Transcript 04. Dynamic lines

Dynamic Lines
Dynamic analysis
Studying of
dynamics of the
phenomena is
very important
for the analysis
of a state of
health
Health of
people and
activity of
medical
establishments
change in time
Analysis of
activity of
system of
public health
services.
Rate of
growth
Rate of gain
Pure
gain
Parameters applied for analysis of changes of a
phenomenon
Parameter
of
correlation
Parameter of
visualization
Intensive,
extensive
parameters
of growth –relation of all
numbers of dynamic lines to
the previous level accepted for
100 %
.
 Rate
Parameters applied for
analysis of changes of a
phenomenon
gain – difference
between next and previous
numbers of dynamic lines.
 Pure
Parameters applied for
analysis of changes of a
phenomenon
of gain – relation of the
pure gain to previous
number.
 Rate
Parameters applied for
analysis of changes of a
phenomenon
of visualization —
relation of all numbers of
dynamic lines to the first level,
which one starts to 100%.
 Parameter
Measures of Association
Dynamic analysis
 Health
of people and activity of
medical establishments change in
time.
 Studying of dynamics of the
phenomena is very important for the
analysis of a state of health and
activity of system of public health
services.
Example of a dynamic line
Year
1994
1995
1996
1997
1998
1999
2000
Bed occupancy (days)
340.1
340.9
338.0
343.0
341.2
339.1
344.2
Statistical Terms
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Mean:  the average of the data
 sensitive to outlying data
Median:  the middle of the data
 not sensitive to outlying data
Mode:  most commonly occurring value
Range:  the difference between the largest observation and
the smallest
Interquartile range:  the spread of the data
 commonly used for skewed data
Standard deviation:  a single number which measures how much
the observations vary around the mean
Symmetrical data:  data that follows normal distribution
 (mean=median=mode)
 report mean & standard deviation & n
Skewed data:  not normally distributed
 (meanmedianmode)
 report median & IQ Range
Measures of Frequency of Events
Prevalence
Incidence
The number
of new events
(e.g. death or
a
particular
disease) that
occur during a
specified
period
Incidence
Rate
A term related
to incidence
that reports
the number of
new events
The number
of persons in
the
population
affected by a
disease at a
specific time
divided
by
the number of
persons in the
population
Measures of Association

