Technological advances continually make new disease prevention and treatment possibilities available for health care.

**WHY STUDY STATISTICS?**

Technological advances continually make new disease
prevention and treatment possibilities available for health care. Consequently,
a substantial body of medical research explores alternative methods for
treating diseases or injuries. Because out-comes vary from one patient to
another, researchers use statistical methods to quan tify uncertainty in the
outcomes, summarize and make sense of data, and compare the effectiveness of
different treatments. Federal government agencies and private companies rely
heavily on statisticians’ input.

The U.S. Food and Drug Administration (FDA)
requires manufacturers of new drugs and medical devices to demonstrate the effectiveness
and safety of their products when compared to current alternative treatments
and devices. Because this process requires a great deal of statistical work,
these industries employ many statisticians to design studies and analyze the
results. Controlled clinical trials, described later in this chapter, provide a
commonly used method for assessing product efficacy and safety. These trials
are conducted to meet regulatory requirements for the market release of the
products. The FDA considers such trials to be the gold standard among the study
approaches that we will cover in this text.

Medical device and pharmaceutical company
employees—clinical investigators and managers, quality engineers, research and
development engineers, clinical research associates, database managers, as well
as professional statisticians—need to have basic statistical knowledge and an
understanding of statistical terms. When you consider the following situations
that actually occurred at a medical device company, you will understand why a
basic knowledge of statistical methods and terminology is important.

*Situation 1: *You are the clinical coordinator
for a clinical trial of an ablation* *catheter
(a catheter that is placed in the heart to burn tissue in order to eliminate an
electrical circuit that causes an arrhythmia). You are enrolling patients at
five sites and want to add a new site. In order to add a new site, a local
review board called an institution review board (IRB) must review and approve
your trial protocol.

A member of the board asks you what your stopping
rule is. You do not know what a stopping rule is and cannot answer the
question. Even worse, you do not even know who can help you. If you had taken a
statistics course, you might know that many trials are constructed using group
sequential statistical methods. These methods allow for the data to be compared
at various times during the trial. Thresholds that vary from stage to stage
determine whether the trial can be stopped early to declare the device safe
and/or effective. They also enable the company to recognize the futility of
continuing the trial (for example, because of safety concerns or because it is
clear that the device will not meet the requirements for efficacy). The
sequence of such thresholds is called the stopping rule.

The IRB has taken for granted that you know this
terminology. However, group sequential methods are more common in
pharmaceutical trials than in medical device trials. The correct answer to the
IRB is that you are running a fixed-sample-size trial and, therefore, no
stopping rule is in effect. After studying the material in this book, you will
be aware of what group sequential methods are and know what stopping rules are.

*Situation 2: *As a regulatory affairs associate
at a medical device company that* *has
completed a clinical trial of an ablation catheter, you have submitted a
regulatory report called a premarket approval application (PMA). In the PMA,
your statistician has provided statistical analyses for the study endpoints
(performance measures used to demonstrate safety or effectiveness).

The reviewers at the Food and Drug Administration
(FDA) send you a letter with questions and concerns about deficiencies that
must be addressed before they will approve the device for marketing. One of the
questions is: “Why did you use the Greenwood approximation instead of Peto’s
method?” The FDA prefers Peto’s method and would like you to compute the
results by using that method.

You recognize that the foregoing example involves a
statistical question but have no idea what the Greenwood and Peto methods are.
You consult your statistician, who tells you that she conducted a survival
analysis (a study of treatment failure as a function of time across the
patients enrolled in the study). In the survival analysis, time to recurrence
of the arrhythmia is recorded for each patient. As most patients never have a
recurrence, they are treated as having a rightcensored recurrence time (their
time to event is cut off at the end of the trial or the time of the analysis).

Based on the data, a Kaplan–Meier curve, the common
nonparametric estimate for the survival curve, is generated. The survival curve
provides the probability that a patient will not have a recurrence by time *t.* It is plotted as a function of *t* and decreases from 1 at time 0. The
Kaplan–Meier curve is an estimate of this survival curve based on the trial
data (survival analysis is covered in Chapter 15).

You will learn that the uncertainty in the
Kaplan–Meier curve, a statistical estimate, can be quantified in a confidence
interval (covered in general terms in Chapter 8). The Greenwood and Peto
methods are two approximate methods for placing confidence intervals on the
survival curve at specified times *t.*
Statistical research has shown that the Greenwood method often provides a lower
confidence bound estimate that is too high. In contrast, the Peto method gives
a lower and possibly better estimate for the lower bound, particularly when *t* is large. The FDA prefers the bound
obtained by the Peto method because for large *t,* most of the cases have been rightcensored. However, both methods
are approximations and neither one is “correct.”

