Issue in Analysis and Presentation

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• Issue in Analysis and Presentation
• of Dietary Data
• Nutritional Epidemiology
• Walter Willet

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• The underlying objectives of data analysis and
  presentation are to learn as much as possible
  from the available data and to present what has
  been learned to readers completely and w/ maximum
  clarity.
• The approaches for presentation should vary
  depending on the intended readership
• - simpler analytic approaches and greater use
  of figures may be appropriate for a general
  medical journal
• - for an epidemiologic publication, more
  complex methods and primarily tabular results may
  be best.

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• DATA CLEANING BLANKS and OUTLIERS
• A common issue w/ dietary data is the treatment
  of questionnaires in which some food items have
  been left blank.
• Two issues arise frequently (1) should subjects
  w/ more than a specific number of blanks be
  excluded, and (2) how should blanks be treated in
  calculating nutrient intakes?
• It is useful to understand why participants may
  not have completed a response for a specific
  food. This could be due to inattention or
  carelessness or because the participant did not
  eat the food (even though they should have
  answered never).
• Several patterns can be seen when examining
  questionnaires w/ multiple blank items
• - For many forms, blank items are interspersed
  w/ plausible and seemingly carefully completed
  responses to other foods and the never category
  is not used, suggesting that blanks meant that
  the food was not consumed.
• - In occasional questionnaires, whole sections
  are left blank, suggesting that they were missed.
  
• ?In calculating nutrient intakes, it seems best
  to consider intermittent blanks as no consumption
  of the food.

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• A firm rule for allowable number of blanks cannot
  be made for all situations, and it is desirable
  to conduct evaluations of decision rules whenever
  possible
• - Nurses Health Study allowed up to 70 (out
  of about 130 items) blanks as long as no whole
  sections or pages were blank.
• - This criterion has been evaluated empirically
  within a validation study by examining the
  correlation between number of blanks on a
  questionnaire and measurement error (calculated
  for each person as the absolute value of the
  difference between the FFQ and diet record
  values).
• - For all nutrients examined there was no
  appreciable correlation.

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• Once nutrients are calculated, some responses
  will be implausibly high or low, necessitating
  additional decisions regarding allowable ranges.
  
• - The use of total energy intake as a primary
  criterion can be justified because it is the only
  nutrient for which intake is physiologically
  fixed within a fairly narrow and predictable
  range.
• - It is generally considered that total energy
  intakes below approximately 1.2 times the resting
  or basal metabolic rate estimated from age,
  gender and weight are unlikely to be correct, and
  intakes of gt4000 kcal/day are unlikely to be true
  for even relatively active men.
• - Usually an arbitrary allowable range of 500
  to 3500 kcal/day for women and 800 to 4000
  kcal/day for men are used. Although the extremes
  within this range rarely are correct, adjustment
  of nutrient intakes for total energy intake will,
  to a large extent, compensate for overall under
  or overreporting.

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• Dietary data are highly sensitive to coding and
  data entry errors because nutrients are
  calculated from large numbers of foods.
• - Miscoding a teaspoon to a cup for one food on
  a questionnaire or in a 1-week food record can
  seriously misclassify an individual for many
  nutrients.
• - Multiple choice formats and machine-readable
  questionnaires are less prone to such errors, but
  if any hand-coded or open-ended questions are
  included, such errors may occur.
• - Extreme values are primarily at the high end
  of the distribution due to the skewed
  distributions of most nutrients, and they can be
  heavily influential when nutrients are considered
  as continuous variables.
• - Sometimes such extreme values will be
  indicative of improper completion of
  questionnaires, such as marking the top category
  for all foods in a section.
• - In other cases, coding, data entry, or food
  composition database errors may be discovered.
• - Some values will just reflect unusual food
  intake patterns without obvious error.

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• CATEGORIZED vs. CONTINUOUS PRESENTATION of
  INDEPENDENT VARIABLES
• Intakes of nutrients and food groups are
  primarily continuous.
• As the traditional presentation of epidemiologic
  data has been in the form of rate ratios and rate
  differences for levels of exposure, and
  statistical methods have been developed for such
  purposes, it is not surprising that most
  continuous dietary data have been categorized for
  analysis in nutritional epidemiologic studies.
• Approaches for the creation of categories (1)
  use of arbitrarily defined quantiles (e.g.,
  quartiles or quintiles) (2) use of standard
  round-numbered cutpoints (3) use of cut points
  that are determined a priori to have biologic
  relevance such as RDA or the intake at which an
  enzyme is saturated.
• - Finer divisions of extreme categories may
  often useful to extend an examination of the
  dose-response relationship.

