An overview of a key statistical technique in epidemiology – standardization - is introduced. The process and application of both direct and indirect standardization in improving the validity of comparisons between populations are described.
Standardization of rates by Dr. Basil TumainiBasil Tumaini
Standardization of rates by Dr. Basil Tumaini, presented during the residency at Muhimbili University of Health and Allied Sciences, Epidemiology class
Incidence (Epidemiology lecture)
short ppt to understand incidence. primary incidence rate, secondary incidence rate, incidence rate, examples of incidence, incidence rate related question are discussed in this lec.
An overview of a key statistical technique in epidemiology – standardization - is introduced. The process and application of both direct and indirect standardization in improving the validity of comparisons between populations are described.
Standardization of rates by Dr. Basil TumainiBasil Tumaini
Standardization of rates by Dr. Basil Tumaini, presented during the residency at Muhimbili University of Health and Allied Sciences, Epidemiology class
Incidence (Epidemiology lecture)
short ppt to understand incidence. primary incidence rate, secondary incidence rate, incidence rate, examples of incidence, incidence rate related question are discussed in this lec.
Measurements of morbidity and mortality
At the end of the session, the students shall be able to
List the basic measurements in epidemiology
Select an appropriate tools of measurement
Measure morbidity & mortality
Perform standardization of rates
This PPT discusses
Basics measurements in epidemiology
Basics requirements of measurements
Tools of measurements
Measures of morbidity
Measures of disability
Measures of mortality
Measurements of morbidity and mortality
At the end of the session, the students shall be able to
List the basic measurements in epidemiology
Select an appropriate tools of measurement
Measure morbidity & mortality
Perform standardization of rates
This PPT discusses
Basics measurements in epidemiology
Basics requirements of measurements
Tools of measurements
Measures of morbidity
Measures of disability
Measures of mortality
Report Back from SGO 2024: What’s the Latest in Cervical Cancer?bkling
Are you curious about what’s new in cervical cancer research or unsure what the findings mean? Join Dr. Emily Ko, a gynecologic oncologist at Penn Medicine, to learn about the latest updates from the Society of Gynecologic Oncology (SGO) 2024 Annual Meeting on Women’s Cancer. Dr. Ko will discuss what the research presented at the conference means for you and answer your questions about the new developments.
Prix Galien International 2024 Forum ProgramLevi Shapiro
June 20, 2024, Prix Galien International and Jerusalem Ethics Forum in ROME. Detailed agenda including panels:
- ADVANCES IN CARDIOLOGY: A NEW PARADIGM IS COMING
- WOMEN’S HEALTH: FERTILITY PRESERVATION
- WHAT’S NEW IN THE TREATMENT OF INFECTIOUS,
ONCOLOGICAL AND INFLAMMATORY SKIN DISEASES?
- ARTIFICIAL INTELLIGENCE AND ETHICS
- GENE THERAPY
- BEYOND BORDERS: GLOBAL INITIATIVES FOR DEMOCRATIZING LIFE SCIENCE TECHNOLOGIES AND PROMOTING ACCESS TO HEALTHCARE
- ETHICAL CHALLENGES IN LIFE SCIENCES
- Prix Galien International Awards Ceremony
micro teaching on communication m.sc nursing.pdfAnurag Sharma
Microteaching is a unique model of practice teaching. It is a viable instrument for the. desired change in the teaching behavior or the behavior potential which, in specified types of real. classroom situations, tends to facilitate the achievement of specified types of objectives.
Lung Cancer: Artificial Intelligence, Synergetics, Complex System Analysis, S...Oleg Kshivets
RESULTS: Overall life span (LS) was 2252.1±1742.5 days and cumulative 5-year survival (5YS) reached 73.2%, 10 years – 64.8%, 20 years – 42.5%. 513 LCP lived more than 5 years (LS=3124.6±1525.6 days), 148 LCP – more than 10 years (LS=5054.4±1504.1 days).199 LCP died because of LC (LS=562.7±374.5 days). 5YS of LCP after bi/lobectomies was significantly superior in comparison with LCP after pneumonectomies (78.1% vs.63.7%, P=0.00001 by log-rank test). AT significantly improved 5YS (66.3% vs. 34.8%) (P=0.00000 by log-rank test) only for LCP with N1-2. Cox modeling displayed that 5YS of LCP significantly depended on: phase transition (PT) early-invasive LC in terms of synergetics, PT N0—N12, cell ratio factors (ratio between cancer cells- CC and blood cells subpopulations), G1-3, histology, glucose, AT, blood cell circuit, prothrombin index, heparin tolerance, recalcification time (P=0.000-0.038). Neural networks, genetic algorithm selection and bootstrap simulation revealed relationships between 5YS and PT early-invasive LC (rank=1), PT N0—N12 (rank=2), thrombocytes/CC (3), erythrocytes/CC (4), eosinophils/CC (5), healthy cells/CC (6), lymphocytes/CC (7), segmented neutrophils/CC (8), stick neutrophils/CC (9), monocytes/CC (10); leucocytes/CC (11). Correct prediction of 5YS was 100% by neural networks computing (area under ROC curve=1.0; error=0.0).
