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Question for HN readers: We have defined about 50 spots (loci) in the mouse genome that contain DNA differences that modulate mortality rates. Most of them have

Question for HN readers: We have defined about 50 spots (loci) in the mouse genome that contain DNA differences that modulate mortality rates. Most of them have complex age-dependent “actuarial” effects. We would like to predict age at death. Would stochastic calculus be a useful approach in actuarial prediction of life expectancies of mice? (And this is why I am pleased to see this high on HN.)

seanhunter 2y ago
Can’t speak about mice, but stochastic calculus is used in modelling for life insurance for humans I believe. eg https://www.soa.org/globalassets/assets/Files/static-pages/research/arch/2008/arch-2008-iss1-gorvett.pdf https://www.soa.org/globalassets/assets/Files/static-pages/r...
- joe_the_user 2y ago
  Your link doesn't demonstrate the use of stochastic calculus by life insurance companies or for life insurance. It's just an undergraduate curriculum for actuarial students (that they learn all this stuff doesn't imply that's what life insurance companies use).
- layer8 2y ago
  This is rather https://en.mwikipedia.org/wiki/Stochastic_modelling_(insurance) https://en.mwikipedia.org/wiki/Stochastic_modelling_(insuran...
whatshisface 2y ago
Stochastic calculus is like ordinary calculus in that it is most useful when one time is like another except for a few variables that describe a state, and least useful when one time is unlike another. Because you have as many questions (loci) as you have segments that you can reasonably expect to divide time into (changing the time of death by 1/50th of a mouse lifespan would be impossible to detect unless I am wrong?), and because the time intervals are not that numerous, and also because you wouldn't really have a model for the interaction of the state variables and would be using model-free statistical methods, I think you would get all of the value there is to get out of noncontinuous methods.
joe_the_user 2y ago
(Just spitballing) I think stochastic calculus looks at a system whose output value is a smooth/real value. Basically, it is for modeling systems like random walks where there is a little bit of random up-and-down jumping in each interval. However, if you are basically looking time versus dead-or-alive, your output is binary and time-of-death is really all the info you get and you wouldn't need/want a random walk model, just a more ordinary statistical model. Maybe if there was some other variable besides dead-or-alive you were measuring or aware of a stochastic model could help then (which is a bit like saying "if we had bacon, we could have bacon-and-eggs, if we had eggs"). Also, if what you're saying is you have 50*X bytes of information that all influence life expectancy, it sounds like a challenging problem. But also it's kind of Taylor-made for neural networks; many discreet inputs versus a single smooth output. You might try a neural network and linear model and see how much better the neural network is - then you could determine if more complex-than-linear interactions were occurring.
bbminner 2y ago
Just in case you missed it, https://en.m.wikipedia.org/wiki/Survival_analysis https://en.m.wikipedia.org/wiki/Survival_analysis exists to answer specifically this question. In more practical terms, if I were to approach this problem, I'd discretize it in time and apply classical ml to predict "chance to die during month X assuming you survived that long" and fit it to data - that'd be much easier to spot errors and potential issues with your data. I'd go for the stochastic calculus or actual survival analysis only if you wanted to prove/draw a connection between some pre-existing mathematical properly such as memory-less-ness and a physical/biological properly of a system such as behavior of certain proteins (that'd be insanely cool, but rather hard, esp if data is limited). In my (very vague) understanding, that's what finance papers that use stochastic analysis do - they make a mathematical assumption about some universal mathematical properly of a system (if markets were always near optimal with probability of deviation decaying as XYZ, the world economy would react this way to these things), and then prove that it actually fits the data. Happy to chat more, sounds like a fun project :)
etiam 2y ago
I'm not prepared to say "no", and as has been noted already, it depends on the application, but from your description it seems to me more like a task for Bayesian statistics organized on graphs (the nodes & vertices kind).
- btown 2y ago
  And going beyond this: my layman's understanding of biology is that the way in which genes are expressed can be highly nonlinear and modulated by all sorts of different pathways. If you have some clarity on how these pathways work, probabilistic programming might be a helpful tool here in a Bayesian context. It's been a number of years since I've looked at these things, but https://www.theactuary.com/2024/04/04/bayesian-revolution https://www.theactuary.com/2024/04/04/bayesian-revolution and https://arxiv.org/abs/2310.14888 https://arxiv.org/abs/2310.14888 are recent articles that may be relevant.
nextos 2y ago
I was coming here to say this is a survival analysis problem, and thus a different branch of probability and statistics. However, you can also frame it as a stochastic process if you have extra epigenetic data that is associated to those 50 DNA loci or some genes they regulate. For example, your DNA loci of interest could have a state (methylated or unmethylated). And you could come up with a stochastic process where death occurs when a function of methylation changes at those loci (e.g. a linear model) crosses a threshold (first passage in stochastic process jargon). Omer Karin & Uri Alon have published a similar concept to explain how the decreased capacity of immune cells to remove senescent cells leads to a Gompertz-like law of longevity, something that originates from actuarial studies! Their model is simpler as they deal with a univariate problem [1]. [1] https://www.nature.com/articles/s41467-019-13192-4 https://www.nature.com/articles/s41467-019-13192-4
deleted 2y ago
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evanfrommaxar 2y ago
I would apply an L1-regularized regression where the variables are simple 0-1 for the presence of the gene. The L1-regularization helps you deal with the high-dimensionality of the problem. https://en.wikipedia.org/wiki/Lasso_(statistics) https://en.wikipedia.org/wiki/Lasso_(statistics) Since these are ages, I wouldn't assume an underlying Gaussian distribution. Making that change isn't as hard as you think. https://en.wikipedia.org/wiki/Generalized_linear_model https://en.wikipedia.org/wiki/Generalized_linear_model As Always: Consult your friendly neighborhood statistician
paulfharrison 2y ago
As others have said in various ways, start by fitting a survival model using glmnet. That said, here are some folks trying to use SDEs to model cells, they even have a "dW" on their logo. This is a long way from predicting age of death, but it might eventually give insights into the exact mechanism. Also I think they're starting with bacteria and yeast, so mice might be a way off. https://macsys.org/ https://macsys.org/
robwwilliams 2y ago
Thanks for the set of helpful replies. I’m going to be working through your suggestions over the next few months. The study is a follow-up to this work from 2 years ago: https://pubmed.ncbi.nlm.nih.gov/36173858/ https://pubmed.ncbi.nlm.nih.gov/36173858/

