# Quick Reference for Statistics in Medicine

```Quick Reference for
Statistics in Medicine
Developed from material on the SIM website
by Lynsay Lane (Meds 2010)
Study Designs
What is it?
Here, you draw a
random sample of
people and record
Crosshealth in a systematic
sectional
manner. You can
surveys
compare characteristics
of people with and
Observational
(the researcher
without a disease.
studies but does
These are like surveys
Cohort
not alter what
that extend over time.
(aka
occurs)
longitudinal This allows you to
study changes and to
or
prospective) establish a timesequence – e.g.,
between cause and
disease.
This is a retrospective
study. You begin at the
CaseStudy
end, by selecting
control
Designs
people with the disease,
studies
and then work
backwards to hunt for
possible causes.
Normally used in
testing new drugs and
treatments. A sample
of patients with the
condition, who meet
selection criteria, are
RCT
randomly allocated to
treatment or the control
Experimental
(the researcher
(standard or placebo)
intervenes to
treatment. Results are
change reality,
recorded.
then observes
Here, there is an
what happens)
intervention (ex.
reduced coverage of
certain services), but it
is often not completely
Quasiexperiments planned by the
researcher. Also,
people not allocated to
experimental &amp; control
groups randomly.
Quick; can
cover whole
population,
giving
representative
information
whether or not
people are
seeking care
Prospective,
so can
establish
causal
sequence; can
estimate
incidence
Based mainly
on self-report
(biases?);
diagnostic
information
usually
inaccurate;
can’t establish
causal sequence
Timeconsuming;
costly; attrition
of cohort?
Relatively
cheap way of
investigating
causal factors
Requires recall
of past events
(inaccurate?);
controls may
not be
equivalent to
cases
This design
Ethical
controls for all concerns in
main forms of etiological
bias; good for applications;
both
often uses
etiological
selected
and evaluative populations, so
research
issue of
generalizability
of the results
May be more
practical than
RCT; can use
“natural
experiments”
Allocation bias
often significant
(experimental
and control
groups not
equivalent)
Patterns observed
before and after the
intervention are
compared.
Some Concepts in Statistics
Measures of central tendency:
Mean – the average of a set of values
Median – the value of the middle observation in a rank-ordered distribution of values.
Half the observations will fall below the median and half above
Measures of dispersion of a set of values:
Range – the highest value minus the lowest. The simplest indicator of spread, but only
considers 2 of the values; may be affected by an extreme value
Variance – the average of the squared distance between each value and the mean of all
values. This improves on the rage by including information form every observation
Standard Deviation (SD) – the square root of the variance. It has the property that in a
“normal” distribution, roughly ⅔ of all observations fall within 1 SD of the mean. In
addition, roughly 95% of all observations will fall within &plusmn; 2 SD.
Confidence Intervals (CI) – a range within which the true value of a parameter probably
lies. The idea is that you have calculated a value from studying a sample, and want to
show how accurate this estimate is for the whole population. Research reports often
contain statements such as “the prevalence of inebriation among law students was 13.5%
(95% CI 10.1%, 16.9%). This means that your study found 13.5% of students were
drunk, and you’re 95% confident that the true prevalence lies somewhere between 10.1
and 16.9%. The bigger the sample size (n), the narrower the CI (because with a bigger
sample we have more confidence in the result)
Measures of Association:
Relative Risk (RR) – the ratio of the risk of disease among people with a risk factor to
those without. It indicates the strength of a risk, or causal factor. An RR of 1.0 means
that the two incidence rates (disease among those with, and those without, the risk factor)
are equal, so the factor has no effect. An RR of 2.0 would indicate that the exposed
people were twice as likely to get the disease; conversely an RR of 0.5 means they were
half as likely, so the exposure protected them from disease (e.g. Eat your veggies!!)
Odds Ratio (OR) – in a case-control study, the OR provides an estimate of the RR. This
is required because you CANNOT calculate incidence in a case-control study. As with
the RR, an OR above 1.0 indicates increasing risk related to the factor, while values
below 1 indicate protective effect
Chi-square test – a statistical test of the association between two categorical variables
Correlation coefficient – a statistical measure that shows how closely two numerical
variables lie in a linear association. That is, if you know one of the values, how
accurately could you predict the other by means of a straight line interpolation? The
correlation coefficient can range from -1 to +1, the two extremes denoting a perfect linear
relationship and 0 denoting a complete absence of relationship.
Regression analysis – a family of analytical methods that extend correlations and show
how much change occurs in the dependent variable for each unit change in a predictor
variable. In medicine, the dependent variable is typically an aspect of health, like BP,
while the independent (or predictor) variable could be a determinant of health (like the
number of cigarettes smoked daily). In multiple regression, you can see how 2 or more
variables can influence the dependent variable: how much effect do body-weight,
cigarettes and amount of exercise affect BP?
Measures of Statistical Difference:
t-test – a test for comparing the mean values from two samples. It shows how confident
we can be that the two mean values differ in the populations from which the samples
were drawn. This could be used to evaluate the results of a drug trial for antihypertensives: how confident are we that the results of this study indicate that there
would be a similar difference when the drug is applied to other samples of patients?
Basic Definitions
Incidence – the frequency with which something, such as a disease, appears in a
particular population or area. In disease epidemiology, the incidence is the number of
newly diagnosed cases during a specific time period.
Prevalence – the proportion of individuals in a population having a disease. It is a
statistical concept referring to the number of cases of a disease that are present in a
particular population at a given time.
Power – refers to the ability of a study to detect a difference that is real. Power is directly
proportional to sample size.
Reliability – refers to consistency or dependability. More formally, it refers of the
amount of random error that occurs in making a measurement.
Validity – refers to what conclusions we can draw from the results of a study, or of a
measurement. When referring to a screening test, validity is commonly reported in terms
of sensitivity and specificity.
Sensitivity – refers to what fraction of all the actual cases of disease are detected by a
test. Sensitivity is low if a test generates “false negatives” (people score negatively on
the test when they should score positively). This can be serious if early treatment would
have saved the person’s life.
SeNsitivity is inversely associated with false Negative rate
Specificity – refers to whether the test identifies only those with the disease. Specificity
is low if a test generates “false positives” (people without the disease test positive for it).
This can lead to worry and expensive further investigations.
SPecificity is inversely associated with false Positive rate
Positive Predictive Value (PPV) – probability that a positive score is a true positive
Negative Predictive Value (NPV) – probability that a negative score is a true negative
PPV and NPV depend on prevalence of disease, so must be determined for each
clinical setting because it is variable. As prevalence goes down, PPV goes
down and NPV rises (i.e. greater chance of not having the disease)
Likelihood Ratio (LR) – is the likelihood that a given test result would be expected in a
patient with the disease compared to the likelihood that the same result would be
expected in a patient without the disease.
2 x 2 Table for Testing a Test
Disease present
Disease Absent
Positive Test
Negative Test
Validity:
a (TP)
c (FN)
b (FP)
d (TN)
Predictive Values:
PPV = a / (a+b)
NPV = d / (c+d)
Sensitivity = a / (a+c) Specificity = d / (b+d)
*** T = true, F = false, P = positive, N = negative
False Negative rate = (1- seNsitivity), how many cases are missed by the screening test?
False Positive rate = (1-sPecificity), how many are falsely classified as having the
disease?
Pretest Probability of Disease (prevalence of disease among the sample) = (a+c) / N,
can also be expressed as…
Odds of disease (based on sample) = (a+c) / (b+d), if the disease is rare.
LR for positive test = Sensitivity / (1-specificity)
LR for negative test = (1-sensitivity) / specificity
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