Download Table 6-11. Calculating a Life Table

HSS4303B – Introduction to Epidemiology
Feb 1, 2010 – Life Tables and Stuff
Women’s Health Research Day
• March 24, 2010, from 10AM to 1PM
• TBT 083 (Senate Room)
• Email [email protected] to register
• There will be poster presentations
Midterm Exam
• Poll closed this morning with 90 respondents
– I’d decided beforehand that it would take at least
an 80% majority to move the midterm
• Feb 11 = 18 respondents
• Feb 25 = 72 respondents (80%)
• Therefore, the midterm is moved to Feb 25
Life Table Analysis
• “A summarizing technique used to describe
the pattern of mortality and survival in
populations.” -John Last
– First used in 1693 by Edmund Halley
– In 1815 in UK, first accurate tables published
Two Types of Life Tables
• “Current Life Table”
– Summary of mortality of pop over short period (13 years)
– Data refers to the middle of time interval
• “Cohort (or Generation) Life Table”
– Actual survival experience of a cohort born about
the same time
Life tables for Canadians 2004
90
80
70
Years
60
50
40
30
20
10
0
<1
5-9
1519
2529
3539
4549
5559
Age groups
Both
M ales
Females
6569
7579
8589
95100
Calculating Life Expectancy
• Age-specific death rates are calculated for
each group of interest (typically age and
gender defined)
• Life table constructed from which one can
determine the probability of surviving to any
given age
• Total life expectancy is computed by
integrating the survival curve from 0 to infinity
– Positive infinity is also called “omega”
Life Expectancy Curve Is Estimated
by “Gompertz” Function
Assumptions in using life table
• Two assumptions need to be considered:
– That there is no change in the effectiveness of treatment
or diagnosis over the period of time
• This factor is a concern if the period is long and if there has been
substantial changes in treatment or method of diagnosis
– Survival experience of the people who are lost to follow-up
is the same as the experience of those who were followed
• The real reason of loss to follow-up is never known
• Life table is used not only for death as an endpoint
but also for effectiveness of treatment or
development of disease
Notation
x
Time interval
lX
Number alive at beginning of interval
dX
Number who have died in the interval
wX
Number withdrawn or lost to follow-up in interval
l'X
Effective number exposed = lX – (0.5) wX
qX
Effective proportion who died during interval = dX/l'X
pX
Effective proportion who did not die during interval = 1-qX
PX
Cumulative proportion who survived from the very beginning =
(PX-1 )(pX)
Remember These Data?
Table 6-3. Analysis of Survival in Patients Treated from 2000 to 2004 and Followed to 2005 (None Lost to
Follow-up): I
Number Alive at End of Year
Year of
Treatment
No. of Patients
Treated
1st
Year
2nd
Year
3rd
Year
4th
Year
5th
Year
2000
84
44
21
13
10
8
2001
62
31
14
10
6
2002
93
50
20
13
2003
60
29
16
2004
76
43
Totals
375
197
71
36
16
8
Life table calculations
Table 6-10. Rearrangement of Data in Standard Format for Life Table Calculations
(1) Interval Since Beginning
Treatment
(2) Alive at Beginning of
Interval
(3) Died During
Interval
(4) Withdrew During
Interval
lX
dX
wX
1st year
375
178
0
2nd year
197
83
43
3rd year
71
19
16
4th year
36
7
13
5th year
16
2
6
x
Calculations for life-table
Table 6-11. Calculating a Life Table
(1)
Interval
Since
Beginning
Treatment
x
(2)
Alive at
Beginning
of Interval
(3)
Died
During
Interval
(4)
Withdrew
During
Interval
(5)
Effective
Number
Exposed to
Risk of Dying
During
Interval:
Col (2) –
1/2Col (4)
(6)
Proportion Who
Died During
Interval:
Col (3) / Col (5)
(7)
Proportion
Who Did Not
Die During
Interval: 1 Col (6)
(8) Cumulative
Proportion
Who Survived
From
Enrollment to
End of
Interval:
Cumulative
Survival
pX
PX
lX
dX
wX
l'X
qX
1st year
375
178
0
375.0
.475
2nd year
197
83
43
175.5
.527
.277
3rd year
71
19
16
63.0
.698
.193
4th year
36
7
13
.237
.763
.147
5th year
16
2
6
.154
.846
.124
.525
Review of Kaplan-Meier method
• Fixed periods or intervals for observation of
events are not used rather the exact point in
time when each death occurred is used
• The number of persons who died at that point
is used as the numerator and the number
alive up to that point (including those who
died at that point) is used as the denominator
• Each event terminates an interval and starts
another interval
Events in Kaplan-Meier method
Calculating survival using Kaplan-Meier method
Table 6-12. Calculating Survival Using the Kaplan-Meier Method*
(1)
Times to
Deaths From
Starting
Treatment
(mo)
(2)
No. Alive at
Each Time
(3)
No. Who
Died at Each
Time
(4)
Proportion Who Died
at That Time:
(5)
Proportion
Who Survived
at That Time:
1 - Col (4)
(6)
Cumulative Proportion
Who Survived to That
Time: Cumulative
Survival
4
6
1
.167
.833
.833
10
4
1
.250
.750
.625
14
3
1
.333
.667
.417
24
1
1
1.000
.000
.000
This is a much simpler example than the one from last time. How?