seanhunter 2y ago

Can’t speak about mice, but stochastic calculus is used in modelling for life insurance for humans I believe. eg https://www.soa.org/globalassets/assets/Files/static-pages/research/arch/2008/arch-2008-iss1-gorvett.pdf https://www.soa.org/globalassets/assets/Files/static-pages/r...

joe_the_user 2y ago
Your link doesn't demonstrate the use of stochastic calculus by life insurance companies or for life insurance. It's just an undergraduate curriculum for actuarial students (that they learn all this stuff doesn't imply that's what life insurance companies use).
layer8 2y ago
This is rather https://en.mwikipedia.org/wiki/Stochastic_modelling_(insurance) https://en.mwikipedia.org/wiki/Stochastic_modelling_(insuran...

whatshisface 2y ago

Stochastic calculus is like ordinary calculus in that it is most useful when one time is like another except for a few variables that describe a state, and least useful when one time is unlike another. Because you have as many questions (loci) as you have segments that you can reasonably expect to divide time into (changing the time of death by 1/50th of a mouse lifespan would be impossible to detect unless I am wrong?), and because the time intervals are not that numerous, and also because you wouldn't really have a model for the interaction of the state variables and would be using model-free statistical methods, I think you would get all of the value there is to get out of noncontinuous methods.

joe_the_user 2y ago

(Just spitballing) I think stochastic calculus looks at a system whose output value is a smooth/real value. Basically, it is for modeling systems like random walks where there is a little bit of random up-and-down jumping in each interval. However, if you are basically looking time versus dead-or-alive, your output is binary and time-of-death is really all the info you get and you wouldn't need/want a random walk model, just a more ordinary statistical model. Maybe if there was some other variable besides dead-or-alive you were measuring or aware of a stochastic model could help then (which is a bit like saying "if we had bacon, we could have bacon-and-eggs, if we had eggs"). Also, if what you're saying is you have 50*X bytes of information that all influence life expectancy, it sounds like a challenging problem. But also it's kind of Taylor-made for neural networks; many discreet inputs versus a single smooth output. You might try a neural network and linear model and see how much better the neural network is - then you could determine if more complex-than-linear interactions were occurring.

