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Measures of disease frequency (II)

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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Measures of disease frequency (II)

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  1. Measures of disease frequency (II)

  2. 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):

  3. 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:

  4. 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:

  5. 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

  6. 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

  7. 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

  8. 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:

  9. 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:

  10. 81 82 83 84 86 87 88 89 1980 1985 1990 1 2 Women 3 4

  11. Assigning person-time to time scale categories • Two time scales (Lexis diagram) Source: Breslow & Day, 1987.

  12. 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)

  13. 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)

  14. 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

  15. Based on individual data: Based on midpoint population: Note:

  16. 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

  17. 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

  18. PREVALENCE

  19. 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

  20. ODDS

  21. 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.

  22. 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.).

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