CONCLUSIONS: 5YS of LCP after radical procedures significantly depended on: 1) PT early-invasive cancer; 2) PT N0--N12; 3) cell ratio factors; 4) blood cell circuit; 5) biochemical factors; 6) hemostasis system; 7) AT; 8) LC characteristics; 9) LC cell dynamics; 10) surgery type: lobectomy/pneumonectomy; 11) anthropometric data. Optimal diagnosis and treatment strategies for LC are: 1) screening and early detection of LC; 2) availability of experienced thoracic surgeons because of complexity of radical procedures; 3) aggressive en block surgery and adequate lymph node dissection for completeness; 4) precise prediction; 5) adjuvant chemoimmunoradiotherapy for LCP with unfavorable prognosis.
Anti ulcer drugs and their Advance pharmacology ||
Anti-ulcer drugs are medications used to prevent and treat ulcers in the stomach and upper part of the small intestine (duodenal ulcers). These ulcers are often caused by an imbalance between stomach acid and the mucosal lining, which protects the stomach lining.
||Scope: Overview of various classes of anti-ulcer drugs, their mechanisms of action, indications, side effects, and clinical considerations.
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These lecture slides, by Dr Sidra Arshad, offer a quick overview of physiological basis of a normal electrocardiogram.
Learning objectives:
1. Define an electrocardiogram (ECG) and electrocardiography
2. Describe how dipoles generated by the heart produce the waveforms of the ECG
3. Describe the components of a normal electrocardiogram of a typical bipolar leads (limb II)
4. Differentiate between intervals and segments
5. Enlist some common indications for obtaining an ECG
Study Resources:
1. Chapter 11, Guyton and Hall Textbook of Medical Physiology, 14th edition
2. Chapter 9, Human Physiology - From Cells to Systems, Lauralee Sherwood, 9th edition
3. Chapter 29, Ganong’s Review of Medical Physiology, 26th edition
4. Electrocardiogram, StatPearls - https://www.ncbi.nlm.nih.gov/books/NBK549803/
5. ECG in Medical Practice by ABM Abdullah, 4th edition
6. ECG Basics, http://www.nataliescasebook.com/tag/e-c-g-basics
Tom Selleck Health: A Comprehensive Look at the Iconic Actor’s Wellness Journeygreendigital
Tom Selleck, an enduring figure in Hollywood. has captivated audiences for decades with his rugged charm, iconic moustache. and memorable roles in television and film. From his breakout role as Thomas Magnum in Magnum P.I. to his current portrayal of Frank Reagan in Blue Bloods. Selleck's career has spanned over 50 years. But beyond his professional achievements. fans have often been curious about Tom Selleck Health. especially as he has aged in the public eye.
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Introduction
Many have been interested in Tom Selleck health. not only because of his enduring presence on screen but also because of the challenges. and lifestyle choices he has faced and made over the years. This article delves into the various aspects of Tom Selleck health. exploring his fitness regimen, diet, mental health. and the challenges he has encountered as he ages. We'll look at how he maintains his well-being. the health issues he has faced, and his approach to ageing .
Early Life and Career
Childhood and Athletic Beginnings
Tom Selleck was born on January 29, 1945, in Detroit, Michigan, and grew up in Sherman Oaks, California. From an early age, he was involved in sports, particularly basketball. which played a significant role in his physical development. His athletic pursuits continued into college. where he attended the University of Southern California (USC) on a basketball scholarship. This early involvement in sports laid a strong foundation for his physical health and disciplined lifestyle.
