Friday, October 21, 2011
Wednesday, October 19, 2011
The Senate acted to save potatoes from school nutrition rules
Random and fun helath care news from the US (Ezra Klein):
The Senate acted to save potatoes from school nutrition rules, reports Robert Pear: "The Senate stood up Tuesday for the humble white potato and rebuffed an effort by President Obama to limit its consumption by millions of schoolchildren around the country. The administration has proposed limiting the amount of potatoes and other starchy vegetables that can be served in school lunches to one cup per student per week, and banning them from school breakfasts. The Senate on Tuesday moved to block the proposal by adopting an amendment to the 2012 spending bill for the Agriculture Department. The amendment, approved by unanimous consent, prohibits the department from setting 'any maximum limits on the serving of vegetables in school meal programs.'"
Tuesday, October 18, 2011
Health (film)
Interesting film about health politics by Robert Altman, the director behind several other well known movies.
'via Blog this'
Monday, October 17, 2011
Update on topics and exam
Anki - The flashcards (http://ankisrs.net/)
Go to the document in the link below and write your name next to the document you have signed up for. If you do not do so withing a week, somebody else will be allowed to take "your" chapter:
https://docs.google.com/document/d/19GwhIAghWFEhGcp6glq11_WsaM4LVHO8d5rG2OwkwhQ/edit?hl=en_US
About the exam
Some of you have asked about how much calculation you have to do, how much you neet to know about the things we do in class in addition to the topics in the book and so on. The short answer is: The exam will consists of several small questions asking you to define concepts and give examples. It will also consists of some questions involving calculations like we did in volumen-profit analysis (calculate break-even volumen and so on). Finally, the main part will be from the Drury book, but there may be one or two small questions about concepts we have covered in class. A list of the topics I expect you to know something about (with links) is listed below.
List of topics
Some of you have asked for a list of topics that are not in the Drury textbook. I have listed the topics below with some links and to more information. For the exam, you will be expected to know something about some of these concepts. It will not be a major part of the exam - concepts from the Drury book will cover that - but you may get some questions on the following: the concept of expected value, some of the mechanisms that create economies of scale and diseconomies of scale, and the problem of regression to the mean. I will update this list so you will always know the concepts that you are supposed to know.
Decision theory
(Define, Difference between expected value and expected utility, St. Petersburg paradox, Allais paradox, Net Present Value, Overconfidence, Bayes' Rule and screening)
System of Health Accounts
(Importance ans use of health accounts, Boundary problems, Conversion problems, Quantification of problems)
The document itself is here: http://www.who.int/nha/sha_revision/sha_2011_final1.pdf
Economies and diseconomies of scale
(Average cost curve, mechanisms that create economies of scale, learning by doing, distribution of fixed costs, mechanisms that create diseconomies of scale, coordination costs, information costs, principal agent problems in hierarchies, chains of principal agent relationships)
Cost containment
Lorenz curve, distribution of health cost among different groups, Atul Gawande, regression to the mean
Why projects often go over budget
1. Political reasons
2. Technical reasons (Ths sum of most likely events is not always the most likely outcome)
Health care fraud
Examples of different kinds of fraud, estimating the size of fraud, fee-for-service vs. per capipta may lead to different frauds
Less relevant, but since I mentioned it in class:
Can you buy love?
Here is a blog with lots of statistics about this and other things based on data from a net dating site (warning, not for the faint hearted): http://blog.okcupid.com/
Go to the document in the link below and write your name next to the document you have signed up for. If you do not do so withing a week, somebody else will be allowed to take "your" chapter:
https://docs.google.com/document/d/19GwhIAghWFEhGcp6glq11_WsaM4LVHO8d5rG2OwkwhQ/edit?hl=en_US
About the exam
Some of you have asked about how much calculation you have to do, how much you neet to know about the things we do in class in addition to the topics in the book and so on. The short answer is: The exam will consists of several small questions asking you to define concepts and give examples. It will also consists of some questions involving calculations like we did in volumen-profit analysis (calculate break-even volumen and so on). Finally, the main part will be from the Drury book, but there may be one or two small questions about concepts we have covered in class. A list of the topics I expect you to know something about (with links) is listed below.
