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‫‪RATES AND‬‬
‫‪STANDARDIZATION‬‬
‫שיעורים ותקנון‬
‫דר' רונית קלדרון‬
‫אוקטובר ‪2014‬‬
‫‪1‬‬
‫נושאי השיעור‬
‫‪ ‬מדדי סיכום לשכיחות ארועים באוכלוסיה‬
‫‪ ‬יחס‪ ,‬פרופורציה‪ ,‬שיעור‬
‫‪ ‬תכונות ודוגמאות‬
‫‪ ‬תקנון‬
‫‪ ‬תקנון ישיר‬
‫‪ ‬תקנון עקיף‬
‫‪2‬‬
‫מדדי סיכום לשכיחות אירועים‬
‫באוכלוסייה‬
‫‪ .1‬יחס – ‪Ratio‬‬
‫חלוקה של שני מספרים מהצורה ‪ c/d‬כאשר ‪ c‬ו‪d -‬‬
‫מתייחסים לשכיחות של מאורע כלשהו‪.‬‬
Properties of Ratios
 R= (c/d)* k. Often the ratio is multiplied
by a value k where k is 1000, 10000 etc.
R>0
 R may or may not have units.
Ratio, Examples
:‫• יחס מיטות אשפוז כלליות למיטות אשפוז פסיכיאטרי‬
13,200
 2.44
5,400
# beds per doctor •
850 beds/10 doctors –
R = 85 beds for 1 doctor –
Male / Female :Sex Ratio •
Female / Male
Odds ratio •
Rate ratio •
5
6
‫היחס בין גברים לנשים‪ ,‬ישראל‪2011 ,‬‬
‫מקור‪ :‬הלשכה המרכזית לסטטיסטיקה‬
‫‪7‬‬
‫מדדי סיכום לשכיחות אירועים‬
‫באוכלוסייה‬
‫‪ .2‬פרופורציה ‪Proportion -‬‬
‫יחס שבו המונה הוא תת‪-‬קבוצה של המכנה‬
‫)‪.c/(c+d‬‬
Properties of Proportions
n - individuals in a population
x - individuals in the populations have
characteristics C
p = x/n proportion in the population with C
Range=?
Properties of Proportions

0  p 1

p has no units

p can be expressed as kp per k where k is a
number such as 1000,10000 in order to avoid
very small numbers.
Properties of Proportions
Example
In 2009 , among Israeli women 19% of all
deaths from cancer were from breast cancer
p=0.19 or 190 per 1000.
12
‫מדדי סיכום לשכיחות אירועים באוכלוסייה‬
‫‪ .3‬שעור ‪Rate -‬‬
‫יחס שבו מופיע אלמנט הזמן במונה וגם במכנה‪:‬‬
‫)‪a*/(a+b‬‬
‫כאשר ‪:‬‬
‫*‪ = a‬מספר האירועים במשך תקופת זמן‬
‫מסוימת‬
‫(‪ = )a+b‬גודל האוכלוסייה בסיכון לאירוע במשך‬
‫תקופת הזמן‪.‬‬
‫השיעור יכול להיות‪ ,‬אך אינו בהכרח‪ ,‬פרופורציה‪.‬‬
Properties of Rates
 Express relative frequency of an event per
unit time.
 Person years and rates.
Properties of Rates
N(t) = number of people exposed to risk of event
during a time period of length T.
Tj= number of time units (years) that person j is
exposed to risk.
A(t)=  (Tj) = person-years of exposure for the
N(T) individuals
D(T) = number of people with event in the time
period.
Properties of Rates
The rate of event is :
#
events
R = D(T) / A(T) = person years of exposure
Properties of Rates
Example
0
10y
time
T1=5
*
*
*
T2=9
T3=5
T4=5
* = event
T5=3
Properties of Rates- Example
R = D(T)/A(T) = 3/(5+9+5+5+3) = 3/27 = 0.11
In vital statistics, we rarely know the exact
exposure times. Instead we approximate A(T)
by NT where N= mid period population size.
