Basic Measures in Epidemiology 9232003

1
Basic Measures in Epidemiology9-23-2003

• Wei J. Chen, MD, ScD
• Institute of Epidemiology
• College of Public Health
• National Taiwan University

2
Evaluation of Scientific Hypothesis

• Qualitative vs. quantitative proposition
• Testing of hypotheses predicated on measurement

3
Quantification of the Occurrence of Disease in
the Population

• Incidence time
• Incidence rate
• Incidence proportion
• Prevalence

4
Incidence Time

• Time of the reference events
• calendar time vs. age time
• Incidence time
• the time span from zero time to the time at which
  the event occurs
• undefined if no event

5
Incidence Rate

• 1. Person-time
• At risk
• Time at risk
• Population at risk
• Total person-time at risk over the period
• Incidence rate has units of measure time
• First occurrence vs. subsequent occurrence
• 2. Closed and open population
• For a closed population
• No new members
• Life table method
• Open population
• Individual contribution not began at the same
  time

6

• 3. Steady state
• incidence density (force of morbidity, hazard
  rate)
• 4. Interpretation of an incidence rate
• should provide the appropriate time units
• In a steady state
• the reciprocal of the average time until disease
  onset (or death)

7
Other Types of Rates

• 1. Absolute rate
• Epidemic curve - number of cases per unit time
• 2. Person-miles (not relating to time)

8
CDC MMWR 200150707-710
9
Incidence Proportion Survival Proportion

• Incidence proportion (R)
• Terms
• Cumulative incidence
• Attack rate (traditional)
• An estimate of average risk
• Need the specification of the time period
• Survival proportion (S)
• S 1-R
• Incidence odds R/S
• R ? I?t
• Case fatality rate

10
Product-limit and Exponential Formulae

• Notation
• tk unique event time (k1, 2, 3, 4, 5)
• AK number of events at time tk
• Nk total number of persons at risk at time tk
• Assumptions
• Closed population
• No competing risk
• Ak / Nk is small

11
Interval from primary AIDS diagnosis until death
for a sample of 12 hemophilic patients at most 40
years of age at HIV seroconversion

• What is the survival of the population of
  hemophiliacs diagnosed in the mid- to late 1980s?

12
Product-limit method of estimating S(t) for
hemophiliac patients
13

• Application with competing risk
• exponential formula will fail to hold if
  competing risk occurs
• Nk1 lt Nk - Ak
• Relation of survival proportion to average
  incidence time
• S0,k Nk/N0

14
Direct Standardization

• Directly standardized rate
• Using the age distribution of a standard
  population as the weighting system

15

• Standard error of standardized rate
• Potential weakness
• The a-priori weights wj take no account of the
  precision with which the component rates are
  estimated

16
(No Transcript)
17

• The cumulative rate
• Taking for wj the length of the jth age interval
  rather than the standard age proportion
• Advantages
• Dispense with the arbitrary selection of standard
  population, while can summarize the age-specific
  data
• Are additive for different age ranges
• Easily converted to cumulative risk (P, the
  actuarial probability)

18

• Cumulative risk up to the jth age group

19
Indirect Standardization

• Indirect standardization
• Using the age distribution of the population to
  be standardized as the weighting system
• The standardized mortality ratio (SMR)
• Pros
• Do not need age-specific number of deaths in the
  population under study
• Cons
• Two SMRs cannot be compared directly because
  different weights are used.

20
SMR

• Point estimate
• Used by William H. Farrs (1855) annual report of
  the Registrar General of Great Britain to compare
  different mortality in different occupational
  groups
• Standard error

21
Example

• Chen W.J., Cheng A.T.A., 1997. Incidence of first
  onset alcoholism among Taiwanese aborigines.
  Psychological Medicine 27, 1363-1371

22
(Chen and Cheng, Psychol Med 1997)
23
(No Transcript)
24
(No Transcript)
25
Further Statistical Analysis

• Standard error of an incidence rate
• Under the assumption of Poisson distribution
• n/(py)2, where n is the number of new cases and
  py is the person-years at risk
• A direct method to standardize the incidence
  rates for age
• the world population (25.4, 35.8, and 38.8
  respectively)
• Variance

26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
A New Method in Mapping Disease Incidence Using
Remotely Sensed Data(Tran et al. Am J Epidemiol
2002156662-668)

• Case density
• To estimate the incidence of Q fever in suburban
  areas (Cayenne, French Guiana)
• Cases
• 112 patients reported in 1996-2000
• Population density
• For each population census district, dividing the
  number of cases in the district by the number of
  inhabitants
• Satellite data

30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
Prevalence

• Focuses on disease status or categorical status
• Reference time
• Point prevalence
• Period prevalence, e.g., 1-month, lifetime (by
  recall)
• Prevalence, incidence, and mean duration
• P/N-P the ratio of diseased to nondiseased
  people in the population
• Utility of prevalence in etiologic research
• Prevalence reflects both the incidence rate and
  the probability of severity with disease
• Mainly used in congenital malformation

34
Prevalence of Substance Use by Grade (Kuo et al.
Drug Alcohol Dependence 20026727-39)
35
(No Transcript)
36
Measures of Effect