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• Arguments for using continuous variables
• (1) the greatest statistical power is
  provided by a continuous variable if the function
  reasonably fits the data, although this advantage
  may be slight w/ the use of five of more
  categories combined w/ an overall test for trend.
  
• (2) when used as a covariate, a crudely
  categorized variable may not fully account for
  the effect of that variable, resulting in
  possible residual confounding.
• (3) the use of continuous variables may
  facilitate comparisons among studies because a
  single relative risk is reported for an
  arbitrarily specified increment of intake (e.g.,
  RR for 100 mg of cholesterol per day) that does
  not depend on the distribution of the dietary
  factor in the particular population or on the
  choice of cut-points of individual studies.
• Tests for nonlinearity, such as the addition of a
  quadratic term, can be used to evaluate the
  presence of nonlinearity.

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• GRAPHICAL PRESENTATION of DATA
• The central data of epidemiologic studies should
  be presented in numerical form to provide the
  actual numbers of exposed subjects and the
  numbers of endpoints.
• Judicious ancillary use of figures summarizing
  the primary findings can be helpful to many
  readers. Also, a clear and attractive summary
  figure is likely to enhance the probability that
  others will include your data in their
  presentations.
• Single Variable Effects
• For presenting the effects of one or a few
  dichotomous exposure variables, a graphic display
  provides little additional perspective and tables
  should be used.
• With multiple ordinal categories, a figure can
  assist in visualizing an overall relationship
  (Fig 13-1).
• The use of histograms to present RRs has
  generally been disfavored because this parameter
  is more correctly represented as a point, and
  C.Is are less readily presented.

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• It might be argued that, if absolute risk is
  really of interest, then the dependent variable
  should be expressed as absolute risk. However,
  one reason that relative rather than absolute
  risks are generally utilized in epidemiologic
  studies is that age is usually the most powerful
  determinant thus, absolute risks are usually
  arbitrary depending on the age to which the data
  have been standardized.
• The actual width of categories of the exposure
  variable should be represented in the graphic
  display.
• Example in Fig 13-1, trans-fatty acid intake
  was divided into quintiles ? the distances
  between quintiles in the figure were made to be
  proportional to the differences between quantile
  medians.
• Usual quantiles
• two groups, tertiles, quartiles, quintiles

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• Actual vs. Predicted Relationships
• In graphic displays of the relationship between
  two variables, one issue that naturally arises is
  whether to provide the actual data or the
  prediction from a model derived from the data.
• - Many epidmiologists believe that the actual
  data should be provided so that the reader can
  view the findings w/o being forced to assume the
  appropriateness of any model assumptions, such as
  whether a linear relationship adequately
  describes the relationship.
• - The best solution may be to do both for
  example, provide the data points for categories
  and superimpose the fitted regression line (Fig
  13-2).

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• One clearly inappropriate approach is to
  analyze the data as continuous, but then present
  the findings as though they were categorical, for
  example, by displaying the odds ratios (and C.Is)
  for multiple discrete levels of intake that are
  all based on a single regression coefficients.
• ? Provides the potentially misleading impression
  of a clearly monotonic relationship and C.I. that
  are too narrow for a specific level because they
  are based on the overall data.

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• Display of Joint Effects
• A common approach to represent the joint effects
  of two exposure variables is the 3-D histogram
  (Fig 13-3A).
• - This has been criticized by some for the same
  reasons that the use of histograms to present
  univariate findings has been discouraged.
• ? alternative display using points (Fig
  13-3B).
• - A display of C.I. is usually incompatible w/
  the 3-D histogram, but this may also be
  problematic w/ the use of points as their C.I.
  are frequently overlapping.
• ? critical C.I. will usually need to be
  presented in tabular form or in text.

