“There are three kinds of lies: lies, damned lies, and statistics.”
Benjamin Disraeli
You open a book on cancer and it would more likely than not start with numbers: So many thousand were diagnosed with the disease in such a period and so many died. They will also give a prognosis as to how these numbers would look like for a period in the future. In the case of prostate cancer in particular we are told that in the coming year so many thousand men will find out that they are afflicted with the disease and another number also in thousand, will succumb to it, some of them unnecessarily. These numbers are significant in as much as they indicate the extent and trend of the disease. But how meaningful are they to an individual? Can he benefit from this knowledge? We can put the answer to these questions also in terms of numbers - fifty for yes fifty for no. There are no known precautions that a man can take to ward off the disease. One can have regular tests and examinations to insure early detection that would help in deciding the course of treatment. But early detection by itself is no guarantee for cure. As long as a person is not a confirmed patient these numbers are impersonal like the statistics on the number of people dead or likely to die in traffic accidents in a given period.
However, the situation changes as soon as the person becomes a part of the statistic. Now he moves into the realm of other numbers. For each treatment option available to him he is confronted with numbers related to the success of these options. He is told of survival rates and now we are talking not just numbers but probabilities. Not that probability is new to us. We deal with them in every day life without even being conscious of it They are wrapped up in weather forecasts, sports, in economic events, and so on. In fact probability and statistics have become an integral part of our lives, even determine the quality of life through processes ranging from mundane ones like quality control of consumer goods to highly sophisticated like space communications.
But statistics by its very nature is impersonal, it deals with a population or sample. Means and averages are meaningless when applied to a particular member of the sample. We have all watched the Dow Jones average soar during the past couple of years. It is supposed to indicate the state of the economy. On the average we would think that everyone playing the stock market would have doubled or tripled his investment. I know several persons whose portfolios shrank during that period. It does not, of course, negate the fact that many stocks soared and people made money in the market. The point is, though, that the statistical results cannot be applied directly to an individual. It is all the more so when we are using statistics in the field of medicine where the unknowns and variables are far more than in other fields.
I have a friend who recently had cataract surgery. These days it is supposed to be a routine procedure with hardly any chance of serious complications. If one insisted on getting numbers, the doctor might put the probability of things going wrong at less than one percent. A month after surgery my friend did develop a problem - for no apparent reason the implanted lens had moved and he had only peripheral vision in that eye. The doctor could not explain it; in fifteen years of his experience with this procedure it had happened only twice. That was, of course, no consolation to my friend; for him the less-than-one percent probability had changed into certainty. He had to get the procedure done again and was terrified at the prospect of things going wrong again. When it comes to personal life there are things over which no one has any control. There is an element of luck in every sphere of activity in life; some may deny its existence but denial does not negate the fact.
There is another aspect of statistics that may present problems; it is the size of the sample or the database. The larger the database, the more reliable are the results. For statisticians, of course, there is never enough data; it may be adequate but it is not the same as enough. In the case of prostate cancer the data is not extensive, at least in some respects, and the statistical inferences may therefore be viewed with caution. For a patient confronted with a decision as to the course of treatment the database for most options is small.
For the options of definitive treatment ten-year survival numbers were available only for radical surgery; for brachytherapy the data did not go that far back for any meaningful analysis. The choice becomes more difficult when the patient has to choose a particular surgeon or oncologist. Then he has to know that particular doctor’s numbers and the size of the sample shrinks to an inadequate level. And then there is the question of luck also. A patient can have problems even with the most experienced and famous surgeon, while another may come out fine with another relatively unknown doctor. One can certainly attempt to obtain the best possible facility and care within his reach not worrying about things beyond his control. To that extent the numbers become less important, they should be used as general guidelines only.
How important is the statistics? If we had to base everything on experience and statistics, there would be no new approaches, no developments. For breaking new grounds it is necessary to venture into the unknown, it is true for any field of knowledge. This is not to belittle the role of accumulated knowledge and experience. To probe the unknown it is imperative to make full use of all that is known. In this process, though, it is sometimes necessary to ignore or go against the accumulated evidence or the statistics. This happens, and not infrequently, in the field of medicine where new data force a revision of opinions based on old. What is considered normal today may not remain so tomorrow.
This brings us to the all-important number for prostate cancer - the prostate specific antigen (PSA) level. This number by itself has nothing to do with statistics. It represents a test result, an observation. However, it provides the raw material for building statistics. After a series of revisions in the past the normal range of PSA is taken to be from zero to four. Without going into the mathematical definition of the word normal, this statement can be interpreted to mean the following: If the PSA is measured for a sufficiently large number of men having no prostate problem, a significant majority of them would have PSA lying between zero and four; the exact percentage will depend on the specific distribution.