Then:
R = D(T)/NT = 3/(3x10) = 3/30 = 0.10
Examples of rates in vital statistics
1). Annual crude death rate =
total # deaths in calendar year
 1000
total population of July 1
2). Annual age-specific death rate.
e.g. death rate ages 1- 4 =
total # deaths aged 1 - 4 in calendar year
 1000
total pop.aged 1 - 4 as of July 1
Examples of rates in vital statistics
3). Percent of all deaths which are aged 1- 4=
total # of deaths aged 1 - 4 in cal. year
 100
total # deaths in cal. year
4). Percent of all death due to cancer =
# cancer deaths in cal. year
 100
total # of deaths in cal.year
Examples of rates in vital statistics
5). Infant mortality rate =
# infant deaths in cal. year
 100
total # live births in cal. year
Example of Age Adjustment
1. Comparison of Total Death Rates in a
Population at Two Different Time Periods
Early Period
Later Period
Population
No. of
Deaths
Death
Rate
per
100,000
Population
No. of
Deaths
Death
Rate
per
100,000
900,000
862
96
900,000
1,130
126
Example of Age Adjustment
2). Comparison of Age-Specific Death Rates
in Two Different Time Periods
Early Period
Later Period
Age
Group
(yr)
Pop.
No. of
Deaths
Death
Rate
per
100,000
Pop.
No. of
Deaths
Death
Rate
per
100,000
All
ages
900,000
862
96
900,000
1,130
126
30-49
500,000
60
12
300,000
30
10
50-69
300,000
396
132
400,000
400
100
70+
100,000
406
406
200,000
700
350
Example of Age Adjustment
3). Carrying
Out an Age Adjustment Using the
Total of the Two Populations as the Standard
Age
Group
(yr)
All
Standard
Population
“Early”
Rate
per
100,000
Expected
No. of
Deaths
Using
“Early”
Rate
“Later”
Rate
per
100,000
Expected
No. of
Deaths
Using
“Later”
Rate
1,800,000
30-49
800,000
12
96
10
80
50-69
700,000
132
924
100
700
70+
300,000
406
1,218
350
1,050
Total no. of deaths expected
2,238
1,830
Example - Age adjustment
In the standard population age-adjusted
rates (per 100000 population):
“Early”=
“Later”=
100,000 *
100,000 *
2238
 124.3
1,800,000
1830
 101.7
1,800,000
‫‪Example - Age adjustment‬‬
‫שיעורי התמותה הגולמיים ל‪ 1,000-‬תושבים במדינת ישראל בשנת‬
‫‪ 2011‬היו ‪ 5.9‬ליהודים ו‪ 2.9-‬למוסלמים‬
‫‪26‬‬
‫יהודים‬
‫‪27‬‬
‫‪0‬‬
‫‪1-4‬‬
‫‪5-9‬‬
‫‪10-14‬‬
‫‪15-19‬‬
‫‪20-24‬‬
‫‪25-29‬‬
‫‪30-34‬‬
‫‪35-39‬‬
‫‪40-44‬‬
‫‪45-49‬‬
‫‪50-54‬‬
‫‪55-59‬‬
‫‪60-64‬‬
‫‪65-69‬‬
‫‪70-74‬‬
‫‪75-79‬‬
‫‪80-84‬‬
‫‪85-89‬‬
‫‪90-94‬‬
‫‪+95‬‬
‫‪2.7‬‬
‫‪0.1‬‬
‫‪0.1‬‬
‫(‪)0.1‬‬
‫‪0.3‬‬
‫‪0.4‬‬
‫‪0.4‬‬
‫‪0.5‬‬
‫‪0.6‬‬
‫‪1.0‬‬
‫‪2.0‬‬
‫‪3.3‬‬
‫‪5.4‬‬
‫‪9.0‬‬
‫‪12.7‬‬
‫‪22.0‬‬
‫‪38.9‬‬
‫‪67.1‬‬
‫‪115.7‬‬
‫‪185.6‬‬
‫‪226.9‬‬
‫מוסלמים‬
‫‪8.1‬‬
‫‪0.4‬‬
‫‪0.2‬‬
‫‪0.2‬‬
‫‪0.6‬‬
‫‪1.1‬‬
‫‪1.1‬‬
‫‪0.9‬‬
‫‪1.0‬‬
‫‪1.5‬‬
‫‪2.5‬‬
‫‪4.7‬‬
‫‪7.6‬‬
‫‪13.2‬‬
‫‪24.2‬‬
‫‪37.3‬‬
‫‪59.6‬‬
‫‪86.9‬‬
‫‪140.9‬‬
‫‪169.7‬‬
‫‪191.6‬‬
‫שיעורי תמותה ספציפיים‬
‫לגיל‪ ,‬ישראל ‪2011‬‬
30
‫השיעורים המתוקננים לגיל ל‪ 1000-‬תושבים (אוכלוסיית‬
‫התקן‪ :‬מפקד ‪ )2008‬היו ‪ 5.6‬ביהודים ו‪ 7.9-‬בקרב מוסלמים‬
‫‪31‬‬
Indirect Standatrdization
‫תקנון עקיף‬
32
Age-specific mortality rates due to cirrhosis.