Transition to Acting
Selleck's transition from an athlete to an actor came with its physical demands. His first significant role in "Magnum P.I." required him to perform various stunts and maintain a fit appearance. This role, which he played from 1980 to 1988. necessitated a rigorous fitness routine to meet the show's demands. setting the stage for his long-term commitment to health and wellness.
Fitness Regimen
Workout Routine
Tom Selleck health and fitness regimen has evolved. adapting to his changing roles and age. During his "Magnum, P.I." days. Selleck's workouts were intense and focused on building and maintaining muscle mass. His routine included weightlifting, cardiovascular exercises. and specific training for the stunts he performed on the show.
Selleck adjusted his fitness routine as he aged to suit his body's needs. Today, his workouts focus on maintaining flexibility, strength, and cardiovascular health. He incorporates low-impact exercises such as swimming, walking, and light weightlifting. This balanced approach helps him stay fit without putting undue strain on his joints and muscles.
Importance of Flexibility and Mobility
In recent years, Selleck has emphasized the importance of flexibility and mobility in his fitness regimen. Understanding the natural decline in muscle mass and joint flexibility with age. he includes stretching and yoga in his routine. These practices help prevent injuries, improve posture, and maintain mobilit
2. CONTENTS
Introduction
Frequency measures- Rates, ratios and proportions
Mortality rates
Definition
Parts
Types of mortality rates
Relevance of mortality rates in public health
5/20/2016 2
3. CONTENTS
Comparing mortality data
Standardization of mortality rates
Definition
Types
Example
Issues of standardization – advantages and disadvantages
Summary
References
5/20/2016 3
4. Introduction
• Statistics are used to summarize the data collected
describe risk
make comparisons
identify high-risk groups
develop hypotheses about the cause(s) of disease
• Most common – frequency measures
Rates, ratios and proportions
5/20/2016 4
5. Frequency Measures
• Ratios –
compares the occurrence of a variable in two different groups
Eg:
No. of male children attending a immunization clinic
No. of female children attending a immunization clinic
5/20/2016 5
6. Frequency Measures
• Proportions:
A proportion is a ratio which indicates the relation in
magnitude of a part of the whole
Eg:
No. Of male children attending the immunization clinic
Total number of children attending the immunization clinic
5/20/2016 6
7. Frequency Measures
• Rates:
Type of frequency measure used with two-category
variables
Measure the occurrence of an event in a population over
time
Reflect groupings of people based on time, place and
person.
5/20/2016 7
8. Frequency Measures
• Comprises the following – numerator, denominator, time
specification and multiplier.
• Usually expressed as per 1000 or 1, 00,000 according to
convenience or convention to avoid fractions.
5/20/2016 8
9. Frequency Measures
• a ratio to compare two independent groups
• a proportion to compare one group with a larger one to
which it belongs
• a rate to measure an event in a population over time
5/20/2016 9
11. Mortality rates
• Mortality rates measure the frequency of occurrence of death
in a defined population during a specified interval
• Difference in the risk of dying from a disease
• Can serve as measures of disease severity
• Serve as surrogates for incidence rates when the disease being
studied is severe and lethal one.
5/20/2016 11
12. Mortality rates
• Essential components of death rates:
• A population group exposed to the risk of death
• A time period
• The number of deaths occurring in the population during that
time period
5/20/2016 12
13. Types of mortality rates
Crude Death Rate:
Number of deaths in an area in a year per 1000 population
counted at midyear
Total No. of Deaths from all causes in 1 year X 1000
No. of persons in the population at mid year
5/20/2016 13
14. Mortality rates
Specific mortality rates:
• To calculate the rate specifically for a group eg. Age, sex,
ethnic groups
Age specific mortality rate :
No. of deaths among children < 10 years in one year X 1000
No. of children in the population < 10 years of age at mid year
5/20/2016 14
15. Mortality rates
• Eg:
Annual mortality rate from leukemia
in children < 10 years of age
= No. of deaths from leukemia in one year in children < 10 years
No. of children in the population < 10 years at mid year
5/20/2016 15
16. Mortality rates
Case Fatality Rates:
• What percentage of people who have a certain disease die
within a certain time after their disease was diagnosed
• It is the measure of disease severity
No. of individuals dying during a specified
period of time after disease onset or diagnosis X 100
No. of individuals with the specified disease at that particular
time
5/20/2016 16
17. Mortality rates
Proportional Mortality Rate:
• Represents the no. of deaths due to particular cause per 100/
1000 total deaths
• Expressed as percentage
No. of deaths from a specific cause X 100
Total No. of deaths in the population
5/20/2016 17
18. Example:
Assume a population of 1,00,000 of whom, 20 are sick with the
disease X and in that year 18 die from the disease X and total
deaths from all causes is 36.
