Age-Based Risk Estimates for C9orf72RE-related Diseases: Theoretical Developments and Added Value for Genetic Counselling

When a parent is diagnosed with a neurodegenerative condition like Amyotrophic Lateral Sclerosis (ALS) or Frontotemporal Dementia (FTD), the conversation for their children often centers on a single number: 50%. Under the standard laws of Mendelian inheritance—the rules governing how traits pass from parents to offspring—a child of a carrier of an autosomal dominant mutation has a 50% chance of inheriting that mutation.

However, this mathematical shorthand is incomplete. It treats the risk as a static coin flip. It ignores the biological reality that these diseases do not strike all at once. Instead, they exhibit age-dependent penetrance (the likelihood that a person with a mutation will actually show symptoms). For a 20-year-old, the risk of being a carrier is theoretically 50%. But for a 70-year-old who has lived a healthy life, that 50% figure becomes a profound statistical inaccuracy.

Beyond the Mendelian Coin Flip

The core problem in genetic counseling for C9orf72-related diseases is the gap between theoretical inheritance and clinical reality. The C9orf72 mutation involves a hexanucleotide repeat expansion (a segment of DNA where a specific six-letter sequence repeats many times). This is the leading genetic driver of both ALS and FTD. While the inheritance of the mutation follows Mendelian logic, the expression of the disease does not.

Currently, relatives are often given the "prior" probability—the 50% for children or 25% for grandchildren—without adjusting for their current age. This fails to account for the fact that the disease typically has a unimodal distribution of onset (a pattern where most cases cluster around a central age), centered around 58 years of age [Figure 1A]. If an individual has passed the typical age of onset without symptoms, the probability that they carry the mutation must logically decrease. Relying on static percentages may misguide the decision-making process for those considering genetic testing.

A Bayesian Framework for Age-Adjusted Risk

To resolve this, the authors developed a theoretical framework based on Bayesian inference. Bayesian probability allows us to update the likelihood of a hypothesis as new evidence becomes available. In this case, the "evidence" is the person's current age and their lack of symptoms.

The researchers' approach decomposes the problem into several layers:

1. Defining Penetrance ($\pi_t$): The model starts with the probability that a carrier will show symptoms by a certain age $t$. They use empirical data to map how this probability climbs as a person ages [Figure 1B].
2. Accounting for Non-Penetrance ($x$): The authors introduce a variable, $x$, representing the fraction of carriers who are "non-penetrant." These are individuals who carry the mutation but will never develop the disease.
3. Updating Carrier Probability: Using Bayes' theorem, the model calculates the probability of being a carrier given that the individual is currently unaffected. For a child, the formula $P(M|A_t) = \frac{1 - \pi_t}{2 - \pi_t}$ filters the initial 50% risk through the lens of the person's age.
4. Extending to Multiple Generations: The complexity increases for grandchildren. The model considers both the grandchild's age and the age of their parent. If the parent is 70 and healthy, it lowers the probability that the parent is a carrier. This, in turn, reduces the risk for the grandchild.

Quantifying the Shift in Risk

The authors applied this framework to a cohort of 1,146 symptomatic individuals from the Murphy et al. dataset. The resulting metrics reveal a massive divergence from traditional Mendelian estimates.

For an asymptomatic child, the risk of being a carrier drops sharply as they age. The paper reports that while the risk is near 50% in the early 20s, it falls to 27% by age 60. By age 70, the risk is only 6% (assuming complete penetrance) [Figure 2A]. Even if we assume 20% of carriers are non-penetrant ($x = 0.2$), the risk for a 70-year-old is 20%. This is still far below the 50% traditionally cited.

The impact on grandchildren is even more dramatic. The risk for a grandchild is highly sensitive to the age of the intervening parent. For a 45-year-old grandchild whose parent is 70 and asymptomatic, the probability of being a carrier is only 2.5% (assuming $x=0$). This is ten times lower than the 25% Mendelian prior. Furthermore, the model predicts future risk. For a child, the probability of developing the disease in the next 10 years peaks at age 55 with a value of 0.26 [Figure 3A].

Limitations and Uncertainties

The authors are transparent about the limitations of the underlying data. First, the empirical penetrance values come from the Murphy et al. cohort. This group may under-represent very elderly individuals. Second, the dataset is mostly from European, North American, or Australian populations. While the authors note that founder effects (genetic changes that occur in a small, isolated population) suggest some universality, the model's precision in other ethnic groups is unknown.

Most importantly, the value of $x$ (the fraction of non-penetrant carriers) is not a known constant. It is influenced by complex interactions between environment and genetics. While the authors show how varying $x$ affects the results, they cannot pinpoint an exact value. Thus, the model provides a range of possibilities rather than a single truth.

The Verdict: A Necessary Tool for Clinical Precision

The shift from "Mendelian probability" to "age-adjusted risk" is a significant step for genetic counseling. By replacing a blunt instrument with a nuanced Bayesian model, the authors align mathematical theory with clinical reality. For many older adults, the "50% risk" is a statistical shadow that no longer applies.

The researchers have made their findings actionable via an online simulator. This tool translates complex equations into an intuitive interface for clinicians .

The code for the analysis and the simulator is available at https://github.com/damiendevienne/ftd-als/. This framework is not limited to C9orf72. It serves as a generalizable blueprint for any autosomal dominant disease where the timing of onset is critical.

Figures from the paper