Excursions in Modern Mathematics, 7e: 13.6 - 2Copyright © 2010 Pearson Education, Inc. 13 Collecting Statistical Data 13.1The Population 13.2Sampling

Excursions in Modern Mathematics, 7e: 13.6 - 2Copyright © 2010 Pearson Education, Inc.

13 Collecting Statistical Data

13.1 The Population

13.2 Sampling

13.3 Random Sampling

13.4 Sampling: Terminology and Key Concepts

13.5 The Capture-Recapture Method

13.6 Clinical Studies


A survey typically deals with issues and questions that have direct and measurable answers. If the election were held today, would you vote for candidate X or candidate Y? How many people live in your household? How many catfish have tags? In these situations data collection involves some combination of observing, measuring, and recording but no active involvement or interference with the phenomenon being observed.

Survey


A different type of data collection process is needed when we are trying to establish connections between a cause and an effect. Does taking a math class increase your chances of getting a good paying job? Does repeated exposure to secondhand smoke significantly increase your risk for developing lung cancer? Does a daily dose of aspirin reduce your chances of a heart attack? Do the benefits of hormone replacement therapy for women over 50 outweigh the risks?

Cause and Effect


These kinds of cause-and-effect questions cannot be answered by means of an immediate measurement and require observation over an extended period of time. Moreover, in these situations the data collection process requires the active involvement of the experimenter–in addition to observation, measurement, and recording, there is also treatment.

Cause and Effect


When we want to know if a certain cause X produces a certain effect Y, we set up a study in which cause X is produced and its effects are observed. If the effect Y is observed, then it is possible that X was indeed the cause of Y. We have established an association between the cause X and the effect Y.The problem, however, is the nagging possibility that some other cause Z different from X produced the effect Y and that X had nothing to do with it.

Cause and Effect


Just because we established an association, we have not established a cause-and-effect relation between the variables. Statisticians like to explain this by a simple saying: Association is not causation.

Cause and Effect


Alar is a chemical used by apple growers to regulate the rate at which apples ripen. Until 1989, practically all apples sold in grocery stores were sprayed with Alar. But in 1989 Alar became bad news, denounced in newspapers and on TV as a potent cancer-causing agent and a primary cause of cancer in children. As a result of these reports, people stopped buying apples, schools all over the country removed apple juice from their lunch menus, and the Washington State apple industry lost an estimated $375 million.

CASE STUDY 5 THE ALAR SCARE


The case against Alar was based on a single 1973 study in which laboratory mice were exposed to the active chemicals in Alar. The dosage used in the study was eight times greater than the maximum tolerated dosage–a concentration at which even harmless substances can produce tissue damage. In fact, a child would have to eat about 200,000 apples a day to be exposed to an equivalent dosage of the chemical.



Subsequent studies conducted by the National Cancer Institute and the Environmental Protection Agency failed to show any cause-and-effect relationship between Alar and cancer in children. While it is generally accepted now that Alar does not cause cancer, because of potential legal liability, it is no longer used.



The Alar scare turned out to be a false alarm based on a poor understanding of the statistical evidence. Unfortunately, it left in its wake a long list of casualties, among them the apple industry, the product’s manufacturer, the media, and the public’s confidence in the system.For most cause-and-effect situations, especially those complicated by the involvement of human beings, a single effect can have many possible and actual causes.



What causes cancer? Unfortunately, there is no single cause–diet, lifestyle, the environment, stress, and heredity are all known to be contributory causes. The extent to which each of these causes contributes individually and the extent to which they interact with each other are extremely difficult questions that can be answered only by means of carefully designed statistical studies.



We will illustrate an important type of study called a clinical study or clinical trial. Generally, clinical studies are concerned with determining whether a single variable or treatment (usually a vaccine, a drug, therapy,etc.) can cause a certain effect (a disease, a symptom, a cure, etc.). The importance of such clinical studies is self-evident: Every new vaccine, drug, or treatment must prove itself by means of a clinical study before it is officially approved for public use.

Clinical Study


Likewise, almost everything that is bad for us (cigarettes, caffeine, trans fats, etc.) gets its official certification of badness by means of a clinical study.Properly designing a clinical study can be both difficult and controversial, and as a result we are often bombarded with conflicting information produced by different studies examining the same cause-and-effect question. The basic principles guiding a clinical study, however, are pretty much established by statistical practice.

Clinical Study


The first and most important issue in any clinical study is to isolate the cause (treatment, drug, vaccine, therapy, etc.) that is under investigation from all other possible contributing causes (called confounding variables) that could produce the same effect. Generally, this is best done by controlling the study.

Isolate the Cause


In a controlled study, the subjects are divided into two different groups: the treatment group and the control group.The treatment group consists of those subjects receiving the actual treatment; the control group consists of subjects that are not receiving any treatment–they are there for comparison purposes only (that’s why the control group is sometimes also called the comparison group).

Controlled Study


If a real cause-and-effect relationship exists between the treatment and the effect being studied, then the treatment group should show the effects of the treatment and the control group should not.To eliminate the many potential confounding variables that can bias its results, a well-designed controlled study should have control and treatment groups that are similar in every characteristic other than the fact that one group is being treated and the other one is not.

Controlled Study


The most reliable way to get equally representative treatment and control groups is to use a randomized controlled study. In a randomized controlled study, the subjects are assigned to the treatment group or the control group randomly.

When the randomization part of a randomized controlled study is properly done, treatment and control groups can be assumed to be statistically similar.

Randomized Controlled Study


But there is still one major difference between the two groups that can significantly affect the validity of the study–a critical confounding variable known as the placebo effect.The placebo effect follows from the generally accepted principle that just the idea that one is getting a treatment can produce positive results.

