Occurrence and timing of events depend on

1
Occurrence and timingofeventsdependon
exposure
Risk depends on exposure
Exposure to the risk of an event
2
Age at first marriage and age at change in
education Person-years file
Educ 0 not in school full-time 1
secondary eduction 2 postsecondary
education Marriage MS 0 not married
1 married
All age periods prior to marriage and age at
marriage are included.
Source Yamaguchi, 1991, p. 22
3
Exposure examples

• To risk of conception
• To risk of infection (e.g. malaria, HIV)
• To marriage
• To risk of divorce
• To risk of dying
• Health risk

4
Exposure to risk

• Whenever an event or act gives rise to gain or
  loss that cannot be predicted
• Risk of the unexpected

Williams et al., 1995, Risk management and
insurance, McGraw-Hill, New York, p. 16
5
Exposure analysis

• Being exposed or not
• If exposed, level of exposure (intensity)
• Factors affecting level of exposure
• (e.g. age, contacts, etc.)
• Interventions may affect level of exposure
• Contraceptives and sterilisation are used to
  prevent unwanted pregnancies
• Breastfeeding prolongs postpartum amenorrhoea
  (PPA)
• Immunisation prevents (reduces) risk of
  infectious disease
• Lifestyle reduces/increases risk of lung cancer
• Which mechanism(s) determines level of exposure
• e.g. Breastfeeding stimulates production of
  prolactin hormone, which inhibits ovulation

Hobcraft and Little, ??
6
Risk levels and differentialsRisk
measuresPrediction of risk levelsDeterminants
of differential risk levels
Risk potential variation in outcome
7
(Objective) risk measures

• Count Number of events during given period
  (observation window)
• Count data
• Probability probability of an outcome
  proportion of risk set experiencing a given
  outcome (event) at least once
• Basis Risk set
• Risk set all persons at risk at given point in
  time.
• Rate number of events per time unit of exposure
  (person-time)
• Basis duration of exposure (duration at risk)
• Rate (general) change in one quantity per unit
  change in another quantity (usually time other
  possible measures include space, miles travelled)

8
Risk measures

• Difference of probabilities p1 - p2 (risk
  difference)
• Relative risk ratio of probabilities (focus
  risk factor)
• prob. of event in presence of risk factor/ prob.
  of event in absence of risk factor (control
  group reference category) p1 / p2
• Odds odds on an outcome ratio of favourable
  outcomes to unfavourable outcomes. Chance of one
  outcome rather than another p1 / (1-p1)
• The odds are what matter when placing a bet on a
  given outcome, i.e. when something is at stake.
  Odds reflect the degree of belief in a given
  outcome.

Relation odds and relative risk Agresti, 1996,
p. 25
9
Risk measures

• Odds two categories (binary data)

In regression analysis, ? is linear predictor ?
?0 ?1 x1 ?2 x2
Parameters of logistic regression ln(odds) and
ln(odds ratio)
10
Risk measures

• Odds multiple categories (polytomous data)

Select category 3 as reference category
Parameters of logistic regression ln(odds) and
ln(odds ratio)
11
Risk measures

• Odds ratio ratio of odds (focus risk
  indicator, covariate)
• odds in target group / odds in control group
  reference category ratio of favourable
  outcomes in target group over ratio in control
  group. The odds ratio measures the belief in a
  given outcome in two different populations or
  under two different conditions. If the odds ratio
  is one, the two populations or conditions are
  similar.
• Target group k1 Control group k2

Parameters of logistic regression ln(odds) and
ln(odds ratio)
12
Risk measures in epidemiology

• Prevalence proportion (refers to status)
• Incidence rate rate at which events (new cases)
  occur over a defined time period events per
  person-time. Incidence rate is also referred to
  as incidence density (e.g. Young, 1998, p. 25
  Goldhaber and Fireman, 1991).
• Case-fatality ratio proportion of sick people
  who die of a disease (measure of severity of
  disease). Is not a rate!! (Young, 1998, p. 27)

Being
Becoming
Confusion Birth defect prevalence proportion of
live births having defects Birth defect
incidence rate of development of defects among
all embryos over the period of gestation (Young,
1998, p. 48)
13
Risk measures in epidemiology

• Attributable risk (among the exposed) proportion
  of events (diseases) attributable to being
  exposed p1-p2/p1 (since non-exposed can also
  develop disease)

14
(Subjective) risk measures

• Subjective probability degree of belief about
  the outcome of a trial or process, or about the
  future. It is the perception of the probability
  of an outcome or event. It is highly dependent
  on judgment (Keynes, 1912, A treatise on
  probability, Macmillan, London). Keynes regarded
  probability as a subjective concept our judgment
  (intuition, gut feeling) about the likelihood of
  the outcome.
• See also Value-expectancy theory attractiveness
  of an alternative (option) depends on the
  subjective probability of an outcome and the
  value or utility of the outcome (Fishbein and
  Ajzen, 1975).

15
In case of multiple categories,select a
reference category
Reference category is coded 0 Various coding
schemes!
16
Coding schemes

• Contrast coding one category is reference
  category (simple contrast coding dummy coding).
  Model parameters are deviations from reference
  category.
• Indicator variable coding indicator (0,1)
  variables
• Cornered effect coding (Wrigley, 1985, pp.
  132-136) 0,1)
• Effect coding the mean is the reference. Model
  parameters are deviations from the mean.
• Centred effect coding (Wrigley, 1985, pp.
  132-136) -1,1
• Other types of coding see e.g. SPSS Advanced
  Statistics, Appendix A

Vermunt, 1997, p. 10
17
Coding schemes

• Categories are coded
• Binary 0,1, -1,1, 1,2
• Multiple 0,1,2,3,.., set of binary
• e.g. 3 categories

18
Coding schemes
Important
Selection of reference category depends on
research question
19
Example
20
Descriptive statistics
21
Reference categories Late ?20, Males Odds on
leaving home early (rather than late)
Logit - Males 74/178 0.416
-0.877 - Females
135/143 0.944
-0.058 Odds ratio (?) 0.944/0.416 2.27
0.820 (if we bet
that a person leaves home early, we should bet on
females they are the winners - leave home
early) Var(?) ?2 1/1351/1431/741/178
0.1725 ln ? 0.819 Var(ln ? )
1/1351/1431/741/178 0.0335
Selvin, 1991, p. 345
22
Leaving home
23
Relation probabilities, odds and logit
24
Risk analysis modelsPrediction of risk levels
and differentials risk levelsProbability models
and regression models

• Counts ? Poisson r.v. ? Poisson distribution ?
  Poisson regression / log-linear model
• Probabilities ? binomial and multinomial r.v. ?
  binomial and multinomial distribution ? logistic
  regression / logit model
• (parameter p, probability of occurrence, is also
  called risk e.g. Clayton and Hills, 1993, p. 7)
• Rates ? Occurrences/exposure ? Poisson r.v. ?
  log-rate model