How to calculate incidence rate changing for a given year period?

[dinyae1]

A series of incidence and population data is given. How can the incidence change, CI and p-value for the change be determined for the time series:

Year	Male	Male population
2012	19	3809086
2013	20	3813246
2014	21	3812580
2015	25	3811591
2016	12	3807555
2017	14	3795242
2018	16	3790916
2019	12	3797092
2020	7	3803236
2021	4	3787284

Thanks for the help if you provide the running code.

[ballardw]

P-value implies some sort of statistical test is run. Which test do you want a p-value for?

What is your "incidence rate change" measured in? Percent of change, per some standardized value such as per 100,000 individuals?

[dinyae1]

Hi. Thanks. Figures absolute numbers of melanoma (per 1000 000 individuals). I did Poisson model for mean annual change. 

Now the % incidence change for the entire time series should be +CI and the p-value for the change.

Thanks for the help again.

Alex

[PaigeMiller]

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@dinyae1 wrote:

A series of incidence and population data is given. How can the incidence change, CI and p-value for the change be determined for the time series:

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Do you want the combined incidence rate over all of the years? Is that the sum of all of the values of MALE divided by the sum of all of the values of MALE POPULATION? Or is the statistic you are thinking about different? If so what are the calculations? Exactly how should we handle the different years shown?

[dinyae1]

Hi. I did Poisson model for mean annual change. 

Now the % incidence change for the entire time series should be +CI and the p-value for the change. What is correct SAS code for this problem?

Thanks for the help again.

Alex

[PaigeMiller]

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@dinyae1 wrote:

Hi. I did Poisson model for mean annual change. 

Now the % incidence change for the entire time series should be +CI and the p-value for the change. What is correct SAS code for this problem?

---

I don't think this answers any of my questions. EDIT: I see @Quentin has similar questions and it would be very helpful for you to explain what you want to do with this data, show examples of the calculation, etc., as I asked for.

The only new information you have provided is that you "did Poisson model". Okay, tell us (or better yet show us the code) how you did the Poisson model. Also please show us the output.

[dinyae1]

proc genmod data=insure;

model male = year / dist=poisson link=log offset=ln;
  effectplot / clm moff;
run;

[ballardw]

Uses a variable LN not defined in any example data so a bit hard to discuss accurately:

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@dinyae1 wrote:

proc genmod data=insure;

model male = year / dist=poisson link=log offset=ln;
  effectplot / clm moff;
run;

---

[Quentin]

I'm assuming this is a homework problem, since I can't believe melanoma rates would decrease that quickly.  It's fine to ask for help with homework questions, but it's helpful to describe them as such.

It's not clear what you are trying to estimate.  Let's assume for a moment you can fit a perfect model, which will allow you to predict the number of male cases in any year.  What is the incidence change you want to estimate?  Is it 2021 incidence - 2012 incidence? Or is it some sort of average annual change (would seem weird for this data)?

If you have a model that fits this data reasonably well, so incidence=f(year), and you have an estimate of a parameter for year, with a standard error, that would allow you to predict incidence in any year, and calculate a confidence interval for that prediction.  And you could subtract the predictions for any two years to get a predicted change between those two years...

[dinyae1]

Thank you for your comments. This is a very rare melanoma. I want to estimate the incidence % change for the entire 2012-2021 period.

[Quentin]

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@dinyae1 wrote:

Thank you for your comments. This is a very rare melanoma. I want to estimate the incidence % change for the entire 2012-2021 period.

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When you say " incidence % change for the entire 2012-2021 period", do you mean change from 2012 incidence (19/3809086) to 2021 incidence  (4/3787284)?

What would be the point estimate for the change, just (4/3787284 - 19/3809086) / (19/3809086) = -79% ?

[dinyae1]

Rather, I would like to ask if, apart from the Poisson model, is there any other suitable model for examining changes in incidence, time series analysis? Or does the Poisson model give a convincing enough result on its own?

[Quentin · Accepted solution]

How well does the model fit your data?  You didn't show any fit statistics, but it looks like you've modeled it as a straight line that doesn't fit very well.  The estimate for the year parameter is not significant. Maybe explore some other models.  The raw incident rates are:

Year	Male	Male population	Incidence
2012	19	3809086	0.000005
2013	20	3813246	0.000005
2014	21	3812580	0.000006
2015	25	3811591	0.000007
2016	12	3807555	0.000003
2017	14	3795242	0.000004
2018	16	3790916	0.000004
2019	12	3797092	0.000003
2020	7	3803236	0.000002
2021	4	3787284	0.000001

That doesn't look linear to me.  Maybe try adding a quadric term (year**2) and see if that helps.

[dinyae1]

Thanks for the suggestion, it helped. Homework is done. Merry Christmas.