Conversely if the measured PSA for a man is within this range, he most probably does not have any prostate problem. The remaining may have PSA beyond this range, i.e. greater than four, since negative values are not possible, and still be disease free. The farther the number from four, the smaller would be the percentage of men having that PSA level. Mathematically this percentage will never become zero, but for all practical purposes there must be a limit. A man having PSA higher than this limit would certainly have a prostate problem. What is this limit and where can one draw the line? I do not think anyone can answer these questions. So the mathematical aspects of the term ‘normal’ are ignored and a rule of thumb is applied: Any test result yielding PSA of greater than four is suspect and further tests are needed. If the additional tests do not show an obvious problem, the person is put in the wait and watch mode. He is not a patient yet but may soon be.
However, even with this ‘primary’ number we run into ambiguities. If the PSA level for a person is below four, it does not automatically mean that he is cancer free. About twenty percent of prostate cancer patients have PSA below four. As a corollary it may be expected that an equal number of men having PSA greater than four would not have the cancer. So PSA alone cannot unambiguously reveal the presence of the cancer.
Once the cancer has been detected there is another number that indicates the degree of activity of the tumor. It is called Gleason score and is determined from pathological analysis of the biopsy samples; it ranges from two to ten. The higher the number, the more active is the cancer. A score of seven and above usually means a highly active fast growing cancer, perhaps in an advanced stage. Gleason score plays an equally important role in the choice of a treatment but by its very nature it is no more reliable than the PSA level.
On the other hand if the tests confirm the presence of cancer, the person is faced with immediate decision. The first question that comes up - and this has to be answered by the doctor - is whether the cancer is contained within the gland or it has spread outside. Even the doctor cannot answer without recourse to surgery and with that too he can not say anything with certainty. The absence of malignant cells at the lymph node does not preclude the possibility of the cells having migrated into the areas just outside the prostate. Again a rule of thumb is applied: If the PSA is not too far out of the normal range, the cancer is assumed to be localized. Now we are stuck with the problem of defining the term ‘too far’. I do not think any urologist would be willing to draw the line or even set a reasonable range. Unfortunately the survivability numbers, thrown at the patient, are affected by this uncertainty.
Dharmbir Rai Sharma
Dharmbir Rai Sharma is a retired professor with electrical engineering and physics background. He obtained his M.S. degree in physics in India and Ph.D. in electrical engineering at Cornell University. He has taught in universities here and also in Brazil, where he spent sometime. He maintains a website http://www.cosmosebooks.com devoted mainly to philosophy and science.
Benjamin Disraeli
You open a book on cancer and it would more likely than not start with numbers: So many thousand were diagnosed with the disease in such a period and so many died. They will also give a prognosis as to how these numbers would look like for a period in the future. In the case of prostate cancer in particular we are told that in the coming year so many thousand men will find out that they are afflicted with the disease and another number also in thousand, will succumb to it, some of them unnecessarily. These numbers are significant in as much as they indicate the extent and trend of the disease. But how meaningful are they to an individual? Can he benefit from this knowledge? We can put the answer to these questions also in terms of numbers - fifty for yes fifty for no. There are no known precautions that a man can take to ward off the disease. One can have regular tests and examinations to insure early detection that would help in deciding the course of treatment. But early detection by itself is no guarantee for cure. As long as a person is not a confirmed patient these numbers are impersonal like the statistics on the number of people dead or likely to die in traffic accidents in a given period.
However, the situation changes as soon as the person becomes a part of the statistic. Now he moves into the realm of other numbers. For each treatment option available to him he is confronted with numbers related to the success of these options. He is told of survival rates and now we are talking not just numbers but probabilities. Not that probability is new to us. We deal with them in every day life without even being conscious of it They are wrapped up in weather forecasts, sports, in economic events, and so on. In fact probability and statistics have become an integral part of our lives, even determine the quality of life through processes ranging from mundane ones like quality control of consumer goods to highly sophisticated like space communications.
But statistics by its very nature is impersonal, it deals with a population or sample. Means and averages are meaningless when applied to a particular member of the sample. We have all watched the Dow Jones average soar during the past couple of years. It is supposed to indicate the state of the economy. On the average we would think that everyone playing the stock market would have doubled or tripled his investment. I know several persons whose portfolios shrank during that period. It does not, of course, negate the fact that many stocks soared and people made money in the market. The point is, though, that the statistical results cannot be applied directly to an individual. It is all the more so when we are using statistics in the field of medicine where the unknowns and variables are far more than in other fields.
I have a friend who recently had cataract surgery. These days it is supposed to be a routine procedure with hardly any chance of serious complications. If one insisted on getting numbers, the doctor might put the probability of things going wrong at less than one percent. A month after surgery my friend did develop a problem - for no apparent reason the implanted lens had moved and he had only peripheral vision in that eye. The doctor could not explain it; in fifteen years of his experience with this procedure it had happened only twice. That was, of course, no consolation to my friend; for him the less-than-one percent probability had changed into certainty. He had to get the procedure done again and was terrified at the prospect of things going wrong again. When it comes to personal life there are things over which no one has any control. There is an element of luck in every sphere of activity in life; some may deny its existence but denial does not negate the fact.