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• Locally Smoothed Regression Curves and Regression
  Splines
• Locally smoothed regression curves and regression
  splines have been used increasingly to display
  epidemiologic findings w/ a continuous exposure
  variable.
• - With smoothed regression curves, the values
  of the dependent variable, such as a relative
  risk, are estimated for a continuously moving
  window of values of the independent variable.
• - In using regression splines, separate linear
  or nonlinear functions are fit between specified
  points (knots) on the exposure distribution,
  and functions are connected at the knots to
  produce a smooth curve.
• The principal advantages of these approaches are
  that a priori assumptions are not imposed
  regarding the shape of the dose-response
  relationship and that maximal use is made of the
  continuous nature of the dependent variable.
• Example relation of alcohol intake to risk of
  breast cancer
• (Fig 13-4)

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Example - those data fit using regression
splines provide a strong sense that the
relationship is approximately linear and that a
significant increase in risk is seen even at
about 10g (1 drink) per day.
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• Example2 Use of smoothing techniques to
  evaluate the relationship between vitamin A
  intake and risk of neural crest congenital
  malformations (Fig 13-5)
• - This analysis suggested the existence of a
  threshold at 10,000 IU, above which risk
  increased substantially.
• - One possible concern is that inflection
  points may be accepted too literally, especially
  when the data are sparse (e.g., the method does
  not provide a C.I. For the apparent threshold,
  which would probably be quite wide).
• ? this might be regarded as an over-fitting of
  the data (analogous to an extreme form of
  selecting optimal cut-points to demonstrate a
  relationship).

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• The degree to which the conclusions are affected
  by somewhat arbitrary choices such as the width
  of the window used for smoothing and the number
  and spacing of knots deserves further
  consideration.
• Although smoothing methods and regression splines
  for analyses involving dietary intake may prove
  valuable, particularly in exploratory data
  analysis, their use deserves further evaluation.
• EXAMINATION of FOODS and NUTRIENTS
• A full evaluation of the relationship between
  diet and a disease should involve the analysis of
  data on both food and nutrient intakes.
• - If an association w/ disease is found for a
  specific nutrient, it is important to examine and
  report whether the major foods contributing to
  this nutrient (as seen in the same dataset,
  defined in terms of either absolute contribution
  or contribution to between-person variance) are
  also related similarly to risk of disease.

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• One serious problem w/ analyses of specific foods
  is the large number of items on a typical
  questionnaire.
• - Some argue that the p value used for
  statistical significance should be adjusted
  according to the number of variables examined.
• - The general consensus in epidemiology is that
  this unduly reduces power and that individual
  associations should be evaluated on their own
  merits, and conclusions should be made in the
  light of consistency w/ other information
  internal and external to the study.
• - When a large number of foods (or nutrients)
  are screened for associations w/o a prior
  hypothesis, the likelihood that some
  statistically significant relationships will
  occur by chance must be considered when
  interpreting the findings.
• - This issue is complicated by the large number
  of foods because an association w/ a food is
  generally more likely to be reported if
  statistically significant, particularly if
  consistent w/ prior expectations. Reporting the
  association for each food on a questionnaire, and
  possibly for groups of foods, is impossible in
  most journals.
• ? the literature on foods is likely to be
  highly biased, and any summary of the published
  literature cannot avoid this bias.

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• No simple solution exists for publication bias
• - A partial solution may be to deposit data in
  the National Auxiliary Publications Service or on
  the internet for all foods when an analysis on a
  particular disease is published.
• ? at least such data will be available to
  others attempting to summarize the literature.
• - The best approach for avoiding publication
  bias on specific foods is probably to analyze
  collaboratively the primary data from all
  available studies on a topic.

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• The widespread use of multiple vitamins and other
  nutritional supplements adds complexity to
  dietary analyses, but can also provide important
  insight by greatly extending the range of
  observable nutrient intakes.
• - Details on dose and duration of supplement
  use are usually obtainable w/ substantially
  greater precision than is possible for foods.
• - When examining associations w/ foods or w/
  nutrient intakes, not including supplements, it
  will be important to conduct analyses excluding
  supplement users, because any effects of
  nutrients from foods may be swamped by the
  relatively high levels of intakes from
  supplements.
• - Stratification by nutrient intake from foods
  may also be important when examining the effect
  of the same nutrient from supplements because
  little effect of supplementation might be
  expected when intake from foods is high.
• - The greatest contrast in risk would usually
  be expected when long-term supplement users w/
  high intakes from diet are compared w/
  nonsupplement users w/ low intakes from diet.

