Plane inclinations: A critique of hypothesis and model choice in Barbi et al

Abstract

This study highlights how the mortality plateau in Barbi and colleagues can be generated by low-frequency, randomly distributed age-misreporting errors. Furthermore, sensitivity of the late-life mortality plateau in Barbi and colleagues to the particular age range selected for regression is illustrated. Collectively, the simulation of age-misreporting errors in late-life human mortality data and a less-specific model choice than that of Barbi and colleagues highlight a clear alternative hypothesis to explanations based on evolution, the cessation of ageing, and population heterogeneity.

Fig 1. Generation of late-life mortality plateau by random errors.

The introduction of symmetrically distributed age-coding errors (a) into the log-linear model (orange line) fit as a 'best estimate’ to the 1904 cohort data in Barbi and colleagues [1] generates late-life mortality patterns (green and pink lines) similar to observed data (blue points) [4]. Residuals from observed data (b) illustrate the skewed residuals of this model compared with more representative regressions of hazard rates, such as the ages 50–80 model shown (grey).

Fig 2. Effect of model selection on the size of apparent mortality plateaus.

(a) Observed hazard rate data (blue) from Barbi and colleagues [1], fitted by log-linear hazard rate regressions for 861 diverse age ranges (grey lines). The Barbi and colleagues [1] age range (orange) produces the largest late-life mortality plateau and (b) produces the greatest overestimate of observed data (orange cross) at advanced ages (blue line, age 105 shown). Seeding random errors into other representative models—e.g., the 50- to 80-years-old regression (green point in (b), green line in (c))—produces (c) late-life mortality deceleration (pink points; p = 2 × 10⁻⁴) and constant hazard-rate regressions (black line) past age 105.