There is another aspect of statistics that may present problems; it is the size of the sample or the database. The larger the database, the more reliable are the results. For statisticians, of course, there is never enough data; it may be adequate but it is not the same as enough. In the case of prostate cancer the data is not extensive, at least in some respects, and the statistical inferences may therefore be viewed with caution. For a patient confronted with a decision as to the course of treatment the database for most options is small.
For the options of definitive treatment ten-year survival numbers were available only for radical surgery; for brachytherapy the data did not go that far back for any meaningful analysis. The choice becomes more difficult when the patient has to choose a particular surgeon or oncologist. Then he has to know that particular doctor’s numbers and the size of the sample shrinks to an inadequate level. And then there is the question of luck also. A patient can have problems even with the most experienced and famous surgeon, while another may come out fine with another relatively unknown doctor. One can certainly attempt to obtain the best possible facility and care within his reach not worrying about things beyond his control. To that extent the numbers become less important, they should be used as general guidelines only.
How important is the statistics? If we had to base everything on experience and statistics, there would be no new approaches, no developments. For breaking new grounds it is necessary to venture into the unknown, it is true for any field of knowledge. This is not to belittle the role of accumulated knowledge and experience. To probe the unknown it is imperative to make full use of all that is known. In this process, though, it is sometimes necessary to ignore or go against the accumulated evidence or the statistics. This happens, and not infrequently, in the field of medicine where new data force a revision of opinions based on old. What is considered normal today may not remain so tomorrow.
This brings us to the all-important number for prostate cancer - the prostate specific antigen (PSA) level. This number by itself has nothing to do with statistics. It represents a test result, an observation. However, it provides the raw material for building statistics. After a series of revisions in the past the normal range of PSA is taken to be from zero to four. Without going into the mathematical definition of the word normal, this statement can be interpreted to mean the following: If the PSA is measured for a sufficiently large number of men having no prostate problem, a significant majority of them would have PSA lying between zero and four; the exact percentage will depend on the specific distribution.
Conversely if the measured PSA for a man is within this range, he most probably does not have any prostate problem. The remaining may have PSA beyond this range, i.e. greater than four, since negative values are not possible, and still be disease free. The farther the number from four, the smaller would be the percentage of men having that PSA level. Mathematically this percentage will never become zero, but for all practical purposes there must be a limit. A man having PSA higher than this limit would certainly have a prostate problem. What is this limit and where can one draw the line? I do not think anyone can answer these questions. So the mathematical aspects of the term ‘normal’ are ignored and a rule of thumb is applied: Any test result yielding PSA of greater than four is suspect and further tests are needed. If the additional tests do not show an obvious problem, the person is put in the wait and watch mode. He is not a patient yet but may soon be.
However, even with this ‘primary’ number we run into ambiguities. If the PSA level for a person is below four, it does not automatically mean that he is cancer free. About twenty percent of prostate cancer patients have PSA below four. As a corollary it may be expected that an equal number of men having PSA greater than four would not have the cancer. So PSA alone cannot unambiguously reveal the presence of the cancer.
Once the cancer has been detected there is another number that indicates the degree of activity of the tumor. It is called Gleason score and is determined from pathological analysis of the biopsy samples; it ranges from two to ten. The higher the number, the more active is the cancer. A score of seven and above usually means a highly active fast growing cancer, perhaps in an advanced stage. Gleason score plays an equally important role in the choice of a treatment but by its very nature it is no more reliable than the PSA level.
On the other hand if the tests confirm the presence of cancer, the person is faced with immediate decision. The first question that comes up - and this has to be answered by the doctor - is whether the cancer is contained within the gland or it has spread outside. Even the doctor cannot answer without recourse to surgery and with that too he can not say anything with certainty. The absence of malignant cells at the lymph node does not preclude the possibility of the cells having migrated into the areas just outside the prostate. Again a rule of thumb is applied: If the PSA is not too far out of the normal range, the cancer is assumed to be localized. Now we are stuck with the problem of defining the term ‘too far’. I do not think any urologist would be willing to draw the line or even set a reasonable range. Unfortunately the survivability numbers, thrown at the patient, are affected by this uncertainty.
Dharmbir Rai Sharma
Dharmbir Rai Sharma is a retired professor with electrical engineering and physics background. He obtained his M.S. degree in physics in India and Ph.D. in electrical engineering at Cornell University. He has taught in universities here and also in Brazil, where he spent sometime. He maintains a website http://www.cosmosebooks.com devoted mainly to philosophy and science.
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