TIME SERIES ANALYSIS FOR STUDIES OF WEATHER AND

HEALTH

Paul WilkinsonPublic & Environmental Health Research Unit

London School of Hygiene & Tropical MedicineKeppel Street

London WC1E 7HT (UK)

www.lshtm.ac.uk paul.wilkinson@lshtm.ac.uk

02

55

07

51

00

12

51

50

Ca

rdio

vasc

ula

r d

ea

ths/

da

y

01jan1990 01jan1991 01jan1992 01jan1993 01jan1994

CVD deaths Mean temperature

LONDON, 1990 - 1994

CLIMATE OR WEATHER?

TWO APPROACHES

• Episode analysis- transparent- risk defined by comparison to local baseline

• Regression analysis of all days of year- uses full data set- requires fuller data and analysis of

confounders- can be combined with episode analysis

EPISODES

No.

of

death

s/day

Date

Influenza ‘epidemic’

Period of heat

Smooth function of date with control for

influenza

Smooth function of date

Triangle: attributable deaths

PRINCIPLES OF EPISODE ANALYSIS

INTERPRETATION

• Common sense, transparent• Relevant to PH warning systems

But• How to define episode?

- relative or absolute threshold- duration- composite variables

• Uses only selected part of data• Most sophisticated analysis requires same

methods as for regression of all days of year

REGRESSION OF ALL DAYS

TIME-SERIES

• Short-term temporal associations

• Usually day to day fluctuations over several years

• Similar to any regression analysis but with specific features

• Methodologically sound(same population compared with itself day by day)

• Time-varying confoundersinfluenzaday of the week, public holidayspollution

• Secular trend

• Season

STATISTICAL ISSUES 1

STATISTICAL ISSUES 1I

• Shape of exposure-response functionsmooth functionslinear splines

• Lagssimple lagsdistributed lags

• Temporal auto-correlation

Source: Anderson HR, et al. Air pollution and daily mortality in London: 1987-92. Br Med J 1996; 312:665-9

Sofia

Temperature (2 day mean) -12 0 10 20 30

85

100

140

London

Temperature (2 day mean)-12 0 10 20 30

85

100

140

Temperature (2 week mean)-12 0 10 20 30

85

100

140

Temperature (2 week mean)-12 0 10 20 30

85

100

140

TEMPERATURE DEPENDENCE OF DAILY MORTALITY, LONDON

THE MODEL…

(log) rate = ß0 +

ß1(high temp.) +

ß2(low temp.)

ß1=heat slopeß2=cold slope

+

ß3(pollution) +

ß4(influenza) +

ß5(day, PH)