List of topics
Some of you have asked for a list of topics that are not in the Drury textbook. I have listed the topics below with some links and to more information. For the exam, you will be expected to know something about some of these concepts. It will not be a major part of the exam - concepts from the Drury book will cover that - but you may get some questions on the following: the concept of expected value, some of the mechanisms that create economies of scale and diseconomies of scale, and the problem of regression to the mean. I will update this list so you will always know the concepts that you are supposed to know.
Decision theory
(Define, Difference between expected value and expected utility, St. Petersburg paradox, Allais paradox, Net Present Value, Overconfidence, Bayes' Rule and screening)
System of Health Accounts
(Importance ans use of health accounts, Boundary problems, Conversion problems, Quantification of problems)
The document itself is here: http://www.who.int/nha/sha_revision/sha_2011_final1.pdf
Economies and diseconomies of scale
(Average cost curve, mechanisms that create economies of scale, learning by doing, distribution of fixed costs, mechanisms that create diseconomies of scale, coordination costs, information costs, principal agent problems in hierarchies, chains of principal agent relationships)
Cost containment
Lorenz curve, distribution of health cost among different groups, Atul Gawande, regression to the mean
Why projects often go over budget
1. Political reasons
2. Technical reasons (Ths sum of most likely events is not always the most likely outcome)
Health care fraud
Examples of different kinds of fraud, estimating the size of fraud, fee-for-service vs. per capipta may lead to different frauds
Less relevant, but since I mentioned it in class:
Can you buy love?
Here is a blog with lots of statistics about this and other things based on data from a net dating site (warning, not for the faint hearted): http://blog.okcupid.com/
Wednesday, October 5, 2011
Management and decision making 102: Bayes' theorem
Imagine yourself as the leader of a health agency and that you have to decide whether to go ahead with a large universal screening program e.g. screening for cancer. You have been told that the test used in the screening is 99% correct and that about 0.5% of the population has the disease.
Many people at this point simply conclude that the screening is a good thing: We will pick up a lot of cases at an early stage, they will get treatment and may even survive because the cancer was discovered early. You, however, are not most people. You try to think about this carefully.
First of all you might wonder about the cost of the screening and how many cases it discovers compared to the no universal screening case. Those with high risk migh go to the doctor anyway and so on, so the question is how many extra cases you will find and be able to cure. This is all true, but you also start to wonder about potential harmful effects.What about those who will get the message "you have cancer" because of mistakes in the test. Well, the test seems good, 99% certain, som maybe this is nothing to worry about?
Unfortunately, this is wrong. We can show this using an example as well as more formally using Bayes' Rule.
To illustrate the problem, imagine 1 000 000 people doing the test. Out of these, 5 000 have the disease and 995 000 do not have the disease. Given an accuracy of 99%, this implies that:
- Among the 5000 with the disease, 4950 will get the message "you have the disease" and 50 will get "you do not have the disease"
- Among the 995 000 who do not have the disease, 985 050 will be told "you do not have the disease" and 9950 will be told "you have the disease"
Altogether this means that 14 900 have been told that the have the disease (9950 + 4950). Out of these only 4950 really have the disease ie. 33.2% In other words, given the information in this example, when a person in the screening program is told "you have the disease" the probability of actually having the disease is only 33.2%
Why? The key problem is the fact that although the test itself seems accurate, the probability of not having the disease is very high. For every case the probability of making a mistake is small, but since there are so many cases, and since most of them are people who do not have the disease, even a small probability of making a mistake will result in many false alarms.
Formally we can use Bayes rule to calculate the probability of actually having a disease given a positive test. We want to know the probability of having the disease (A) given a positive test result (B): P(A|B). From basic probability theory we know:
P(AB) = P(A) P(B|A)
That is, the probability that both A and B will happen can be found by multiplying the probability that A will happen and the probability that B will happen given that A has happened.
Similarly we know
P(BA) = P(B) P(A|B)
Since P(BA) = P(AB), we also have
P(B) P(A|B)= P(A) P(B|A)
Rearranged:
P(A|B)= P(A) P(B|A) / P(B)
This is called Bayes rule and it can be used to calculate the correct probability. Recall
P(A) : Probability that a person the disease = 0.005
P(-A) : Probability that a person does not have the disease = 0.995
P(B): Probability that a person tests positive
P(B|A): Probability that a person tests positive given that she has the disease = 0.99
P(B|-A): Probability that a person tests positive given that she does not have the disease = 0.01
To work out the probability that a random person tests positive, remember that there are two ways of testing positive: Either you have the disease and test positive, or you do not have the disease and test positive.