Placebo Effect


Thus, when subjects in a study are getting a pill or a vaccine or some other kind of treatment, how can the researchers separate positive results that are consequences of the treatment itself from those that might be caused by the placebo effect?

When possible, the standard way to handle this problem is to give the control group a placebo.

Placebo


A placebo is a make-believe form of treatment–a harmless pill, an injection of saline solution, or any other fake type of treatment intended to look like the real treatment. A controlled study in which the subjects in the control group are given a placebo is called a controlled placebo study.

Controlled Placebo Study


By giving all subjects a seemingly equal treatment (the treatment group gets the real treatment and the control group gets a placebo that looks like the real treatment), we do not eliminate the placebo effect but rather control it–whatever its effect might be, it affects all subjects equally. It goes without saying that the use of placebos is pointless if the subject knows he or she is getting a placebo.

Controlled Placebo Study


Thus, a second key element of a good controlled placebo study is that all subjects be kept in the dark as to whether they are being treated with a real treatment or a placebo. A study in which neither the members of the treatment group nor the members of the control group know to which of the two groups they belong is called a blind study.

Blind Study


To keep the interpretation of the results (which can often be ambiguous) totally objective, it is important that the scientists conducting the study and collecting the data also be in the dark when it comes to who got the treatment and who got the placebo. A controlled placebo study in which neither the subjects nor the scientists conducting the experiment know which subjects are in the treatment group and which are in the control group is called a double-blind study.

Double-Blind Study


Polio (infantile paralysis) has been practically eradicated in the Western world. In the first half of the twentieth century, however, it was a major public health problem. Over one-half million cases of polio were reported between 1930 and 1950, and the actual number may have been considerably higher. Because polio attacks mostly children and because its effects can be so serious (paralysis or death), eradication of the disease became a top public health priority in the United States.

CASE STUDY 6 THE 1954 SALK POLIO VACCINE FIELD TRIALS


By the late 1940s, it was known that polio is a virus and, as such, can best be treated by a vaccine that is itself made up of a virus. The vaccine virus can be a closely related virus that does not have the same harmful effects, or it can be the actual virus that produces the disease but that has been killed by a special treatment. The former is known as a live-virus vaccine, the latter as a killed-virus vaccine.



In response to either vaccine, the body is known to produce antibodies that remain in the system and give the individual immunity against an attack by the real virus. Both the live-virus and the killed-virus approaches have their advantages and disadvantages. The live-virus approach produces a stronger reaction and better immunity, but at the same time, it is also more likely to cause a harmful reaction and, in some cases, even produce the very disease it is supposed to prevent.



The killed-virus approach is safer in terms of the likelihood of producing a harmful reaction, but it is also less effective in providing the desired level of immunity.These facts are important because they help us understand the extraordinary amount of caution that went into the design of the study that tested the effectiveness of the polio vaccine.



By 1953, several potential vaccines had been developed, one of the more promising of which was a killed-virus vaccine developed by Jonas Salk at the University of Pittsburgh. The killed-virus approach was chosen because there was a great potential risk in testing a live-virus vaccine in a large-scale study.



The testing of any new vaccine or drug creates many ethical dilemmas that have to be taken into account in the design of the study. With a killed-virus vaccine the risk of harmful consequences produced by the vaccine it-self is small, so one possible approach would have been to distribute the vaccine widely among the population and then follow up on whether there was a decline in the national incidence of polio in subsequent years.



This approach, which was not possible at the time because supplies were limited, is called the vital statistics approach and is the simplest way to test a vaccine. This is essentially the way the smallpox vaccine was determined to be effective. The problem with such an approach for polio is that polio is an epidemic type of disease, which means that there is a great variation in the incidence of the disease from one year to the next.



In 1952, there were close to 60,000 reported cases of polio in the United States, but in 1953, the number of reported cases had dropped to almost half that (about 35,000). Since no vaccine or treatment was used, the cause of the drop was the natural variability typical of epidemic diseases.



But if an ineffective polio vaccine had been tested in 1952 without a control group, the observed effect of a large drop in the incidence of polio in 1953 could have been incorrectly interpreted as statistical evidence that the vaccine worked.The final decision on how best to test the effectiveness of the Salk vaccine was left to an advisory committee of doctors,public officials,and statisticians convened by the National Foundation for Infantile Paralysis and the Public Health Service.



Approximately 750,000 children were randomly selected to participate in the study. Of these, about 340,000 declined to participate, and another 8500 dropped out in the middle of the experiment. The remaining children were randomly divided into two groups–a treatment group and a control group–with approximately 200,000 children in each group.



Neither the families of the children nor the researchers collecting the data knew if a particular child was getting the actual vaccine or a shot of harmless solution. The latter was critical because polio is not an easy disease to diagnose–it comes in many different forms and degrees. Sometimes it can be a borderline call, and if the doctor collecting the data had prior knowledge of whether the subject had received the real vaccine or the placebo, the diagnosis could have been subjectively tipped one way or the other.



A summary of the results of the Salk vaccine field trials is shown on the next slide. These data were taken as conclusive evidence that the Salk vaccine was an effective treatment for polio, and on the basis of this study, a massive inoculation campaign was put into effect. Today, all children are routinely inoculated against polio, and the disease has essentially been eradicated in the United States. Statistics played a key role in this important public health breakthrough.



Documents

Excursions in Modern Mathematics, 7e: 13.6 - 2Copyright © 2010 Pearson Education, Inc. 13 Collecting Statistical Data 13.1The Population 13.2Sampling