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EVIDENCE-BASED-HEALTH  February 2015

EVIDENCE-BASED-HEALTH February 2015

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Subject:

survival statistics

From:

Piersante Sestini <[log in to unmask]>

Reply-To:

Piersante Sestini <[log in to unmask]>

Date:

Tue, 24 Feb 2015 16:57:43 +0100

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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

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