Crude Death rate = 36 per 1 lakh population
Case fatality rate = 18/20 X 100 = 90%
Proportional mortality rate = 18/36 x 100= 50%
5/20/2016 18
19. Relevance of mortality rates in public health
• Single indicator which can signal a broad range of health
problems
• Clearly an index of the severity of a disease from both clinical
and public health stand points
• Also be used as an index of the risk the disease
5/20/2016 20
20. Relevance of mortality rates in public health
Are good reflection of incidence rates under 2 conditions:
• When the case fatality rate is high
• When the duration of disease is short
Eg: Ca. Pancreas is a highly lethal disease and death generally
occurs within months of diagnosis. Hence mortality rates from
ca pancreas can be taken as the incidence of the disease.
5/20/2016 21
21. Limitations of mortality data:
• Incomplete reporting of deaths
• Lack of accuracy - inaccuracies in the recording of age and
cause of death
• Lack of uniformity
• Choosing a single cause of death
• Diseases with low fatality
5/20/2016 22
22. Comparing mortality in different population
• Important for the evaluation of community health status
• Used to compare two or more populations or one population in
different time periods
• populations may differ in regard to many characteristics & so
comparisons of crude rates can be misleading
• Differences in determinants can distort comparisons between
populations
5/20/2016 23
23. Advantages Disadvantages
Crude Death Rate Actual summary rates
Readily calculable
Since populations vary
in composition (e.g.,
age), differences in
crude rates difficult to
interpret
Specific Rates Homogenous
subgroups
Detailed rates useful
for
epidemiologic and public
health purposes
Cumbersome to
compare many
subgroups of two or
more populations
5/20/2016 24
24. Comparing mortality in different population
Two criteria:
• Rates should relate the number of events to
the population at risk
• Because many health outcomes vary by
age, the effect of the population’s age
distribution must be taken into account
5/20/2016 25
25. Several techniques for adjusting age-specific rates:
• Direct and indirect standardization
• The comparative mortality index
• Equivalent average death rates
• Life table rates
• Yerushalmy’s index
• Cumulative death rates
• Regression analysis & multivariate techniques
Source: WHO: Age standardization of rates
5/20/2016 26
26. Standardization of rates
• Set of techniques used to remove as far as possible the effects
of differences in age or other confounding variables when
comparing two or more variables
• Age and sex are two of the most common variables used for
standardization - called standardized rates
• Involves taking weighted averages of the stratum-specific
outcome measures
5/20/2016 27
27. Standardization of rates
• A standard is a set of weights that is used in taking weighted
average
Eg: if the only stratification variable is age, a standard might be
the amount of person-time or number of persons in a standard
population that fall into each of the age categories
5/20/2016 28
29. Direct standardization
• To compare health outcomes among populations that may have
different age distributions
• Used when age specific rates of disease are known for the
populations being compared.
• A standard population is used in order to eliminate the effects
of any differences in age between the two or more populations
being compared
5/20/2016 30
30. Standard population
Defined as one for which the numbers in each age and sex
group are known.
"Artificial populations" with fictitious age structures
uniform basis for the calculation of comparable measures for
the respective reference population
5/20/2016 31
31. Choice of standard population: considerations
• When several different populations are being compared, a
‘pooled’ standard minimizes the variance of the adjusted rates
• In examining trends, an appropriate standard is one that
reflects the average structure of the population over the time
period
• The standard should be similar to the population of interest
• It should not change frequently (all historic data would need to
be recomputed)
5/20/2016
32
32. One of the following is used for a standard age distribution:
• The distribution of one of the populations being compared
• An independent standard, e.g. national population in an
arbitrarily chosen year
• A distribution constructed by combining the populations, e.g.
by averaging or totalling
5/20/2016 33
33. Steps in calculating age adjusted rate:
Step 1:
A hypothetical “standard population” is created
Step 2:
The age-specific rates of the population whose crude death rate
has to be standardized is applied to the standard population
5/20/2016 34
34. Steps in calculating age adjusted rate:
Step 3: For each age group an expected number of deaths in the
standard population is obtained.