measured confounders+

ß6(season) +

ß7(trend)unmeasured confounders

LAGS

• Heat impacts short: 0-2 daysCold impacts long: 0-21 days

• Vary by cause-of-death- CVD: prompt- respiratory: slow

• Should include terms for all relevant lags

LONDON, 1986-96: LAGS FOR COLD-RELATED MORTALITY

% I

NC

RE

AS

E I

N M

OR

TA

LIT

Y/

ºC F

ALL

IN

TE

MP

ER

AT

UR

E

DAYS OF LAG

ALL CAUSE

0 5 10 151.65

1.7

1.75

1.8

1.85

CARDIOVASCULAR

0 5 10 151.7

1.75

1.8

1.85

1.9

RESPIRATORY

0 5 10 153.8

3.9

4

4.1

4.2

NON-CARDIORESPIRATORY

0 5 10 15.7

.8

.9

1

Lag

RR

0 5 10 15 20

1.0

00

1.0

05

1.0

10

*

**

** * * *

**

**

**

** * *

* *

*

*

*

* * **

**

**

**

** * * * * *

*

*

SANTIAGO: COLD-RELATED MORTALITYCARDIO-VASCULAR DISEASE

Lag

RR

0 5 10 15 20

0.9

95

1.0

00

1.0

05

1.0

10

1.0

15

*

* **

* * * * * * * * * * **

* * *

*

*

*

*

* * **

* * * * * * * * ** * *

* *

*

SANTIAGO: COLD-RELATED MORTALITYRESPIRATORY DISEASE

LJUBLJANA

-10 0 10 20 30 40

80100120140

BUCHAREST

-10 0 10 20 30 40

80100120140

SOFIA

-10 0 10 20 30 40

80100120140

DELHI

-10 0 10 20 30 40

80100120140

MONTERREY

-10 0 10 20 30 40

80100120140

MEXICO

-10 0 10 20 30 40

80100120140

CHIANGMAI

-10 0 10 20 30 40

80100120140

BANGKOK

-10 0 10 20 30 40

80100120140

SALVADOR

-10 0 10 20 30 40

80100120140

SAO PAULO

-10 0 10 20 30 40

80100120140

SANTIAGO

-10 0 10 20 30 40

80100120140

CAPE TOWN

-10 0 10 20 30 40

80100120140

LAG: 0-1 DAYSHEAT

LJUBLJANA

-10 0 10 20 30 40

80100120140

BUCHAREST

-10 0 10 20 30 40

80100120140

SOFIA

-10 0 10 20 30 40

80100120140

DELHI

-10 0 10 20 30 40

80100120140

MONTERREY

-10 0 10 20 30 40

80100120140

MEXICO

-10 0 10 20 30 40

80100120140

CHIANGMAI

-10 0 10 20 30 40

80100120140

BANGKOK

-10 0 10 20 30 40

80100120140

SALVADOR

-10 0 10 20 30 40

80100120140

SAO PAULO

-10 0 10 20 30 40

80100120140

SANTIAGO

-10 0 10 20 30 40

80100120140

CAPE TOWN

-10 0 10 20 30 40

80100120140

LAG: 0-13 DAYSCOLD

Threshold for heat effect

Threshold for cold effect

CONTROLLNG FOR SEASON

TEMPERATURE

MORTALITYSEASON

Infectious disease

Diet

UNRECORDED FACTORS

Human behaviours

X X

• Moving averages

• Fourier series (trigonometric terms)

• Smoothing splines

• Stratification by date

• Other…

METHODS OF SEASONAL CONTROL

All cause

0

0.5

1

1.5

2

2.5

3

3.5

4df 7df 10df 12df 4df 7df 10df 12df 4df 7df 10df 12df 4df 7df 10df 12df

decade 1 decade 2 decade 3 decade 4

% c

hang

eEFFECT OF INCREASING SEASONAL CONTROLGradient of cold-related mortality, London

Unadjusted

Rel

ativ

e m

orta

lity

month1 2 3 4 5 6 7 8 9 10 11 12

50

75

100

125

150

Adjusted for low temperature

Rel

ativ

e m

orta

lity

month1 2 3 4 5 6 7 8 9 10 11 12

50

75

100

125

150

Adjusted for influenza count

Rel

ativ

e m

orta

lity

month1 2 3 4 5 6 7 8 9 10 11 12

50

75

100

125

150

Adjusted for month low temperature and influenza

Rel

ativ

e m

orta

lity

month1 2 3 4 5 6 7 8 9 10 11 12

50

75

100

125

150

SEASONAL MORTALITY, GB

Month-to-month variation in mortality (adjusted for region and time-trend) accounted for 17% of annual all-cause mortality but only:

- 7.8% after adjustment for temperature- 12.6% after adjustment for influenza A

counts- 5.2% after adjustment for both

SEASONAL FLUCTUATION IN MORTALITY, GB

FUTURE IMPACTS

01jan1991 01jan1993 31dec19940

20

40

60

Seasonal mortality pattern, DelhiD

aily

death

s

Delhi,

India: Average annual pattern of temperature, rainfall and

daily mortality (data for all 1991-94 years, averaged, by day of year)

1st Jan 1st July

0

50

100

150

-10

0

10

20

30

40

Jan 1 July 1 Dec 31

150

100

50

0

40

30

20

10

0

-10

Daily deaths

Daily temperature

Monthly rainfall

TemperatureDeaths

McMichael et al, in press

0 10 20 30 40

80

100

120

140

Heat-related mortality, DelhiR

ela

tive m

ort

alit

y (

% o

f d

aily

avera

ge)

