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Research and
Medical Statistics
A review for USMLE Step 3 and board exams
Michael Thomas Kitchell MD
Dutifully Ripped Off By
Logan Matthew Atkins MD
Note
Information which is important for Step 3, but may or
may not necessarily be covered in depth today is listed
in red italics.
This powerpoint is readily available and may be found
on the wiki.
Part I
Basics of Medical Statistics
Null Hypothesis
The stance or position that two events are not
linked in a causal manner.
True and False Positives
● True Positive - A positive test which is
correct and can be validated on a “Gold
Standard”
● False Positive - A positive test which is
incorrect.
False positive is also known as a Type I error, which is
failure to reject the null hypothesis.
True and False Negatives
● True Negative - A negative test which is
correct
● False Negative - A negative test which is
incorrect.
False negative also known as Type II error, or when the
null hypothesis is incorrectly accepted.
Spin and Snout
Specificity - Proportion of people who do not
have a disease that will test negative for it.
(True negatives/(True negatives + False positives)
Value is Unrelated to prevalence.
Sensitivity - Proportion of people who have a
disease who will test positive for it.
(True positives/(true positive + false negative))
Value is Unrelated to prevalence.
Question
In testing for a condition, the best screening
test has a:
A.)High Sensitivity
B.)Low Sensitivity
C.)High Specificity
D.)Low Specificity
E.)Long name
Answer
High Sensitivity
Question
In testing for a said condition, the best
confirmatory test has a:
A.)High Sensitivity
B.)Low Sensitivity
C.)High Specificity
D.)Low Specificity
E.)High Risk
Answer
High Specificity
Question
To establish a diagnosis of diabetes, a fasting
blood sugar of 126 or higher on two separate
occasions is considered positive. What would
happen to the sensitivity and specificity of the
test if this value was increased to 136?
Answer
Sensitivity - Decrease
Specificity - Increase
Prevalence & Incidence
Prevalence - proportion of a group found to have the
disease or condition. Expressed as a percentage.
Number of total cases/Total population
Incidence - Amount of new cases of the disease or condition
within an allotted amount of time.
Number of new cases in a time period/Total non-diseased population
Incidence can also be stated as the amount of new cases per
patient year.
Number of new cases observed in a period /
[(Total non-diseased population) (years of observation)]
Question
Populations exist with varying incidences and prevalences
of Scrofula.
1.)Incidence - 5.2%
Prevalence - 3.2%
2.)Incidence - 2.8%
Prevalence - 7.8%
3.)Incidence - 4.3%
Prevalence - 4.1%
4.)Incidence - 1.8%
Prevalence - 6.3%
5.)Incidence - 8.9%
Prevalence - 5.1%
Which populations would offer someone the least and
greatest likelihood of developing Scrofula?
Answer
4.)Incidence - 1.8%
5.)Incidence - 8.9%
Prevalence - 9.3%
Prevalence - 1.1%
Least Likely
Most Likely
Positive Predictive Value
● Proportion of positive tests in a given
population which are true positives.
● Takes into account the prevalence of the
disease in the population tested.
Number of true positives/ (Number of true positives +
number of false positives)
Must know the prevalence to calculate
Question
The Modified Bruce Protocol exercise stress test has a 50-74% specificity at
detecting coronary artery disease.
A 27 year medical student, with no relevant past medical, family, or social
history undergoes a stress test to calibrate a new exercise treadmill machine.
The result is positive. He comes into your clinic worried. What should you
advise him regarding his risk for coronary disease?
A.)The positive test means he has CAD.
B.)The positive test means he likely has CAD.
C.)The positive test means he will develop CAD by the time he is 50.
D.)The positive test is likely a false positive.
E.)The positive test means he does not have CAD.
Answer
D.)The positive test is likely a false positive.
Negative Predictive Value
● Proportion of negative tests in a given
population which are true negatives.
● Takes into account the prevalence of a
disease in the tested population.
Number of true negatives/(number of true negatives +
number of false negatives)
Must know the prevalence to calculate
Question
Modified Bruce Protocol has a sensitivity of up to 90%
A 67 year old obese diabetic male with a past medical history of HLD, and HTN
as well as a 60 pk/year history and 2 previous MI’s is sent for cardiac stress test
after having left sided exertional chest pain that has been worsening over the
last several months and is relieved with nitroglycerin. He comes into your
office relieved that the result is negative. What should you advise him in
regards to his risk of coronary disease?
A.)A negative test rules out CAD in his case, his pain is likely costochondritis.
Recommend NSAIDs
B.)A negative test means he is extremely unlikely to have CAD.
C.)He still is at high risk for CAD, and needs further testing.
D.)A negative test means he has CAD.
E.)A negative test could be a result of small cell lung cancer. Recommend a
bronchoscopy.
Answer
C.)He still is at high risk for CAD, and needs further testing.
Absolute and Relative Risk
Absolute Risk:
Relative Risk:
Risk of an event happening
over a given time period.
Used when dealing with
only one group.