From the present text, you will learn about
confidence bounds and survival distributions; eventually, you will be able to
compute both the Greenwood and Peto bounds. (You already know enough to respond
to the FDA question, “Why did you use the Greenwood approximation . . . ?” by
asking a statistician to provide the Peto lower bound in addition to the
Greenwood.)

*Situation 3: *Again, you are a regulatory
affairs associate and are reviewing an* *FDA
letter about a PMA submission. The FDA wants to know if you can present your
results on the primary endpoints in terms of confidence intervals instead of
just reporting *p*-values (the *p*-value provides a summary of the
strength of evidence against the null hypothesis and will be covered in Chapter
9). Again, you recognize that the FDA’s question involves statistical issues.

When you ask for help, the statistician tells you
that the *p*-value is a summary of the
results of a hypothesis test. Because the statistician is familiar with the
test and the value of the test statistic, he can use the critical value(s) for
the test to generate a confidence bound or confidence bounds for the hypothesized
parameter value. Consequently, you can tell the FDA that you are able to
provide them with the information they want.

The present text will teach you about the
one-to-one correspondence between hypothesis tests and confidence intervals
(Chapter 9) so that you can construct a hy-pothesis test based on a given
confidence interval or construct the confidence bounds based on the results of
the hypothesis test.

*Situation 4: *You are a clinical research
associate (CRA) in the middle of a clinical trial. Based on data provided by
your statistics group, you are able to change your chronic endpoint from a
six-month follow-up result to a three-month follow-up result. This change is
exciting because it may mean that you can finish the trial much sooner than you
anticipated. However, there is a problem: the original protocol required
follow-ups only at two weeks and at six months after the procedure, whereas a
three-month follow-up was optional.

Some of the sites opt not to have a three-month
follow-up. Your clinical manager wants you to ask the investigators to have the
patients who are past three months postprocedure but not near the six-month
follow-up come in for an unscheduled follow-up. When the investigator and a
nurse associate hear about this request, they are reluctant to go to the
trouble of bringing in the patients. How do you convince them to comply?

You ask your statistician to explain the need for
an unscheduled follow-up. She says that the trial started with a six-month
endpoint because the FDA viewed six months to be a sufficient duration for the
trial. However, an investigation of Kaplan–Meier curves for similar studies
showed that there was very little decrease in the survival probability in the
period from three to six months. This finding convinced the FDA that the
three-month endpoint would provide sufficient information to determine the
long-term survival probability.

The statistician tells the investigator that we
could not have put this requirement into the original protocol because the
information to convince the FDA did not exist then. However, now that the FDA
has changed its position, we must have the three-month information on as many
patients as possible. By going to the trouble of bringing in these patients, we
will obtain the information that we need for an early approval. The early
approval will allow the company to market the product much faster and allow the
site to use the device sooner. As you learn about survival curves in this text,
you will appreciate how greatly survival analyses impact the success of a
clinical trial.

*Situation 5: *You are the Vice President of the
Clinical and Regulatory Affairs* *Department
at a medical device company. Your company hired a contract research
organization (CRO) to run a randomized controlled clinical trial (described in
Section 1.3.5, Clinical Trials). A CRO was selected in order to maintain
complete objectivity and to guarantee that the trial would remain blinded
throughout. Blinding is a procedure of coding the allocation of patients so
that neither they nor the investigators know to which treatment the patients
were assigned in the trial.

You will learn that blinding is important to
prevent bias in the study. The trial has been running for two years. You have
no idea how your product is doing. The CRO is nearing completion of the
analysis and is getting ready to present the report and unblind the study
(i.e., let others know the treatment group assignments for the patients). You
are very anxious to know if the trial will be successful. A successful trial
will provide a big financial boost for your company, which will be able to
market this device that provides a new method of treatment for a particular
type of heart disease.

The CRO shows you their report because you are the
only one allowed to see it until the announcement, two weeks hence. Your
company’s two expert statisticians are not even allowed to see the report. You
have limited statistical knowledge, but you are accustomed to seeing results
reported in terms of *p*-values for
tests. You see a demographic analysis comparing patients by age and gender in
the treatment and the control groups. As the *p*-value is 0.56, you are alarmed, for you are used to seeing small *p*-values. You know that, generally, the
FDA requires *p*-values below 0.05 for
acceptance of a device for marketing. There is nothing you can do but worry for
the next two weeks.

