Nonrandom sequence of slope-intercept estimates in longitudinal gompertzian analysis suggests biological relevance

The significance of intersections in age-specific mortality rate distributions could be attributed to a fundamental statistical relationship between estimates of slope and intercept. A strong negative correlation between estimates of slope and intercept is often observed in simple linear regression problems. The net result is that the family of lines generated by repetitive estimates of slope and intercept in a static experimental situation will tend to intersect at a common point. This statistical relationship between slope and intercept, however, should be random with respect to the time-ordered sequence of slope and intercept estimates. Annual paired slope and intercept estimates derived using the method of longitudinal Gompertzian analysis of age-specific mortality rates for men and women in the United States from 1900 to 1988 were analyzed to determine if they varied randomly. The probability that the observed sequence in these annual paired slope-intercept estimates was random is less than 10(-50) for both men and women. This finding essentially excludes the possibility that intersections in age-specific mortality rate distributions reflect a fundamental statistical relationship between slope and intercept and further suggests biological relevance for the method of longitudinal Gompertzian analysis.