoothWixel
283 provided by xDrip-BluetoothWixel
286 provided by xDrip-BluetoothWixel
287 provided by xDrip-BluetoothWixel
289 provided by xDrip-BluetoothWixel
290 provided by xDrip-BluetoothWixel
292 provided by xDrip-BluetoothWixel
292 provided by xDrip-BluetoothWixel
294 provided by xDrip-BluetoothWixel
296 provided by xDrip-BluetoothWixel
299 provided by xDrip-BluetoothWixel
303 provided by xDrip-BluetoothWixel
310 provided by xDrip-BluetoothWixel

That's all folks, back to my obscure useless stuff.