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• The Effect of Time
• Dietary factors may operate at various stages of
  the sequence of events (e.g., an antioxidant
  might reduce the effect of ionizing ration, which
  is an early event or alcohol may influence
  endogenous hormone metabolism, which is most
  likely to be most important later in
  carcinogenesis).
• The effect of diet may also be cumulative so that
  risk is related to a function of both dose and
  duration of exposure.
• Dietary factors may also have effects at specific
  periods in life far removed from the time of
  diagnosis (e.g., high growth rates before puberty
  appear to increase breast cancer risk by
  advancing the age at menarche, and effects of
  maternal diet during pregnancy on the offsprings
  risk of breast cancer have been hypothesized).
• Our knowledge is often not sufficient to be
  confident that an effect of diet would be limited
  to only a particular period, it will usually be
  difficult to exclude an effect of a dietary
  factor until a fairly wide range of temporal
  relationships have been examined.

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• Ideally, a comprehensive dietary assessment would
  include a measurement of current diet and also
  diet at various times in the past.
• - Unfortunately, a comprehensive assessment of
  even current diet is already a major burden on
  participants. Moreover, the validity of recall
  diminishes w/ time, and the reporting of past
  diet is heavily influenced by current diet, so
  that truly independent retrospective assessments
  of various periods appear impossible.
• - In practice, in cohort studies an assessment
  of current diet (usually over the past year) is
  used, and in case-control studies a period in the
  past thought to be most plausibly relevant to the
  disease (typically 5 to 10 years ago for cancer)
  is the focus of recall.
• For intake of vitamin and mineral supplement,
  information on duration of use can be readily
  collected and can be critical (e.g., vitamin E
  supplements in relation to CHD risk, or for
  vitamin C supplements in relation to risk of
  cataracts the associations were limited to longer
  term users).

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• Prospective studies provide important additional
  means of assessing temporal relationships w/
  diet.
• - Baseline data on current diet can be examined
  in relation to disease incidence at various
  follow-up periods under the reasonable
  assumption that diet varies over time, the
  maximum relative risk should provide information
  on the true induction period.
• - The limitation of this approach is largely
  practical as few cohorts will be sufficiently
  large to provide statistically stable estimates
  of risk during multiple time periods.
• Prospective studies w/ replicate dietary
  assessment provide the opportunity to examine
  various intervals between dietary intake and
  disease diagnosis w/ much greater power.

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• THE USE of MULTIPLE DIETARY ASSESSMENTS in
  PROSPECTIVE STUDIES
• A powerful feature of cohort studies is the
  opportunity to collect repeated dietary data over
  time. Such repeated measurement of dietary
  intake provide many possible analytic
  opportunities to reduce the effects of
  measurement error and to evaluate various
  hypothesized temporal relationships between the
  dietary factor

and the disease outcome (Table 13-2).
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• Measured changes in diets of individuals over
  time are a mix of true variation and measurement
  error.
• - the comparison of persons whose intakes are
  consistently high w/ those whose intakes are
  consistently low provide a strong test of
  cumulative exposure, as well as both long and
  short latency, because it is highly likely that
  these persons were truly high or truly low over
  long durations.
• - The major limitation of this strategy is the
  loss of power due to the exclusion of the many
  persons who changed categories and the need to
  exclude cases that occur before the repeated
  measurement if the analyses are to be truly
  prospective.
• The use of cumulative average measurements (i.e.,
  the average of all measurements for an individual
  up to the start of each follow-up interval) takes
  advantage of all prior data and thus should
  provide a statistically more powerful test of an
  association of cumulative exposure.
• - This approach deserves further methodologic
  development, though, to take into account the
  different degrees of measurement error and
  information provided at each interval.

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• Because our understanding of disease etiology is
  often inadequate to specify a temporal
  relationship w/ confidence, the use of several
  rather than just one analytic strategy to examine
  various temporal relationships will generally be
  appropriate.
• Clear evidence that an association is strongest
  w/ a particular temporal relationship can provide
  important information on the pathogenetic process
  and possibilities for intervention.
• - If no association is observed, the
  demonstration that this lack of relationship is
  seen when a full range of temporal relationship
  is examined provides the most compelling evidence
  that an important association has not been
  missed.
• Example Analysis of the relationship between
  coffee consumption and risk of CHD in women
  (Table 13-3)

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• MULTIVARIATE ANALYSES
• Multivariate methods may be particularly
  important in nutritional epidemiology because
  dietary factors tend to be intercorrelated,
  sometimes strongly so.
• A common reason for using multivariate analysis
  in a study of diet and disease is to address the
  question of whether an observed association
  between a specific dietary factor and disease
  risk is only secondary to its correlation w/
  another, truly causal dietary factor.
• - A standard approach is simply to include both
  variables together in the same model.
• - As the focus will typically be on dietary
  composition rather than on absolute amounts, the
  specific nutrients should usually be expressed as
  energy-adjusted residuals or nutrient densities,
  and total energy should be included as a term
  unless it is unrelated to disease risk.
• - Many possible alternative dietary factors
  could be considered as potential confounding
  variables, and the temptation may be to simply
  include these all simultaneously in a model.

