Download Controlled Study

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
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 2
Survey
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 3
Cause and Effect
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?
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 4
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 5
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 6
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 7
CASE STUDY 5 THE ALAR SCARE
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 cancercausing 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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 8
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 9
CASE STUDY 5 THE ALAR SCARE
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 10
CASE STUDY 5 THE ALAR SCARE
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 11
CASE STUDY 5 THE ALAR SCARE
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 12
Clinical Study
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 selfevident: Every new vaccine, drug, or
treatment must prove itself by means of a
clinical study before it is officially approved
for public use.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 13
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 14
Isolate the Cause
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 15
Controlled Study
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).
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 16
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 welldesigned 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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 17
Randomized 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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 18
Placebo Effect
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 19
Placebo
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 20
Controlled Placebo Study
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 21
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 22
Blind 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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 23
Double-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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 24
CASE STUDY 6
THE 1954 SALK POLIO
VACCINE FIELD TRIALS
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 25
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 livevirus vaccine, the latter as a killed-virus
vaccine.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 26
CASE STUDY 6
THE 1954 SALK POLIO
VACCINE FIELD TRIALS
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 27
CASE STUDY 6
THE 1954 SALK POLIO
VACCINE FIELD TRIALS
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 28
CASE STUDY 6
THE 1954 SALK POLIO
VACCINE FIELD TRIALS
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 29
CASE STUDY 6
THE 1954 SALK POLIO
VACCINE FIELD TRIALS
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 30
CASE STUDY 6
THE 1954 SALK POLIO
VACCINE FIELD TRIALS
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 31
CASE STUDY 6
THE 1954 SALK POLIO
VACCINE FIELD TRIALS
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 32
CASE STUDY 6
THE 1954 SALK POLIO
VACCINE FIELD TRIALS
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 33
CASE STUDY 6
THE 1954 SALK POLIO
VACCINE FIELD TRIALS
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 34
CASE STUDY 6
THE 1954 SALK POLIO
VACCINE FIELD TRIALS
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 35
CASE STUDY 6
THE 1954 SALK POLIO
VACCINE FIELD TRIALS
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.
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 36
Copyright © 2010 Pearson Education, Inc.
Excursions in Modern Mathematics, 7e: 13.6 - 37