Using Statistical Methods for Environmental Science and Management

1
Using Statistical Methods for Environmental
Science and Management

• Graham McBride, NIWA, Hamilton
• g.mcbride_at_niwa.co.nz
• Statistics Teachers Day, 25 November 2008
• What do statisticians really do?

2
THE ROLE OF STATISTICAL METHODS MY VIEW

• Separate randomness from pattern
• Make inferences about the world, based on data
  from samples
• Help to design sampling programmes (use resources
  efficiently)
• Help to establish cause and effect
• Cant prove anything with statistics

3
Three kinds of lies Insult, or compliment?

• There are three kinds of lies
• lies, damned lies, and statistics
• Who said that?
• Mark Twain (1835 1910)
• Figures often beguile me, particularly when I
  have the arranging of them myself
• Benjamin Disraeli (1804 1881)
• Sought to discredit true British soldier casualty
  figures in the Crimean War (1853 1856)
• Who came first? (Twain cites Disraeli!)

4
What you should do

• Establish the context of your work (what do
  people want to know, and why do they want to know
  that?)
• Consult with others, e.g., to discuss whether a
  proposed sampling programme can actually be done
• Discuss the appropriate burden-of-proof (e.g.,
  drinking water standards minimise the consumers
  risk, not the producers risk)

5
What you should not do

• Confuse association and causation (pp. 267-8 of
  Barton, Sigma Mathematics)
• Ignore other lines-of-evidence (Bradford-Hill
  criteria), such as
• Can the cause reach the location of the effect?
• Is the finding plausible?
• Can you explain inconsistencies with other
  evidence?
• Be ignorant of how statistical procedures work
• The computer said so

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What you should not do

• Believe that there is only one statistically
  correct way of analysing data
• There are lots of good ways many more bad and
  wrong ways too
• Not consider bias and imprecision in your data

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Bias and Imprecision
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What you might have to do

• Use non-standard methods, e.g.,
• non-parametric (rank) methods for highly skewed
  data (very common in aquatic studies)
• e.g., linear trend or monotonic trend?
• Read rather widely
• Statistics is not a cut-and-dried subject there
  are still some fundamental debates about
  statistical inference, especially the Bayesians
  versus the frequentistsboth approaches have
  their place

9
What you also might have to do

• Answer this question What is P
• Result of a hypothesis test
• Used (over-used!) routinely, so youll need to
  know
• P Prob(data at least as extreme if the tested
  hypothesis is true)
• Not the probability of the truth of the
  hypothesis
• Relate results to confidence intervals

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EXAMPLEIncreasing pressure on freshwaters
Is there evidence of associated deterioration (or
improvements) in rivers?
11
600000
4
Total Nitrogen
3.5
Total Phosphorus
500000
Cows
3
400000
2.5
Fertilizer consumption (tonnes)1
Cow numbers (millions)2
300000
2
1.5
200000
1
100000
0.5
0
0
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Data source 1Fertilizer consumption UN Food
Agriculture Organisation 2Cows Livestock
Improvement NZ Dairy Statistics
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A National River Water Quality Network for New
Zealand (1989)

• GOAL
• To provide scientifically defensible information
  on the important physical, chemical, and
  biological characteristics of a selection of the
  nations rivers as a basis for advising the
  Minister of Science and other Ministers of the
  Crown of the trends and status of these waters
• OBJECTIVES
• Detect significant trends in water quality
• Develop better understanding of water resources,
  and hence to better assist their management

13
NRWQNstructure

• 77 sites on 35 rivers
• All sites have reliable flow data
• Sites are sampled by regional Field Teams
• 14 WQ parameters (monthly)
• Data available (search for WQIS www.niwa.co.nz

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WQ state land use
Correlations with Pasture Temperature 0.50 Co
nductivity 0.55 pH -0.19 Dissolved
oxygen -0.17 Visual clarity -0.60 NOx-N 0.71
NH4-N 0.77 Total nitrogen 0.84 DRP 0.67
Total phosphorus 0.74 E. coli 0.79
P lt 0.001 Spearman rank correlation
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WQ Trends 1989-2005

• Calculated annual medians from monthly data at
  each site for each parameter
• Took the 77 datapoints for each year and
  calculated the 5th, 50th, and 95th percentile
  values
• The 50th percentile gives us a picture of what is
  happening in a national average river in terms
  of annual median water quality data
• The 5th and 95th percentiles tell us about
  changes over time in our best and worst
  rivers.
• Trends in these values were assessed using the
  Spearman rank correlation coefficient (rS).

