How to adjust poisson regression to census age group data? Which approach is statistically more robust?

Dear statistical enthusiasts, I'm trying to assess the relationship between the cancer incidence and the various environmental exposure (&ejvar) using poisson regression model at census tract level. Since cancer incidence is highly age-dependent, I have to adjust my poisson regression model to age.

My question is how to adjust my model to the effect of age?

I came across two main approaches, that could be used but I'm not sure if any of these two are more stat robus than another.

1. The first approach is to use percent of people for all 14 age groups for each census tract. In this case, my data has 4918 points which is the length to contain all distinct census tract of NY state. (wide format)

2. The second approach is to use number of people for all 14 age group and listed vertically thus my data has around 4918*14 age groups ~ 68,852 points (long format).

I hope attached images would help to understand what I mean by wide and long formats.

I thought, either way would do and lead to comparable results. However, model fit statistics show that wide format data with percent of each group fit data better based on AIC, BIC and the full likelihood statistics. Also, final results vary depending on the choice of either of these two approaches for the age adjustment.

I greatly appreciate to learn from your suggestions, which approach is statistically more robust? and worked better from your expeience, or any alternatives?

SAS code for wide format data. PROC GENMOD DATA=MYDATA; MODEL N_TRACT= &ejvar AGE5 AGE59 AGE85 AGE1014 AGE1519 AGE2024 AGE2529 AGE3034 AGE3539 AGE4044 AGE4549 AGE5054 AGE5559 AGE6064 AGE6569 AGE7074 AGE7579 AGE8084 POVERTY/DIST=POISSON LINK=LOG OFFSET=LN MAXITER=1000; RUN;

SAS code for long format data. PROC GENMOD DATA=MYDATA; CLASS AGECAT(REF='10')/PARAM=REF; MODEL N_TRACT= &ejvar AGECAT POVERTY/DIST=POISSON LINK=LOG OFFSET=LN MAXITER=1000; RUN;

Again my question is, which appraoch do you think is mor statitically robust?

• Please don't shout. Thank you. – Stephan Kolassa Jan 27 at 21:16
• @StephanKolassa, I'm sorry. Just edited. – Maggie Jan 27 at 21:25
• how many data points do you actually have? is it 4803 or 68684? my initial thought was that your wide format might need a weight statement, or your "long" format might need to delete some observations. Additionally, you can also add the "wide" dataset predictors to the "long" dataset and do a formal test (estimate statement I think?). – probabilityislogic Jan 27 at 22:04
• NY state has 4918 census tracts so is wide-format, the long format has 4918*14 age groups=68,852 points. – Maggie Jan 28 at 1:07
• Did your data come from a representative survey? If not, are there post-stratification weights in your data by chance? Otherwise, you should be able to simply weight up or weight down your estimates to match population totals. – StatsStudent Jan 28 at 3:07