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Statistics for Health Care
Biostatistics
Phases of a Full Clinical Trial
• Phase I – the trial takes place after the
development of a therapy and is designed to
determine doses, strengths and safety – it is preexperimental – there is no control group
• Phase II – the trial is looking for evidence of
effectiveness – it is pre-experimental or quasiexperimental and similar to a pilot test – it seeks
to determine feasibility of further testing and
signs of potential side effects
Phases of a Full Clinical Trial
• Phase III – it is a full experimental test of
the therapy with randomly assigned
treatment and control groups. It is
designed to determine whether the
intervention is more effective than a
standard treatment. It may be referred to
as and RCT or randomized clinical trial
and often studies large groups from
multiple sites.
Phases of a Full Clinical Trial
• Phase IV – it occurs after the decision to
adopt an innovative therapy and involves
study of its long-term consequences –both
side effects and benefits. It rarely requires
true experimental design.
Prevalence Studies
• Prevalence studies are a type of
descriptive study that come from the field
of epidemiology. They are conducted to
determine the prevalence rate of some
condition. They are cross-sectional
designs that obtain data from one
population at risk for the condition
Prevalence Studies
• The formula for a prevalence rate (PR) is:
# of cases with the condition at a given point in time
_____________________________________
x K
# in the population at risk for being a case
Example:
80 cases
____________ x 100 (# we want the PR established for) = 16 per 100
500 at risk
Incidence Studies
• Incidence studies measure the frequency
of developing new cases. This requires a
longitudinal design, because we need to
determine who is at risk for becoming a
new case.
Incidence Studies
• The formula for an incidence rate (IR) is:
# of new cases with the condition over a given period of time
_____________________________________
# in the population at risk for being a new case
Example:
21 new cases (in one year since original count)
____________ x 100
= 5 per 100
420 at risk (from previous example: 500-80 =420 now at risk
x K
Relative Risk
• Relative risk (RR is the risk of becoming a
case if in one group compared to being in
another group.
• Example:
If the risk of becoming a new case was 7 per
hundred in men and 14 per hundred in
women, we would divide the rate of women by
the rate of men, and find that women were
twice as likely to become a new case over a
year’s time.
Relative Risk
• Relative Risk can also be used in examining
new therapies.
• Relative Risk is the ratio of an outcome (such as
PONV) in the treatment group (those receiving a
bolus of fluid before induction) to the rate of the
outcome (PONV) in the controls.
An RR of < 1.0 means the experimental group had
less (PONV) than the control group. An RR of > 1.0
would mean that the experimental group had more
(PONV) than did the controls.
Developing
Screening/Diagnostic
Instruments
• Goal is to establish a cutoff point
that balances sensitivity and
specificity
Positive Predictive Value
• The Positive Predictive Value (PPV) - the precision rate, or the posttest probability of disease - is the proportion of patients with positive
test results who are correctly diagnosed. It indicates the probability
with which a positive test might show the disease or condition being
tested for. It is a measure of the diagnostic test. A low number
means a high “false positive” rate.
•
• PPV =
•
•
No. of true positives
No. of true positives + No. of false positives
(total who test positive)
Negative Predictive Value
• The Negative Predictive Value (NPV) is
the proportion of patients with negative
test results who are correctly diagnosed.
(They do not have the disease or
condition.)
• NPV =
No. of true negatives
•
No. of true negatives + No. of false negatives
•
(total who test negative)
•
Criteria for Assessing Screening/Diagnostic
Instruments
• Sensitivity: the instrument’s ability to
correctly identify a “case”—i.e., to
diagnose a condition
• Specificity: the instrument’s ability to
correctly identify “noncases”, that is, to
screen out those without the condition
EMPIRICAL
Test
Outcome
EVIDENCE
of
CONDITION
True
False
Positive
True positive
False
Positive
(Type I error)
Positive
Predictive
Value
Negative
False
negative
(Type II error)
True negative
Negative
Predictive
Value
Sensitivity
Specificity
BOWEL CA
Fecal
Occult Blood
Test
(POSITIVE ON
COLONOSCOPY
and BIOPSY)
True
False
Positive
True positive =
2
False
Positive = 18
PPV
2/20 = 10%
Negative
False negative
=1
(Type II error)
True
negative =
182
NPV
182/183 =
99.5%
Sensitivity
2/ (2+1) =
66.7%
Specificity
182/ (18
+182) = 91%
Information from Slide 19
• Looking at the slides you can see that the
large number of false positives and the low
number of false negatives indicate that the
occult blood test is poor at confirming
colon cancer. However, it is good as a
screening test since 99.5 % of the
negative tests will be correct and the
sensitivity indicates that further testing
needs to be done on at least 66.7% of
those testing positive.
Confidence Interval
• The Confidence Interval (CI) is the range
of values around a sample mean that are
calculated to contain the population mean
with a 95% (or 99%) degree of certainty.
Many researchers believe that these
values give more clinical data than do p
values.
Confidence Interval
• The POINT ESTIMATE is a single point
estimated to be the mean for the population,
based on a sample. When a confidence interval
(CI) is reported, it is an INTERVAL ESTIMATE,
a range of values that estimate the mean for a
population. If a math test was given to a sample
of nursing students and there was a mean of 55,
then 55 would be the point estimate. If the 95%
CI was reported as 52-57, there would be a 95%
chance that the true mean of all nursing students
would be between 52-57.
•
Confidence Interval
• The STANDARD ERROR OF THE MEAN is used to calculate the
CI. The standard error of the mean is the error that is due to
sampling. Each sample mean is likely to deviate somewhat from the
true population mean. The SEM is the difference between the
sample mean and the unknown population mean. It is the margin of
error to allow for when estimating the population mean from a
random sample. It allows for chance errors. It is calculated as
follows:
•
SD (of the sample)
•
Square root of the No. of people in the sample
Confidence Interval
• If the SEM is 3 and the mean is 100 and you
want a confidence interval of 95% - that is
between -1.96 and +1.96 SD from the mean,
you would use the following formula: X + (1.96 x
SEM) = CI
•
•
100 + (1.96 x 3)
=
100 + 5.88
• We can say, with 95% confidence, that the
population mean would fall between 94.12 and
105.88
•
Confidence Interval
• For a 68% CI, add the standard error of
the mean (SEM) to the mean, then
subtract it from the mean. For a 95% CI ,
multiply the SEM by 1.96, then add and
subtract. For a 99% CI, multiply by 2.58,
then add and subtract. Note: The intervals
obtained by using these multipliers are
only precise with large numbers (60 or
more cases).