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NOx-N Trends 1989-2005

1200
1000
)
3
800
-N (mg/m
600
x
NO
400
200
0
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Year
Concentrations of NOx-N increased dramatically
between 1989 2005 in our most enriched rivers
18
Trends 1989-2005

• Results indicative of
• Warming in our coolest rivers
• Drops in pH
• Increasing nitrogen enrichment
• Decreases in BOD5 most rivers

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Trends 1989-2003

• More formal analysis of trends carried out on
  monthly data (1989-2003) at all 77 sites
• Seasonal Kendall test
• Data were flow-adjusted using LOWESS (many WQ
  parameters can be strongly influenced by
  discharge)
• Used a binomial test to indicate a national
  trend
• Discriminate between significant (i.e. P lt
  0.05) and meaningful trends (i.e., P lt 0.05 and
  slope gt 1 of median value per annum).

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Trends in TN
Total nitrogen exhibited a strong increasing
trend at the national scale during 1989-2003 (P lt
0.001). Increasing trends in TN were
particularly evident in the South Island, where
25 of 33 sites showed meaningful increases.
21
Trends in DRP
There was a strong national trend of increasing
DRP concentrations during 1989-2003 (P lt
0.001). This result contrasts with the
relatively weak trends observed for 1989-2005.
22
Summary of trends 1989-2003
No significant trend
Significant improving trend
Significant deteriorating trend
23
Links between land use and trends
The magnitude of trends in DRP increase with
pastoral land use
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Land use and trends
RSKSE
SKSE
Parameter
0.20
0.19
Temperature
0.40
0.47
Conductivity
-0.28
-0.28
pH
-0.27
-0.27
Dissolved oxygen
-0.11
-0.26
Visual clarity
0.23
0.30
Oxidised nitrogen
0.68
0.29
Ammoniacal nitrogen
-0.01
0.35
Total nitrogen
0.48
0.59
Dissolved reactive phosphorus
0.18
0.31
Total phosphorus
Spearman rank correlation coefficients (bold P lt
0.01)
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Conclusions

• Strong associations between nutrient
  concentrations and pastoral land cover at the
  national scale (State)
• Rivers draining large areas of pastoral land have
  deteriorated significantly over the last 17 years
  with respect to nitrogen concentrations (Trends)
• The magnitude of trends in some parameters is
  associated with extent of pastoral land use
• Decreasing trends in NH4-N and BOD5 indicative of
  improvements in point source management
• Increasing trends in nutrients indicative of
  increasing pressure from agriculture

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EXAMPLEWater quality-human health risk
assessment, quantitative approach Christchurch
City Wastewater Outfall
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Quantitative Microbial Health Risk Assessment
(QMHRA)

• Identify hazards (pathogens)
• Quantify exposure (swimming, shellfish
  consumption)
• Assess dose-response
• Characterise risk

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Hazard vs. Risk

• Hazards can cause harm, after exposure
• Risk cannot occur if no exposure
• Can have hazard without risk
• But not vice versa!

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Christchurch hazardsviruses only

• From an extensive list (next slide)
• Swimming
• adenovirus (respiratory)
• rotavirus
• enterovirus (Echovirus 12)
• Shellfish consumption (raw)
• enteroviruses
• rotavirus
• hepatitis A

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Dose-response curves
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Accounting for variability and uncertainty

• Exposure is variable
• e.g., individuals swim duration
• Dose-response is uncertain
• only some pathogen strains in clinical trials
• trials limited to healthy adults
• Describe using statistical distributions in a
  Monte Carlo analysis

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Scenariosis!

• 1,000 people 1,000 occasions
• 8 beaches
• 2 influent virus conditions (normal outbreak)
• 2 seasons summer/winter
• 3 viruses for 2 activities
• 2 outfall lengths
• 2 virus inactivation regimes
• 2 UV options (with without)
• ? 1536 x 106 calculations

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Calculation sequence
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Dose-response models

• Constant susceptibilitysimple exponential (d
  average dose, Prinf infection prob)
• Variable susceptibilitybeta-Poisson
• Calculations performed using _at_RISK (an Excel
  plug-in)

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Occasion 1, Individual 1
Volume ingested
Dose
Probability of infection
Binomial distribution
Infected?
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Occasion 1, Individual 2
Volume ingested
Dose
Probability of infection
Binomial distribution
Infected?
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Occasion 1, Individual 3
Volume ingested
Dose
Probability of infection
Binomial distribution
Infected?
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Occasion 1, Individual 1000
Volume ingested
Dose
Probability of infection
Binomial distribution
Infected?
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Occasion 2, Individual 1
Volume ingested
Dose
Probability of infection
Binomial distribution
Infected?
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Occasion 2, Individual 2
Volume ingested
Dose
Probability of infection
Binomial distribution
Infected?
43
Occasion 2, Individual 3
Volume ingested
Dose
Probability of infection
Binomial distribution
Infected?
44
Characterising the results

