title: Progression of mean age and mean expected mortality rate by duration of follow up in cohorts with a wide range of age.
abstract: BACKGROUND
  [corrected] In a previous article, it was demonstrated that use of mean age to enter a life table to obtain a mean expected mortality rate of a cohort with a wide age range invariably underestimates the true mean expected mortality rate, q'. This is due to the bias introduced by the average 10% annual increase in q' in the approximate age range of 45 to 90 years (rates in the population life table, ages 0-109 years were analyzed to illustrate this). The magnitude of the error was demonstrated in various examples. All of these data were limited to the first year of FU (follow-up) duration. In this article, we analyze progression of mean age, x, and mean expected mortality rate, q', with FU duration in cohorts with all ages combined. When the age range is only 5 or 10 years, the mean age of the survivors does increase very nearly a full year with each year of FU duration.
  
  
  RESULTS
  We utilized a 1973-1987 cohort in the SEER database for prostate cancer, all ages and all stages combined, and from this derived a comparative mortality table. We first demonstrated the difference between cumulative expected survival rate, P', as calculated in the SEER database, and the actuarial calculation of P'. The SEER method results in a 5% underestimate of P' vs the actual P' at a duration 14-15 years, and a corresponding overestimate of Q' and q'. Second, we found that the annual mean age of the survivors in the prostate cancer cohort increased from 72.4 years at entry to 80.2 years in a FU of 15 years. Mean expected q' increased from 66.7 per 1000 in the first year to 93.1 per 1000 in the 15th year. The geometric mean annual increase in mean q' was only 2.4% per year, instead of the approximate 10% seen in the life table from about age 45 to 90. Progression patterns by duration for mean age and mean q' are very different in female thyroid cancer, all ages and all stages combined, again for a 1973-1987 cohort. In thyroid cancer, females outnumber males; in both sexes, the proportion of younger patients, under age 45, is much greater than in typical cancer sites, such as prostate cancer. In female thyroid cancer, both mean age and mean q' actually decreased from the mean values at entry for 5 years or more. At entry, mean age was 43.9 years, and mean q' was 8.2 per 1000. These values decreased to 43.5 years and 6.8 per 1000, respectively, at duration 1-2 years, then leveled off and began a gradual increase. At duration 14-15 years, mean age was 53.7 years, and mean q' was 11.4 deaths per 1000 per year.
  
  
  CONCLUSIONS
  Progression of mean q' is erratic and unpredictable, because annual mean age of survivors is highly dependent on the proportion of younger patients in the cohort being followed. If the proportion of patients under age 45 years is high enough, both mean age and mean q' may show an initial decrease from the values found in the year of entry, because, even though each survivor is a year older, the progression of mean age is so heavily biased by the slower progression of q' at the younger than at the older ages. However, with the SEER database, if annual expected survival rates are converted to annual expected mortality rates, the derivation of mean expected mortality rate, q' is accurate, regardless of the width of the age range in the cohort selected and being analyzed. The user of the SEER database is warned that the expected cumulative survival rate, P', is derived in the SEER survival tables on the basis of the first-year age distribution, not on the basis of the changing age distribution that is actuarially observed.
authors.forename: Richard B
authors.initials: RB
authors.lastname: Singer
mesh_terms: D000293:Adolescent; D000328:Adult; D000367:Age Factors; D000368:Aged; D015982:Bias; D002648:Child; D002675:Child, Preschool; D015331:Cohort Studies; D005500:Follow-Up Studies; D006801:Humans; D007223:Infant; D007231:Infant, Newborn; D015993:Life Tables; D008297:Male; D008875:Middle Aged; D009026:Mortality / Q000639:trends*; D011471:Prostatic Neoplasms / Q000401:mortality; D018426:SEER Program; D014481:United States / Q000453:epidemiology