Kaplan-Meier plot of survival
Uses of Kaplan-Meier plots
• Rosenhek and colleagues in 2000 studied aortic
stenosis in asymptomatic patients
– Should patients with asymptomatic disease have their
aortic valves replaced
– Compared survival among aortic stenosis patients with
general population (age and sex matched)
– Moderate and severe calcification of the aortic valve was a
significant predictor of subsequent cardiac events and
poor prognosis
– Event free survival was much worse in patients with
moderate or severe valve calcification
Kaplan-Meier survival in asymptomatic patients
compared with general population
Consider this abstract
Feinstein et al, New England Journal of Medicine. 312(25):1604-8, 1985 Jun 20
•
•
•
We found that a cohort of patients with lung cancer first treated in 1977
had higher six-month survival rates for the total group and for subgroups
in each of the three main TNM stages (tumor, nodes, and metastases)
than a cohort treated between 1953 and 1964 at the same institutions.
The more recent cohort, however, had undergone many new diagnostic
imaging procedures. According to the "old" diagnostic data for both
cohorts, the recent cohort had a prognostically favorable "zero-time shift."
In addition, by demonstrating metastases that had formerly been silent
and unidentified, the new technological data resulted in a stage
migration.
–
•
•
Many patients who previously would have been classified in a "good" stage were assigned to a
"bad" stage.
Because the prognosis of those who migrated, although worse than that
for other members of the good-stage group, was better than that for other
members of the bad-stage group, survival rates rose in each group
without any change in individual outcomes.
When classified according to symptom stages that would be unaltered by
changes in diagnostic techniques, the two cohorts had similar survival
rates.
Summary:
• Feinstein et al compared survival in patients with lung cancer
first treated in 1977 with a cohort of patients treated from
1953-1964
• Six months survival was higher in the later group (adjusted for
disease stage)
• The apparent improvement in survival was due in part to
stage migration
– “Stage migration” is a term used to describe the gradual and
apparently continuing tendency for patients to be diagnosed
with much earlier clinical and pathological stages of their disease than
was historically the case
• Categorization of patients as good or bad stage depends on
the diagnostic technology, improvement in technology could
help in better diagnosis even though there was no change in
treatments.
Will Rogers Phenomenon
• “When the Okies left Oklahoma
and moved to California, they
raised the average intelligence
level in both states.” –Will Rogers
• In medical stage migration,
improved detection of illness
leads to the movement of people
from the set of healthy people to
the set of unhealthy people
November 4, 1879 – August 15, 1935
Impact of improved diagnosis
Impact of improved diagnosis
Impact of improved diagnosis of micrometastases on
age-specific case-fatality
Median survival time
• Median survival is defined as the length of time that
half of the study population survives
• Median survival time is a measure of prognosis
• Median survival is a better index than mean survival
because:
– It is less affected by outliers
– It can be calculated with only half the population whereas
in mean the whole population need to included in the
calculation
Review: Relative survival rate
• Relative survival for any group with a disease
is the comparative survival to a similar group
without the disease
• Relative survival rate is defined as the ratio of
the observed survival to the expected survival
Observed survival in people with disease
Relative survival rate = -----------------------------------------------------Expected survival if disease were absent
The relative survival rate shows
whether the disease shortens life.
Gives necessary adjustment for expected mortality
from causes other than the disease under study
without requiring information on causes of death
Five-year observed and relative survival rates
Table 6-13. Five-Year Observed and Relative Survival Rates (%) by Age for Colon and Rectum Cancer:
SEER Program (Surveillance, Epidemiology, and End Results Study), 1990-1998
Age
(yr)
Observed Rate (%) Relative
Rate (%)
Relative Rate
(%)
<50
60.4
61.5
50-64
59.4
63.7
65-74
53.7
63.8
>75
35.8
58.7
From Edwards BK, Howe HL, Ries LAG, et al: Annual report to the nation on the status of cancer, 1973-1999, featuring implications of age and
aging on U.S. cancer burden. Cancer 94:2766-2792, 2002.
How do you interpret this?