Daily mean temperature /degrees Celsius

Temperature distribution

Health impact model Generates comparative estimates of the regional impact of each climate scenario on specific health outcomes

Conversion to GBD ‘currency’ to allow summation of the effects of different health impacts

GHG emissions scenarios Defined by IPCC

GCM model: Generates series of maps of predicted future distribution of climate variables

Level Age group (years)0-4 5-14 15-29 30-44 45-59 60-69 70+

1 1.0 1.0 1.0 1.0 1.0 1.0 1.02 1.2 1.2 1.2 1.2 1.2 1.2 1.23 1.7 1.7 1.7 1.7 1.7 1.7 1.71 1.0 1.0 1.0 1.0 1.0 1.0 1.02 1.2 1.2 1.2 1.2 1.2 1.2 1.23 1.7 1.7 1.7 1.7 1.7 1.7 1.71 1.0 1.0 1.0 1.0 1.0 1.0 1.02 1.2 1.2 1.2 1.2 1.2 1.2 1.23 1.7 1.7 1.7 1.7 1.7 1.7 1.71 1.0 1.0 1.0 1.0 1.0 1.0 1.02 1.2 1.2 1.2 1.2 1.2 1.2 1.23 1.7 1.7 1.7 1.7 1.7 1.7 1.71 1.0 1.0 1.0 1.0 1.0 1.0 1.02 1.2 1.2 1.2 1.2 1.2 1.2 1.23 1.7 1.7 1.7 1.7 1.7 1.7 1.7

RISK ASSESSMENT FOR CLIMATE CHANGE

• EXTRAPOLATION(going beyond the data)

• VARIATION(..in weather-health relationship -- largely unquantified)

• ADAPTATION(we learn to live with a warmer world)

• MODIFICATION(more things will change than just the climate)

BUT FOUR REASONS TO HESITATE…

Source: Checkley et al, Lancet 2000

Daily hospitalizations for diarrhoea

Daily temperature

19971993

HOSPITALIZATIONS FOR DIARRHOEA, LIMA PERUShaded region corresponds to 1997-98 El Niño event

• Changes in population- Demographic structure (age)- Prevalence of weather-sensitive

disease

• Environmental modifiers

• Adaptive responses- Physiological habituation

(acclimatization)- Behavioural change- Structural adaptation- PH interventions

CHANGING VULNERABILITY

• Provide evidence on short-term associations of weather and health

• ‘Robust’ design

• Repeated finding of direct h + c effects

• Some uncertainties over PH significance

• Uncertainties in extrapolation to future(No historical analogue of climate change)

SUMMARY: TIME-SERIES STUDIES

INTERMISSION…

TIME SERIES ANALYSIS FOR STUDIES OF WEATHER AND

HEALTH

Part 2

HARVESTING

FRAILTY MODEL

General populatio

n

Frail population

, Nt

Death

DtIt

Nt = Nt-1 + It - Dt-1

IDEALIZED SCHEMA

MORTALITY

HEAT

A

B

weaker absen

t

strong correlationPeriod of

averaging

** **

******

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*********

***

**

** ****************************** ****** ********************************* ****************** **** * ** * *

* *

**** * * ********* ** ** ******************* *** *********************** ****

*

* *** *

**

**

***

** ** **********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

**************************************************************************************************************************

*****************************************************************

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*********************************

*****

Mean temperature, average(lags 0-1)

Pe

rce

nta

ge

of

me

an

nu

mb

er

of

de

ath

s

5 10 15 20 25

95

10

01

05

110

115

12

0

** ** * *****

********

******** ********************************************* *** ** *************************************************************************

***********************

** *

** ** ******* *********************** ****** ********************************* ****************** **** * ** * *

* *

**** * * ********* ** ** ******************* *** *********************** ****

** **

* ***

*****

*

***

**************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

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*

***

******

********

******** ********************************************* *** ** *********************************************************************

