Scientific Concept of the National Cohort (status ... - Nationale Kohorte

A.6 Planned statistical analyses and statistical power considerations
Longer-term replicate risk factor assessments and measurements errors
For many specific exposure types, short-term variations (e.g., a 1-year interval) may reasonably
be considered “random” variations around average exposure level at that time point
(or within a comparatively short time window around that time point) that are nondifferential
with respect to disease outcome. Over longer time intervals, however, this assumption may
progressively lose validity and risk of disease may show stronger associations with risk factors
assessed at a more recent time before diagnosis. For the latter type of situation, Frost
and white (2005) 742 also demonstrated that a regression calibration approach to correct
for (presumed “random”) errors in baseline measurements, using replicate measurements
taken over long time intervals, may overcorrect and lead to biased RR estimates.
Frost and White (2005) 742 proposed a basic longitudinal (“life course”) modeling approach
�1 �
that provides 193 a useful, basic framework � � �for � the statistical modeling of disease risks in rela-
b � � w � �b
�
tion to long-term repeat measurements in prospective cohort studies. Following that approach,
a simple statistical model for the (first) two risk factor/exposure measurements
planned within the National Cohort is:
194 log( risk) � � � �1
xi1
� � 2 xi2
,
�1 �
where, for individual 193 i, x is the centered error-free (true) risk factor level in the latest index
i2 � � �� b � � w � �b
�
period of risk factor assessment, and x is the true �1risk factor �
193 � �
level in first (initial recruitment)
i1 �� b � � w � �b
�
period. In this basic model, coefficient β can be interpreted as the “history-adjusted” (log)
2 194 log( odds) � � � ( �
RR (or log-odds ratio) associated with an 1 � �
error-free 2 ) xi1
� �
risk 2 ( xifactor
2 � xi1)
(which may be expressed for
a 1-unit increase), 194 adjusted for all log( past risk error-free ) � � � levels. � The history-adjusted current as-
1 xi1
� � 2 xi2
sociation describes the short-term, potentially modifiable risk, measuring the difference in
risk between
194
two subjects who log( risk have ) � different � � �1
xrisk
i1
�factor
� 2 xi2
levels now but had identical levels
in the 194 past. With just two exposure log( riskperiods, ) � � � the � L �wmodel 1xi1
� wcan
2x
i2be
� rewritten as
194 log( odds) � � � ( �1
� �2
) xi1
� �2
( xi
2 � xi1)
,
which 194 indicates that log( the odds coefficient ) � � � in ( �1the
� above �2
) xi1
�models
�2
( xi
2 �actually
xi1)
estimates the change in
(log)disease risk associated with the P(
change D)
� P(
in D over | E ) time (x -x ) true exposure level.
195
PAR �
i2 i1
A second way of rewriting the above, basic
P(
D
model
)
194 log( risk) � � � is: � L �w1 xi1
� w2x
i2
�
risk) � � � � w x � w x ,
log( L 1 i1
2 i2
194 � �
where β = Σ β and wi = β / β , that is, exposures assessed in visits (time periods) 1 and
L i2 i i L P(
D)
� P(
D*)
2 are 195 weighted by the strength GIF � of their log-linear P(
D)
� Prelationship
( D | E ) with risk (i.e., weighted by
their respective 195 β-coefficients). In this PARP
second � ( D)
model, reflects the long-term association
P(
D)
� P(
D | PE
( ) D)
for subjects 195 whose risk factor PARlevel
� has differed by 1 unit throughout the full cohort study
period, and for modifiable exposures this P(
can D)
be interpreted as measuring the long-term
potentially modifiable risk, with respect to a long-term exposure history. In the special case
where β = β , the latter model will � provide 1 �estimates
for a single regression coefficient, β 1 2 L
203
VIF �
(= β = β ), relating (log) disease risk �
� P
to the �
� ( D)
� P(
D*)
195
GIF 2 (equally weighted) average of the exposures, x 1 2 �1
� ��
CE
i1
and x , in the two index periods. Averaging P(
D)
� P�
( the D*)
Pexposures
( D)
195
from two index periods will give
i2 GIF �
a corresponding increase in statistical power P(
D)
and estimated accuracy (confidence interval)
of RR estimates, as intraindividual (time-related) variations in exposure will be reduced by
taking an integrated measure of the 2exposures
at the two time points. However, if β > β
203
�
1 2
CE
(or vice versa, β < β ), then unequal weights � 1will
be � given to the exposures in the different
203 1 2 VIF �
index periods and, depending on the degree �
�
to which �
�
2
� 1 ��1
� � �
the relative weighting predominantly
CE
favors 203 the exposure at just VIF one �of �
�the
time �
�
2 points, x or x , the potential gains in statistical
1 2
power by averaging exposures over �1
� �CE
time �(testing
the null hypothesis β = 0 for long-term
L
association) will be smaller.
2
203
� CE
2
203
�
CE
173
A.6