Age
group
(yr)
Mortality
per
million
men per
year
Number
of men
Number
of
doctors
15-24
5.859
3,584,320
1080
25-34
13.050
3,065,100
12,860
35-44
46.937
2,876,170
11,510
45-54
161.503
2,965,880
10,330
55-64
271.358
2,756,510
7790
Age group
Standard
mortality rate,
all men
(a)
15-24
0.000005859
1080
0.0063
25-34
0.000013050
12860
0.1678
35-44
0.000046937
11510
0.5402
45-54
0.000161503
10330
1.6683
55-64
0.000271358
7790
2.1139
Total
Observed pop.
Number of
doctors
(b)
(a) x (b)
4.4965
By indirect standardization
 Number expected = 4.4965
Number observed=14
Ratio observed/expected = 3.1
Standardized Mortality Ratio
 Frequently
SMR
=
used statistic in epidemiology
# observed deaths in group
100
# expected deaths if standard rates apply
Cause-specific Mortality of Grand
Multiparous Women in Finland.
Hinkula, Am J Epidemiol, 2006
Types of Adjustment Procedures
Stratified or subgroup analysis
 Direct or indirect standardization of rates
 Multivariate statistical analysis
Example - Israeli Data
-2012 ‫שנתון סטטיסטי‬
Period: 2008-2010
Mortality rates to 1000 persons, men
Overall:
Jews-5.8; Arabs-3.1
Age group: 70-74: Jews-22.7; Arabs-35.7
Age group: 75-79: Jews-39.6; Arabs-60.8
‫תמותה לפי מין‪ ,‬קבוצת אוכלוסיה ושנה‬
‫שיעורים גולמיים‬
‫‪800‬‬
‫‪700‬‬
‫‪600‬‬
‫‪500‬‬
‫‪JM‬‬
‫‪400‬‬
‫‪JF‬‬
‫‪AM 300‬‬
‫‪AF‬‬
‫‪200‬‬
‫‪100‬‬
‫‪0‬‬
‫תמותה לפי מין‪ ,‬קבוצת אוכלוסיה ושנה‬
‫שיעורים מתוקננים למאה אלף‬
‫‪700‬‬
‫‪600‬‬
‫‪500‬‬
‫‪JM 400‬‬
‫‪JF‬‬
‫‪300‬‬
‫‪AM‬‬
‫‪AF 200‬‬
‫‪100‬‬
‫‪0‬‬
Example - Israeli Data - 2002
 Deaths, crude rate per 100,000, women =571
 Adjusted* mortality rate per 100,000:
Spain 438
Italy 444
Sweden 491
Israel 512
* Standard population = European population
Example - Israeli Data - 2002
 Deaths, crude rate per 100,000, among men =597
 Adjusted* mortality rate per 100,000:
Iceland 681
Israel 723
Sweden 740
Italy 751
EU-15 826
* Standard population = European population
Direct method - Properties
 Calculate what rates in each group would be if
the groups had the same age distribution or
composition (that of the standard population)
 Results :
1. Actual values of adjusted rates are
meaningless
2. Compare directly adjusted rates to each
other.
Direct method - Properties
 Does require the
1. Age-specific rates for each group.
2. Age distribution of the standard
population.
Indirect method - Properties
 Calculate how many deaths would be expected
in each group if the age-specific rates of the
reference population were applicable
 Results:
1. Actual values of adjusted rates are
meaningless
2. Compare indirectly standardized (adjusted)
rates to the crude rate for the reference
population.
Indirect method - Properties
 Does not require age-specific rates for
each group

Does require:
1. Age distribution of each group
2. Total deaths in each group
3. Age-specific rates for a standard
population.