Calculating annual increase or decrease in mortality after multivariate logistic regression model

[Muhammad Rashid]

Dear Stata user

Can anyone please help me to figure out how can I calculate and report adjusted changes in mortality after logistic regression. I have a longitudinal data over 30 years where I am calculating mortality changes over time. obviously I am adjusting for all the potential confounders in the model. I have introduced "year" as a continuous variable in the model which gives me adjusted odd ratio for each year. However, I am interested to report these odds ratio as a percentage change per year. I have tried margins, atmeans, but this given my means for all the variables including the means for all years. am I right to think that this is not a percentage increase or decrease in mortality? sorry to be nob I will be extremely grateful for your help in this matter.

[Clyde Schechter]

Well, you don't show your actual logistic regression command, so I'm not sure what you've done. And I don't know what the range of values for the year variable is. For illustration purposes I'll assume that year ranges from 1 to 30. Modify the code accordingly:

margins, dydx(year) at(year = (1(1)29))

This will give you the adjusted increments in mortality (assuming mortality was in fact the outcome variable in the logistic model) each year. As written, the command will do the adjustment to the observed distribution of all of the model covariates in your estimation sample. From your original attempt, however, it seems you may prefer rather to adjust all the covariates to their mean values. If so, just add -atmeans- to the end of the command.

Added: In the future, it is best to show the estimation commands you have actually run when you want help with interpretation of the results or help with post-estimation commands. One or two lines of code is usually much more informative than several paragraphs of narrative. And it usually doesn't hurt to fire up -dataex- and show example data, too.

[Muhammad Rashid]

Dear Clyde

Thank you so much for the help, the data is very big over 30 years, Please see below the short example of the model output I have run over the later years. I obviously get the yearly adjusted odds ratios ( which become significant with narrow point estimates once I adjust for more confounders) I am really sorry for not posting this earlier. I am not familiar with -dataex- and right now looking at a youtube video to see how I can do this as well.



logistic death i.SHF c.AGE i.YEAR

Logistic regression Number of obs = 351,144
LR chi2(13) = 1914.97
Prob > chi2 = 0.0000
Log likelihood = -33876.671 Pseudo R2 = 0.0275

------------------------------------------------------------------------------
death | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.SHF1 | 1.486133 .0422969 13.92 0.000 1.405502 1.571389
AGE | 1.038926 .0009917 40.01 0.000 1.036984 1.040871
|
YEAR |
2005 | .9379712 .0779373 -0.77 0.441 .7970068 1.103868
2006 | .9448996 .0766574 -0.70 0.485 .8059902 1.10775
2007 | .9423053 .0753371 -0.74 0.457 .8056349 1.102161
2008 | 1.153527 .0834659 1.97 0.048 1.001007 1.329285
2009 | 1.199922 .0853529 2.56 0.010 1.043771 1.379433
2010 | 1.211955 .0857572 2.72 0.007 1.055008 1.392249
2011 | 1.205718 .0829562 2.72 0.007 1.053613 1.379782
2012 | 1.252829 .0866294 3.26 0.001 1.094041 1.434663
2013 | 1.305883 .0888665 3.92 0.000 1.142824 1.492208
2014 | 1.236164 .0834829 3.14 0.002 1.082907 1.41111
2015 | 1.210767 .0840903 2.75 0.006 1.056678 1.387325
|
_cons | .0009848 .0000916 -74.45 0.000 .0008207 .0011817



As per my question, instead of reporting an adjusted odds ratio per year, I want to report the annual percentage change in mortality with respective 95%CI and P values. if I got it right then my post estimation command after running the model would something like
margins, dydx(YEAR) at (YEAR=2004(1)2015))

[Muhammad Rashid]

My final results table should look something like this, I am obviously looking to get the adjusted death per year in the third row in the table below.

Death	2004	2005	2006	2007	2008	2010	2011	2012	2013	2014	2015	Odds ratio per year
Unadjusted death	3.1%	3.3%	3.9%	4.7%	4.8%	5.1%	5.6%	5.9%	6.6%	6.9%	7.1%	OR 0.968 (0.982-0.971)
Adjusted death

I have now run your command as below which has produced the following results which I don't understand all now.

margins, dydx(YEAR) at(YEAR = (2004(1)2015))

Average marginal effects Number of obs = 351,149
Model VCE : OIM

Expression : Pr(DIED), predict()
dy/dx w.r.t. : 2005.YEAR 2006.YEAR 2007.YEAR 2008.YEAR 2009.YEAR 2010.YEAR 2011.YEAR 2012.YEAR 2013.YEAR 2014.YEAR 2015.YEAR

