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Table 1 Numerical example: expected person-year contributions and calculation procedure for a single individual

From: Estimating the standardized incidence ratio (SIR) with incomplete follow-up data

   Rates (per 1000) E(pyj)    Sensitivity analysis
E(pyj)
Year (j) Age (i) μij νij λij   Var(pyj) (fixed rates) Var(pyj) (variable rates) Factor for μij 0.5 and νij 1.5
1990 40 2 13 0.5 0.992 0.004 0.01725 0.9925 0.9775
1991 41 2 13 0.5 0.978 0.019 0.03384 0.9851 0.9558
1992 42 2 13 0.5 0.963 0.035 0.04979 0.9777 0.9449
1993 43 2 13 0.5 0.949 0.050 0.06513 0.9704 0.9238
1994 44 2 13 0.5 0.934 0.066 0.07988 0.9632 0.9031
1995 45 3 10 0.8 0.921 0.078 0.09252 0.9569 0.8840
1996 46 3 10 0.8 0.908 0.087 0.1047 0.9507 0.8670
1997 47 3 10 0.8 0.896 0.097 0.11655 0.9446 0.8500
1998 48 3 10 0.8 0.884 0.106 0.12798 0.9385 0.8335
1999 49 3 10 0.8 0.872 0.114 0.13903 0.9324 0.8173
2000 50 5 7 1.2 0.860 0.122 0.14909 0.9268 0.8008
2001 51 5 7 1.2 0.849 0.129 0.15884 0.9213 0.7854
2002 52 5 7 1.2 0.838 0.136 0.16830 0.9157 0.7700
2003 53 5 7 1.2 0.827 0.143 0.17748 0.9103 0.7552
2004 54 5 7 1.2 0.816 0.149 0.18638 0.9048 0.7404
Total total     13.487 1.335 1.677 14.190 12.830
  1. Date of birth:January 1st, 1950; Begin of follow-up: January 1st, 1990;
  2. End of follow-up:December 31st, 2004
  3. μij - mortality rate (all causes other than disease of interest), age i, year j
  4. νij - migration rate, age i, year j
  5. λij - incidence rate (disease of interest), age i, year j