Wednesday, May 28, 2014

Predicting the World Cup

Using ELO ratings, we can predict how far each team will make it in the 2014 World Cup.

Probability of each team reaching the Round of 16 (Ro16), Quarterfinals (QtrF), Semifinals (SemiF), and Finals, as well as the probability of winning the World Cup (Champ).  These data are not cumulative (e.g. Brazil has probabilities of 94% 65%,  52%, 38%, and 26% of reaching Ro16, QtrF, SemiF, Final, and Champ).

ELO is a ratings system originally devised for chess players.  Each player (or in this case, each soccer team) has a numerical rating.  When two teams play, the winner takes some points from the loser.  The amount of points exchanged depends on the relative ratings of the two teams.  I've used the ratings from www.eloratings.net, which uses data from www.world-results.net to track the results of every international soccer match and calculate a current ELO rating for each national team.

Based on the ELO rating of two teams, I calculate the probability of either team winning.  ELO is somewhat limited, in that it can only predict a binary outcome (win or loss), whereas in the World Cup group stages, there are 3 outcomes (win, loss, draw).  Luckily, Lars Schiefler at www.clubelo.com has come up with a model that uses ELO ratings to predict the number of goals scored by each team.  I've used that model to predict the outcomes of the group stages, and I use the regular ELO system to calculate the win probabilities of the knockout rounds.

Using these probabilities, I performed 100,000 random simulations of the entire tournament.  The full summary is in the figure above.  Here's the breakdown by group of the probabilities (in %) for each team.

"Grp1" is the winner of the group and "Grp2" is the runner-up. RO16, QtrF, SemiF, and Final are the knockout stages, and Win is the winner of the World Cup.
Finally, I wanted to look at how group selection affected each team's chances.  I did a regression between the ELO rating of each team and its probability to advance to the knockout round.  I've highlighted teams that stray from the regression line - team above the line have a higher chance of advancing than their rating would suggest, and teams below the line have a lower chance.



You can see that the USA and Ghana will have a hard time due to their match-up with Germany and Portugal.  Chile is also in a tough group, having to face Spain and the Netherlands.  Belgium and Russia have an easy go of it, being matched in Group H with Algeria and South Korea.  I was surprised that France didn't show up in this analysis, but then again, they are only ranked 12th in the world according to ELO, and Ecuador is a better team than a lot of people realize.

Sunday, July 28, 2013

How does cancer treatment work?

"Cancer" is an umbrella term for hundreds of different diseases.  Cancer arises when cells in the body become unable to regulate their division, and grow out of control.  Since cancer can arise from almost any cell in the body, and each of these cells have different characteristics, each different site of cancer (breast, prostate, lung, etc) behaves almost as its own distinct disease.  On top of that, the underlying DNA mutations which give the tumors their malignant traits can also differ.  For example, in breast cancer, tumors can harbor a number of distinct gene mutations (such as estrogen/progesterone receptors or HER-2 receptors).  Each one of these is a different subtype of breast cancer, and has its own prognosis and treatment options.  Some drugs may work on one type, but not on another.

I think that one of the most difficult parts of undergoing cancer treatment is the myriad of options one is presented with.  Will you undergo surgery, chemo, radiation?  What kind of radiation will you get?  Which surgeon will you go to?  How much treatment can you avoid while still giving yourself the best chance at survival?  I can't write an end-all, be-all guide to cancer treatment options.  But I can try to explain what cancer treatment does, the strengths and weaknesses of each type of treatment, and how they work together to extend life.  

Cancer progression and the goals of treatment


To understand what cancer treatment does, we need to understand how cancer progresses.  A tumor is made of cells that grow and divide out of control.  These cells form a mass in the site where they arise (the primary tumor).  The primary tumor will grow and press on nearby tissue, but on its own it is usually not life-threatening.  The danger comes when the tumor spreads to other parts of the body.  

Tumors typically will first spread to nearby lymph nodes, which are organs of the immune system that act as a trap for foreign particles.  If a tumor cell drains into a lymph node, it can start growing into a new mass.  Even more dangerous is when the tumor metastasizes.  If left unchecked, tumors tend to begin invading and degrading nearby tissue.  This can lead to tumor cells entering the blood stream and traveling to distant parts of the body.  Metastases commonly arise in organs with a large blood supply - the brain, liver, or bones.  Tumor cells which land here can form secondary tumors, and are almost always life-threatening. 

