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Measures of disease frequency (II)

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Calculation of incidence Strategy #2 ANALYSIS BASED ON PERSON-TIME CALCULATION OF PERSON-TIME AND INCIDENCE RATES Example 1Observe 1 st graders, total 500 hours Observe 12 accidents Accident rate (or Accident density):

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Person ID 0 12 4 1 (24) 2 (6) 3 (18) (15) 5 (12) 6 (3) Follow-up time (years) CALCULATION OF PERSON-TIME AND INCIDENCE RATES Example 2 Person ID No. of person-years in Total FU 1 st FU year2 nd FU year 625431625431 3/12=0.25 6/12=0.50 12/12=1.00 0 3/12=0.25 6/12=0.50 12/12=1.00 0.25 1.00 1.25 1.50 2.00 Total4.751.756.50 Step 1: Calculate denominator, i.e. units of time contributed by each individual, and total:

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Step 2: Calculate rate per person-year for the total follow-up period: 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: Person ID No. of person-years in Total FU 1 st FU year2 nd FU year 625431625431 3/12=0.25 6/12=0.50 12/12=1.00 0 3/12=0.25 6/12=0.50 12/12=1.00 0.25 1.00 1.25 1.50 2.00 Total4.751.756.50 Person ID 0 12 4 1 (24) 2 (6) 3 (18) (15) 5 (12) 6 (3) Follow-up time (years)

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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

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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

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Confidence intervals and hypothesis testing Assume that the number of events follow a Poisson distribution (use next pages table). Example: 95% CLs for accidental falls in 1 st 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

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Assigning person-time to time scale categories One time scale, e.g., age: 25 30 35 40 45 50 Age Number of person-years between 35-44 yrs of age: 30 Number of events between 35-44 yrs of age: 3

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1980 1985 1990 8182838486878889 4 3 2 1 Women 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:

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1980 1985 1990 8182838486878889 4 3 2 1 Women

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

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Approximation: Incidence rate based on mid- point population (usually reported as yearly average) Person ID 0 12 4 1 (24) 2 (6) 3 (18) (15) 5 (12) 6 (3) Follow-up time (years) Midpoint population Midpoint population: estimated as the average population over the time period Example:

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Person ID 0 12 4 1 (24) 2 (6) 3 (18) (15) 5 (12) 6 (3) Follow-up time (years) Midpoint population This approach is used when rates are calculated from aggregate data (e.g., vital statistics)

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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

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

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Person ID 0 12 4 1 (24) 2 (6) 3 (18) (15) 5 (12) 6 (3) Follow-up time (years) SUMMARY OF ESTIMATES MethodEstimateValue Life-table Kaplan-Meier q (2 years)0.60 0.64 Person-year Midpoint popn Rate (per year)0.46/py 0.43 per year In actuarial life-table:

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Use of person-time to account for changes in exposure status (Time-dependent exposures) Example: Is menopause a risk factor for myocardial infarction? ID1 2 3 4 5 6 7 8 9 10 No. PY PRE meno No. PY POST meno C C : Myocardial Infarction; C: censored observation. 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 3 4 0 5 6 0 0 1 5 5 3 3 17 18 Year of follow-up Note: Event is assigned to exposure status when it occurs

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PREVALENCE

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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

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ODDS

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Odds The 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.

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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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