Probability of an event
occurring to one group as
opposed to another group.
Relative Risk =
Odds of event in test group/Odds of
event in control group.
Relative Risk example
A retrospective cohort study shows these looks
into the risk of bladder cancer in smokers vs.
nonsmokers.
Positive for bladder cancer
Negative for bladder cancer
Group A (Smokers)
29 (a)
714 (b)
Group B (Non-Smokers)
35 (c)
1975 (d)
Set up and Solve for Relative Risk.
Relative Risk example
Positive for bladder cancer
Negative for bladder cancer
Group A (Smokers)
29 (a)
714 (b)
Group B (Non-Smokers)
35 (c)
1975 (d)
Relative risk = (a/[a+b])/(c/[c+d])
(29/[29+714])/(35/[35+1975])
Relative Risk = 2.24
In other words, you are 2.24 times more likely to develop bladder cancer if
you are a smoker (in this completely made up example)
Odds Ratio: Similar to Relative risk, measures strength of an effect. Measures
“odds” instead of probability. Less intuitive.
Odds Ratio = ad/bc
Absolute Risk Reduction
Change in the risk of a given event based on an
intervention in a specific amount of time.
percent with condition in 1 year
Placebo
16%
Chemical X
12%
What is the Absolute Risk Reduction of
Chemical X?
Absolute Risk Reduction
4%
Absolute Risk Reduction =
(probability of condition without treatment) - (probability
of condition with treatment)
Relative Risk Reduction
The proportional change in risk from one group
to another.
Percent with condition in 1 year
Placebo
16% (a)
Chemical X
12% (b)
What is the Relative Risk Reduction.
Relative Risk Reduction
25%
Relative Risk Reduction =
([percent with condition without treatment] - [percent
with condition with treatment]) / (percent with condition
without treatment)
Number Needed to Treat
● Used to address the effectiveness of a particular
intervention.
● Relevant in issues dealing with economics of a specific
treatment.
● Many similar concepts are found which start with
“Number needed to” such as number needed to harm,
vaccinate, treat, prophylax. They are all the same
calculation
● Inverse of Absolute Risk Reduction
Number Needed to Treat
Calculate the NNT for Influenza Vaccination,
Note: Numbers are estimations, but percentages are accurate based on
Cochrane Review.
Positive for Flu
Negative for Flu
Vaccinated
245
24255
Unvaccinated
1820
43680
NNT = 1/(Probably without treatment - Probability with
treatment)
Number Needed to Treat
Calculate the NNT for Influenza Vaccination,
Note: Numbers are estimations, but percentages are accurate based on
Cochrane Review.
Positive for Flu
Negative for Flu
Vaccinated
245 (a)
24255 (b)
Unvaccinated
1820 (c)
43680 (d)
NNT = 1/{(c/[c+d]) - (a/[a+b])}
NNT = 1/{(1820/[1820+43680]) - (245/[245+24255])}
NNT = 1/([1820/45500] - [245/25500])
NNT = 1/(0.04 - 0.01)
NNT = 1/0.03
NNT = 33 ⅓
p-value
● Probability of obtaining similar results in a
study assuming the null hypothesis is true.
● In general a p-value of 0.05 (a 5% chance of
these results being from chance) is accepted
to be adequate.
● If the p-value is <0.05 it is “statistically
significant”
http://xkcd.com/882
Confidence Interval
Used associated with relative risk or odds ratio.
In our previous example of relative risk of bladder cancer in smokers (2.24). A
confidence interval would be, for example:
95% confidence interval from 1.63-3.12
Meaning, we are 95% sure the relative risk falls somewhere between 1.63 and
3.12.
Question
A double blind randomized control trial shows a linkage
between ingestion of Lisinopril and alopecia (No, not really).
The relative risk is found to be 1.8 (95% CI = 0.93-2.54)
What should you do with this information?
Answer
Nothing!
Anytime the confidence interval crosses the number 1, the
result is not statistically significant!
Question
In the previous question, what could have been
done to help us reach statistical significance?
Answer
Increase the power of the study.
Increasing the power of the study will narrow the confidence interval
Power
The probability a study will reject the null hypothesis when
the null hypothesis is false.
Primary factors which influence power.
1. Definition of Statistical Significance - If a p-value of 0.1
is accepted, it is easier to meet.
2. Magnitude of effect - It is easier to prove the link
between knife juggling and lacerations than it is to
prove the link between phenergan and tardive
dyskinesia.
3. Sample Size - The larger the study, the more minute of
an effect can be noticed.
As power increases Confidence Interval narrows
Part II
Study Analysis
Blinding
The process in which information which may lead to bias is
withheld from certain groups within a study.
Single Blind - Information is withheld from participants.
Experimenters are aware.
Double Blind - Information regarding the experiment is
withheld from both the participants and the experimenters.
Independent & Dependent
Variables
Independent Variable:
Dependent Variable:
A variable which is changed
between the treatment and
control groups. Looked at as
a possible cause of change in
the dependent variable.
