using statistical methods for environmental science and management

Using Statistical Methods for Environmental Science and Management

Graham McBride, NIWA, [email protected]

Statistics Teachers’ Day, 25 November 2008

What do statisticians really do?

• 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

• Can’t “prove anything with statistics”

THE ROLE OF STATISTICAL THE ROLE OF STATISTICAL METHODS: MY VIEWMETHODS: MY VIEW

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!)

““Three kinds of lies”Three kinds of lies”InsultInsult, or , or complimentcompliment??

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 consumer’s risk, not the producer’s risk)

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

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

Bias and Imprecision

INACCURATE INACCURATE INACCURATE ACCURATE

(a) Biased, imprecise (b) Unbiased, imprecise (c) Biased, precise (d) Unbiased, precise

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 frequentists—both approaches have their place

What you also might have to do

• Answer this question: “What is P” – Result of a hypothesis test– Used (over-used!) routinely, so you’ll 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

EXAMPLEEXAMPLEIncreasing pressure on freshwatersIncreasing pressure on freshwaters

Is there evidence of associated deterioration (or improvements) in rivers?

0

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Total Nitrogen

Total Phosphorus

Cows

Data source: 1Fertilizer consumption – UN Food & Agriculture Organisation2Cows –Livestock Improvement NZ Dairy Statistics

GOAL

To provide scientifically defensible information on the important physical, chemical, and biological characteristics of a selection of the nation’s 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

1. Detect significant trends in water quality

2. Develop better understanding of water resources, and hence to better assist their management

A National River Water Quality A National River Water Quality Network for New Zealand (1989)Network for New Zealand (1989)

• 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

NRWQNNRWQNstructurestructure

Correlations with % Pasture

Temperature 0.50***

Conductivity 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 < 0.001; Spearman rank correlation

WQ state & land WQ state & land useuse

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).

NONOxx-N Trends 1989-2005-N Trends 1989-2005

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x -N

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g/m

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5th 50th 95th

Concentrations of NOx-N increased dramatically between 1989 & 2005 in our most enriched rivers

Trends 1989-20055th 50th 95th

TEMP 0.70 0.33 0.28

COND 0.30 0.48 0.22

PH -0.27 -0.11 -0.64

DO -0.09 -0.25 -0.11

CLAR 0.13 0.39 0.44

NOx-N -0.81 0.37 0.80

NH4-N -0.96 -0.94 0.44

TN 0.39 0.59 0.71

DRP -0.26 0.48 0.05

TP -0.10 0.24 -0.37

BOD5 -0.75 -0.88 -0.70

Results indicative of:

• Warming in our coolest rivers

• Drops in pH

• Increasing nitrogen enrichment

• Decreases in BOD5 most rivers

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 < 0.05) and “meaningful” trends (i.e., P < 0.05 and slope > 1% of

median value per annum).

Trends in TN

Total nitrogen exhibited a strong increasing trend at the national scale during 1989-2003 (P < 0.001).

Increasing trends in TN were particularly evident in the South Island, where 25 of 33 sites showed meaningful increases.

Trends in DRP

There was a strong national trend of increasing DRP concentrations during 1989-2003 (P < 0.001).

This result contrasts with the relatively weak trends observed for 1989-2005.

Summary of trends 1989-2003

No significant trend Significant improving trend Significant deteriorating trend

Plot 1

Temp Cond pH DO Clar NOx-N NH4-N TN DRP TP BOD5

RS

KS

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Links between land use and trends

The magnitude of trends in DRP increase with % pastoral land use

y = 0.0406x - 0.0027

R2 = 0.31

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% Pastoral land use

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LowerManawatu Rv.

Land use and trends

0.180.31Total phosphorus

0.480.59Dissolved reactive phosphorus

-0.010.35Total nitrogen

0.680.29Ammoniacal nitrogen

0.230.30Oxidised nitrogen

-0.11-0.26Visual clarity

-0.27-0.27Dissolved oxygen

-0.28-0.28pH

0.400.47Conductivity

0.200.19Temperature

RSKSESKSEParameter

Spearman rank correlation coefficients (bold P < 0.01)

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

EXAMPLE:Water quality-human health risk assessment, quantitative approach

Christchurch City Wastewater Outfall

Pipeline route

Pump Station

Oxidation PondsAvon-Heathcote Estuary

Quantitative Microbial Health Risk Assessment (QMHRA)

• Identify hazards (pathogens)

• Quantify exposure (swimming, shellfish consumption)

• Assess dose-response

• Characterise risk

Hazard vs. Risk

• Hazards can cause harm, after exposure

• Risk cannot occur if no exposure

• Can have hazard without risk

• But not vice versa!