• Meaning of effect
• The endpoint of a causal mechanism
• The amount of change in a populations disease
  frequency caused by a specific factor
• Absolute effects (difference) vs. relative
  effects (ratio)
• Wish to estimate the effects of exposure on risk
• Observe the association of exposure with risk

37
Notations

• Nsize of a closed cohort
• Exposed cohort
• A1cases occurred during the T1 person- time
• Nonexposed cohort
• A0cases occurred during the T0 person- time
• Rate
• I1 and I0 incidence rate for the exposed and the
  nonexposed, respectively
• Risk (average)
• R1 and R0 incidence proportion for the exposed
  and the nonexposed, respectively
• S11-R1 and S01-R0
• Odds ratio
• R1/S1 / R0/S0

38
Simple Effect Measures

• Relative effect
• Rate ratio
• (I1-I0)/I0I1/I0 1? I1/I0
• Risk ratio
• Odds ratio
• Features
• Depends on the magnitude of the baseline
  occurrence
• Excess relative risk
• (R1-R0)/R0
• Relative risk
• R1/R0

• Absolute effect
• Rate difference
• I1-I0
• Risk difference
• Excess risk

39
Relations among Relative Risk

• Ratios of the risks, ratio, and odds
• Odds ratio ? risk ratio, if both S1and S0 ? 1
• Rate ratio ? risk ratio, if the size of the
  population at risk decline only slightly
• Closeness to null
• Risk ratio is always close to the null than the
  odds ratio
• Risk ratio is always close to the null than the
  rate ratio
• Rate ratio is close to the null than the odds
  ratio
• Thus, risk ratio ? rate ratio ? odds ratio

40
Relation of Stratum-specific Measures to Overall
Measures

• Effect-measure modification (heterogeneity)
• Either absolute or relative effect measure are
  uniform across strata
• For risk differences and ratios
• Value of the entire cohort fall in the midst of
  the stratum-specific measures
• For the odds ratio
• Value of the entire cohort may be closer to the
  null than any of the strata

41
Noncollapsibility

• Odds ratio
• The OR for the total cohort is not a weighted
  average of the stratum-specific OR
• Rate ratio
• Can display noncollapsibility too
• Not a concern unless the outcome is very common
  in at least one stratum-specific exposure group

42
Attributable Fraction

• Two sets of sufficient causes
• CE
• Contain a specific cause (exposure E)
• C
• Represent many different combinations of causal
  components, which do not contain E
• I1 (observed incidence rate among the exposed)
• Reflects the incidence of cases in both sets of
  sufficient causes
• I1 I0 dose not necessarily equal the rate of
  disease with the exposure as a component cause
  (because some cases with E did not go via CE
  pathway)
• Difficult to distinguish these two types of cases

43
I1-I0 Not Necessarily Equal the Rate of Disease
with the Exposure as a Component Cause

• In a hypothetical cohort
• C will be completed before the C
• If the cohort is unexposed
• Every case must be attributed to C
• If the cohort is exposed
• Every case occurs when C is completed (E being
  already present), thus must be attributed to CE
• The incidence rate of cases caused by exposure
• I1 when exposure is present. Thus, AF100
• Not I1-I0

44

• Definitions of fraction incorrectly interpreted
  as the fraction of cases caused by exposure
  (etiological fraction)
• Rate fraction
• (I1 I0) / I1(IR-1)/IR
• Commonly used in public-health projections
• Not generally equal to the fraction of cases in
  which exposure played a role in the disease
  etiology
• Excess fraction
• (A1 A0) / A1,
• A1, A0 case number who are exposed and
  nonexposed, respectively
• (R1 R0) / R1 (A1 A0) / A1 or (RR-1) / RR
• Rate fraction is not equal to the excess fraction
  

45
For Convenience (Rothman Greenland, 1998)

• Attributable fractions
• Including the etiologic, excess, and rate
  fractions
• Also called
• Attributable risk percent
• Attributable risk (??????)
• For use with exposures that have a net causal
  effect
• Preventable fractions
• Interchanging I1 with I0, R1 with R0, A1 with A0,
  and T1 with T0
• (A0-A1)/A0 1-RR the fraction of the caseload
  under nonexposure that could be prevented by
  exposure

46
Etiologic Measures

• F (a fraction)
• The fraction of completions of C was preceded by
  completions of C
• Case with (A1) or without exposure (A0)
• (1 F) of A0 would be unaffected by exposure
• Etiological fraction (or probability of
  causation)
• Cannot be estimated without knowing F

47
Susceptibility to Exposure

• If completion of C and C occur independently
• F (R1 R0) / (1 R0)
• R0 A0/N (unexposed incidence proportion)
• R1 A1/N (exposed incidence proportion)
• Relative difference
• An index of susceptibility to exposure effects
• Depends on the independence assumptions

48
Smoking-Attributable Fraction (SAF)

• Smoking-attributable fraction of each disease
  category
• p0percentage of never smoker
• p1percentage of current smoker
• p2percentage of former smoker
• RR1relative risk for current smoker/never smoker
• RR2relative risk for former smoker/never smoker

49
CDC MMWR 1987 (reprinted in MMWR 199746444-451)
50
CDC MMWR 200251300-303