Incidence Rate for surveillance study

[Sandy Royston]

Hello, I would like to seek some advice on incidence rate calculation (person-years) for a surveillance study.

I'm calculating incidence rate (with CIs) and my data set in Stata (16MP) so far only includes those cases we have recorded with disease. All children in the cohort are at risk (at least until they develop the disease) and there is no exposure variable. They include some x33 cases, and I've started by calculating the survival time for these cases (in days).

The problem I've got is creating in Stata the correct denominator, as we are aiming to calculate incidence of disease across the 5-15yr old population in UK and RoI. As this is a surveillance study I am effectively exploring a population size of 10,355,298 children but these are not represented anywhere in my data set. I'm not sampling the population, as this is a surveillance study and we are aiming to catch every incident case.

I can't find a way for Stata to allow me to input this figure in anywhere. I can't realistically create data entries for 10 million non-diseased children, and if I could I don't think Stata would like it. The page: https://www.stata.com/features/table...idemiologists/ is of limited use for my calculation.

Could I have some advice please? I realise using Stata for this application might seem overkill for a straight-forward calculation but I would use it to obtain the CIs.

Many thanks in advance.

Sandy

[Carlo Lazzaro]

Sandy:
welcome to this forum.
I would seem a job for -weight-.

[Bjarte Aagnes]

see -help ci-

    Confidence intervals for means, Poisson distribution

        ci means [varlist] [if] [in] [weight], poisson [exposure(varname) options]

        cii means #exposure #events, poisson [level(#)]

[Sandy Royston]

Dear Carlo and Bjarte,

Thanks so much for your combined support, it's enormously helpful and I would be lost without it.

My study showed a prevalence of 33 severe cases but only 10 were incident within the period of observation.

So using weight I have constructed the following chart (it was a 393 day long study period, so my population of over 10 million children who weren't diagnosed as severe during that time were given a survival time of 393 days, is this correct?):

ID Severe Incident Population Survivaldays Survivalyears Persondays Personyears A 1 1 1 28 0.076712329 28 0.076712329 B 1 1 1 155 0.424657534 155 0.424657534 C 1 1 1 120 0.328767123 120 0.328767123 D 1 1 1 273 0.747945205 273 0.747945205 E 1 1 1 62 0.169863014 62 0.169863014 F 1 1 1 297 0.81369863 297 0.81369863 G 1 1 1 59 0.161643836 59 0.161643836 H 1 1 1 195 0.534246575 195 0.534246575 I 1 1 1 28 0.076712329 28 0.076712329 J 1 1 1 195 0.534246575 195 0.534246575 K 0 0 10,355,298 393 1.076712329 4069632114 11149677.02 TOTAL 4069633526 11,149,680.89

so, using ci means command:

"ci means Severe [fweight=Population], exposure(Survivalyears)"

-- Poisson Exact --
Variable | Exposure Mean Std. Err. [95% Conf. Interval]
-------------+---------------------------------------------------------------
Severe | 1.11e+07 8.97e-07 2.84e-07 4.30e-07 1.65e-06


And then using the cii means command I can calculate:


"cii means 11149680.89 11, poisson level(95)"

-- Poisson Exact --
Variable | Exposure Mean Std. Err. [95% Conf. Interval]
-------------+---------------------------------------------------------------
| 1.11e+07 9.87e-07 2.97e-07 4.92e-07 1.77e-06


so that is 10 cases/11,149,680.89

Which I presume gives me an incidence rate of:

0.89 case per 1 million person-years

[LL, UL] 95%CIs are therefore: [0.49, 1.77]

A few questions:

1. Is the use of frequency weights correct here? I assume the indication of duplicate values is the intention
2. I have stated the exit time of 373 days (1.077 years) for those not diagnosed as Severe. Is this correct or is there another way to state that they were at risk for the entire period but did not develop disease?
3. Have I taken the correct figures for my CIs?


I apologise for my ponderous calculations and simple questions. Many thanks

Sandy

[Carlo Lazzaro]

Sandy:
1) yes, -fweight- indicate replicated data.
2) the exit time should be 393 days; patients at risk who did not develop the disease are right-censored.
3) yes, it seems so.

[Sandy Royston]

Amazing, thanks Carlo

[Bjarte Aagnes]

3. Have I taken the correct figures for my CIs?

seem like the ci are based on 11 cases not 10?

* Example generated by -dataex-. For more info, type help dataex
clear
input double(Severe Population Survivalyears)
1 1  .076712329
1 1  .424657534
1 1  .328767123
1 1  .747945205
1 1  .169863014
1 1   .81369863
1 1  .161643836
1 1  .534246575
1 1  .076712329
1 1  .534246575
0 10355298 1.076712329
end

ci means  Severe [fweight=Population], exposure(Survivalyears)

qui {
   
   su Severe  
   local cases = r(sum)
   su Survivalyears [fweight=Population]
   local pyrs = r(sum)
}

di "pyrs: `pyrs'  "_n " cases: `cases' "

cii means `pyrs' `cases', poisson level(95)
cii means `= `pyrs' * 10^-6 '  `cases', poisson level(95)  

local fmt %3.2f
di `fmt' r(mean) " [" `fmt' r(lb) "," `fmt' r(ub) "]"

. ci means  Severe [fweight=Population], exposure(Survivalyears)

                                                            Poisson exact    
    Variable |   Exposure        Mean    Std. err.       [95% conf. interval]
-------------+---------------------------------------------------------------
      Severe |   1.11e+07    8.97e-07    2.84e-07        4.30e-07    1.65e-06

. 
. qui {

. 
. di "pyrs: `pyrs'  "_n " cases: `cases' "

pyrs: 11149680.89556219  
cases: 10 

. 
. cii means `pyrs' `cases', poisson level(95)

                                                            Poisson exact    
    Variable |   Exposure        Mean    Std. err.       [95% conf. interval]
-------------+---------------------------------------------------------------
             |   1.11e+07    8.97e-07    2.84e-07        4.30e-07    1.65e-06

. cii means `= `pyrs' * 10^-6 '  `cases', poisson level(95)  

                                                            Poisson exact    
    Variable |   Exposure        Mean    Std. err.       [95% conf. interval]
-------------+---------------------------------------------------------------
             |   11.14968    .8968867    .2836205         .430092    1.649406

. 
. local fmt %3.2f

. di `fmt' r(mean) " [" `fmt' r(lb) "," `fmt' r(ub) "]"
0.90 [0.43,1.65]