• Risk percentilespercent of time the risk is
  below a stated value
• IIRIndividual Infection Risk (total number of
  calculated infections divided by total number of
  exposures)

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Results
South New Brighton
Integers are cases per 1000 exposures
46
IIR Normal influent, South Brightonadenovirus,
swim
Numbers are percentages. MfE/MoH (2003)
guidelines lt0.3 Very good.
47
IIR Normal influent, South Brighton rotavirus,
shellfish
Numbers are percentages.
48
IIR Outbreak influent, South Brighton
adenovirus, swim
Numbers are percentages. MfE/MoH (2003)
guidelines 1.9 - 3.9 Fair - Poor.
49
IIR Outbreak influent, South Brighton
rotavirus, shellfish
Numbers are percentages.
50
IIR Outbreak influent, South Brighton hepatitis
A, shellfish
Numbers are percentages.
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Statistical modelling can reveal important
information gaps

• Bioaccumulation factors for NZ shellfish
• Dose-response for norovirus (new study published)
• Detailed exposure data (ingestion rates etc.)
• Constancy of virulence?
• Campylobacter in shellfish?
• Better methods for uncertainty analysis
• Better models for illness, cf. infection

52
Conclusions

• Longer outfall no UV still has higher risk than
  shorter outfall with UV
• But risks low
• What if UV doesnt work 24/7 (technology
  breakdown, power outage,)
• Decision longer outfall, no UV

53
Semi-Quantitative approach

• Use when hazards and exposures are less
  well-defined and more widespread
• Paradigm is
• Risk score Likelihood x Consequences
• Use scores as a relative measure of risk.
• Use panel of experts may solicit list of
  hazards from affected community

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Hazards

• Pathogens (from humans and animals)
• Chemicals
• Algal toxins
• Physical objects

57
End-points (exposures)

• Recreational contact
• Drinking water consumption
• Consumptions of aquatic organisms
• Food? (more difficult)

58
The delivery chain

• Can be called hazardous event
• How does the hazard get from its origin to the
  point of exposure?

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Likelihood

• Probability of an exposure event (for at least
  one person) in a year (cf. any year) to a
  sufficient degree to cause harm. Scores

0 Impossible 0 1 Extremely unlikely
1 2 Very unlikely 1 5 4 Unlikely 6
40 6 Even 41 60 8 Likely 61 95 10 Very
likely gt95
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Consequences
Scale Severity Duration 1 lt1 1
Asymptomatic 1 Day 2 15 2 Discomfort 2
Week 3 510 3 Visit doctor 3 Month 4
1020 4 Hospitalisation 4 Year 5 gt20 5
Death 5 Permanent Percent of total community
Refers to health effect
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Typical results
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Conclusions

• Use QRA for well-defined local problems
• Use semi-quantitative methods for broader-scale
  problems
• Risk assessment identifies many knowledge gaps,
  some need urgent attention
• Most difficult gap often the delivery chain
• Can update assessments with new data
• Especially useful in ranking risks

63
EXAMPLECompliance with Drinking Water Standards
How to assess compliance with microbial limits?

• Cant sample everything
• Need high assurance that supply isnt
  contaminated in some assessment period cant be
  fully assured
• MoH then said We want to be 95 confident that
  the water is uncontaminated for 95 of the time.
  What should the compliance rule be?

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What kind of a question is this?

• Bayesian
• It asks about the probability of an hypothesis,
  given data that we will collect
• Frequentist (classical methods) ask about the
  probability of data assuming an hypothesis to be
  true
• Precautionary (not permissive)
• Benefit of doubt goes to the consumer, not to the
  supplier
• One-sided
• Hypothesis to be tested is breach, not compliance

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Results
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Results
67
Policy Implications

• Results in Table 8.2 now incorporated into 2005
  Drinking-water Standards for New Zealand
• http//www.moh.govt.nz/moh.nsf/0/12F2D7FFADC900A4C
  C256FAF0007E8A0/File/drinkingwaterstandardsnz-200
  5.pdf

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EXAMPLEEffect of microbial contamination on
swimmers health
Epidemiological study at 7 NZ beaches
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Main Findings

• Using generalized regression models
• Evidence of respiratory illness effects related
  to microbial contamination
• Human- and animal-waste impacted beaches not
  separable in terms of health effects
• Both were separable from control beaches

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Policy implications

• Human and animal wastes no longer distinguished
  in terms of health risks
• Result incorporated into new guidelines
• http//www.mfe.govt.nz/publications/water/microbio
  logical-quality-jun03/