Outline Some field sampling issues Overview of approach to understanding a system Example 1 KPBS Exa

1
OutlineSome field sampling issuesOverview of
approach to understanding a systemExample 1
KPBSExample 2 XooExample 3 SIR
modelThrough approach again with these three
examples

• Karen A. Garrett
• Kansas State University

2
Cercospora apii infects both humans and celery
Phytophthora infestans, an oomycete
Rust fungi
Wheat curl mite, vector of Wheat streak mosaic
virus
3
Designed experiments vs. observational experiments

• Designed experiments generally have a more
  straightforward analysis
• Observational experiments rely more on
  correlation, so that interpreting causality may
  be more difficult
• Many experiments in disease ecology have some
  designed elements and some observational elements

4
Ratio of Phaeosphaeria nodorum to Mycosphaerella
graminicola compared to sulfur dioxide emissions
Bearchell et al. 2005 PNAS
5
Defining an inference space

• The inference space of an experiment is the group
  to which the experimental conclusions can be
  correctly applied
• The pool from which the experimental units are
  randomly drawn will clearly be part of the
  inference space
• Logic outside statistical inference may be used
  to extend results to broader set of units
• Definition of this space allows definition of the
  appropriate experimental unit

6
Pseudoreplication

• Pseudoreplication occurs when repeated
  observations of a subject are substituted for
  replicated applications of a treatment on
  different subjects
• In general, if it seems that the number of
  replicates can be increased indefinitely by
  splitting samples in increasingly smaller units,
  these are probably pseudoreplicates
• What is objectionable is when the tentative
  conclusions derived from unreplicated treatments
  are given an unmerited veneer of rigor by the
  erroneous application of inferential statistics
  - Hurlbert

7
Classic example of pseudoreplication
True replicates
Pseudoreplicates
Scenario in which an individual mite is the
appropriate experimental unit
8
Pseudoreplication ex 2 pseudoreplication in
spatial samples
Suppose that a treatment has been applied at the
larger scale
Pseudoreplication
9
Suppose there is no treatment application or
experimental design?

• Defining pseudoreplication in an observational
  study is more challenging
• The variance associated with sampling at
  different spatial scales or across different
  types of groups of individuals can be compared to
  determine what are the largest sources of
  variation

10
Important note about correlation and newer
statistical packages

• Recall the standard assumption for typical
  analyses of variance that observations are
  independent
• In the past, and sometimes in the present, people
  might disregard the possibility of using packages
  like SAS Proc GLM because they knew their samples
  were not truly independent
• Newer programs like SAS Proc Mixed (and programs
  in R?) make it easier to specify more complicated
  correlation matrices for the errors in an
  analysis of variance

11
Statistical power

• Statistical power the probability of detecting
  treatment effects that really exist
• Scientists have tended to emphasize controlling
  the Type I error rate (the probability of
  designating an effect as significant when it is
  not real) rather than maximizing power
• This seems to be based on the idea that journals
  should not be cluttered with reports of a lot of
  effects that are not real
• However, if you want to manage a disease,
  discarding an effect because the associated
  p-value is greater than 0.05 may lead you to
  leave out important effects
• Real effects may be difficult to detect because
  of noise
• Sensitivity analyses can be used to explore the
  implications of removing an effect when it is
  actually real

12
Parsimony

• On the other hand, parsimony is a good general
  goal
• Statistical models need to strike a balance to
  avoid leaving out important predictors and also
  to avoid overparameterizing
• Mechanistic models can be applied to explore the
  potential impacts of many predictors

13
Statistical power

• Power is increased by reducing measurement errors
  and by increasing sample size
• Just because a null hypothesis has not been
  rejected doesnt mean that there are no treatment
  effects

14
Testing for bioequivalence

• Bioequivalence tests can be used to formally test
  whether there is no difference between the
  effects of treatments (within some tolerance)

15
Garrett 1997
16
Defining a biological tolerance level

• A sensitivity analysis might be used to define a
  tolerance level for effects below which there is
  not expected to be any important impact
• Formal discrimination between statistical
  significance and biological significance
• BUTyou would need to have a great deal of
  confidence in your model to rely on this for
  management decisions

17
Meta-analysis applications in plant pathology

• Comparisons across studies can be formalized in
  meta-analyses
• We have illustrated the application of
  meta-analysis to the large quantities of data
  available from plant pathology field trials

Rosenberg, Garrett, Su, and Bowden 2004
Phytopathology
18
Metadata

• The National Center for Ecological Analysis and
  Synthesis works with metadata and metadata
  standards as one of its many projects
• http//www.nceas.ucsb.edu/nceas-web/resources/meta
  data.html

19
For discussing the disease data set analyses

• Here are some suggestions for pondering your data
  sets and projects
• You might consider addressing these questions in
  your discussions and final presentation

20
Defining the goals of the project

• A. What is the motivation for the project?
• Understanding the system better
• In what way in particular?
• Learning to manipulate the disease
• What are the potential methods for manipulation?
• B. What are the hypotheses to be tested or
  parameters to be estimated?
• Will the project be sufficient to test
  hypotheses?
• Or will it more appropriately generate hypotheses
  to be tested in a more controlled context?

21
Variables and parameters

• What are the potential predictor and response
  variables?
• What are the parameters to be estimated?
• When using parameter estimates from an experiment
  in a mechanistic simulation model, the estimates
  might be viewed as values to emphasize while
  considering a wider range of possible values

22
Studying the distribution of variables

• It may be necessary to split variables into
  logical groups, such as by environment
• For example, if environment has a large effect,
  analyzing the disease severity for samples from
  all environments in the same analysis might
  produce a multi-model distribution

23
What are sources of bias?

• Since samples may not have been collected
  specifically to answer later questions, estimates
  may be biased for some questions
• For example, rather than random sampling,
  specific individuals may have been sampled
  because of their observed characteristics
  (symptoms, family size, )
• True random sampling is often a challenge, anyway

24
Deciding what to average prior to analysis

• Once the appropriate experimental unit is
  identified, you might average the subsamples
  within a unit
• Possibly the subsample variance is interesting in
  its own right and you would like to include it in
  analyses
• You can keep all the individual subsample
  measures in the analysis if you are careful to
  use the correct error estimates for testing
  effects

25
Is there a widely accepted model for this system
already available?

• Can your data be used to further validate this
  model or perhaps as an example of a case in which
  the model does not hold?
• Does your data add a new component to this model,
  such as considering the effects of a novel
  environmental parameter?

26
If there are not already accepted models for your
system

• Is there a related system that has been studied
  more, modeled, and might be used as a starting
  point for considering your system?
• For example, SIR models might be generally
  applied for many types of disease

27
Iteration between input from experimental
analyses and input from modeling
Modeling Construction of new hypotheses and
predictions
Empirical experimentation Testing of hypotheses
in experiments generation of new parameter
estimates generation of new hypotheses
Modeling Construction of new hypotheses and
predictions
Empirical experimentation Testing of hypotheses
in experiments generation of new parameter
estimates generation of new hypotheses
28
Sensitivity analysis

• Analysis of model output for a range of parameter
  and variable inputs analysis of the sensitivity
  of outputs to changes in the inputs
• The distribution of outputs for a particular set
  of inputs can be evaluated in terms not only of
  the mean or median, but also the maxima and minima

29
Model validation

• A data set might be split by location, so that a
  model developed based on one subset of locations
  is validated using another subset
• A data set might be split by time, so that a
  model developed based on earlier time points is
  validated using later time points