Probabability of having the disease and testing positive: P(A) P(B|A) = 0.005 * 0.99
Probabability of not having the disease and testing positive: P(-A) P(B|-A) = 0.995 * 0.01
We then find
P(B) = P(A) P(B|A) + P(-A) P(B|-A)
P(B) = 0.005 * 0.99 + 0.995 * 0.01 = 0.0149
We then have all the information neede to use Bayes rule to calculate the probability of having the disease given a positive test:
P(A|B)= P(A) P(B|A) / P(B)
P(A|B) = 0.005 * 0.99 / 0.149 = 0.32
In short, knowing a three hundred year old mathematical rule, will enable you to make a better decision. You need not even know its precise formulation - all you have to remember is that the importance of considering not only the accuracy of the test (high), but also the base rate prevalence of the disease (low) and that the end result will be in between.
Many people at this point simply conclude that the screening is a good thing: We will pick up a lot of cases at an early stage, they will get treatment and may even survive because the cancer was discovered early. You, however, are not most people. You try to think about this carefully.
First of all you might wonder about the cost of the screening and how many cases it discovers compared to the no universal screening case. Those with high risk migh go to the doctor anyway and so on, so the question is how many extra cases you will find and be able to cure. This is all true, but you also start to wonder about potential harmful effects.What about those who will get the message "you have cancer" because of mistakes in the test. Well, the test seems good, 99% certain, som maybe this is nothing to worry about?
Unfortunately, this is wrong. We can show this using an example as well as more formally using Bayes' Rule.
To illustrate the problem, imagine 1 000 000 people doing the test. Out of these, 5 000 have the disease and 995 000 do not have the disease. Given an accuracy of 99%, this implies that:
- Among the 5000 with the disease, 4950 will get the message "you have the disease" and 50 will get "you do not have the disease"
- Among the 995 000 who do not have the disease, 985 050 will be told "you do not have the disease" and 9950 will be told "you have the disease"
Altogether this means that 14 900 have been told that the have the disease (9950 + 4950). Out of these only 4950 really have the disease ie. 33.2% In other words, given the information in this example, when a person in the screening program is told "you have the disease" the probability of actually having the disease is only 33.2%
Why? The key problem is the fact that although the test itself seems accurate, the probability of not having the disease is very high. For every case the probability of making a mistake is small, but since there are so many cases, and since most of them are people who do not have the disease, even a small probability of making a mistake will result in many false alarms.
Formally we can use Bayes rule to calculate the probability of actually having a disease given a positive test. We want to know the probability of having the disease (A) given a positive test result (B): P(A|B). From basic probability theory we know:
P(AB) = P(A) P(B|A)
That is, the probability that both A and B will happen can be found by multiplying the probability that A will happen and the probability that B will happen given that A has happened.
Similarly we know
P(BA) = P(B) P(A|B)
Since P(BA) = P(AB), we also have
P(B) P(A|B)= P(A) P(B|A)
Rearranged:
P(A|B)= P(A) P(B|A) / P(B)
This is called Bayes rule and it can be used to calculate the correct probability. Recall
P(A) : Probability that a person the disease = 0.005
P(-A) : Probability that a person does not have the disease = 0.995
P(B): Probability that a person tests positive
P(B|A): Probability that a person tests positive given that she has the disease = 0.99
P(B|-A): Probability that a person tests positive given that she does not have the disease = 0.01
To work out the probability that a random person tests positive, remember that there are two ways of testing positive: Either you have the disease and test positive, or you do not have the disease and test positive.
Probabability of having the disease and testing positive: P(A) P(B|A) = 0.005 * 0.99
Probabability of not having the disease and testing positive: P(-A) P(B|-A) = 0.995 * 0.01
We then find
P(B) = P(A) P(B|A) + P(-A) P(B|-A)
P(B) = 0.005 * 0.99 + 0.995 * 0.01 = 0.0149
We then have all the information neede to use Bayes rule to calculate the probability of having the disease given a positive test:
P(A|B)= P(A) P(B|A) / P(B)
P(A|B) = 0.005 * 0.99 / 0.149 = 0.32
In short, knowing a three hundred year old mathematical rule, will enable you to make a better decision. You need not even know its precise formulation - all you have to remember is that the importance of considering not only the accuracy of the test (high), but also the base rate prevalence of the disease (low) and that the end result will be in between.
