Inference Modeling for COVID Data I am trying to build a model to analyze the relationship between COVID-19 mortality rate in each U.S. state or county (y) and independent variables (x) including:

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*Vaccination rate: 1st, 2nd, booster

*COVID-19 policies: mask mandate, vaccine mandate, social distancing, quarantine mandate

*Amount of healthcare resources: number of doctor / 1k population, % GDP spent on health

Need to control for:

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*Demographics: sex, race, income, age

*Major health conditions that increase COVID-19 mortality: cardio-pulmonary diseases, diabetes, obesity, age

I am struggling to select the appropriate model. I don't know how to account for the time component of the pandemic, i.e. the 4 COVID waves, in an inference model. I have thought of some modeling ideas, but they  all seem to have some issues:

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*Linear model


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*Pick one point in time, e.g. peak of the 2nd wave, do a linear model between the dependent and independent variables. Observational unit: state or county. Can also pick one period of time (e.g. the entire 2nd COVID wave) and aggregate the predictors for each state/county.

*Issue: Linear models assume independence between data points but COVID mortality at a given time point is likely related to that from its preceding time point(s)



*Time series model


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*Issue: Time series models are made for predictions, but I would like to make inferences.



*Causal Impact analysis: would enable me to estimate the impact of an intervention


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*Issues: (1) I have multiple interventions/mandates that I want to assess, and (2) there are variables that I need to control for (see listed above).

*Is there a way to address these two issues while using Causal Impact analysis?

I would really appreciate any help! Thank you for your time in advance!
Data I am considering using:
https://apidocs.covidactnow.org/?utm_term=coronavirus%20dashboard&utm_campaign=API&utm_source=adwords&utm_medium=ppc&hsa_acc=2362348058&hsa_cam=12135623891&hsa_grp=119598093249&hsa_ad=493383798453&hsa_src=g&hsa_tgt=kwd-867918059411&hsa_kw=coronavirus%20dashboard&hsa_mt=b&hsa_net=adwords&hsa_ver=3

