57ª Reunião Anual da Rbras
Workshop in Design of Experiments (DOE)
Analysis for Repeated
Crossover Designs
Carla A. Vivacqua
André L. S. de Pinho
Federal University of Rio Grande do Norte
UFRN – Brazil
Outline
• Motivation
• Good milking practices study
• Experimental Design
• Double-reversal crossover design
• Analysis
• Future Work
3
Motivation
• Safety of dairy products:
• Human health
• Environment
• Animal well-being
4
Somatic Cells Count
• Somatic cells count - SCC (Andrade
et al., 2004):
• Quality of milk
• Health of mammal glands
5
Good Milking Practices
• Set of guidelines for milking process:
•
•
•
•
Cleaning of all equipments
Hygiene of operators
Cleaning of the environment
Cleaning solutions used before and after each milking
6
Objective
• Evaluate the influence of good milking
practices on somatic cell count
7
Previous Studies
• Other variables that may affect
somatic cells count :
• Parity order
• Lactation period
8
Experimental
Design
Experimental Units and
Treatments
• Experimental units:
• Holstein crossbred cows
• Treatments :
• Milking using good practices guidelines
• Milking without good practices guideline (control)
• Just washed the mammal glands with water
10
Completely
Randomized Design
11
Randomized Block
Design
 Grouped by parity order and lactation period
12
How homogeneous
are the
experimental units?
Crossover Design
• AB/BA design
14
Crossover Design
•
Longitudinal study in which experimental units receive
different treatments at different periods of time, in a predetermined sequence
•
Objective: Reduce the effect of differences among
experimental units on the comparison between
treatments
•
Simplest crossover design (AB/BA): involves two
treatments and two periods of time
•
Two concepts are fundamental: the time interval
between applications of different treatments (washout)
and residual effect of treatments (carryover).
15
Washout Period
16
Case Study
• Washout:
- Ideally, the time interval should be
large enough so that the residual
effects of the previous treatment is
eliminated;
• Milking good practices study:
- Washout period of 7 days
17
Carryover Effect
• Residual effect of a treatment
• Treatment effect may persist a long
time after its application
• Main concern during the analysis of a
crossover
design
Kenward, 2003)
18
(Jones
and
Double-Reversal
Design
• Four periods of time (four weeks)
• Two sequences of treatments:
• ABAB
• BABA
• 16 Holstein crossbred cows
• Grouped by:
• Parity order
• Lactation period
• Four cows in each group
19
Analysis
Linear Model
• Terms:
•
•
•
•
Intercept
Period effect
Y
Direct treatment effect
Carryover (additive and treatment by
carryover interactions)
• Effect associated with an animal on a
sequence (parity order, lactation period
effects and interactions)
21
Basic Command in R
• Specify the correct error terms
• Error
22
Future Work
• During the execution of the experiment:
• One cow got sick before the start of the experiment
• Delay in the start of the experiment led to the
classification of a cow on a different lactation period
• One cow got sick during the experiment, some
observations periods are missing
• How do these affect the analysis?
• Would another design be better?
23
References
• ANDRADE et al. (2004) “Influência da
contagem de células somáticas sobre a
produção de leite em diferentes fases da
lactação”, V Simpósio da Sociedade
Brasileira de Melhoramento Animal
• JONES, B., KENWARD, M.G. Design
and Analysis of Cross-Over Trials,
Chapman & Hall/CRC, New York, 2003.
24
Carla A. Vivacqua
[email protected]
André L. S. de Pinho
[email protected]
Thank you!