Controlled interrupted time series with count data using glm, panel data, and Newey-West standard errors

[Tim Jones]

Hi,

I am trying to conduct an interrupted time series analysis with an intervention group and a control group and count (Poisson) data.

My dependent variable is hospital admission rates, and I am considering this to be Poisson distributed (using count of admissions, called 'freq', and log(population) as an offset - my population is in the variable 'dementia').

I have a variable "index_num" to identify intervention and control groups (zero for control, one for intervention), and each has 60 monthly timepoints (in the variable 'timepoint' going from 0 to 59).

I would like to estimate Newey-West standard errors to account for autocorrelation. I would normally include a bunch of other variables to make the interrupted time series comparisons (e.g. level change, slope change after intervention), but here I am going to show a model without additional variables to demonstrate my issue as simply as possible because it doesn't seem to matter how many other variables are in the model.

If I 'tsset' for panel data (panel being intervention and control counts) and try to run a poisson regression with newey-west errors on the panel data as follows:

tsset index_num timepoint
glm freq, family(poisson) link(log) vce(hac nwest) exposure(dementia) eform

I get this error message: "repeated time values in sample r(451);".

I am sure this is because I do have repeated time values (one time series each for intervention and control). I have searched around on the internet and seen a few people mention similar issues but no solution so far.

If I run the same regression on just one of my groups (e.g. the intervention group) as follows, there are no problems:

keep if index_num == 1
tsset timepoint
glm freq, family(poisson) link(log) vce(hac nwest) exposure(dementia) eform

Alternatively, I can run the regression with both groups and without using Newey West errors (e.g. robust standard errors instead) and this runs fine.

I think that GLM can't do the Newey-West errors with panel data.

Does anyone have any solution to this issue?

I have thought of a couple of options but can't figure out how to do this:
1. Somehow differencing the intervention and control groups to get a single time series (however, the intervention and control have different underlying populations so I'm not sure how I could appropriately subtract one from the other?)
2. Find a way to program my own kernel for the vce(hac ...) option that works with panel data - I'm not an expert mathematician so I'm not sure what the kernel should look like for panel data Newey-West errors, or how I pass this into the Stata command.

Any help with the above or any other possible solutions would be very welcome.

Thanks in advance for any help.

Tim

[Fei Wang]

Tim, I think one choice is -xtpoisson, pa- with -corr()- specifying some sort of serial correlation. This can be equivalently implemented using -xtgee- with -poisson- family and -log- link. But as N is only 2, I don't think you would lose much by separately analyzing two time-series with -glm-. Let's wait and see what others would suggest.

[Tim Jones]

Thanks a lot Fei, I've got that to run using xtset and xtpoisson for population average data.

Do you have any tips on specifying an appropriate AR lag for the correlation structure? Can I just try a few out and choose the one with the lowest deviance? (The AR lag doesn't seem to make any difference to the degrees of freedom, unless I'm missing something, so I don't think AIC/BIC or other penalisation terms would make any difference?)

I wanted to be able to include both groups (intervention and control) in the same model to make a direct comparison between them (i.e. check that any change in level or slope of the intervention group was different from that in the control group). I can include terms that indicate this (or not) in the model with both groups. But otherwise I could just run the two groups as separate GLM poisson models with Newey-West errors and descriptively compare them.

Thanks again,

Tim

[Fei Wang]

Tim, I would specify -corr(uns)- as it's less restrictive than -corr(ar #)-.

[Ronald Kakeeto]

Hi,
I am also trying to conduct an interrupted time series analysis with an intervention group and a control group using the command, however, whenever I type in the command
. "itsa treatment_Cases, treat(3) trperiod(13) lag(1) replace trpost figure" I get this error "treatid requires a tsset panel variable" which I have failed to work around yet I have a short time frame to submit my thesis.

Thanks a lot for your support in advance
Ronald

[Jared Greathouse]

Ronald Kakeeto you need to xtset your data with a panel and time variable