1._at : YEAR = 2004

2._at : YEAR = 2005

3._at : YEAR = 2006

4._at : YEAR = 2007

5._at : YEAR = 2008

6._at : YEAR = 2009

7._at : YEAR = 2010

8._at : YEAR = 2011

9._at : YEAR = 2012

10._at : YEAR = 2013

11._at : YEAR = 2014

12._at : YEAR = 2015

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
2005.YEAR |
_at |
1 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
2 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
3 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
4 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
5 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
6 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
7 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
8 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
9 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
10 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
11 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
12 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
-------------+----------------------------------------------------------------
2006.YEAR |
_at |
1 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
2 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
3 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
4 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
5 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
6 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
7 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
8 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
9 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
10 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
11 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
12 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
-------------+----------------------------------------------------------------
2007.YEAR |
_at |
1 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
2 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
3 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
4 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
5 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
6 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
7 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
8 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
9 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
10 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
11 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
12 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
-------------+----------------------------------------------------------------
2008.YEAR |
_at |
1 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
2 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
3 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
4 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
5 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
6 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
7 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
8 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
9 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
10 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
11 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
12 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
-------------+----------------------------------------------------------------
2009.YEAR |
_at |
1 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
2 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
3 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
4 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
5 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
6 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
7 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
8 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
9 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
10 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
11 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
12 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
-------------+----------------------------------------------------------------
2010.YEAR |
_at |
1 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
2 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
3 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
4 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
5 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
6 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
7 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
8 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
9 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
10 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
11 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
12 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
-------------+----------------------------------------------------------------
2011.YEAR |
_at |
1 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
2 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
3 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
4 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
5 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
6 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
7 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
8 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
9 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
10 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
11 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
12 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
-------------+----------------------------------------------------------------
2012.YEAR |
_at |
1 | .0031294 .0013115 2.39 0.017 .000559 .0056998
2 | .0031294 .0013115 2.39 0.017 .000559 .0056998
3 | .0031294 .0013115 2.39 0.017 .000559 .0056998
4 | .0031294 .0013115 2.39 0.017 .000559 .0056998
5 | .0031294 .0013115 2.39 0.017 .000559 .0056998
6 | .0031294 .0013115 2.39 0.017 .000559 .0056998
7 | .0031294 .0013115 2.39 0.017 .000559 .0056998
8 | .0031294 .0013115 2.39 0.017 .000559 .0056998
9 | .0031294 .0013115 2.39 0.017 .000559 .0056998
10 | .0031294 .0013115 2.39 0.017 .000559 .0056998
11 | .0031294 .0013115 2.39 0.017 .000559 .0056998
12 | .0031294 .0013115 2.39 0.017 .000559 .0056998
-------------+----------------------------------------------------------------
2013.YEAR |
_at |
1 | .0037156 .0013007 2.86 0.004 .0011663 .006265
2 | .0037156 .0013007 2.86 0.004 .0011663 .006265
3 | .0037156 .0013007 2.86 0.004 .0011663 .006265
4 | .0037156 .0013007 2.86 0.004 .0011663 .006265
5 | .0037156 .0013007 2.86 0.004 .0011663 .006265
6 | .0037156 .0013007 2.86 0.004 .0011663 .006265
7 | .0037156 .0013007 2.86 0.004 .0011663 .006265
8 | .0037156 .0013007 2.86 0.004 .0011663 .006265
9 | .0037156 .0013007 2.86 0.004 .0011663 .006265
10 | .0037156 .0013007 2.86 0.004 .0011663 .006265
11 | .0037156 .0013007 2.86 0.004 .0011663 .006265
12 | .0037156 .0013007 2.86 0.004 .0011663 .006265
-------------+----------------------------------------------------------------
2014.YEAR |
_at |
1 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
2 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
3 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
4 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
5 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
6 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
7 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
8 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
9 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
10 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
11 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
12 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
-------------+----------------------------------------------------------------
2015.YEAR |
_at |
1 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
2 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
3 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
4 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
5 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
6 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
7 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
8 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
9 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
10 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
11 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
12 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

[Clyde Schechter]

OK, sorry, I forgot that when you do -dydx()- with a discrete variable you get all of its levels reported. So you can simplify the margins command to just -margins, dydx(YEAR)- without the -at()- option. That way you won't get 12 repetitions of every result.

[Muhammad Rashid]

Dear Clyde

I am really sorry to be a dumb here, I have following table after using the command
margins, dydx (YEAR)

. margins, dydx(YEAR)

Average marginal effects Number of obs = 351,149
Model VCE : OIM

Expression : Pr(DIED), predict()
dy/dx w.r.t. : 2005.YEAR 2006.YEAR 2007.YEAR 2008.YEAR 2009.YEAR 2010.YEAR 2011.YEAR 2012.YEAR 2013.YEAR 2014.YEAR 2015.YEAR

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
YEAR |
2005 | -.0009253 .0014474 -0.64 0.523 -.0037622 .0019116
2006 | -.000664 .0014246 -0.47 0.641 -.0034562 .0021282
2007 | -.0007212 .0014028 -0.51 0.607 -.0034708 .0020283
2008 | .0019428 .001348 1.44 0.150 -.0006993 .0045849
2009 | .0026055 .0013405 1.94 0.052 -.0000218 .0052328
2010 | .0027016 .0013342 2.02 0.043 .0000867 .0053166
2011 | .0025827 .0012907 2.00 0.045 .0000529 .0051124
2012 | .0031294 .0013115 2.39 0.017 .000559 .0056998
2013 | .0037156 .0013007 2.86 0.004 .0011663 .006265
2014 | .0024123 .0012691 1.90 0.057 -.000075 .0048997
2015 | .0019275 .0013014 1.48 0.139 -.0006232 .0044781
------------------------------------------------------------------------------

I still don't get it whether these are percentage changes per year, for instance, -0.0009 in 2005 is equivalent to what?

[Clyde Schechter]

It means that compared to 2004, mortality probability declined by 0.0009, or, equivalently, by 0.09 percentage point. And in, say, 2007 compared to 2004, it declined by 0.07 percentage point.

If you want to compare each year to the preceding year, you can do that with

contrast ar.year

[Muhammad Rashid]

Thank you Clyde, This is perfect. very very helpful indeed.