Assessing the relationship between continuous variables   Age.of.Diagnosis Native.American European  African
                60             0.5      0.4      0.1

I have the ancestry data on ~100 individuals with cancer, and I would like to know how ancestry affects the age of diagnosis. Essentially I have 2 continuous predictors (ancestry) and 1 continuous response variable (age of diagnosis). What statistical method might be appropriate here?
 A: There are examples of using Multiple Linear Regression for similar studies[1]
Here is an notebook example of doing this in R.
[1] Genomic ancestry and somatic alterations correlate with age at diagnosis in Hispanic children with B-cell ALL
A: Here is a somewhat simplistic (Bayesian) model for your problem. I did not complete it (I am not 100% positive I can). Let me know if this seems reasonable, it looks like a nice problem!
Imagine a human being is made of three independent parts: a native american part (1), a european part (2) and an african part (3). Thus, a person is represented as $x \in \mathbb{R}_{+}^3$ (meaning $x_1,x_2, x_3 \geq 0$) with the constraint $x_1+x_2+x_3 = 1$.
In order to get cancer, a human must get "enough" cancer in their inidividual parts. So if a person $x = (\frac{1}{3},\frac{1}{3},\frac{1}{3})^t$, then they can get cacner if each part gets cancer independently. Alternatively, they can get cancer by summing: say the european part gets cancer twice, the african part gets cancer once and the native american doesn't get cancer at all. In this context it is assumed that getting cancer and being diagnosed are the same (I know it might not hold but we can make things complicated later).
The probability for a part to get some number of cancers in time $T$ is modeled as Poisson process(very reasonable: it counts how many hits one gets in a given time) with some corresponding parameter $\lambda_i$. Consequently, for and individual $x$, the occurence of cancers until time $T$ is distributed like $ \sum_{i=1}^3 x_i N_i(T)$, where each $N_i(t)$ is a Poisson process with parameter $\lambda_i$. We are only interested in the first time the individual gets a total of 1 cancer or more. I believe this time should be exponential random variable with parameter that is a kind of average of the $\lambda_i$'s (I don't know that for sure, this is the missing part). 
\begin{eqnarray}
\begin{split}
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P( \text{Cancer before time } t|\lambda, x)&= P( \sum_i x_i N_i(t) \geq 1) \\
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&= \sum_{k_1,k_2,k_3} \prod_{i=1}^3 \frac{e^{-\lambda_i} (\lambda_it)^{k_i}}{k_i!} \\
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&= \sum_{k_1,k_2,k_3} \frac{e^{\lambda_1+\lambda_2+\lambda_3} \lambda_1^{k_1}\lambda_2^{k_2}\lambda_3^{k_3}t^{k_1+k_2+k_3}}{k_1!k_2!k_3!} 
\end{split}
\end{eqnarray}
where the sum is over triplets $(k_1,k_2,k_3)$ such that $\sum_i k_i x_i \geq 1$. This seems to be the hard part. However, it looks like one can estimate it numerically, so that might just be enough.
If one has this distribution $P( \text{Cancer before time } t|\lambda, x)$, then calculating the data likelihood $p(\text{Data} | \lambda )$ should be trivial (a product of iids with the above distributions). Choose a reasonable prior for $\lambda$ and Bayes rule will allow you to get the probability $p(\lambda | \text{Data})$. For a new individual $x$, the distribution of age they get cancer is going to be the predictive distribution
$$
p( \text{Cancer} | x, \text{Data} ) = \int p( \text{Cancer} | \lambda, x) p(\lambda | \text{Data} ) d\lambda,
$$
 which can (probably) be estimated using Gibbs sampling.