bbminner 2y ago

Just in case you missed it, https://en.m.wikipedia.org/wiki/Survival_analysis https://en.m.wikipedia.org/wiki/Survival_analysis exists to answer specifically this question. In more practical terms, if I were to approach this problem, I'd discretize it in time and apply classical ml to predict "chance to die during month X assuming you survived that long" and fit it to data - that'd be much easier to spot errors and potential issues with your data. I'd go for the stochastic calculus or actual survival analysis only if you wanted to prove/draw a connection between some pre-existing mathematical properly such as memory-less-ness and a physical/biological properly of a system such as behavior of certain proteins (that'd be insanely cool, but rather hard, esp if data is limited). In my (very vague) understanding, that's what finance papers that use stochastic analysis do - they make a mathematical assumption about some universal mathematical properly of a system (if markets were always near optimal with probability of deviation decaying as XYZ, the world economy would react this way to these things), and then prove that it actually fits the data. Happy to chat more, sounds like a fun project :)

etiam 2y ago

I'm not prepared to say "no", and as has been noted already, it depends on the application, but from your description it seems to me more like a task for Bayesian statistics organized on graphs (the nodes & vertices kind).

btown 2y ago
And going beyond this: my layman's understanding of biology is that the way in which genes are expressed can be highly nonlinear and modulated by all sorts of different pathways. If you have some clarity on how these pathways work, probabilistic programming might be a helpful tool here in a Bayesian context. It's been a number of years since I've looked at these things, but https://www.theactuary.com/2024/04/04/bayesian-revolution https://www.theactuary.com/2024/04/04/bayesian-revolution and https://arxiv.org/abs/2310.14888 https://arxiv.org/abs/2310.14888 are recent articles that may be relevant.

nextos 2y ago

I was coming here to say this is a survival analysis problem, and thus a different branch of probability and statistics. However, you can also frame it as a stochastic process if you have extra epigenetic data that is associated to those 50 DNA loci or some genes they regulate. For example, your DNA loci of interest could have a state (methylated or unmethylated). And you could come up with a stochastic process where death occurs when a function of methylation changes at those loci (e.g. a linear model) crosses a threshold (first passage in stochastic process jargon). Omer Karin & Uri Alon have published a similar concept to explain how the decreased capacity of immune cells to remove senescent cells leads to a Gompertz-like law of longevity, something that originates from actuarial studies! Their model is simpler as they deal with a univariate problem [1]. [1] https://www.nature.com/articles/s41467-019-13192-4 https://www.nature.com/articles/s41467-019-13192-4

deleted 2y ago

[deleted]

evanfrommaxar 2y ago

I would apply an L1-regularized regression where the variables are simple 0-1 for the presence of the gene. The L1-regularization helps you deal with the high-dimensionality of the problem. https://en.wikipedia.org/wiki/Lasso_(statistics) https://en.wikipedia.org/wiki/Lasso_(statistics) Since these are ages, I wouldn't assume an underlying Gaussian distribution. Making that change isn't as hard as you think. https://en.wikipedia.org/wiki/Generalized_linear_model https://en.wikipedia.org/wiki/Generalized_linear_model As Always: Consult your friendly neighborhood statistician

paulfharrison 2y ago

As others have said in various ways, start by fitting a survival model using glmnet. That said, here are some folks trying to use SDEs to model cells, they even have a "dW" on their logo. This is a long way from predicting age of death, but it might eventually give insights into the exact mechanism. Also I think they're starting with bacteria and yeast, so mice might be a way off. https://macsys.org/ https://macsys.org/

robwwilliams 2y ago

Thanks for the set of helpful replies. I’m going to be working through your suggestions over the next few months. The study is a follow-up to this work from 2 years ago: https://pubmed.ncbi.nlm.nih.gov/36173858/ https://pubmed.ncbi.nlm.nih.gov/36173858/