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Important definitions in statistics
ABOUBAKR ELNASHAR
Benha University Hospital, Egypt
ABOUBAKR ELNASHAR
Sensitivity:
Probability of test to be positive when the disease
is present
True positive test
Specificity
Probability of the test to be negative when the
disease is absent
True negative test
Systematic review
is qualitative reports
Meta-analysis
Qualitative analysis of systematic review
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Precision
a description of a level of measurement that
yields consistent results when repeated. It is
associated with the concept of "random error", a
form of observational error that leads to
measurable values being inconsistent when
repeated.
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Precision or positive predictive value
the proportion of the true positives against all the
positive results (both true positives and false
positives)
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Accuracy
two definitions:
a level of measurement with no inherent
limitation (i.e. free of systematic error, another
form of observational error).
ISO definition
a level of measurement that yields true (no
systematic errors) and consistent (no random
errors) results.
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Accuracy
used as a statistical measure of how well a binary
classification test correctly identifies or excludes a
condition.
Accuracy
is the proportion of true results (both true
positives and true negatives) among the total
number of cases examined.
To make the context clear by the semantics, it is
often referred to as the "Rand accuracy" or "Rand
index". It is a parameter of the test.
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Accuracy may be determined from sensitivity and specificity,
provided prevalence is known, using the equation:
The accuracy paradox for predictive analytics states that
predictive models with a given level of accuracy may have
greater predictive power than models with higher accuracy. It
may be better to avoid the accuracy metric in favor of other
metrics such as precision and recall.
In situations where the minority class is more important, F-
measuremay be more appropriate, especially in situations
with very skewed class imbalance.
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Another useful performance measure is the balanced accuracy which avoids inflated performance estimates on
imbalanced datasets.
It is defined as the arithmetic mean of sensitivity and
specificity, or the average accuracy obtained on either class:
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Confidence interval
A way of expressing certainty about the findings
from a study or group of studies, using statistical
techniques.
A confidence interval describes a range of
possible effects (of a treatment or intervention)
that is consistent with the results of a study or
group of studies.
I am confident 95% that the range is between so
and so
If the range cross 1 , it is insignificant
95% CI (1.05-1.15)= I am 95% confident that the
risk between 1.05 and 1.15
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A wide confidence interval indicates a lack of
certainty or precision about the true size of the
clinical effect and is seen in studies with too few
patients.
Where confidence intervals are narrow they
indicate more precise estimates of effects and a
larger sample of patients studied.
It is usual to interpret a ‘95%’ confidence interval
as the range of effects within which we are 95%
confident that the true effect lies
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In case control study
It is better to have more controls than cases
In clinical studies
It is better for cases and control to be the same
For numbers: t test
For %: chi square
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Relative risk
A summary measure which represents the ratio
of the risk of a given event or outcome (e.g. an
adverse reaction to the drug being tested) in one
group of subjects compared to another group.
When the ‘risk’ of the event is the same in the
two groups the relative risk is 1.
In a study comparing two treatments, a relative
risk of 2 would indicate that patients receiving
one of the treatments had twice the risk of an
undesirable outcome than those receiving the
other treatment.
Relative risk is sometimes used as a synonym
for risk ratio.
RR
If 1: no association
<1: negative association
>1: positive association
RR= 2 i.e. risk is doubled
= 5 i.e. risk is 5 times
= 0.5 i.e. negative association ad the risk is
halfed
OR
Is like RR and interpreted as it
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Odds ratio
a way of representing probability, especially
familiar for betting.
They provide an estimate (usually with a
confidence interval) for the effect of a treatment.
Odds are used to convey the idea of ‘risk’ and an
odds ratio of one between two treatment groups
would imply that the risks of an adverse outcome
were the same in each group.
For rare events the odds ratio and the relative
risk (which uses actual risks and not odds) will be
very similar.
