Is Poisson regression possible with row level mixed numeric / factor data?

Question

I checked different sources here and here but was still unclear of the response so I am asking. I am thinking of using a Poisson regression for several reasons. One: response is a count, two: data not all numeric three: distribution is not normal. The problem is my data is not aggregated, it is row level and I'm no sure if it's possible to use Poisson (Note: management does not want a logistic regression). If my data must be rearranged to use Poisson, I am unsure which rearrangement to use. I am using R so here is my data frame

## patient hospital data

id <- c(123, 234, 456, 567, 678, 789, 890, 901, 1000)  # factor
year <- c(2015, 2017, 2016, 2017, 2015, 2016, 2016, 2015, 2017)  # factor
state <- c('NY', 'CA', 'NY', 'MI', 'NV', 'CA', 'CA', 'NY', 'NH')  # factor
stage <- c('adv','early','adv','stg1','stg2','adv','early','stg1','stg2') # factor
age <- c(25, 45, 67, 24, 17, 34, 75, 22, 51) # integer
wagesWk <- c(200, 1220.75, 500, 600, 500.5, 1200, 900, 200.5, 400.5) # continuous
numStateHosp <- c(45, 100, 54, 100, 37, 90, 71, 92, 52) # integer
residence <- c("condo", "shelter", "hospice", "rental", "parents", "condo", "hospice", "parents", "rental") #factor
ethnicity <- c('group1','group4','group3','group1','group1','group4','group2','group1','group4') #factor
underPhysCare <- c('N','Y','Y','N','Y','N','Y','Y', 'N')  #factor

df <- data.frame(id, year, state, stage, age, wagesWk, numStateHosp, residence, ethnicity, underPhysCare)

response: count of number patients by year and ethnicity a = year b = ethnicity

therefore: response: countPatients with subscripts ab explanatory variables: year, state, stage, age, wagesWk, ethnicity, underPhysCare

The problem is this is row level data. If I aggregate like this:

num_patients_2015_group1
num_patients_2015_group2
num_patients_2015_group3...
num_patients_2016_group1
num_patients_2016_group2
num_patients_2016_group3...

Wouldn't this require multiple Poisson regressions? If so, how do I incorporate my explanatory variables? If Poisson is not a good choice, what other choice can I use? For sure I cant OLS because the normality assumption is violated and I am not allowed to use logistic.

Note: I am not asking for code. I am asking for advice as to how to tackle this problem. Thanx in advance for your help

Answer 1

If I've understood correctly, you're looking to do a Poisson regression in which the data can be aggregated by year and ethinicity into a contingency table which may look like (using the data you provide)

     ethnicity
year   group1 group2 group3 group4
  2015      3      0      0      0
  2016      0      1      1      1
  2017      1      0      0      2

If that is correct, Poisson regression is an excellent way to do this. In fact, Poisson regression is one of the main ways you can analyze contingency tables like this (the other way is logistic regression and I find it strange they won't allow you to use it). You can simply group by year and ethnicity and count the number of rows in each group. This would be the outcome and you can adjust the expected mean by year and group very simply.

Using some R code...

library(tidyverse)
tabl = xtabs(~year + ethnicity, data = df)
model_data = tabl %>% 
  as.data.frame() %>% 
  mutate(year = as.numeric(year))


model = glm(Freq ~ year + ethnicity, data = model_data, family = poisson)
summary(model)

You can add additional predictors quite naturally by adding them to the xtabs formula.