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Dr. N. Birkett, Department of Epidemiology & Community Medicine, University of Ottawa

EPI 5344: Survival Analysis in Epidemiology Epi Methods: why does ID involve person-time? March 13, 2014. Dr. N. Birkett, Department of Epidemiology & Community Medicine, University of Ottawa. The Issue (1). Epidemiology focuses on: Incidence Proportion or Cumulative Incidence (CI)

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Dr. N. Birkett, Department of Epidemiology & Community Medicine, University of Ottawa

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  1. EPI 5344:Survival Analysis in EpidemiologyEpi Methods: why does ID involve person-time?March 13, 2014 Dr. N. Birkett, Department of Epidemiology & Community Medicine, University of Ottawa

  2. The Issue (1) • Epidemiology focuses on: • Incidence Proportion or Cumulative Incidence (CI) • Incidence Density or Incidence Rate (ID). • Standard formulae are:

  3. The Issue (2) • How do these measures relate to survival analysis? • Why does ID involve person-time?

  4. Incidence Density (rate) • Rate of getting disease. • A number with units (time-1) • Ranges from 0  ∞ • Often measured from time ‘0’ (recruitment) • Can be measured for any time interval • Separate ID’s for each year of follow-up • If the time units get smaller, we approach the ‘instantaneous ID’

  5. Incidence Density (rate) • Rate of getting disease (outcome) at time ‘t’ given (conditional on) on having survived to time ‘t’ • Instantaneous ID is the same as the hazard • Average ID is more common in epidemiology

  6. Epidemiology formulae ignore ID variability over time and compute average ID (ID`) • Actuarial method (density method) lets each interval have a different ID • Linked to piecewise exponential model

  7. Why does ID relate to person-time? • Let’s look at a simple situation (assumption): • No losses (i.e. no censoring) • A constant ID over time (I) • Then, we have:

  8. Why does ID relate to person-time?

  9. So, how can we figure out the area under S(t)? • Let’s look at the next page

  10. Graph of S(t) Actually a curve but we assume it’s a straight line Area under S(t) from 0 to 1

  11. In general, area under S(t) from ‘0’ to ‘t’ is given by: How does this help? In the formula we derived for ID, multiply top and bottom by ‘N’ (the initial # of people at risk) Now, CI(t) * N = # new cases by time ‘t’.

  12. This is the standard Epidemiology definition of ID

  13. Person-time approach to ID assumes that ID (hazard) is constant • Can be seen as estimating an average ID • BUT, constant hazard gives the exponential survival model which does not reflect real-world S(t)’s.

  14. Why does epidemiology ignore this and use a constant ID? • Lack of data • Lack of measurement precision • Tradition • ”teaching” • Old fashioned methods or learning by rote • What can we do? • Piece-wise constant hazard approach is better • Density methods • Survival methods

  15. Density method (1) GOAL: to estimate CI for outcome by year ‘t*’ • Select a time interval (usually 1 year) • Divide follow-up time into intervals of this size • Within each interval, compute the ID of surviving the interval given you are disease-free at start:

  16. Density method (2) • Compute: • Then, we have:

  17. Density method (3) • Very similar to the methods based on H(t). • When h(t) is piecewise constant, we have:

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