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• A problem w/ including a large number of dietary
  factors simultaneously is that the remaining
  independent variation in the primary dietary
  factor may become quite small because,
  collectively, the other variables can account for
  almost all of its variation.
• An alternative strategy is to conduct a series of
  analyses including standard non-dietary factors
  at a time. In this process, it may be possible
  to eliminate several or all alternative variables
  by showing that they have no independent
  association w/ disease and that the association
  w/ the primary variable remains.
• There is no clear limits as to the number of
  nutrients that may be included simultaneously as
  this will depend on their intercorrelation as
  well as size of the dataset. However, because
  many dietary variables are strongly correlated w/
  many others, the maximum number is likely to be
  modest before C.I. became uninformatively wide.

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• Another common situation arises when one or more
  dietary factors are subcomponents of another
  (e.g., saturated, monounsaturated, and
  polyunsaturated fats are the components of total
  fat) entering all four variables simultaneously
  is impossible as they are redundant.
• - Options (using types of fat as an example)
  are listed in Table 13-4.
• - Model 1a a standard multivariate model and
  does address the independent effect of saturated
  fat. The term total fat no longer has the
  biologic meaning of total fat because a major
  component, saturated fat, is included separately
  its meaning then becomes mono- and
  polyunsaturated fat.

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• - Model 1b Total fatres E sat fatres total
  fat energy
• the residual from the regression of
  energy-adjusted saturated fat on energy-adjusted
  saturated fat is included. This will provide the
  same coefficient for saturated fat as in model
  1a, but the full biologic meaning of total fat is
  retained ? this model describes disease risk in
  relation both to the total fat composition of the
  diet and to the type of fat.
• - Model 1c Total fat/E sat fat/E energy
• the term for saturated fat (as a nutrient
  density) can be interpreted as substituting
  certain percentage of energy from saturated fat
  for the same amount of other types of fat. The
  term for total fat as a nutrient density reflects
  primarily the energy density of mono- and
  polyunsaturated fats.
• - Models 2a Total fat sat fat poly fat
  energy
• 2b Total fatres E sat fatres total fat
  poly fatres total fat energy
• 2c Total fat/E sat fat/E poly fat/E
  energy
• analogous to models 1a-1c, but more
  specifically address the substitution of
  saturated fat for monounsaturated fat because
  polyunsaturated fat is included as a separate
  term. Can be used for testing the general
  question Does the type of fat add independently
  to the prediction of disease above and beyond
  total fat?

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• - Models 3a Sat fat mono fat energy
• 3b Sat fatres E mono fatres E poly
  fatres E energy
• 3c Sat fat/E mono fat/E poly fat/E
  energy
• are not fat substitution models because the
  total fat composition of the diet is not
  constrained. These models address a somewhat
  different issue Are each of the types of fat,
  substituted for other sources of energy,
  independently associated w/ disease risk?
• Another common example of a dietary factor w/
  nested subcomponents is alcohol intake, where the
  question frequently arises whether an observed
  association is due to a certain type of alcoholic
  beverage.
• The interpretation of multivariate analyses
  including two or more dietary factors should
  always be tempered by knowledge that non of the
  dietary variables are measure perfectly.
  Moreover, the degree of measurement error may
  vary among different dietary factors.
• - One dietary factor may appear to be the true
  predictor and the other a confounder only because
  the former is better measured.

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• EMPERICAL DIETARY SCORES
• Two traditional methods of combining data on
  intakes of various foods have been (1) to compute
  nutrient intakes using food composition tables,
  and (2) to create food groups based on
  similarities in nutrient content.
• - Use of global scores to describe dietary
  patterns or quality has also been suggested.
• Factor Analysis
• Can be used to identify two or more uncorrelated
  dietary patterns based on foods that tend to be
  used (or avoided) by the same persons.
• A score is created for each person for each
  factor by assigning weights to their frequency of
  use of each food. Once the scores are computed
  for each person, their relation to risk of
  disease can be examined.