Step 4: The expected number of deaths are added together for all
age groups to get the total expected deaths.
Step 5: Divide the total expected deaths by the total of the
standard population, which yields the standardized or age-
adjusted rate.
5/20/2016 35
37. Example 1:
5/20/2016 38
Population A Population B
No. of deaths 862 1130
Total population 900000 800000
Crude mortality rate
(per 1,00,000
population)
96 142
38. Example 1:
5/20/2016 39
Population A Population B
No. of deaths 862 1130
Total population 900000 800000
Crude mortality rate
(per 1,00,000
population)
96 142
39. Age group Population A Population B
Total
number
No. of
deaths
Death
rates/1
00000
Total
number
No. of
deaths
Death
rates/10
0000
30-49 500000 60 12 400000 30 8
50-69 300000 396 132 200000 400 200
>70 100000 406 406 200000 700 350
Total 900000 862 96 800000 1130 142
5/20/2016 40
41. 5/20/2016 42
Age group Standard
populatio
n
Age
specific
mortality
rates –
Pop- A
Expected
number of
deaths I
Age
specific
mortality
rates-
pop- B
Expected
number of
deaths II
30-49 900000 12 108 8 72
50-69 500000 132 660 200 1000
>70 300000 406 1218 350 1050
Total 1700000 96 1986 142 2122
42. 5/20/2016 43
Age group Standard
populatio
n
Age
specific
mortality
rates –
Pop- A
Expected
number of
deaths I
Age
specific
mortality
rates-
pop- B
Expected
number of
deaths II
30-49 900000 12 108 8 72
50-69 500000 132 660 200 1000
>70 300000 406 1218 350 1050
Total 1700000 96 1986 142 2122
43. • Age adjusted rates:
No. of expected deaths X 100000
Total standard population
• Population A = 1986 /1700000= 117 per 100000 population
• Population B = 2122/1700000= 125 per 100000 population
5/20/2016 44
44. Example 2:
Age Total subjects Cases Controls
No Heavy
smokers
% No Heavy
smokers
%
40-49 500 400 200 50 100 50 50
50-59 500 100 10 10 400 40 10
Total 1000 500 210 42 500 90 18
5/20/2016 45
45. Age adjustments are carried out
• By combining number of subjects in both the age groups
(500+500 = 1000) to create a standard population
• Applying the observed age-specific proportions of heavy
smokers to the same standard population
5/20/2016 46
46. 5/20/2016 47
Age Subjects Expected number of heavy smokers
Cases controls
40-49 500 500X50/ 100 = 250 500X50/100 = 250
50-59 500 500X 10/100 = 50 500X 10/100 = 50
Total 1000 300 300
Standardized rates
Cases= 300X 100/1000 = 30
Controls = 300X 100/1000 =30
47. Direct Standardization
• Direct method requires the knowledge of age specific rates of
the events under comparison for each of the communities as
well as the standard population age structure.
• Sometimes, the above data may not be available or the
population in different age or sex groups or may be too small
resulting in large fluctuating of the age specific rates through
the presence of only a few events
5/20/2016 48
48. Indirect method of standardization
• Requires the knowledge of the age and sex structure of the
population as well as the age and sex specific rates of events
under consideration for the standard population
• Used when the number of deaths for each age specific stratum
is not available
5/20/2016 49
49. Indirect method of standardization
• Steps:
• Step 1: Choose a reference or standard population.
• Step 2: Calculate the observed number of deaths in the
population (s) of interest
• Step 3: Apply the age-specific mortality rates from the chosen
reference population to the population(s) of interest.
5/20/2016 50
50. Indirect method of standardization
• Step 4: Multiply the number of people in each age group of the
population(s) of interest by the age-specific mortality rate in
the comparable age group of the reference population.
• Step 5: Sum the total number of expected deaths for each
population of interest.