The variable which is not
changed in the study. Often
the end point in the study.
Independant Variable = Input
In a study which evaluates CT exposure to a link of melanomas, CT exposure is
the independent variable. Incidence of melanoma is the dependant variable.
[Independent variable] causes a change in the [dependent variable]
Question
A study is setup to look at the incidence of bladder cancer in
smokers vs nonsmokers.
What are the independent and dependant variables?
Answer
Independent Variable - smoking status
Dependent Variable - bladder cancer
Bias
● Anything that can skew or change the results
of a study from the true value.
● Detail on each type could easily fill an entire
lecture
● For more information see the website below
for types of bias that are commonly tested on
Step 3
http://www.medicalbiostatistics.com/Types%20of%20bia
s.pdf
Question
A study is constructed to determine the benefit of routine
screening for family members of people affected by
Huntington’s Disease. The study finds routine screening of
first degree relatives at age 30 grants a 19 year increase in
lifespan from the time of diagnosis in comparison to
patients who were screened only with physical exam when
they began to show symptoms.
What type of bias explains this effect?
Answer
Lead time bias
Patients are not living longer, they are only being diagnosed 19 years earlier.
Confounding
Any factor which correlates to both the
independent and dependent variables and is
extrinsic of the study.
Question
A case-control trial is done evaluating a
possible increased risk in lung cancer incidence
in people who carry lighters.
What is the confounding variable?
Answer
Smoking
Randomization
The act of purposely equalizing all variables in a
study which may have an effect on the result
with the exception of the independent variable.
Decrease Bias
Question
A survey is placed in mammography clinics to
assess the likelihood of women to do breast
self-exams in a particular town.
What type of bias is illustrated here?
Answer
Selection Bias
The survey ignores the subset of women who do not get mammograms.
Retrospective & Prospective
Retrospective:
Prospective:
Study looking back in time
from data that is already
available.
More prone to bias and
confounding.
Study which watches for
changes in an outcome
based on different
dependent variables.
Case-Control Trials
● Relatively easy, cost-effective retrospective study
frequently used as a first step.
● Helpful in rare conditions as less numbers are needed.
● Gives an odds-ratio, not a relative risk.
● Example: If looking for a link in renal cell cancer and
ACE inhibitor use. You would find a group of people
with renal cell cancer (the case group) and a group
without renal cell cancer (the control group) then find
the prevalence of ACE inhibitor use in both groups.
Question
A Case-control study is done through a phone survey to
evaluate for a possible link between respiratory illness
during pregnancy and cerebral palsy. Mothers of children
with cerebral palsy are called to ask if there were any
respiratory illnesses in the pregnancy. These are then
broken down by trimester. A control group of mothers of
healthy children are called and asked similar questions.
What is the most likely source of bias in this study?
Answer
Recall Bias
Bias results from mothers of children with cerebral palsy trying to remember
more illness in an effort to find a possible link, while mothers of healthy
children are more likely to disregard any minor illnesses in their pregnancy.
Cohort Study
● Frequent next step after a Case-Control study.
● Expensive, time-consuming.
● Observational, this study does not assign treatment
groups. It only observes similar groups with different
independent variable.
● Require large groups, and long term monitoring.
● Measures relative risk.
● Framingham Heart Study is a common example (started
in 1948, and still in progress)
Randomized Control Trial
● Prospective study
● Randomly assigns a group to either treatment or control
then determines if the treatment (independent variable)
had an effect on the outcome (dependent variable)
● Followed for a specific amount of time but may be
stopped early if significant power is available to show an
effect.
● Less likely to be affected by selection bias.
● Gold Standard of studies.
Meta-Analysis
Several studies are combined after the fact, essentially making one large study.
RCT
Cohort
Cohort
Meta-Analysis
Question: What factor would this primarily affect?
RCT
RCT
Answer
Power
Example
From Rakel’s
HRT was first evaluated for possible risks in case-control and cohort studies,
which showed HRT could reduce the incidence of CAD fractures and colorectal
cancer. A possible increase in breast cancer, stroke and DVT was noted, but
was outweighed by the decrease in CAD. Even several meta-analyses backed
these findings.
Randomized Control Trials done after this showed the actual relation between
CAD and HRT.
It is hypothesized the cause was secondary to healthier people in general being
interested in HRT, causing a selection bias.
This information is found in Rakel’s on page 112-114, and is a good read.
Statistics don’t lie,
Statisticians do.
All images are webcomics from www.xkcd.com
The 7 Dirty Equations
● Relative Risk (RR)
= Risk of event (exposed) / Risk of event (unexposed)
● Absolute Risk (AR)
= Event rate (untreated) - Event rate (treated)
● Number Needed to Treat (NNT)
= 1 / Absolute Risk
● Sensitivity
= TP / (TP + FN)
● Specificity
= TN / (TN + FP)
● Positive Predictive Value (PPV)
= TP / (TP + FP)
● Negative Predictive Value (NPV)
= TN / (TN + FN)