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

A.6 Planned statistical analyses and statistical power considerations
All power calculations in Sects. A.6.4.2 and A.6.4.3 are based on the following assumptions:
� Possible effects of exposure measurement errors are ignored. (Sect. A.6.2.3.1, however,
addresses the issue of random errors, particularly for continuous exposure measurements,
and presents a strategy for reproducibility/calibration substudies embedded
in the National Cohort, to improve quantitative estimation of RRs, adjusting for
regression dilution effects due to random measurement errors.)
� The possibility of missing data was ignored. While imputation methods will be used in
the analysis when necessary, the effects on power can approximately be translated
with the percentage of missing values for a given covariable 811 .
� No confounding is assumed. However, the variance inflation factor (VIF), which is
discussed below, directly translates into the factor for the sample size.
In addition to sample size requirements for detecting RRs, Sect. A.6.4.5 presents estimates
of sample size requirements for nested case-control studies aiming to estimate sensitivity of
a continuous diagnostic marker at a prefixed level of specificity.
A.6.4.2 minimally detectable odds ratios in main effects models
Exposures or risk factors are frequently measured or coded as binary, multiple categorical,
or continuous variables. In nested case-control studies, typical examples of binary exposure
variables based on laboratory measurements include classifying individuals into carriers
or noncarriers of a given infectious agent, or carrier status for a given (polymorphic)
genetic risk allele. In cohort studies, a typical example of binary risk factor classifications
is a comparison between use versus nonuse of exogenous hormones or medical drugs.
Examples of continuously measured risk factors include many biomarkers (e.g., markers
of metabolism) measured in blood or urine samples or quantitative scores based a larger
number of questionnaire responses (e.g., nutrient intakes estimated from a food frequency
questionnaire). In a first step, continuous exposure variables may also be broken down into
quantile categories and RRs (or odds ratios) estimated for each quantile, taking one of the
quantile categories as reference. A statistical instrument for the latter situation is a categorical
model, counting events in cells of a multidimensional contingency table and assuming
an order between the categories of the new quantile variable. This latter approach can thus
be regarded as a general and robust method that should be followed by dose–response
analyses812 .
For continuous exposure or risk factor measurements, it is often appropriate to test the hypothesis
that increasing levels of the exposure are associated with increases in risk on a continuous
(log-)linear scale. The statistical power of such tests is based on a standardized difference
(A). Definition and interpretation of standardized difference are given in Annex C.2.2.
For continuous exposure/risk factor variables that follow skewed (e.g., approximately lognormal)
probability distributions or more complex distributional types, including a spike at
zero situation (e.g., cigarette smoking or alcohol consumption), more complex modeling
strategies, such as fractional polynomials, may be needed813 . Rigorous sample size or statistical
power calculations for these more complex situations are not being considered here.
In multifactorial statistical models that include a number of covariates as adjustment or confounding
factors, the estimates of sample size requirements will increase, compared to the
sample size needed for nonadjusted analyses. A general approximation to this increase in
sample size requirements is given by the VIF814 �1 �
193 � � �� b � � w � �b
�
194 log( risk) � � � �1
xi1
� � 2 xi2
194 log( odds) � � � ( �1
� �2
) xi1
� �2
( xi
2 � xi1)
194 log( risk) � � � � L �w1 xi1
� w2x
i2
�
P(
D)
� P(
D | E )
195
PAR �
P(
D)
P(
D)
� P(
D*)
195
GIF �
P(
D)
:
� 1 �
203
VIF �
�
�
�
� , 2
�1
� �CE
�
203
181
�
2
CE
A.6