Let me begin, your question is ill-posed.  One thing Statistics lacks is a uniqueness theorem.  However, if your question were clearer, I probably could not help you.  What I can tell you is what is probably needed before you start deciding on a model.
There are roughly 5500 counties and roughly 300 tribal jurisdictions.  Each local jurisdiction has its own issues, resources and so forth.  For example, in my locality, the county is about three hours wide by three hours long driving at high speed.  It is the same size as Rhode Island.  For most of that period, there was only one free testing site.  Now there is none.
When testing was free, the numbers from people within 15 minutes of the testing site were high.  The numbers from distant locations were zero or nearly zero.  Now that a test costs $200, only those who are insured and need to go to the ER get tested.  Based on past versus present and quite a bit of local knowledge, I think our official count is off by a factor of 25 from reality.
Because I have a doctorate and know a lot about the geography and history, I can give you a pretty good estimate of what is going on.  I have no clue what is going on in New York City.  Without sitting down with the people that do the work in each of the boroughs and maybe even neighborhoods, I couldn't give you a credible estimate of cases in New York City.
Deaths are equally local.  Some places use death certificate data, some use doctors' notes, some do a full investigation, some do a mixture of things.  Some places are so overrun, that if a hospital calls in a death, that counts.  If the hospital forgot, it does not count.  Policies on cause of death are local.  There is no national certifying body.  Also, based on research last year of 3300 patients that tested positive for COVID, 1% had a heart attack, 25%$ had an arrhythmia and 20% had some level of heart failure.
If a patient is brought in for a heart attack and dies, it is very possible that nobody will ever know COVID caused the heart attack.
Case numbers depend on resources.  If you see a case was opened on July 1, you can be reasonably certain it happened on or after April 1st and almost certainly not before March 1st.  See my notes above.  It easily could have happened on the day reported or the prior day, or that week or weeks earlier.  Since the priority is saving lives, counting is secondary.
Contrary to what most people believe, double counting is actually rare, but not zero.  That is because the software systems involved treat John Smith, JOHN SMITH and john smith as separate people.  If someone was tested by multiple providers, they could easily have duplicate cases.  For a variety of reasons, those are almost always caught, if there is personnel to do it.  It is an easy thing to catch, especially if they have the same birthdate, sex and address.
A non-trivial percentage of patients lie about their address to avoid charges.  So zip code data is very noisy.  See my notes above.
There is no national database of vaccinations.  One person got vaccinated 23 times before it showed up enough in one database for someone to refuse and identify the person.  Certain entities are not required to report the vaccinations they give.
Some states, and this has nothing to do with COVID, require affirmative permission to include medical information such as vaccines in any type of database, other than the providers or the insurers.  If you see that someone has three vaccinations reported, that is probably correct.  If you see zero reported, it is impossible to know how many they had.
If you want to do this type of estimation, I would look for a resource-rich set of counties that have no political incentive to hide cases.  I would try and make an appointment with the media liaison person to get some way into speaking with the Health Officer and get permission to speak with whoever is in charge of actually doing the COVID response.
As that person may be an LPN or someone without medical training, you will probably want to consult a geographer.  Their narrow goal is to mitigate harm by limiting the propagation of infection.  That is all they have to be good at.  Still, they will know what policies were in place in different stages of the various outbreaks, and if they were there at the beginning.  Someone will have the institutional knowledge unless they quit, of course.
You need to find the testing sites.  You need to find the dates that they were opened and closed, maybe reopened or moved.
I would see if I could get access to medical billing data.  If I know that 4000 tests were administered on June 1 but there were only 100 cases, and 100 cases the day before, and 100 cases the day before that, I know a resource limit was hit.
Cross-referencing billing data may be usable to build estimates of timing.
Instead of using time, use variant test data.  Some areas of the United States did a brilliant job with variant testing, some do almost none at all.  Look for behavioral breaks in the data.  That will be your clue that a new variant entered the area.
Look at hospitalization data.  Because most hospitals use electronic medical record systems, they are nearly real time systems.  You can improve that by requesting death certificate data for people that died at home.  Some people do not realize how sick they are or that they have COVID and die before anybody realizes what is going on.
Look at hospital capacity with close eyes.  A hospital with a 100 bed capacity where a specific doctor or the right set of nurses are involved in a motor vehicle accident becomes a 90 bed hospital.  The official bed count isn't the true capacity.
Mortality should be a function of capacity.  If you can, find out what the pediatric capacity is as that will give you a better idea.
Adult bodies can handle a lot of violence in order to keep them alive.  Human children are like puppies or kittens, they are not designed for durability.  Human women used to have many babies so that 2.1 babies per couple survived to reproduce.
Death is a process.  A pediatrician or a pediatric nurse could tell you when a child is beginning to die.  Because you cannot treat them with violence, it takes a lot of spare capacity to keep one alive that has begun to die.
With an adult, you send some to hospice that would have otherwise died unless you have the capacity to do the violence.  Sometimes they make it even in hospice.  With a child, you shoot them up with medicine to make the symptoms vanish and send them home to die with their teddy bears.  They will just suddenly crumple and it will be over.  Capacity and changes in child deaths will give you a better idea of how strained the system is.
If you can get ambulance billing data versus call data, that can also act as a proxy.  If an ambulance system is using home triage, you call an ambulance and if you are not sick enough or too sick, they leave without you.  Hospitals have the same capacity issues as the data entry clerks.  If the hospital is at 150% of capacity and holding, but the ambulances are running empty, the demand has exceeded the 150% in use.  Hospitals can exceed capacity by putting people in hallways, lounges and so forth.  Death rates will change as capacity is met or exceeded.
Get to know your localities.  Understand their geography.  Read the county budgets and hospital financial statements.  Find out how first responders operate.  Find out how symptoms and comorbidities are reported, when they are reported and when they fail to report them for lack of time.  Find out local vaccination policy.  Get U.S. Census data.
One other place I would recommend looking is at the tribes.  Many of the tribal governments kept people alive better than most of the governments in the world, let alone the United States.  That does not imply that Natives did not die at higher rates than others, but they have more strikes against them to start with.
The only thing with the tribes is understanding the background will be far more difficult.  You will likely be horrified if you investigate the background of Native life for a particular tribe.  I would point out that each one is very different and has a very unique culture and history.  You cannot generalize well with them but there are lessons to be learned for the rest of American society.
If I really wanted to use the type of data that you are using, I would choose a European, African or Asian country with an extensive real-time reporting system linked directly to their system of national health care.  I wouldn't use an American system because it does not exist.  There is a Lincoln Nebraska system, a Dade County system, a Marion County system and a Blackfeet system.  There are roughly 5800 separate systems in use, they are noncomparable.