In theory, all it takes is a single tumor cell to grow into a new tumor.  As long as there are tumor cells still present and dividing in the body, there is a risk that they can spread.  So, the goal of cancer treatment is to kill or incapacitate every single tumor cell in the body.  Yet the goal of any medical intervention is to improve the patient's quality of life.  Cancer treatment must kill the tumor, but it must also do as little harm to normal tissue as possible.  So every therapy must balance the benefits of treatment with the risks of side effects.

Surgery


The most straightforward way to remove a tumor is to remove it surgically.  A surgeon cuts open the body, goes in, sees where the tumor is, and cuts out everything that can safely be removed.  Surgery is the most effective treatment in almost any site of disease, and is the standard by which other treatments are usually measured.

Surgery is excellent at removing so-called "bulk" disease.  In chemotherapy, drugs can only reach the tumor cells that have blood supply.  In surgery, the entire bulk tumor is removed at once.  Surgery is also a very targeted therapy, since the only tissues affected by surgery are the ones the surgeon cuts into.  Because of this, surgery is excellent at dealing with early-stage cancer that hasn't had a chance to spread or invade nearby tissue.  If the tumor is confined to a well-defined area, then it can be removed.

On the other hand, surgery is very invasive (as anyone who has had surgery can attest).  The surgeon must cut his/her way through the body in order to get to the tumor, and also cut into nearby tissue to find where the tumor has spread.  If tumor cells have invaded nearby nerves or major blood vessels, it may be impossible to remove without doing serious harm to the patient.     

Chemotherapy


Compared to surgery, chemo is known as a systemic treatment.  When the drug is injected into the body, it travels everywhere that blood can reach.  Strangely enough, tumors themselves have very poor blood supplies, and often times chemotherapy cannot treat the entire bulk tumor (surgery is much better in this regard).  But it is good at reaching places where the tumor may have spread.  This is chemo's best aspect - metastatic disease is dangerous, and chemotherapy can reach microscopic cancer outcroppings before they manifest into clinically significant lesions.

Chemo is a bit simpler to understand, since drugs are very familiar to us.  For instance, if you have a bacterial infection, all you need to do is simply take an antibiotic.  But we might not think as often about a drug's mechanism - how we make it do what we want it to.  How does an antibiotic know to kill the bacteria, but not hurt normal tissue?  There needs to be some difference between the normal and abnormal cells that the drug can exploit.  Take penicillin, for example. Some bacterial cells differ from human cells in that they have a cell wall.  Penicillin works by destroying these cell walls.  This action kills bacteria, but since human cells do not have walls, they are unharmed.

The trouble with treating cancer is that a tumor is composed of the same types of cells as the rest of the body.  Your immune system has trouble telling a cancerous cell from a normal one.  Moreover, there are very few chemical distinctions between cancerous cells and normal cells that allow for a drug to act on one but not the other.  One famous scientist likens searching for chemotherapy agents to finding a drug that can kill your left ear while leaving your right ear unhurt.

Let's say you had a forest full of maple and oak trees.  The maples want more sunlight, but the oaks are too tall.  So to alleviate the problem, you go in and chop down every tree over 100 ft high. In general, this accomplishes your task - you remove most of the oaks, and the maples can bask in the sun.  But you also probably chopped down a fair number of the tall maples, and you also missed all the short oaks.  By targeting a trait of the trees which is shared by other species, your "therapy" had unintended consequences.

One of the defining traits of cancer cells is that they divide very rapidly.  So, the first chemo drugs worked by killing cells that undergo cellular division at a high rate.  However, this has the side effect of harming the other cells which are undergoing normal cell division!  Things like hair, bone marrow, or the intestinal lining will suffer damage from this type of drug, and this is the reason why many types chemotherapy are so toxic to the body.  By targeting traits of cancer, the drug also harms normal cells which exhibit these traits.

More modern chemotherapy drugs target traits that are specific to cancer cell genes.  For instance, a lung tumor may be growing quickly because it overexpresses a gene for something called Endothelial Growth Factor Receptor.  This is a receptor that receives signals to grow and divide, and by making thousands of copies, a tumor cell is hyper-sensitized to growth signals (leading to excess growth).  But this is also a weakness - drugs like erlotnib and gefitnib can bind to these receptors and kill the cell.

Radiation Therapy


Radiation therapy is the red-headed stepchild of cancer treatment.  Many people have never heard of it (which is part of the reason why most people scratch their heads when I say I am a "Medical Physicist").  Yet radiation is perhaps the first treatment to definitively cure a sub-type of cancer (Hodgkin's Lymphoma), and remains an integral part of modern cancer therapy.

When ionizing radiation interacts with cells in the body, it knocks millions of electrons out of their atoms.  Chemically, this leaves these ions in a very reactive state (free-radicals), and they cause lots of errant damage to nearby molecules.  If one of these free radicals is near the DNA of a cell, it can break it.