Relative risk and cohort studies
- The relative risk (or risk ratio) is defined as the
ratio of the incidence of disease in the
exposed group divided by the corresponding
incidence of disease in the unexposed group.
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Odds ratio and case-control studies
- The odds ratio is defined as the odds of
exposure in the group with disease divided by
the odds of exposure in the control group.
Case-control
studies
Relative risk
and cohort
studies
Measures
of
Association
Odds
ratio
Measures of Association
RELATIVE INDICES
Relative Values
In order to acquire a level of the
phenomenon, for comparison of a parameter
in dynamics or with a parameter of other
territory it is necessary to calculate relative
values (parameters, factors) which represent
result of a ratio of statistical numbers between
itself. The basic arithmetic action at
subtraction of relative values is division.
The following kinds of relative
parameters are used in medical
statistics
Correlation
indices
Extensive
indices
Intensive
indices
Relative
intensity
indices
Visualizati
on
indices
The extensive parameter, or a
parameter
of
distribution,
characterizes a parts of the
phenomena (structure), that is it
shows, what part from the general
number of all diseases (died) is
made with this or that disease
which enters into total.
The general formula of its calculation is the
following: (extensive parameters)
part × 100
total
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General formula of the calculation is the
following (intensive parameters)
phenomenon×100 (1000; 10 000; 100 000)
environment
General mortality rate
number of died during the year × 1000
number of the population
Parameters of relative intensity
If it is necessary
this indices to
measure a degree of
a disproportion in
structure of two or
several close
processes
Represent a numerical
ratio of two or several
structures of the same
elements of a set, which
is studied
Used as
auxiliary
reception,
to receive
direct
intensive
parameters
Its allow
determining a
degree of
conformity
(advantage or
reduction) of
similar attributes
The parameter of correlation
Characterizes
the relation
between
diverse values
For example, the
parameter of
average bed
occupancy,
providing by
nurses, doctors
The techniques of
subtraction of the
correlation
parameter is the
same as for
intensive parameter
The parameter of visualization
Characterizes
the relation of
any of
comparable
values to the
initial level
accepted for
100
This parameter is
used for
convenience of
comparison, and
also in case
shows a direction
of process
(increase,
reduction) a level
or the numbers of
the phenomenon
It can be used for
the characteristic of
dynamics of the
phenomena, for
comparison on
separate territories,
in different groups
of the population,
for the construction
of graphic
SIMULATION
Consider a box containing chips or cards,
each of which is numbered either 0 or 1.
We want to take a sample from this box in
order to estimate the percentage of the
cards that are numbered with a 1.
The population in this case is the box of
cards, which we will call the population
box. The percentage of cards in the box
that are numbered with a 1 is the
parameter π.
SIMULATION
In the Harris study the parameter π is
unknown. Here, however, in order to see
how samples behave, we will make our
model with a known percentage of cards
numbered with a 1, say π = 60%. At the
same time we will estimate π, pretending
that we don’t know its value, by examining
25 cards in the box.
SIMULATION
We take a simple random sample with replacement
of 25 cards from the box as follows. Mix the box of
cards; choose one at random; record it; replace it;
and then repeat the procedure until we have
recorded the numbers on 25 cards. Although
survey samples are not generally drawn with
replacement, our simulation simplifies the analysis
because the box remains unchanged between
draws; so, after examining each card, the chance
of drawing a card numbered 1 on the following
draw is the same as it was for the previous draw, in
this case a 60% chance.
SIMULATION
Let’s say that after drawing the 25 cards this way,
we obtain the following results, recorded in 5
rows of 5 numbers:
Parameters applied for analysis
of changes of a phenomenon
of growth –relation of all
numbers of dynamic lines to
the previous level accepted for
100 %.
 Rate
Parameters applied for
analysis of changes of a
phenomenon
gain – difference
between next and previous
numbers of dynamic lines.
 Pure
Parameters applied for
analysis of changes of a
phenomenon
of gain – relation of the
pure gain to previous
number.
 Rate
Parameters applied for
analysis of changes of a
phenomenon
of visualization —
relation of all numbers of
dynamic lines to the first level,
which one starts to 100%.
 Parameter
Measures of Association
Measures of Association
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Absolute risk
- The relative risk and odds ratio provide a measure of risk
compared with a standard.
Attributable risk or Risk difference is a measure of absolute
risk. It represents the excess risk of disease in those exposed
taking into account the background rate of disease. The
attributable risk is defined as the difference between the
incidence rates in the exposed and non-exposed groups.
Population Attributable Risk is used to describe the excess
rate of disease in the total study population of exposed and
non-exposed individuals that is attributable to the exposure.
Number needed to treat (NNT)
- The number of patients who would need to be treated to
prevent one adverse outcome is often used to present the
results of randomized trials.
Relative Values
As a result of statistical research during
processing of the statistical data of
disease, mortality rate, lethality, etc.
absolute numbers are received, which
specify the number of the phenomena.
Though absolute numbers have a
certain cognitive values, but their use is
limited.
Relative Values
In order to acquire a level of the phenomenon,
for comparison of a parameter in dynamics or
with a parameter of other territory it is
necessary to calculate relative values
(parameters, factors) which represent result
of a ratio of statistical numbers between itself.
The basic arithmetic action at subtraction of
relative values is division.
In medical statistics themselves the
following kinds of relative parameters
are used:





Extensive;
Intensive;
Relative intensity;
Visualization;
Correlation.
The extensive parameter, or a
parameter of distribution,
characterizes a parts of the
phenomena (structure), that is it
shows, what part from the general
number of all diseases (died) is
made with this or that disease
which enters into total.
Using this parameter, it is possible to
determine the structure of patients
according to age, social status, etc. It is
accepted to express this parameter in
percentage, but it can be calculated and in
parts per thousand case when the part of
the given disease is small and at the
calculation in percentage it is expressed as
decimal fraction, instead of an integer.
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The intensive parameter characterizes frequency
or distribution.
It shows how frequently the given phenomenon
occurs in the given environment.
For example, how frequently there is this or that
disease among the population or how frequently
people are dying from this or that disease.
To calculate the intensive parameter, it is
necessary to know the population or the
contingent.
SIMULATION
We take a simple random sample with replacement
of 25 cards from the box as follows. Mix the box of
cards; choose one at random; record it; replace it;
and then repeat the procedure until we have
recorded the numbers on 25 cards. Although
survey samples are not generally drawn with
replacement, our simulation simplifies the analysis
because the box remains unchanged between
draws; so, after examining each card, the chance
of drawing a card numbered 1 on the following
draw is the same as it was for the previous draw, in
this case a 60% chance.