Very common 1/1-1/10 A person in family
Common 1/10-1/100 A person in street
Uncommon 1/100-1/1000 A person in village
Rare 1/1000-1/10,000 A person in small town
Very rare <1/10,000 A person in large town
Royal College of Obstetricians and
Gynaecologists
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Incidence
The rate of new (or newly diagnosed) cases of
the disease.
It is generally reported as the number of new
cases occurring within a period of time (e.g.,
per month, per year).
It is more meaningful when the incidence rate
is reported as a fraction of the population at risk
of developing the disease (e.g., per 100,000 or
per million population).
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The accuracy of incidence data depends upon
the accuracy of diagnosis and reporting of the
disease.
In some cases (including ESRD) it may be
more appropriate to report the rate of treatment
of new cases since these are known, whereas
the actual incidence of untreated cases is not.
Incidence rates can be further categorized
according to different subsets of the population
– e.g., by gender, by racial origin, by age group
or by diagnostic category.
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Prevalence
The actual number of cases alive, with the
disease either during a period of time (period
prevalence) or at a particular date in time (point
prevalence).
Period prevalence provides the better measure
of the disease load since it includes all new cases
and all deaths between two dates
Point prevalence only counts those alive on a
particular date.
Prevalence is also most meaningfully reported as
the number of cases as a fraction of the total
population at risk and can be further categorized
according to different subsets of the population.ABOUBAKR ELNASHAR
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Controlled clinical trial (CCT)
A study testing a specific drug or other treatment
involving two (or more) groups of patients with the
same disease.
One (the experimental group) receives the
treatment that is being tested, and the other (the
comparison or control group) receives an
alternative treatment, a placebo (dummy treatment)
or no treatment.
The two groups are followed up to compare
differences in outcomes to see how effective the
experimental treatment was.
A CCT where patients are randomly allocated to
treatment and comparison groups is called a
randomised controlled trial.
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Meta-analysis
Results from a collection of independent studies
(investigating the same treatment) are pooled,
using statistical techniques to synthesise their
findings into a single estimate of a treatment
effect.
Where studies are not compatible e.g. because
of differences in the study populations or in the
outcomes measured, it may be inappropriate or
even misleading to statistically pool results in this
way.
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Systematic review
A review in which evidence from scientific
studies has been identified, appraised and
synthesised in a methodical way according to
predetermined criteria.
May or may not include a meta-analysis.
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Cochrane Collaboration
An international organisation in which people
find, appraise and review specific types of
studies called randomised controlled trials.
The Cochrane Database of Systematic Reviews
contains regularly updated reviews on a variety
of health issues and is available electronically as
part of the Cochrane Library.
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Cochrane Library
The Cochrane Library consists of a regularly
updated collection of evidence-based medicine
databases including the Cochrane Database of
Systematic Reviews (reviews of randomised
controlled trials prepared by the Cochrane
Collaboration).
The Cochrane Library is available on CD-ROM
and the Internet.
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Cohort
A group of people sharing some common
characteristic (e.g. patients with the same
disease), followed up in a research study for a
specified period of time.
Cohort study
An observational study that takes a group
(cohort) of patients and follows their progress
over time in order to measure outcomes such as
disease or mortality rates and make comparisons
according to the treatments or interventions that
patients received.
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Thus within the study group, subgroups of
patients are identified (from information collected
about patients) and these groups are compared
with respect to outcome, e.g. comparing mortality
between one group that received a specific
treatment and one group which did not (or
between two groups that received different levels
of treatment).
Cohorts can be assembled in the present and
followed into the future (a ‘concurrent’ or
‘prospective’ cohort study) or identified from past
records and followed forward from that time up to
the present (a ‘historical’ or ‘retrospective’ cohort
study).
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Because patients are not randomly allocated to
subgroups, these subgroups may be quite
different in their characteristics and some
adjustment must be made when analysing the
results to ensure that the comparison between
groups is as fair as possible.
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