updated version of -itsa- available on SSC

[Ariel Linden]

Thanks to Kit Baum, a revised version of itsa is now available on SSC.
This new version fixes a bug that affected the posttrend estimates in the multiple-group/multiple intervention analysis.

itsa performs interrupted time series analysis for single and multiple groups

itsa estimates the effect of an intervention when the outcome variable is ordered as a time series, and a number of observations are available in both pre- and post-intervention periods. The study design is generally referred to as an interrupted time series because the intervention is expected to "interrupt" the level and/or trend subsequent to its introduction. itsa is a wrapper program for, by default, newey, which produces Newey-West standard errors for coefficients estimated by OLS regression, or optionally prais, which uses the generalized least-squares method to estimate the parameters in a linear regression model in which the errors are assumed to follow a first-order autoregressive process. itsa estimates treatment effects for either a single treatment group (with pre- and post-intervention observations) or a multiple-group comparison (i.e., the single treatment group is compared with one or more control groups). Additionally, itsa can estimate treatment effects for multiple treatment periods.

[Omar Okasha]

Dear Ariel

First, I would like to reiterate my thanks to you for the great work in itsa module, and I hope you have some time to help me figure the answer to the problem below..

I am working on a time-series data from 2000 to 2013, where an intervention was implemented in 2011. The data is in aggregate format, and I had the number of events of a specific outcome that we are assessing before and after the intervention, as well as the total population per year for each age group. Based on that, I calculated the incidence rate of that outcome per 1000 population. I then used your module to estimate changes in level and trend of the incidence, following the intervention. I used the single group option, together with lag(1) and posttrend terms. Below is how the command, and the data after using itsa (the data below if for one of the age groups included in the study):

itsa incidence, single trperiod(2011) lag(1) posttrend

year	incidence	_t	_x2011	_x_t2011	_s_incidence_pred
2000	2,16	1	0	0	2,24
2001	2,72	2	0	0	2,25
2002	2,08	3	0	0	2,25
2003	2,33	4	0	0	2,25
2004	2,10	5	0	0	2,25
2005	2,52	6	0	0	2,26
2006	1,87	7	0	0	2,26
2007	1,84	8	0	0	2,26
2008	2,06	9	0	0	2,27
2009	2,49	10	0	0	2,27
2010	2,66	11	0	0	2,27
2011	3,41	12	1	0	3,33
2012	2,58	13	1	1	2,76
2013	2,27	14	1	2	2,19

Now, I still need to do one more thing so that I can finalize my results, which is to calculate the incidence rate ratio (IRR), which should be based on the ratio between the incidence after intervention to that before the intervention. since you mentioned in your article that lincom was used to estimate the posttrend option, and since the model is based on newey [/Cregression, I looked in the Stata documentation relevant to the two commands to see how I can estimate the IRR. I found an option that can be added to the lincom command to do the job. The problem is I cannot seem to understand how to apply it. I tried the following line, based on the output of the itsa command:

lincom _b[_t]+_b[_x_t2011], irr

But I am quiet sure the results have nothing to do with what I am trying to do I was just trying it.

N.B.Similar studies almost always used negative binomial regression to estimate the IRR (I believe it can be done using the xtnbreg command which is based on xtset). But it seems this cannot be applied in itsa?

Thank you in advance.
Omar

[Omar Okasha]

Hi Ariel..

So couple of thoughts after whole-day attempts:

1. I tried setting the time series using xtset, instead of stset, so that I can use xtnbreg after itsa, and it worked. I compared the output of itsa post-xtset to that post-stset and they are identical. Then I used xtnbreg with the (irr) option to get my estimate.

2. One of the objectives of ITSA, at least I understood it this way, is to estimate the difference between the observed post-intervention outcome measure (i.e. incidence in my case) and the counterfactual (i.e. the outcome measure that would have been observed in absence of the intervention, and as a continuation of the pre-intervention trend). Usually, they estimate the difference between the predicted and observed at the last time point post-intervention, assuming the intervention would have reached its maximum effect. Now I am confused whether this can be done using your itsa module? This intervention effect can be estimated simply as the difference between the full model (i.e. the one with the pre- and post-intervention terms included, thus yielding predicted/counterfactual post-intervention estimates) and the model including only post-intervention terms. I am not sure but it occurred to me that, using the stored estimates of itsa module in my data, this should be the difference between the predicted incidence (_s_event1rate_pred) at 2013 and the observed incidence at 2013?, but I need your opinion about this.

Again, my sincere thanks

[Ariel Linden]

Hi Omar,

Thank you very much for your thoughtful questions!

I apologize if my response it short, but I don't have time at the moment to provide an expansive response.

First, you could certainly use a Poisson or negative binomial model if that is what makes the most sense for your data. I would use itsa first to get the variables you will need for estimation (_t, _x(trperiod), _x_t(trperiod)). Then I would estimate the count model using the variables generated by itsa. I believe you could then use the lincom with either the coefficient or the irr option, depending on how you want to view your results.

As for your question about the counterfactual, you would run a simple model without an intervention ie., outcome regressed on time, save the predicted values, and then for any given month in the intervention period, you would compare the predicted value from itsa to the predicted value without the intervention.

I hope this helps

Ariel

[Omar Okasha]

Hi Ariel,

This is very helpful, I really appreciate it. Now I have the estimates using the method you described..

My best wishes
Omar