If you had a little more statistical training or if
you had a chance to speak to your statistician, you may have heard the
following: Generally, hypothesis tests are set up so that the null hypothesis
states that there is no difference among groups; you want to reject the null
hypothesis to show that results are better for the treatment group than for the
control group. A low *p*-value (0.05 is
usually the threshold) indicates that the results favor the treatment group in
comparison to the control group. Conversely, a high *p*-value (above 0.05) indicates no significant improvement.

However, for the demographic analysis, we want to
show no difference in out-come between groups by demographic characteristics.
We want the difference in the value for primary endpoints (in this case, length
of time the patient is able to exercise on a treadmill three months after the
procedure) to be attributed to a difference in treatment. If there are
demographic differences between groups, we cannot determine whether a
statistically significant difference in performance between the two groups is
attributable to the device being tested or simply to the demographic
differences. So when comparing demographics, we are not interested in rejecting
the null hypothesis; therefore, high *p*-values
provide good news for us.

From the preceding situations, you can see that
many employees at medical device companies who are not statisticians have to
deal with statistical issues and terminology frequently in their everyday work.
As students in the health sciences, you may aspire to career positions that
involve responsibilities and issues that are similar to those in the foregoing
examples. Also, the medical literature is replete with research articles that
include statistical analyses or at least provide *p*-values for certain hypothesis tests. If you need to study the
medical literature, you will need to evaluate some of these statistical
results. This text will help you become statistically literate. You will have a
basic understanding of statistical techniques and the assumptions necessary for
their application.

We noted previously that in recent years, medically
related research papers have included more and increasingly sophisticated
statistical analyses. However, some medical journals have tended to have a poor
track record, publishing papers that contain various errors in their
statistical applications. See Altman (1991), Chapter 16, for examples.

Another group that requires statistical expertise
in many situations is comprised of public health workers. For example, they may
be asked to investigate a disease outbreak (such as a food-borne disease
outbreak). There are five steps (using statistics) required to investigate the
outbreak: First, collect information about the persons involved in the
outbreak, deciding which types of data are most appropriate. Second, identify
possible sources of the outbreak, for example, contaminated or improperly
stored food or unsafe food handling practices. Third, formulate hypotheses
about modes of disease transmission. Fourth, from the collected data, develop a
descriptive display of quantitative information (see Chapter 3), e.g., bar
charts of cases of occurrence by day of outbreak. Fifth, assess the risks
associated with certain types of exposure (see Chapter 11).

Health education is another public health
discipline that relies on statistics. A central concern of health education is
program evaluation, which is necessary to demonstrate program efficacy. In
conjunction with program evaluation, health educators decide on alternative
statistical tests, including (but not limited to) independent groups or paired
groups (paired *t*-tests or
nonparametric analogues) chisquare tests, or one-way analyses of variance. In
designing a needs assessment protocol, health educators conduct a power
analysis for sample surveys. Not to be minimized is the need to be familiar
with the plethora of statistical techniques employed in contemporary health
education and public health literature.

The field of statistics not only has gained
importance in medicine and closely related disciplines, as we have described in
the preceding examples, but it has become the method of choice in almost all
scientific investigations. Salsburg’s recent book “The Lady Tasting Tea”
(Salsburg, 2001) explains eloquently why this is so and provides a glimpse at
the development of statistical methodology in the 20th century, along with the
many famous probabilists and statisticians who developed the discipline during
that period. Salsburg’s book also provides insight as to why (possibly in some
changing form) the discipline will continue to be important in the 21st
century. Random variation just will not go away, even though deterministic
theories (i.e., those not based on chance factors) continue to develop.

The examples described in this section are intended
to give you an overview of the importance of statistics in all areas of
medically related disciplines. The examples also highlight why all employees in
the medical field can benefit from a basic understanding of statistics.
However, in certain positions a deeper knowledge of statistics is required.
These examples were intended to give you an understanding of the importance of statistics
in realistic situations. We have pointed out in each situation the specific
chapters in which you will learn more details about the relevant statistical
topics. At this point, you are not expected to understand all the details
regarding the examples, but by the completion of the text, you will be able to
review and reread them in order to develop a deeper appreciation of the issues
involved.

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