Cells react to DNA damage in several ways.  First off, the cell can simply repair the damage, and go on as normal.  If the damage is not repaired, the cell may die (since DNA encodes for the enzymes and proteins that a cell needs to live).  Or, the cell may detect that its DNA is damaged, and undergo a process called "apoptosis" (cell suicide).  The cell may also enter a state where it is able to live, but is unable to divide (mitotic death).  Any of these things would amount to success, if the goal is to keep a cancer cell from living and dividing.

In order for a cell to repair DNA damage, the repair enzymes must be able to find the damage.  Here's the kicker - if a cell is in the process of dividing, its DNA is bound up tightly into chromosomes.  If the DNA is damaged during division, then it is much harder to repair that damage.  And since cancer cells are undergoing division much more frequently than normal cells, they are very sensitive to radiation (compared to normal tissue).  This is why we use radiation to treat cancer - tumor cells are inherently more sensitive to radiation damage.

Another advantage of radiation therapy is that it is non-invasive.  Using a medical linear accelerator, we can produce a small, focused beam of x-rays.  The patient lays on a movable tabletop, and the accelerator rotates around, delivering radiation from several different angles.  These beams enter the body at different places, and all converge on the tumor.  In this way, the tumor is given as much radiation as possible, and the normal tissue receives a lower dose.

Radiation is very useful for hitting microscopic pieces of the tumor that the surgeons may have missed.  Or, if the surgeons feel that the tumor is inoperable, radiation can be used to treat the bulk disease.  If there are multiple lesions in a nearby place (such as many small lesions in the brain or liver), radiation can be used to treat all of them simultaneously.

Combination Therapy


The reason we use surgery, chemotherapy, and radiotherapy is that they are so effective when used in conjunction with each other.  Surgery removes the original tumor.  Radiation treats the tumor bed, and kills any microscopic spread of the cancerous cells.  Chemotherapy is a systemic treatment that kills any cancer cells that may be working their way around the body, trying to set up new colonies.  Together,  these three treatments will hopefully kill every single tumor cell in the body.  Without radiation, there might be a recurrence in the original tumor site.  Without chemotherapy, there may be metastases.  And without surgery, it may be hard to control the original, bulk tumor.


Each of these therapies also causes harmful side effects.  So when deciding on the best course of treatment, doctors only use as much therapy as is needed.  For instance, early-stage prostate cancer is very unlikely to systematically spread, and is usually confined to the prostate.  So this type of cancer can be treated with only surgery, or local radiation.  In leukemia, the cancer is spread throughout the bloodstream.  So surgery/radiation has little effect, and chemotherapy alone is often the best course of treatment.

Like I said before, this isn't an end-all, be-all guide to cancer therapy.  There are hundreds of different types of cancer, and each one calls for its own specialized course of treatment.  But almost all treatments are going to involve some combination of surgery, radiation, and chemotherapy.

Thursday, February 28, 2013

What ACTUALLY Causes Cancer?

Cell phones.  Microwaves.  Diet soda.  Sugar.  Power lines.  TV screens.

Every day, we are exposed to a laundry list of modern devices and substances.  And I would bet that most of us have wondered what the effects of all those substances are.  The list above is are things that are usually found in news headlines, right before the part that screams "CAUSES CANCER!!"

When you stub your toe, there is no question what the cause was.  But cancer takes years, even decades, to develop.  We carry our cell phones every day, use microwaves to heat our food, and drink our diet sodas at work.  And as humans, we like to attribute things to a cause.  So when someone hears about a diagnosis of brain cancer, it is natural to wonder what really happened over all those years of holding a cell phone to your head.

So, what causes cancer?  There are two ways to answer that question - one way which lends itself to fear mongering, and one way which lends itself to rational public health decisions.  I'll let you guess which one I prefer.

Read more after the break.


Friday, December 14, 2012

Mammograms, PSA Tests, and PAP Smears: The difficulty in screening for cancer

Within a few years, cancer is on track to overtake heart disease as the #1 cause of death among Americans, and one out of every two of us is expected to be diagnosed with cancer at some point in our lives.  Cancer is extremely prevalent, and a big question is how best to fight it.  History has shown us that the survival rates are much higher when treating cancer in its earliest stages, and so one main focus of our healthcare system is to diagnose cancer as soon as possible.

I think almost everyone has had at least some experience with cancer screening.  We are always told to check ourselves for suspicious lumps or weird pains - things like breast or testicular self-exams.  We also undergo screening during our annual checkups.  Mammograms (breast cancer), prostate-specific antigen tests (PSA, prostate cancer), colonoscopy (colon cancer) and PAP smears (cervical cancer) are the most common.  Other tests that can be used are chest x-rays (lung cancer) and MRI or CT scans (for anything else).

