# How do I model monthly count data (the number of lumbar fusion surgeries)?

I have the following data:

• Month-year number of people with back/neck problem
• number of people using surgery (lumbar fusion) as a treatment

The goal is to compute usage rate of surgery (=number of surgeries / number of people with back/neck problem) for each month and hence come up with monthly forecast. What is the best approach to model this data?

I tried to figure out seasonality in the data, but with little success. Is it possible that my data does not have any seasonality? If I use Poisson regression, then do I have to test for normality? Or can I just ignore the distribution of the data. A step by step procedure is requested as I am new to this field.

I have data from January 2006 to May 2012. My counts are anywhere between 1 to 70. I am using sas and sas jmp. There is a limitation on the version of sas that I use. It has no time series license.

There is no seasonality in number with back/neck problem. So, I guess there will be no seasonality in number of surgeries either.

Since, I have count data I am using Poisson Regression to model number of surgeries. But Poisson regression has some strong assumptions. Another possible method is Negative Binomial Regression.

Currently my model contains a lagged dependent variable (lagged number of surgeries) and number with back/neck pain.

I hope I am on the right path. Or do you suggest a better approach?

• A related question that should be of interest, Time series for count data, with counts < 20. – Andy W Aug 30 '12 at 12:32
• Two thoughts. First, perhaps your denominator (number with back/neck problem) is adding a lot of variability to the ratio. Is there seasonality in number with back/neck problem alone? Perhaps evaluate your numerator (number of surgeries) alone, looking for seasonality there. Second, why do you expect seasonality? If you have predictions of what times of years will have least or most operations, perhaps you can test this hypothesis directly and more powerfully by direct comparison. – Joel W. Aug 30 '12 at 12:39
• I think your data are not Poisson distributed, but actually binomially distributed. I'm assuming that only people who report back/neck injuries decide to use lumbar fusion as a treatment. Also, you can't just ignore the distribution of the data - it isn't normal, but if you assume Poisson, Negative Binomial, or Binomial you still have to test the quality of the fit by looking for overdispersion and the distribution of residuals. – atiretoo Aug 30 '12 at 21:55