• Step 6: Divide the total number of observed deaths of the
population(s) of interest by the expected deaths
5/20/2016 51
51. Standardized Mortality Ratio (SMR):
• The simplest and most useful form of indirect standardization
• Ratio of the total number of deaths that occur in the study
group to the number of deaths that would have been expected
to occur if that study group had experienced the death rates of
the standard population
SMR = Observed Deaths X 100
Expected Deaths
5/20/2016 52
52. 5/20/2016 53
Age groups Population A Observed No of
deaths in each
age group
(obs1)
Population B Observed No of
deaths in each
age group
(obs2)
A1 B1
CDR1 = Obs
1/A1
CDR2 =
Obs 2/B1
Age groups Std Age
specific
death rates
S
Populatio
n A
Expected
deaths in
each group
Population B Expected
deaths in
each group
E1 = S* A1 E2 = S*B1
SMR 1 = Obs 1/ E1 SMR 2 = Obs 2/ E2
53. Example 1
• In a population of 5,34,533 miners in a country, 436 deaths
from tuberculosis occurred in 2000.
• The question of interest is whether this mortality experience
from TB is greater than, less than or about the same as that
expected from the general population
5/20/2016 54
54. 5/20/2016 55
Age (yr) Estimated
population of
miners
Observed deaths
from TB in
miners
Death
rate/1,00,000 for
TB in general
population
20-24 74598 10 12.26
25-29 85077 20 16.12
30-34 80845 22 21.54
35-44 148870 98 33.96
45-54 102649 174 56.82
55-59 42494 112 75.23
Total 534533 436
55. 5/20/2016 56
Age (yr) Estimated
population of
miners
Observed deaths
from TB in
miners
Death
rate/1,00,000 for
TB in general
population
20-24 74598 10 12.26
25-29 85077 20 16.12
30-34 80845 22 21.54
35-44 148870 98 33.96
45-54 102649 174 56.82
55-59 42494 112 75.23
Total 534533 436
Std population
56. 5/20/2016 57
Age (yr) Estimated
population of
miners
Death
rate/1,00,000 for
TB in general
population
Expected deaths
from TB in
miners
20-24 74598 12.26 9.14
25-29 85077 16.12 13.71
30-34 80845 21.54 17.41
35-44 148870 33.96 50.55
45-54 102649 56.82 58.32
55-59 42494 75.23 31.96
Total 534533 181.09
57. SMR = 436 / 181.09 X 100
= 241
• SMR = 100 - observed death is same as expected death.
• SMR < 100 - observed death is less than expected death.
• SMR > 100 - observed death is more than expected death.
5/20/2016 58
58. Example: 2
5/20/2016 59
Age Population Std population –
age & sex specific
death rates
Estimated deaths
Males Females Males Females Males Females
0-4 734 685 58.3 70.2 42.8 48.1
5-14 1494 1311 4.5 5.3 6.7 6.9
15-19 471 352 2.1 4.2 1.0 1.5
20-24 397 399 3.9 5.5 1.5 2.2
25-29 386 362 3.7 5.5 1.4 2.0
30-34 339 327 4.1 6.4 1.4 2.1
35-39 293 239 6.5 6.1 1.9 1.5
Total 4114 3675 56.7 64.3
59. • Index death rate for the population =
total estimated events X 1000
total population
Index rate = 121/ 7789 X 1000
= 15.5
Standardising factor = Overall death rate of standard population /
Index rate
= 23.91 / 15.5
= 1.54
5/20/2016 60
60. • Standardised death rate for the community;
Observed rate X standardizing factor
= 12.7 X 1.54
= 19.6
Crude – 12.7
Standardised rate = 19.6
5/20/2016 61
62. Issues in the use of standardisation:
• Standardised rates are used for the comparison of two or more
populations; they represent a weighted average of the age
specific rates taken from a 'standard population' and are not
actual rates.
• The direct method of standardisation requires that the age-
specific rates for all populations being studied are available
and that a standard population is defined.
5/20/2016 63
63. Issues in the use of standardisation:
• The indirect method of standardisation requires the total
number of cases
• As the choice of a standard population will affect the
comparison between populations, it should always be stated
clearly which standard population has been applied.
5/20/2016 64
64. Summary
• Most common statistical measures – Rates, ratios, proportions
• Mortality rates – relevance in public health
• Crude death rates are easy to calculate but distort the
comparisons between population
• Hence standardization is used to enable comparisons
• 2 types – direct and indirect
5/20/2016 65
67. References
• Gordis L. Epidemiology. 4thed. Philadelphia (USA): Elsevier
Saunders; 2009. p.
• RothmanKJ, Greenlands S, lash TL. Modern Epidemiology. 3rd ed.
Philadelphia (USA): Lippincot Williams and Wilkins. 2008. P.
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