Christchurch hazards—viruses only

From an extensive list (next slide):

• Swimming– adenovirus (respiratory)– rotavirus– enterovirus (Echovirus 12)

• Shellfish consumption (raw)– enteroviruses– rotavirus– hepatitis A

Pathogen Main disease caused Comments Include?

Bacteria

Campylobacter spp. Gastroenteritis Poor survival in seawater No

Pathogenic E. coli Gastroenteritis Low concentration expected in sewage No

Legionella pneumophila Legionnaires' disease No evidence of environmental infection route

No

Leptospira sp. Leptospirosis Low concentration expected in sewage No

Salmonella sp. Gastroenteritis Low concentration expected in sewage No

Salmonella typhi Typhoid fever Rare in New Zealand No

Shigella sp. Dysentery Low concentration expected in sewage No

Vibrio cholerae Cholera Rare in New Zealand No

Yersinia enterolitica Gastroenteritis Low concentration expected in sewage No

Helminths

Ascaris lumbricoides Roundworm Rare in New Zealand No

Enterobius vernicularis Pinworm Low concentration expected in sewage No

Fasciola hepatica Liver fluke Rare in New Zealand No

Hymnolepis nana Dwarf tapeworm Rare in New Zealand No

Taenia sp. Tapeworm Rare in New Zealand No

Trichuris trichiura Whipworm Rare in New Zealand No

Protozoa

Balantidium coli Dysentery Low concentration expected in sewage No

Cryptosporidium oocysts Gastroenteritis Can accumulate in shellfish, but virus groups of more concern

No

Entamoeba histolytica Amoebic dysentery Rare in New Zealand No

Giardia cysts Gastroenteritis Poor survival in seawater No

Viruses

adenoviruses Respiratory disease2 Very infective, present in substantial concentrations in raw sewage

Yes (SW only)1

enteroviruses Gastroenteritis Less infective, but health consequences can be more severe than adenovirus

Yes (SW and SF)

hepatitis A virus Infectious hepatitis Low sewage concentration; very infective Can affect surfers in contaminated waters4

Yes (SF)

noroviruses3 Gastroenteritis No reliable method for viability enumeration; limited data on occurrence in water and infectivity.

No

rotaviruses Gastroenteritis Limited evidence of waterborne infection in NZ; infection in children would be of concern.5

Yes (SF and SW)

Dose-response curves

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Variable susceptibility

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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

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

Calculation sequenceViruses in raw sewage

Treatment efficiency

Virus concentrationat beach

Virus concentrationsin shellfish

Meal size

Bioaccumulation Duration of swim

Water ingestion/inhalation rate

Plume dispersion model(including inactivation)

Dose-responserelationships

Dose-responserelationships

UV disinfection, if present

Number of virusesingested

Number of virusesingested or inhaled

Proportion of population infected

Dose-response models• Constant susceptibility—simple exponential

(d = average dose, Prinf = infection prob)

• Variable susceptibility—“beta-Poisson”

• Calculations performed using “@RISK” (an Excel plug-in)

rdd e1)(Prinf

dd 11)(Prinf

Pro

b(in

f)

Volume ingested

Dose

Probability of infection

Infected?

Binomial

distribution

Duration

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Occasion 1, Individual 1

Ingestion rate

Fre

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b(in

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Volume ingested

Dose


Binomial

distribution

Duration

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Ingestion rate

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Infected?

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Dose


Binomial

distribution

Duration

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Ingestion rate

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Infected?

Sum the cases

Pro

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Volume ingested

Dose


Binomial

distribution

Duration

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Ingestion rate

Fre

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Infected?

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Volume ingested

Dose


Binomial

distribution

Duration

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Ingestion rate

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Microorg. concn

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Infected?

Characterising the results

• Risk percentiles—percent of time the risk is below a stated value

• IIR—Individual Infection Risk (total number of calculated infections divided by total number of exposures)

ResultsSouth New Brighton

Integers are cases per 1000 exposures

RAW SHELLFISH CONSUMPTION: NORMAL NONCONSERVATIVE ROTAVIRUS

Summer Winter

2 km 3 km 2 km 3 km

no UV UV no UV UV no UV UV no UV UV

Min 0 0 0 0 0 0 0 0

50%ile 0 0 0 0 0 0 0 0

90%ile 0 0 0 0 0 0 0 0

95%ile 0 0 0 0 1 0 0 0

98%ile 0 0 0 0 4 1 2 1

99%ile 0 0 0 0 6 2 3 1

99.9%ile 1 1 0 0 15 6 7 3

Max 2 1 0 0 16 7 8 4

IIR(%) 0.0005 0.0002 0.0000 0.0000 0.0244 0.0052 0.0089 0.0032

IIR: Normal influent, South Brightonadenovirus, swim

2 km, no UV 2 km, UV 3 km, no UV 3 km, UV

Summer

0.0001 0.0000 0.0000 0.0000

Winter

0.0034 0.0002 0.0016 0.0005

Numbers are percentages. MfE/MoH (2003) guidelines: <0.3% = “Very good”.