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• The role of factor analysis or other multivariate
  methods (e.g., principal components or cluster
  analysis) to create scores for dietary patterns
  in nutritional epidemiology remains unclear.
• - In contrast to calculations of nutrient
  intakes, there is no biologic basis for these
  scores.
• - This approach may be useful for describing
  the intercorrelation of foods and thus the
  identification of potential confounders.
• Empirically Selected Variable Score
• A tempting strategy for developing a prediction
  score is to examine the relation of each food (or
  nutrient) w/ risk of disease, pick the
  significant associations, and create a summary
  score comprised of these variables.
• - The problem w/ this approach can be
  appreciated by considering that, if 100 foods are
  examined as disease predictors, by chance alone
  about 5 will be statistically significant. A
  score based on these 5 variables will be
  extremely significantly predictive of disease,
  all on the basis of chance.

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• One common strategy for cross-validation is to
  divide the dataset into halves, create an
  empirical prediction score in one half (training
  set) and evaluate the score in the other half
  (test or validation set).
• More statistically efficient alternatives for
  cross-validation exist, such as the jack knife,
  which involve successively leaving out one
  observation and fitting the model w/ the
  remaining data to predict the omitted
  observation.
• Nutrient Prediction Models Using an Independent
  Gold Standard
• In calculating nutrient intakes from a FFQ, foods
  are weighted by their frequency of use and their
  nutrient content using a food composition
  database.
• - Ideally, the weight would also take into
  account the validity w/ which intake of each food
  was assessed and the bioavailability of the
  nutrient from each food.
• - This additional weighting can be accomplished
  by using an independent quantitative assessment
  of nutrient intake or a biochemical indicator of
  nutrient intake in a sample of the population.

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• Diet records, which are often used to assess the
  validity of a food-frequency instrument, could be
  used as an independent estimate of true nutrient
  intake to develop a prediction score from foods
  on a FFQ.
• - To do so, the nutrient intake from the diet
  record would be used as the independent variable
  in a multiple regression analysis w/ all foods
  from the FFQ being allowed to enter in a stepwise
  multiple regression analysis. Foods that explain
  the most between-person variance in the nutrient
  intake enter first.
• - If the validity of a food item on the
  questionnaire is low (e.g., if it was worded
  poorly), it should not contribute appreciably to
  the prediction of the nutrient.
• - The nutrient score based on the coefficients
  from the stepwise regression could then be
  computed for each person and used in analyses
  predicting disease.
• - Limitations of this approach (1) a large
  number of subjects are needed to provide stable
  estimates of regression coefficients, probably
  considerably larger than most validation studies
  (2) the regression coefficients will reflect in
  part the respondent characteristics which is a
  desirable feature because they may influence
  validity- but this means that they may not be
  generalizable to other population.

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• A biochemical indicator could also serve as the
  standard for developing a prediction score from
  foods on a FFQ.
• - Such an approach would take into account
  factors such as the bioavailability of the
  nutrient in each food and the validity of each
  food item.
• Example Giovannucci et al. (1995) use this
  approach to develop a prediction score for
  lycopene intake using plasma lycopene levels as a
  standard. They found that cooked tomato products
  predicted plasma lycopene levels better than did
  raw tomato products so this was incorporated
  into the empirical prediction equation. When
  this empirical score was used to examine the
  relation between lycopene intake and risk of
  prostate cancer in the total cohort, a stronger
  association was observed than using the standard
  calculation of intake.
• - The size of substudy is a critical issue
  because it determines the precision of
  coefficients, but the desirable size is not
  clear.

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• SUBGROUP ANALYSES AND INTERACTIONS
• The effects of most dietary factors are likely to
  vary among subgroups, depending on the intake of
  other dietary factors and characteristics of the
  subjects. This issue is generally known as
  effect modification or interaction.
• - A fundamental issue is whether the
  interaction should be assessed on an absolute
  scale (whether the rate difference is constant
  across categories of the third variable) or
  relative scale (whether the rate ratio or RR is
  constant across these categories).
• One general concern has been that an extensive
  search for interactions and associations within
  subgroups of other variables creates a high
  likelihood of statistically significant
  associations arising by chance.
• Although there is no simple solution for
  evaluating subgroups w/ confidence, this should
  not deter investigators from examining them.
• - Some subgroup analyses are so important a
  priori that they must be examined, and failure to
  find evidence of effect modification may even
  cast doubt on an association.