Yet if you read the news, there seems to be a lot of controversy over what kind of tests are necessary.  Recently, the US Preventative Services Task Force advised that healthy men should not receive PSA testing.    The same task force has also advised against mammography for women under the age of 50.  At first glance, this may seem odd - if there is a test that can diagnose cancer, why not perform it all the time?  

A good test must be able to accurately detect when cancer is present.  But what many people don't consider is this: what happens when the test is wrong?  In this post, I'll go over some of the science of screening for cancer, and hopefully explain why the guidelines are set the way they are.

Read more after the break.


Wednesday, November 28, 2012

Is there more cancer today?


Roughly 1 in 2 Americans will be diagnosed with cancer at some point in their lives.  Some of us are screened for cancer with what seems like an ever-increasing frequency.  Cancer is one of the most researched and most publicized illnesses.  Some would say that awareness of cancer is at an all time high, and this often raises many questions.  Have humans always gotten cancer?  Is cancer more prevalent now than it was before?  Why do our lives seem so full of cancer now?


A brief history of cancer



Cancer arises when cells in the body lose their ability to regulate cellular division.  When this happens, a cell begins to divide out of control - dividing more and more until there are so many cancer cells that it impedes the normal function of the body.  Cellular division is part of life, and some people argue that cancer is as old as life itself.  In fact, recent evidence suggests that dinosaurs got cancer over 65 million years ago.

We know that cancer in humans has been around for some time as well.  The ancient Egyptians and Greeks both described cancer in their medical writings, but didn't have much in the way of treatment besides amputation.  Yet until the 20th century, cancer was just a blip on the healthcare radar.

In 1971, Richard Nixon and Congress began the effort which is now known as the "War on Cancer."    This was a response to the massive increase in the rate of cancer deaths since the turn of the 20th century.  Money has poured into cancer research and treatment since then, yet despite our best efforts, cancer is still predicted to overtake heart disease as the #1 cause of death among Americans within the next few years.

Why is cancer so prevalent?  If we analyze the rise of cancer in the 20th century, we learn a lot about the American medical system, as well as how cancer works.

Read more after the break.


Sunday, November 18, 2012

Which College Teams are Over-Ranked in Pre-Season Polls?

As we near Thanksgiving, I like to look back on the college football pre-season rankings.  It always makes for good comedy.  One thing (maybe the only thing?) I admire about the BCS is that they wait until the teams have actually played some games to attempt to rank them.  Pre-season rankings tend to be based on a mix of historical success, recruiting strength, and public perception.  Here is where we stand as of week 13:

              2012 AP Poll
  PreSeason                 Week 13

1 USC 1 Notre Dame
2  Alabama   2 Alabama
3  LSU   3  Georgia
4  Oklahoma   4  Ohio State
5  Oregon   5  Oregon
6  Georgia   6  Florida
7  Florida State  7  Kansas State
8  Michigan   8  LSU
9  South Carolina  9  Texas A&M
10 Arkansas  10 Florida State
11  West Virginia  11  Stanford
12  Wisconsin  12  Clemson
13  Michigan State  13  South Carolina
14  Clemson   14  Oklahoma
15  Texas   15  UCLA
16  Virginia Tech  16  Oregon State
17  Nebraska  17  Nebraska
18  Ohio State  18  Texas
19  Oklahoma State  19  Louisville
20  TCU   20  Michigan
21  Stanford  21  Rutgers
22  Kansas State  22  Oklahoma State
23  Florida   23  Kent State
24  Boise State  24  Northern Illinois
25  Louisville  25  Mississippi State

Friday, November 16, 2012

Is "Gerrymandering" Responsible for the House Majority?

The 2012 election was, by all accounts, a victory for the Democrats.  President Obama was re-elected in spite of the economic downturn that took place during his first term, and the Democrats picked up seats in both the House and Senate.  However, the GOP maintained its majority in the House of Representatives, 234-201 (assuming the current leaders in the 4 un-called races go on to win).

It was predicted for some time that the House wouldn't switch hands, so many people didn't pay much attention to the races.  But there are some excellent election datasets out there - for instance, the Google Elections data browser (edit: it seems as though the google elections data browser has been taken offline).  And if you browse through the results of the Congressional elections, you might see some surprising things.

Case in point: Florida's 5th District.
Fig. 1: Gerrymandering in Florida?  It seems like Democrats are packed into the 5th District, allowing nearby districts to be won more easily by Republicans.