I am struggling to understand a statistical aspect of the National Lung
Screening trial publishen on the NEJM in 2011
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
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?