42

• When two dietary factors act by a similar
  mechanism, it may be difficult to observe an
  association by examining only one of these
  variables at a time an examination of joint
  exposures may be most powerful.
• Purely exploratory analysis of associations among
  subgroups of known risk factors is also a good
  practice even when little a priori reason exists
  because new knowledge may be gained
• - Such explorations w/o strong prior
  expectations should be clearly described as such,
  and the reader should be skeptical of any
  findings.
• - Some would suggest not reporting p values in
  such circumstances.
• Ultimately, the only fail-safe protection against
  spurious conclusions based on subgroups is
  demonstration of reproducibility, perhaps over
  time within the same study and, most importantly,
  in other independent datasets.

43

• ERROR CORRECTION
• Methods to correct observed associations for
  errors in measurement of exposure variables
  require data on either reproducibility or
  validity this information is now being collected
  as part of many large studies.
• The most common use of error correction
  procedures is the de-attenuation of correlation
  coefficients, probably because this only requires
  replicates of one or both measurements being
  compared.
• - This procedure has become quite routine in
  validation studies, where a small number of days
  of diet records or 24-hour recall data are
  collected as an independent representation of
  true long-term intake.
• In studies of disease incidence, the calculation
  of RRs and C.I. Adjusted for measurement error
  has usually been done as a secondary analysis.
• - These analyses address 3 interrelated
  objectives (1) to obtain the best estimate of
  the RR after accounting for attenuation due to
  imperfect measurement of the primary exposure
  (2) to obtain the best estimate of the true C.I.,
  which is particularly important when little
  association is seen, because the central question
  becomes whether the adjusted C.I. Are
  sufficiently narrow to be informative (3) to
  account for residual confounding by imperfectly
  measured covariates.

44

• ROLE of META-ANALYSIS and POOLED ANALYSIS in
  NUTRITIONAL EPIDEMIOLOGY
• The place of meta-analysis in epidemiology has
  been controversial.
• - Some have argued that the combining of data
  from randomized trials is appropriate because
  statistical power is increased w/o concern for
  validity since the comparison groups have been
  randomized, but that in observational
  epidemiology the issue of validity is determined
  large by confounding and bias rather than
  limitations of statistical power ? the great
  statistical precision obtained by the combining
  of data may be misleading because the findings
  may still be invalid.
• - The combining of all available epidemiologic
  data can be of treat value, particularly when a
  body of evidence becomes substantial and
  difficult to assimilate at once and if the
  potential for bias is not ignored.

45

• An alternative to the combining of published
  epidemiologic data is to pool and analyze the
  primary data from all available studies on a
  topic that meet specified criteria.
• - Because of the complexity of dietary data,
  this approach has great advantages in nutritional
  epidemiology and can address many limitations of
  individual studies.
• Any attempt to combine published data on diet and
  disease is immediately confronted w/ the problem
  that various investigators have usually used
  different approaches for presenting their
  findings that make them difficult to combine
• - Sometimes RRs are given for arbitrary
  quantiles and other times for specified
  increments using continuous variables.
• - Adjustments for total energy intake are often
  done using a variety of methods or not at all,
  and the inclusion of other covariates typically
  differs among studies.
• A major advantage of pooling primary data is that
  all data can be analyzed simultaneously using
  common approaches and definitions of exposure.

46

• In a pooled analysis, the range of dietary
  factors that can be addressed can be considerably
  greater than in the separate analyses because any
  one study will have few subjects in the extremes
  of intake and, sometimes, because the studies
  will vary in distribution of dietary factors.
• Example in the pooled analysis of
  prospective studies of diet and breast cancer, it
  was possible to evaluate associations from lt15
  to gt45 of energy from fat, which was a far
  greater range than possible in the individual
  studies.
• - Although few pooled analyses have been
  conducted at the level of specific foods, this
  can provide a less biased assessment of
  relationships based on the total body of
  evidence.
• Evaluation of the consistency of findings in
  subgroup analyses across studies will reduce the
  likelihood of overinterpreting findings that may
  have occurred by chance.

47

• The data quality may differ among studies due to
  differences in the questionnaires used, study
  designs, or populations.
• - This can be addressed if each study includes
  a validation/ calibration substudy so that
  corrections can be made for the study-specific
  measurement error, and the studies w/ more valid
  assessments of diet can be given more weight.
• - The advantages of pooled analyses in
  nutritional epidemiology are so substantial that
  this should become common practice for important
  issues.