Tuesday, October 4, 2011
Relevant articles
The reading list mentions some articles. You have online access to some of these from the University of Oslo. Here are the full references:
Alanen J,
Keski-Nisula L, Laurila J, Suramo I, Standertskjöld-Nordenstam CG, Brommels M
(1998) Costs of plain-film radiography in an partially digitized radiology
department: an activity based analysis. Acta Radiol 39: 200–207
Laurila J,
Suramo I, Brommels M, Tolppanen EM, Koivukangas P, Lanning P,
Standertskjöld-Nordenstam CG (2000) Activity-based costing in radiology:
application in a pediatric radiological unit. Acta
Radiol 41:189–195
Jonas Schreyögg & Oliver Tiemann & Reinhard Busse,
2006. "Cost accounting to
determine prices: How well do prices reflect costs in the German
DRG-system?," Health Care Management Science, Springer, vol. 9(3), pages
269-279.
J.A.
Brickley and R.L. Van Horn (2002), Managerial incentives in nonprofit
organizations. Journal of Law and Economics,
XLV (2002), pp. 225–249.
Kuntz, C.,
and Antonio Vera. 2005. Transfer Pricing in Hospitals and Efficiency of Physicians:
The Case of Anesthesia Services. Health Care Management Review 30(3): 262-269.
Management and decision theory 101: The basics and St Petersburg paradox
The theory
Should you invest in umbrellas or ice-cream? How should you choose between the two?
Some simply to go with their gut feeling. That may work sometimes, but it turns out that gut feeling is often wrong. Being led by your stomack or other bodily parts often lead to systematic mistakes and bad outcomes. To improve the way we make decisions, in life and in business, it is useful to explore both when gut feelings tend to lead us astray as well as what we should do to make better descisions.
How should one make the best possible decisions? Intuitively one should weight the costs and benefits of the two actions. The question is how one can do this in an uncertain world. Should you bring an umbrella or not when going out of the house? The decision depends on your beliefs about the weather, the hassle of carrying an umbrella and how bad you believe it is to be outside in the rain without an umbrella. All of this has to be estimated and somehow integrated into a single value in order to determine the best action.
Continue with the example and imagine that your subjective probability for rainy weather is p. To calculate the expected consequences of bringing an umbrella, you consider the two possible outcomes. If it rains you will avoid getting wet, if it does not rain you will look like a fool with an umbrelly on a sunny day. The higher the probability of rain, the more likely it is that you will experience the first outcome. In this way the probability of the outcome can serve as a weight. The more probable an outcome is, the more weight we should attach to it when calculating the expected consequence. So to make a rational decision we list all the possible outcomes from an action and weight the outcomes according to how probable they are. In short:
Expected consequence of an action = Sum of (probability * Value of outcome) for all outcomes of that action
St. Petersburg Paradox
This may sound obvious, but there are always surprises hidden in the details. To illustrate a potential problem, suppose you are offered a chance to play a game in which a coin is thrown until it lands heads up. If it lands heads up after the first throw, you get two dollars. If it takes two throws to get heads, you get four dollars. Three throws to gives you eight dollars and so on. In short, the money doubles for every time tails comes up and as soon as the coin comes heads up, you get that sum of money. Now, the question is how much you are willing to pay in order to be allowed to play this game.
Should you invest in umbrellas or ice-cream? How should you choose between the two?
Some simply to go with their gut feeling. That may work sometimes, but it turns out that gut feeling is often wrong. Being led by your stomack or other bodily parts often lead to systematic mistakes and bad outcomes. To improve the way we make decisions, in life and in business, it is useful to explore both when gut feelings tend to lead us astray as well as what we should do to make better descisions.
