Il 24/02/2015 16:57, Piersante Sestini ha scritto:
> I am struggling to understand a statistical aspect of the National 
> Lung Screening trial publishen on the NEJM in 2011
> http://www.nejm.org/doi/full/10.1056/NEJMoa1102873
>
> The study reports a 20% reduction in mortality, and this figure is 
> currently used to perform cost analyses and to issue recommendations.
> However, that figure is not relative to a certain time point, using 
> actuarial or survival curves, but is computed using "person-years at 
> risk", which, I suspect, assumes that the effect does not change over 
> time. Furthermore, recruitment was performed between 2002 and 2004  
> and analysis performed in 2009, thus complete data were available only 
> to up to 5 years, while at later time points an increasing percentage 
> of subjects was censored.
>
> Statistical analysis is described as follows:
> Event rates were defined as the ratio of the number of events to the 
> person-years at risk for the event. For the incidence of lung cancer, 
> person-years were measured from the time of randomization to the date 
> of diagnosis of lung cancer, death, or censoring of data (whichever 
> came first); for the rates of death, person-years were measured from 
> the time of randomization to the date of death or censoring of data 
> (whichever came first). The latest date for the censoring of data on 
> incidence of lung cancer and on death from any cause was December 31, 
> 2009; the latest date for the censoring of data on death from lung 
> cancer for the purpose of the primary end-point analysis was January 
> 15, 2009. The earlier censoring date for death from lung cancer was 
> established to allow adequate time for the review process for deaths 
> to be performed to the same, thorough extent in each group. We 
> calculated the confidence intervals for incidence ratios assuming a 
> Poisson distribution for the number of events and a normal 
> distribution of the logarithm of the ratio, using asymptotic methods. 
> We calculated the confidence intervals for mortality ratios with the 
> weighted method that was used to monitor the primary end point of the 
> trial,17 which allows for a varying rate ratio and is adjusted for the 
> design. The number needed to screen to prevent one death from lung 
> cancer was estimated as the reciprocal of the reduction in the 
> absolute risk of death from lung cancer in one group as compared with 
> the other, among participants who had at least one screening test.
>
> My question is: how can this analysis dispense from performing a 
> Kaplan Maier or actuarial analysis? What is the meaning of this 20% 
> reduction?
>
> The paper only provides a graph of cumulative deaths over time, Panel 1B
> http://www.nejm.org/action/showImage?doi=10.1056%2FNEJMoa1102873&iid=f01
>
> Of course, deaths accumulation decreases after almost 5 years in both 
> groups, because there are less patients.
> My instinct was to check at 5 years (actually 4 years and 8.5 months), 
> when data represent the whole population. If I extract the data from 
> the figure with one of the many programs available, at that time I 
> find a difference of about 50 deaths or ~0.2%, with a reduction of  
> less than 15% and an NNT of ~500, which -even with the limits of the 
> method of data extraction- are quite different from those computed by 
> persons-year (2% and 325).
>
> However, the NNT seems to gradually decrease overtime, from more that 
> 1000 at 1 yr, so I cannot exclude that at later time points the effect 
> would become greater than that.
> My question is: how does the analysis per persons-year at risk 
> dispense from an actuarial analysis , and what are the expected effect 
> of the presence of censored data? And by which mechanism it provides a 
> greater estimate compared that computed on mere solid data?
> thanks! If the effect does increase with time, why an estimate 
> computed with more subjects followed for a shorter period should be 
> higher?
> And how do I explain the 20% effect to a patient: that with the 
> screening, for every year that he stays alive,  he has a 20% less 
> probability of dying of cancer?
>
> Thanks!
> Piersante Sestini
>
Dear Piersante,
I totally endorse your question: how can this analysis dispense from 
performing a Kaplan Maier or actuarial analysis? I look forward to hear 
about from the list experts.
Further, I performed a simpler (somewhat raw, maybe) analysis:

CT arm:  356 died from lung cancer out of 26722 =  1,33%
RX arm:  443  died from lung cancer out of 26722 =  1,66%
CT  arm: 87 had most severe complications classified as major = 0,33%
RX arm:  28 had most severe complications classified as major = 0,10%

So, for death from lung cancer, actual absolute risk reduction (ARR) is 
1,66 - 1,33 = 0,33%, (not -20%) while for
most severe complications absolute increase of risk is 0,33 - 0,10 = +0,23%.
20% is RRR (Relative Risk Reduction), that often exaggerates true 
estimate of effectiveness.
Indeed, had the authors used RRR for most severe complications as they 
did for death, they  would say that CT screening actually DOUBLES the 
risk of most severe complications.
But they didn't.
Kind regards.
Federico Barbani
Helth Authority
Modena, Italy


-- 
dott. Federico Barbani
Servizio Committenza
Azienda Unità Sanitaria Locale di Modena
059/435813