Comparison of two proportions (over time)

[Liza de Groot]

Dear all,

I would like to compare two proportions (over time); but I think I have to restructure my dataset.
In 2012 - 2021 organizations tried to increase the notification rate of people living with disease X by applying an intervention.
For example in 2012 in the control group (C) 798 cases out of 606049 (population) were notified vs. 1076 out of 537856 in the intervention group (I). I would like to see whether this difference is statistically significant (including 95% CI). Hopefully it is also possible to study differences over time.
I think I need to restructure my data first. To get 100,000 rows with 0 (not notified) and 1 (notified), the CNRAF and CNRBC are case notification rates (per 100,000 people).

Thanks in advance, Liza

YEAR AF  BC              POP    C/I %        CNRAF    CNRBC    
2012  798 450            606049 0  56.39098 131.67252  74.25142
2013  686 392            624398 0  57.14286 109.86582  62.78047
2014  723 450 647319.4766528223 0  62.24067 111.69137  69.51745
2015  583 379 664842.2501385728 0 65.008575  87.68997    57.006
2016  547 403 551020.5399679504 0  73.67459  99.27035  73.13702
2017  432 291 564495.6774984105 0 67.361115  76.52849  51.55044
2018  620 468            574951 0  75.48387 107.83527  81.39824
2019  659 464            590396 0  70.40971    111.62  78.59132
2020  694 548            606028 0  78.96254 114.51616  90.42487
2021  897 681            622067 0  75.91973 144.19669 109.47374
2012 1076 515            537856 1  47.86245 200.05354  95.75053
2013 1226 521            570573 1  42.49592  214.8717  91.31171
2014 1264 596            583449 1   47.1519 216.64276 102.15118
2015 1276 591            601421 1  46.31662  212.1642  98.26727
2016 1342 693            618517 1  51.63934  216.9706  112.0422
2017 1511 760            683966 1  50.29782  220.9174 111.11664
2018 1554 754            694664 1  48.51995 223.70528 108.54169
2019 1187 724            596525 1   60.9941  198.9858  121.3696
2020 1233 756            611564 1  61.31387 201.61423 123.61748
2021 1179 758            637763 1  64.29177  184.8649 118.85293
end

[Joseph Coveney]

Hopefully it is also possible to study differences over time.
I think I need to restructure my data first.

Maybe not.

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿquietlyÿinputÿint(YEARÿAFÿBC)ÿdoubleÿPOPÿbyteÿtrtÿdouble(cnrafÿcnrbc)ÿ//ÿC/Iÿ%ÿCNRAFÿCNRBCÿÿÿÿ

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.ÿrenameÿ*,ÿlower

.ÿlist,ÿnoobsÿseparator(0)

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ÿÿÿÿÿÿÿÿÿÿafÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
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note:ÿpopÿhasÿnonintegerÿvalues

GeneralizedÿlinearÿmodelsÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿ=ÿÿÿÿÿÿÿÿÿ20
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Linkÿfunctionÿÿÿÿ:ÿg(u)ÿ=ÿln(u/(pop-u))ÿÿÿÿÿÿÿÿÿÿÿ[Logit]

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.ÿtestparmÿi.trt#i.year

ÿ(ÿ1)ÿÿ[af]1.trt#2013.yearÿ=ÿ0
ÿ(ÿ2)ÿÿ[af]1.trt#2014.yearÿ=ÿ0
ÿ(ÿ3)ÿÿ[af]1.trt#2015.yearÿ=ÿ0
ÿ(ÿ4)ÿÿ[af]1.trt#2016.yearÿ=ÿ0
ÿ(ÿ5)ÿÿ[af]1.trt#2017.yearÿ=ÿ0
ÿ(ÿ6)ÿÿ[af]1.trt#2018.yearÿ=ÿ0
ÿ(ÿ7)ÿÿ[af]1.trt#2019.yearÿ=ÿ0
ÿ(ÿ8)ÿÿ[af]1.trt#2020.yearÿ=ÿ0
ÿ(ÿ9)ÿÿ[af]1.trt#2021.yearÿ=ÿ0

ÿÿÿÿÿÿÿÿÿÿÿchi2(ÿÿ9)ÿ=ÿÿ200.03
ÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿÿÿÿ0.0000

.ÿ
.ÿexit

endÿofÿdo-file


.

Are some of those population numbers estimates?

[Liza de Groot]

Dear Joseph,

Thanks for your reaction; however, I have to study it more in detail.
The population numbers aren't estimates.

[Joseph Coveney]

The population numbers aren't estimates.

OK; I was just wondering how they had managed to become nonintegers in the control treatment group for a few years.

Also, forgive my error. That data-input command should have been

quietly input int(YEAR AF BC) double POP byte trt double(pct cnraf cnrbc) // C/I % CNRAF CNRBC

[Liza de Groot]

I also wonder, I'll check how this is possible

[Liza de Groot]

Dear Joseph,

I "studied" your two options to analyze my data.
Could I also use a log link function in your GLM option? Or should I change family to poisson then?

Best, Liza

[Joseph Coveney]

Could I also use a log link function in your GLM option?

glm allows you to use the log link function with the binomial distribution family; the regression table will show risk ratios when you specify the eform option.

Or should I change family to poisson then?

I think that with the observed proportions in your case it doesn't matter practically between fitting Poisson, odds ratio or risk ratio regression models.

If it were my research project, I would concern myself more with other things, for example, I would be taken aback to see numbers of order 10^-10, 10^-11 in the regression output, and chi-square test statistics that are more than twentyfold their degrees of freedom.

[Liza de Groot]

glm allows you to use the log link function with the binomial distribution family; the regression table will show risk ratios when you specify the eform option.

I think that with the observed proportions in your case it doesn't matter practically between fitting Poisson, odds ratio or risk ratio regression models.

If it were my research project, I would concern myself more with other things, for example, I would be taken aback to see numbers of order 10^-10, 10^-11 in the regression output, and chi-square test statistics that are more than twentyfold their degrees of freedom.

Yes I also saw this, but I don't know why this is, or how to solve it