Factorial Design and CrossOver Design

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Factorial Design and Cross-Over Design

• ? ? ? (Yue-Cune Chang)
• ? ? ? ? ? ? ?
• ???????????

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How to Control Structural Bias?

• Randomization (Combine Some Appropriate
  Experiment Designs Could be Necessary)
• Masking (Blinding)
• Concurrent Controls
• Objective Assessments
• Active Follow-up and Endpoint Ascertainment
• No Post-hoc Exclusions

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Contents

• Factorial Design (Chapter 15)
• Cross-Over Design (Chapter 16)

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Factorial Design

• Definition
• In a factorial design each level of a factor
  occurs
• with every level of every other factor.
• Experimental units are assigned randomly to
• treatment combinations.

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Example

• Suppose there are three factors
• A with three levels
• B with two levels
• C with four levels
• There are 324 24 treatment combinations.
• If there are 3 observations per combination,
• 72 experiment units are needed.

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Why Factorial Design?

• To test the effect of two or more treatments and
  allow to assess the interaction effects among
  those treatments in a single design.
• Factorial designs offer certain advantages over
  conventional comparative designs, even those
  employing more than two treatment arms.
• The factorial structure permits certain
  comparisons to be made that cannot be achieved by
  any other design.

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Example
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Eight Treatment Groups in a Balanced 222
Factorial Design

 
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Restrictions for Using Factorial Design

• The treatments must be amenable to being
  administered in combination without changing
  dosage in the presence of each other.
• It must be ethically acceptable not to administer
  the individual treatments (Control group).
• We must be genuinely interested in learning about
  treatment combinations or else some of the
  treatment groups might be unnecessary.
• The therapeutic questions must be chosen
  appropriately.

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Partial (Fractional) Factorial Design

• Partial, or fractional, factorial designs are
  that omit certain treatment groups by design.
• For higher-order designs, if some interactions
  are known biologically not to exist, certain
  treatment combinations can omitted from the
  design and still permit estimates of other
  effects of interest. e.g. in the 222 design,
  if interaction between A, B, and C is known not
  to exist, that treatment cell could be omitted
  from the design and still permit estimation of
  all main effects.

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Factorial Designs are Useful in Two Circumstances

• When two or more treatments do not interact,
  factorial designs can test the main effects of
  each using smaller sample sizes and greater
  precision than separate parallel groups designs.
• When it is essential to study treatment
  interactions, factorial designs are the only way
  to do so.

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• Example 1 A study is conducted to determine the
  effect of water level and type of plant on the
  overall stem length of pea plants. Three water
  levels and two plant types are used. Eighteen
  leafless plants are available for study. These
  plants are randomly divided into three subgroups,
  and then water levels are randomly assigned to
  the groups. A similar procedure is followed with
  18 conventional plants. The response is the stem
  length in centimeters.
• Data Factorial Design Ex 1

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• Example 2 A study is run of the effect of
  photoperiod and genotype on the latent period of
  infection of barley mildew isolate AB3. Fifty
  leaves of each of four genotypes are obtained and
  randomly split into five subgroups, each of size
  10. Each group is infected and then is exposed to
  a different photoperiod. The response noted is
  the number of days until the appearance of
  visible symptoms.
• Data Factorial Design Ex 2

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• Example 3 A study is run of the capsular
  solubility in biological fluids of two of the
  most commonly encapsulated enzyme preparations.
  The purpose is to determine the effect of capsule
  type and biological fluid on the time until
  dissolution of the capsule. Two biological fluid,
  gastric and duodenal juices, and two capsule
  types, C and V, are used. Thus two factors are
  involved, each being studies at two levels. To
  conduct the study, 10 empty capsules of each type
  are obtained and randomly divided into two
  subgroups, each of size 5. One group is dissolved
  in gastric juices the other, in duodenal juice.
  The response noted is the time (in min.) at which
  the first air bubbles are released through
  perforations in the capsules.
• Data Factorial Design Ex 3

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• Example 4 Cotinine is a major metabolite of
  nicotine. It is currently considered to be the
  best indicator of tobacco smoke exposure. A study
  is conducted to detect possible racial
  differences in cotinine level in young adults.
  The data are obtained on the cotinine level in
  milligrams per milliliter.
• Data Factorial Design Ex 4

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• Example 5 A study of the effect of wastewater
  plant discharge water on freshwater ecology is
  conducted. Two sampling sites are used in the
  study. One site is upstream from the point at
  which the plant introduces effluents into the
  stream the other is downstream. Samples are
  taken over a 3-week period. These data are
  obtained on the number of diatoms (??) found.
• Data Factorial Design Ex 5

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Cross-Over Design

• Definition
• An experiment is a cross-over experiment if the
• same experimental unit receives more than one
• treatment, or is investigated under more than
• one condition of the experiment. The different
• treatments are given during non-overlapping
• time period.

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Notes

• In factorial designs, some patients also receive
  more than one treatment. However, basic
  cross-over are different from these because some
  patients receive more than one treatment
  simultaneously in factorial trials.
• In a cross-over trial, only the order of
  administering the treatments is randomized
• (not the study subjects).

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Cross-Over Design ????

• Random Assignment
• Carry-over Effects
• Changes Over Time (Period Effects)
• Permanently Change the Subjects in the first
  Period

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????(Perycit) ? HBL ? DHBL ????? ---Cross-Over
Design
Order 1 (A to B) 2 (B to A) where A ???,
B????(Perycit) Ref ??, ???(2000)???????? (??)
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• Note
• Cross-over trials are those in which
  study participants receive all treatments under
  investigation, each in a different study period.
  Between periods, a washout period is used to
  allow the effects of the previous treatment to
  disappear. Because the treatment effect is
  estimated within rather than between patients,
  cross-over are more efficient than parallel
  groups designs.
• Ancillary measurements, such as baseline
  covariates at the beginning of each treatment
  period, can improve the performance of cross-over
  designs.

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• Note Despite the potential benefits and
  efficiencies of the cross-over design, there are
  serious limitations to its widespread use shown
  as follows
• The investigators must have some knowledge of the
  sign and magnitude of the within-patient
  correlation between responses.
• The underlying disease must have a constant
  intensity during ALL treatment period. If the
  disease is cured by one of the treatments or can
  be expected to disappear in a short (relative to
  the treatment period) time, the cross-over design
  will not be applicable.
• The effect of the treatment needs to be
  restricted to the period in which it is applied.
  Equivalently, the treatment periods must be
  separated by a sufficient length of time for the
  effects of the earlier treatment to subside.