Sporadic, late-onset, and multistage diseases

Abstract

Multistage disease processes are often characterized by a linear relationship between the log of incidence rates and the log of age. Examples include sequences of somatic mutations, that can cause cancer, and have recently been linked with a range of non-malignant diseases. Using a Weibull distribution to model diseases that occur through an ordered sequence of stages, and another model where stages can occur in any order, we characterized the age-related onset of disease in UK Biobank data. Despite their different underlying assumptions, both models accurately described the incidence of over 450 diseases, demonstrating that multistage disease processes cannot be inferred from this data alone. The parametric models provided unique insights into age-related disease, that conventional studies of relative risks cannot. The rate at which disease risk increases with age was used to distinguish between "sporadic" diseases, with an initially low and slowly increasing risk, and "late-onset" diseases whose negligible risk when young rapidly increases with age. "Relative aging rates" were introduced to quantify how risk factors modify age-related risk, finding the effective age-at-risk of sporadic diseases is strongly modified by common risk factors. Relative aging rates are ideal for risk-stratification, allowing the identification of ages with equivalent-risk in groups with different exposures. Most importantly, our results suggest that a substantial burden of sporadic diseases can be substantially delayed or avoided by early lifestyle interventions.

Keywords: UK Biobank; aging; epidemiology; multimorbidity; multistage; risk factors; somatic mutations.

Fig. 1.

A multistage model can describe any process that arises through one or more independent pathways, with one or more sequential or non-sequential steps. (a) The sequential Armitage–Doll (Weibull) model requires that stages occur sequentially. (b) The non-sequential model (NSM), allows the stages to occur in any order.

Fig. 2.

Left: For each disease a dot indicates the probability of first hospital admission at 50, plotted versus the relative increase in probability of disease by age 100. Disease incidence was classified in tertiles to indicate how sporadic or late-onset it was (see main text). Results for the Weibull model are shown, the NSM model gave similar results (Supplementary Material). Right: The composition of sporadic and late-onset diseases in terms of ICD-10 chapters, with N the number of diseases.

Fig. 3.

Relative risks (top), and relative aging rates (bottom), for potential risk factors associated with sporadic diseases (left), and late-onset diseases (right). Box plots show the median, the interquartile range, and whiskers at 1 × the interquartile range. Relative risks for diabetes and smoking tended to be larger for late-onset disease. Relative aging rates tended to be larger for sporadic diseases, suggesting that your effective age-at-risk is more modifiable for sporadic than late-onset diseases. After an FDR multiple-testing adjustment, a t-test identified statistically significant differences in mean values at the 0.05 level, for all associations except: height, or between regular drinking and sporadic disease.

Fig. 4.

Multistage disease processes will usually have a straight line when log (H(age)) is plotted versus log (age) (A) If an exposure increases the rates of disease processes, but the number of stages are unchanged, then a plot for the exposed group will be displaced vertically upwards. (B) If an exposure increases the rates of one or more processes sufficiently to reduce the number of rate-limiting stages m, then the exposed group’s plot will be displaced vertically upwards and reduced in slope. (C) In a proportional hazards Weibull model with H = e^βX(t/L)^m, then log (H) = βX + mlog (t/L), and risk factors X displace lines vertically.

Fig. 5.

The incidence of three common smoking-related diseases in men (top) and women (bottom), stratified by smoking status, with Kaplan–Meier estimates adjusted using Eq. 5. Data for smokers differ by vertical displacements and changes in slope, that can be interpreted as changes in the rates of processes, and numbers of steps in disease (see main text). Dashed lines indicate 95% confidence intervals.