How should one make the best possible decisions? Intuitively one should weight the costs and benefits of the two actions. The question is how one can do this in an uncertain world. Should you bring an umbrella or not when going out of the house? The decision depends on your beliefs about the weather, the hassle of carrying an umbrella and how bad you believe it is to be outside in the rain without an umbrella. All of this has to be estimated and somehow integrated into a single value in order to determine the best action.
Continue with the example and imagine that your subjective probability for rainy weather is p. To calculate the expected consequences of bringing an umbrella, you consider the two possible outcomes. If it rains you will avoid getting wet, if it does not rain you will look like a fool with an umbrelly on a sunny day. The higher the probability of rain, the more likely it is that you will experience the first outcome. In this way the probability of the outcome can serve as a weight. The more probable an outcome is, the more weight we should attach to it when calculating the expected consequence. So to make a rational decision we list all the possible outcomes from an action and weight the outcomes according to how probable they are. In short:
Expected consequence of an action = Sum of (probability * Value of outcome) for all outcomes of that action
St. Petersburg Paradox
This may sound obvious, but there are always surprises hidden in the details. To illustrate a potential problem, suppose you are offered a chance to play a game in which a coin is thrown until it lands heads up. If it lands heads up after the first throw, you get two dollars. If it takes two throws to get heads, you get four dollars. Three throws to gives you eight dollars and so on. In short, the money doubles for every time tails comes up and as soon as the coin comes heads up, you get that sum of money. Now, the question is how much you are willing to pay in order to be allowed to play this game.
Being rational, you start to calculate the expected value of playing the game. The outcomes are easy, you can end up winning 2, 4, 8, 16 dollars and so on. The probabilities are also quite easy. The probability of getting heads on the first throw is 1/2. To win four dollars, the coin has to land with tails up on the first throw (p=1/2) and heads on the second throw (p=1/2). Each event has probability a half, so the probability for both to happen is 1/2*1/2 = 1/4. next, the third outcome - winning eight dollars - implies tails, tails, head or a probability of 1/2 * 1/2 * 1/2 = 1/8. If we go on we have:
Outcomes (2 , 4 , 8 , 16 , 32 , ...)
Probabilities (1/2, 1/4, 1/8, 1/16, 1/32, ...)
Multiplying each outcome with the probability that it will happen, we then have (2 * 1/2) + (4*1/4) + 8 * 1/8 and so on:
Expected value of the gamble = 1 + 1 + 1 + 1 ...
Retunr to the question of how much you would be willing to pay to play the game. Since the expected value is infinite (1 + 1 + 1 forever), one might think that we should be willing to pay whatever we have available to play the game. In reality this is not what happens. Most people are only wiling to pay a dollar or two in order to play the game. Either the theory about how to make a good decision is wrong, or there is something wrong with the example!
As promised the interesting and surprising devil is in the details. The relevant outcome is not that you get a certain amount of money, but how much utility you get from that money. You do not care about the money in itself, only the utility it gives you. This small distinction is vitally important and it was first pointed out by the brilliant Bernoulli several hundred years ago: What we want to maximize when making a decision is not expected value, but expected utility. Each outcome should be transformed into the utility we get from that outcome before we multiply it with its probability:
Expected value = Sum of (probability * outcome) for all outcomes of that action
Expected value = Sum of (probability * utility of outcome) for all outcomes of that action
In the case of the coin game, we then have
Expected utility of coin game = 1/2 * utility of (2 dollars) + 1/4 * utility (4 dollars) + 1/8 * utility (8 dollars)
How does this solve the problem? The basic problem when using the expected value, is that the sum became infinite because the growth of the money balanced the decrease in probability so we got an infinite sum of 1 + 1 + 1 + ... When using utilities, this is no longer the case. 4 dollars is twice as much money as 2, but the utility we get from four dollars is probably not twice as high as the utility we get from two. A billionaire is not a thousand times happier than a millionaire. This means thet the value of the outcome will not increase as much when we use utilities as outcome: the probabilities will decrease faster than the increase in the value of the outcomes and the sum no longer becomes infinite.
A rational decision
The lesson? Being rational implies, first of all, to consider all the possible actions, outcomes and their respective probabilities. The best decision is then the one that maximizes expected utility, defined as the sum of the utility of the outcomes associated with the action weighted by the probabilities of these outcomes.
This is, at least, the starting point!
Subscribe to:
Posts (Atom)