IIR: Normal influent, South Brighton

rotavirus, shellfish2 km, no UV 2 km, UV 3 km, no UV 3 km, UV

Summer

0.0005 0.0002 0.0000 0.0000

Winter

0.0244 0.0052 0.0089 0.0032

Numbers are percentages.

IIR: Outbreak influent, South Brighton adenovirus, swim


Summer

0.0568 0.0179 0.0009 0.0003

Winter

2.1135 0.5552 1.0959 0.3016

Numbers are percentages. MfE/MoH (2003) guidelines: 1.9 - 3.9% = “Fair” - “Poor”.

IIR: Outbreak influent, South Brighton rotavirus, shellfish


Summer

0.3882 0.1034 0.0033 0.0005

Winter

4.9911 2.1668 2.3916 1.1779


IIR: Outbreak influent, South Brighton hepatitis A, shellfish


Summer

0.0343 0.0107 0.0000 0.0001

Winter

0.9441 0.2477 0.4633 0.1733


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

Conclusions• Longer outfall no UV still has higher risk than shorter

outfall with UV• But risks low• What if UV doesn’t work 24/7 (technology

breakdown, power outage,…)• Decision: longer outfall, no UV

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

Hazards

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

“End-points” (exposures)

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

The delivery chain

• Can be called “hazardous event”

• How does the hazard get from its origin to the point of exposure?

LikelihoodProbability 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 >95%

Consequences

Scale# Severity* Duration*

1: <1% 1: Asymptomatic 1: Day

2: 1–5% 2: Discomfort 2: Week

3: 5–10% 3: Visit doctor 3: Month

4: 10–20% 4: Hospitalisation 4: Year

5: >20% 5: Death 5: Permanent# Percent of total community

* Refers to health effect

Typical resultsExposure Population Score Hazardous event

Recreational Water

Normal 250 Toxic algal bloom (marine) – inhalation

Recreational Water

Normal 250 Strong rips and current in bathing areas

Recreational Water

Normal 240 Urban stormwater discharge in streams and beaches

Recreational Water

Normal 240 Bird defecation into freshwater margins

Recreational Water

Normal 200 Toxic algal blooms (f/w) – inhalation

Recreational Water

Normal 200 Algae from overflow of oxidation ponds – inhalation

Recreational Water

Normal 200 Algae released from farm dams etc. – inhalation

Recreational Water

Susceptible 200 Bather shedding of infectious organisms

Recreational Water

Susceptible 200 Urban stormwater discharge in streams and beaches

Recreational Water

Susceptible 200 Bird defecation into coastal waters

Recreational Water

Normal 180 Dry weather sewage overflows in streams and beaches

Recreational Water

Normal 180 Cuts from naturally-occurring objects (oyster shells etc.)

Recreational Water

Normal 160 Bather shedding of infectious organisms

Recreational Water

Normal 160 Slipping on slimy surfaces

Recreational Water

Susceptible 150 Dry weather sewage overflows in streams and beaches

Drinking-water Mainland 125 Toxic algal blooms (f/w) – ingestion

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

EXAMPLEEXAMPLECompliance with Drinking Water StandardsCompliance with Drinking Water Standards

How to assess compliance with microbial limits?

• Can’t sample everything• Need high assurance that supply isn’t contaminated

in some assessment period; can’t 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?”

What kind of a question is this?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

ResultsResults

Policy Implications

• Results in Table 8.2 now incorporated into 2005 Drinking-water Standards for New Zealand– http://www.moh.govt.nz/moh.nsf/

0/12F2D7FFADC900A4CC256FAF0007E8A0/$File/drinkingwaterstandardsnz-2005.pdf

EXAMPLEEXAMPLEEffect of microbial contamination on Effect of microbial contamination on

swimmers’ healthswimmers’ health

Epidemiological study at 7 NZ beaches

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

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/microbiological-quality-jun03/

using statistical methods for environmental science and management

Documents

nonstandard methods

statistical inference

water standards

nonparametric rank methods

fertilizer consumption

consumption tonnes100

skewed data

good ways