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Measures of disease frequency (II). Calculation of incidence Strategy #2 ANALYSIS BASED ON PERSON-TIME. CALCULATION OF PERSON-TIME AND INCIDENCE RATES Example 1 Observe 1 st graders, total 500 hours Observe 12 accidents Accident rate (or Accident density ):. Person ID. (3). 6. (6).

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calculation of incidence strategy 2 analysis based on person time
Calculation of incidenceStrategy #2ANALYSIS BASED ON PERSON-TIME

CALCULATION OF PERSON-TIME AND INCIDENCE RATES

Example 1 Observe 1st graders, total 500 hours

Observe 12 accidents

Accident rate (or Accident density):

slide3

Person ID

(3)

6

(6)

2

(12)

5

(15)

4

(18)

3

(24)

1

1

2

0

Follow-up time (years)

CALCULATION OF PERSON-TIME AND INCIDENCE RATES

Example 2

Step 1: Calculate denominator, i.e. units of time contributed by each individual, and total:

slide4

Person ID

(3)

6

(6)

2

(12)

5

(15)

4

(18)

3

(24)

1

1

2

0

Follow-up time (years)

It is also possible to calculate the incidence rates per person-years separately for shorter periods during the follow-up:

For year 1:

For year 2:

Step 2: Calculate rate per person-year for the total follow-up period:

notes
Notes:
  • Rates have units (time-1).
  • Proportions (e.g., cumulative incidence) are unitless.
  • As velocity, rate is an instantaneous concept. The choice of time unit used to express it is totally arbitrary. Depending on this choice, the value of the rate can range between 0 and .

E.g.:

0.024 per person-hour = 0.576 per person-day

= 210.2 per person-year

0.46 per person-year = 4.6 per person-decade

notes1
Notes:
  • Rates can be more than 1.0 (100%):
    • 1 person dies exactly after 6 months:
      • No. of person-years: 1 x 0.5 years= 0.5 person-years
slide7
Confidence intervals and hypothesis testingAssume that the number of events follow a Poisson distribution (use next page’s table).

Example:

95% CL’s for accidental falls in 1st graders:

  • For number of events: Lower= 120.517=6.2

Upper= 121.750=21.0

  • For rate: Lower= 6.2/500=0.0124/hr

Upper= 21/500=0.042/hr

assigning person time to time scale categories

Age

50

45

40

35

30

25

Assigning person-time to time scale categories
  • One time scale, e.g., age:

30

Number of person-years between 35-44 yrs of age:

3

Number of events between 35-44 yrs of age:

slide10

81

82

83

84

86

87

88

89

1980

1985

1990

1

2

Women

3

4

When exact entry/event/withdrawal time is not known, it is usually assumed that the (average) contribution to the entry/exit period is half-the length of the period.

Example:

slide11

81

82

83

84

86

87

88

89

1980

1985

1990

1

2

Women

3

4

slide12

Assigning person-time to time scale categories

  • Two time scales (Lexis diagram)

Source: Breslow & Day, 1987.

approximation incidence rate based on mid point population usually reported as yearly average

Midpoint population

Approximation: Incidence rate based on mid-point population(usually reported as “yearly” average)

Midpoint population: estimated as the average population over the time period

Example:

Person ID

(3)

6

(6)

2

(12)

5

(15)

4

(18)

3

(24)

1

1

2

0

Follow-up time (years)

slide14

Midpoint population

Person ID

(3)

6

(6)

2

(12)

5

(15)

4

(18)

3

(24)

1

1

2

0

Follow-up time (years)

This approach is used when rates are calculated from aggregate data

(e.g., vital statistics)

correspondence between individual based and aggregate based incidence rates
Correspondence between individual-based and aggregate-based incidence rates

When withdrawals and events occur uniformly, average (midpoint)-rate per unit time (e.g., yearly rate) and rate per person-time (e.g., per person-year) tend to be the same.

Example: Calculation of mortality rate

12 persons followed for 3 years

slide16

Based on individual data:

Based on midpoint population:

Note:

slide17

Person ID

(3)

6

(6)

2

(12)

5

(15)

4

(18)

3

(24)

1

1

2

0

Follow-up time (years)

In actuarial life-table:

SUMMARY OF ESTIMATES

slide18

No. PY

PRE meno

No. PY

POST meno

7

3

10

6

2

9

5

ID

1

8

4

C

5

0

0

6

1

0

C

5

5

3

3

18

17

: Myocardial Infarction; C: censored observation.

Use of person-time to account for changes in exposure status (Time-dependent exposures)

Example:

Is menopause a risk factor for myocardial infarction?

Year of follow-up

4

3

Note: Event is assigned to exposure status when it occurs

Rates per person-year:

Pre-menopausal = 1/17 = 0.06 (6 per 100 py)

Post-menopausal = 2/18 = 0.11 (11 per 100 py)

Rate ratio = 0.11/0.06 = 1.85

slide20

Prevalence“The number of affected persons present at the population at a specific time divided by the number of persons in the population at that time”Gordis, 2000, p.33

Relation with incidence --- Usual formula:

Prevalence = Incidence x Duration*

P = I x D

* Average duration (survival) after disease onset. It can be shown to be the inverse of case-fatality

slide22

OddsThe ratio of the probabilities of an event to that of the non-event.

Example: The probability of an event (e.g., death, disease, recovery, etc.) is 0.20, and thus the odds is:

That is, for every person with the event, there are 4 persons without the event.

notes about odds and probabilities
Notes about odds and probabilities:
  • Either probabilities or odds may be used to express “frequency”
  • Odds nearly equals probabilities when probability is small (e.g., <0.10). Example:
        • Probability = 0.02
        • Odds = 0.02/0.98 = 0.0204
  • Odds can be calculated in relation to any kind of probability (e.g., prevalence, incidence, case-fatality, etc.).