The answer depends on what specific question you want to address.
Say that your interest is whether the age of onset of a disease differs with gender, your population of interest is only those who have been diagnosed with the disease, and you have reason to believe that you have a reliable sample of that population (addressing the first question from Jeremy Miles). Then you could just do a t-test for age at diagnosis versus gender, or otherwise compare the distribution of age at diagnosis versus gender.
If your interest extends outside those who have been diagnosed with the disease and you want to evaluate time (age) to event, then the second question from Jeremy Miles becomes relevant: "What about the people who never get the disease?" This might be an example of right truncation, when "only individuals for which the event has occurred by a given date are included in the study" (Klein and Moeschberger, Section 5.3, page 149). That's complicated. It requires reversing the time axis to convert to left-truncated times, and then dealing with the problems inherent in left truncation (see Section 4.6 of Klein and Moeschberger).
In response to comment and linked article
The article by Li et al., Genome-wide analyses identify NEAT1 as genetic modifier of age at onset of amyotrophic lateral sclerosis, Molecular Neurodegeneration 18: Article number 77 (2023), takes the population of interest to be only those who have been diagnosed with the disease.
Amyotrophic lateral sclerosis (ALS) is a very rare disease, with a prevalence of only 9.1 per 100,000 individuals in the US. Standard survival analysis assumes that all individuals eventually experience the event. A model of a rare disease like ALS in the entire population could instead be a cure model, evaluating both whether that event (onset of ALS) occurs at all, and the age at onset if it does.
You can think about this study as omitting the "cure" part of the cure model, and only evaluating the age at onset for those who have already been diagnosed. In this situation the age at onset is known for all individuals, so there is no right censoring of event times as you typically have in a survival model.
Although the authors call their analysis a "Cox proportional hazards model" and used survival-analysis software, it might be better to think of this as the equivalent semi-parametric continuation-ratio ordinal regression. That's a way to model ordered outcomes (age at ALS onset, here) as a function of predictors without making assumptions about the underlying statistical distributions.
Instead, there's an assumption that the log of the hazard, the probability of having an event at a certain time given that you haven't had one yet, is a linear function of predictor variables. In the cited paper, it seems that the associations between age at onset and the predictors were further assumed to be independent of age per se.
There's nothing wrong with that as a modeling tool, but interpretation of results must be very cautious. This analysis says nothing about the risks of those who haven't been diagnosed with ALS, as they weren't incorporated into the analysis at all. For example, it's possible that the FRMD8 genetic locus found to be associated with earlier age at onset among those with ALS has nothing to do with the risk of developing ALS but instead accelerates the time that the underlying disease becomes clinically apparent.
Even when restricted to those with ALS, it's critical that the sample be representative of those who develop the disease. That's where the importance of the sampling design comes in. If you analyze a cohort of newly diagnosed ALS patients, then you might have a good sample of those who develop the disease. If instead you sample from all those who have a typically fatal disease like ALS at some calendar date, you run a risk of survivorship bias. Those who currently have ALS will under-represent individuals with a more rapid progression between diagnosis and death.