Change of Topic…
Dynamics of disease transmission
• Disease results from interaction between
–
–
–
–
_______ (person)
_______ (bacterium, virus)
____________ (contaminated water)
____________ (mosquitoes)
HSS4303: Introduction to epidemiology
Factors associated with increased risk
Table 2-1. Factors That May Be Associated With Increased Risk of Human Disease
Host Characteristics
Types of Agents and Examples
Environmental Factors
Age
Biologic (bacteria, viruses)
Temperature
Sex
Chemical (poison, alcohol, smoke)
Humidity
Race
Physical (trauma, radiation, fire)
Altitude
Religion
Nutritional (lack or excess)
Crowding
Customs
Housing
Occupation
Neighbourhood
Genetic profile
Water
Marital status
Milk
Family background
Food
Previous diseases
Radiation
Immune status
Air pollution
Noise
HSS4303: Introduction to epidemiology
Infectious Disease
• An infectious disease is a clinically evident
illness resulting from the presence of
pathogenic microbial agents
•Viruses
•Bacteria
•Protozoans
•Fungi
•Multicellular parasites
•Prions
Infection
• Infection is not the same thing as infectious
disease
• An infection may not cause symptoms or
impair function
Infectivity
• The ability of a pathogen to establish an
infection
• Positively correlated with virulence
• What is virulence?
The ability of a pathogen to cause disease
How Do Pathogens Cause Disease?
•
•
•
•
•
Adhesion
– By binding to the cell, normal processes are affected
Colonization
– Spreading stuff to make themselves at home (and thus making us sick)
Invasion
– Physically destroying tissue to gain entry
Immune response inhibitors
– Eg. Release proteins that bind to antibodies
Toxins
– Eg. Food poisoning
Vectors and Fomites
• Vector
– Living thing that carries an infection
– Typically arthropods, but not exclusively
• Fomite
– Inanimate object capable of carrying an infection
Eg, clothing, money
Locus
• In transmission, a locus is the point on the
body where a pathogen enters
– In droplet contact and other airborne transmission it is
generally the respiratory system
– In direct physical and indirect contact it is generally
through a wound in the skin or through a mucous
membrane
– In fecal-oral transmission, it is through the mouth.
– In vector borne transmission, it is at the bite or sting of the
vector.
Modes of transmission of disease
Figure 2-2 Droplet dispersal following a
violent sneeze. (Reprinted with
permission from Jennison MW:
Aerobiology, No. 17, 1947, p 102.
Copyright 1947 American Association for
the Advancement of Science.)
Figure 2-3 Body surfaces as sites of microbial
infection and shedding. (From Mims CA, Dimmock
NJ, Nash A, et al: Mims' Pathogenesis of Infectious
Disease, ed 4. London, Academic Press, 1995, p
10.)
HSS4303: Introduction to epidemiology
Vertical Transmission
• Parent to offspring
– Typically a mother gives a disease to child through
breastfeeding or other body fluid
– Usually during perinatal period
Eg, HIV or Hep
Horizontal Transmission
• from one individual to another in the same
generation (peers in the same age group)
• Direct contact or indirect contact (eg, vectors)
• One can say that “infectivity” is a pathogen’s
capacity for “horizontal transmission”
– How frequently it spreads among hosts
Eg, common cold
Droplet Contact
• Also known as the respiratory route, it is a typical mode of
transmission among many infectious agents. If an infected
person coughs or sneezes on another person the
microorganisms, suspended in warm, moist droplets, may
enter the body through the nose, mouth or eye surfaces.
•Bacterial Meningitis
•Chickenpox
•Common cold
•Influenza
•Mumps
•Strep throat
•Tuberculosis
•Measles
•Rubella
•Whooping cough
Viral Droplet Nuclei Transmission
• When viruses are shed by an infected person through
coughing or sneezing into the air, the mucus coating on the
virus starts to evaporate. Once this mucus shell evaporates
the remaining viron is called a droplet nucleus or quantum(a)
– The lower the humidity, the quicker the mucus shell evaporates thus
allowing the droplet nuclei to stay airborne and not drop to the groun
– “Wells-Riley” equation predicts the infection rates of persons who
shed quanta within a building and is used to calculate indoor infection
outbreaks within buildings
•Common cold
•Influenza A & B
•Mumps
•Measles
•Rubella
•SARS
Fecal-Oral Transmission
• Eating sh*t
– Direct contact is rare
– More common is indirect route: contaminated
food, water, poor handwashing, sewage overflow
•Cholera
•Hepatitis A
•Polio
•Rotavirus
•Salmonella
Sexual Transmission
• During sexual activity with another person,
including vaginal or anal sex
•HIV/AIDS
•Chlamydia
•Genital warts
•Gonorrhea
•Hepatitis B
•Syphilis
Oral Sex Transmission
• Contact between mouth and genitalia
•Herpes simplex 1
•Some STDS
•Maybe HIV
Direct Contact
• Diseases that can be transmitted by direct
contact are called contagious
– Contagious is not the same as infectious; although
all contagious diseases are infectious, not all
infectious diseases are contagious
– Common outbreaks in schools
•Athlete’s foot
•Warts
Iatrogenic Transmission
• Transmission due to medical procedures, such
as injection or transplantation of infected
material.
•CJD
•MRSA
Transmission of disease
• _________________
– When a disease is transmitted from person to
person by direct contact
• __________________
– When a disease is transmitted through a common
vehicle such as a contaminant or a vector
HSS4303: Introduction to epidemiology
Homework
• Lots of good ones in the textbook