******************

*********

***

**

*********

*********************** ****** ********************************* ****************** **** * ** * *

* *

**** * * ********* ** ** ******************* *** ***********************

*****

* **

**

**

*

****

*

***

************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

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ALL-CAUSE MORTALITY

ALL CAUSE MORTALITY: HEAT DEATHS

Lag

PER

CEN

TA

GE IN

CR

EA

SE IN

MO

RTA

LITY

PER

ºC

BELO

W C

OLD

TH

RESH

OLD

0 5 10 15 20

-0.5

00.5

11.5

**

*

** * *

* * * * * * * **

* * **

*

*

*

**

* * * **

* * * * * * * **

* *

*

LondonE

xces

s ris

k (9

5% C

I)

lag0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

-4

-2

0

2

4

6

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

CUMULATIVE EXCESS RISK OF HEAT DEATH AS AFUNCTION OF INCREASING LAG: LONDON

CUMULATIVE EXCESS RISK OF HEAT DEATH AS AFUNCTION OF INCREASING LAG: DELHIDelhi

Exc

ess

risk

(95%

CI)

lag0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

-4

-2

0

2

4

6

- - - - - - - - - - - - - - - - - - - - - - - - - -- -

- - -

- - - - - - - - - - - - - - - - - - - - - - - - - - - -- - -

CUMULATIVE EXCESS RISK OF HEAT DEATH AS AFUNCTION OF INCREASING LAG: SAO PAULO

Sao PaoloE

xces

s ris

k (9

5% C

I)

lag0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

-4

-2

0

2

4

6

- - - - - - - - - - - - - - - - - - - - --

- - - - - - - --

- - - - - - - - - - - - - - - - - - - - -- - - - - - - -

--

UNCERTAINTIES IN FUTURE HEALTH IMPACTS

(1) EXTRAPOLATION

LJUBLJANA

-10 0 10 20 30 40

80100120140

BUCHAREST

-10 0 10 20 30 40

80100120140

SOFIA

-10 0 10 20 30 40

80100120140

DELHI

-10 0 10 20 30 40

80100120140

MONTERREY

-10 0 10 20 30 40

80100120140

MEXICO

-10 0 10 20 30 40

80100120140

CHIANGMAI

-10 0 10 20 30 40

80100120140

BANGKOK

-10 0 10 20 30 40

80100120140

SALVADOR

-10 0 10 20 30 40

80100120140

SAO PAULO

-10 0 10 20 30 40

80100120140

SANTIAGO

-10 0 10 20 30 40

80100120140

CAPE TOWN

-10 0 10 20 30 40

80100120140

MEAN DAILY TEMPERATURE/ degrees Celsius

MORTALITY (% of annual average)

?

HEAT DEATHSMonterrey, Mexico

(2) VARIATION

LJUBLJANA

-10 0 10 20 30 40

80100120140

BUCHAREST

-10 0 10 20 30 40

80100120140

SOFIA

-10 0 10 20 30 40

80100120140

DELHI

-10 0 10 20 30 40

80100120140

MONTERREY

-10 0 10 20 30 40

80100120140

MEXICO

-10 0 10 20 30 40

80100120140

CHIANGMAI

-10 0 10 20 30 40

80100120140

BANGKOK

-10 0 10 20 30 40

80100120140

SALVADOR

-10 0 10 20 30 40

80100120140

SAO PAULO

-10 0 10 20 30 40

80100120140

SANTIAGO

-10 0 10 20 30 40

80100120140

CAPE TOWN

-10 0 10 20 30 40

80100120140

Mortality (% of annual average)

Mean daily temperature in degrees Celsius

Daily mortality in relation to mean temperature during preceding two days

LJUBLJANA

-10 0 10 20 30 40

80100120140

BUCHAREST

-10 0 10 20 30 40

80100120140

SOFIA

-10 0 10 20 30 40

80100120140

DELHI

-10 0 10 20 30 40

80100120140

MONTERREY

-10 0 10 20 30 40

80100120140

MEXICO

-10 0 10 20 30 40

80100120140

CHIANGMAI

-10 0 10 20 30 40

80100120140

BANGKOK

-10 0 10 20 30 40

80100120140

SALVADOR

-10 0 10 20 30 40

80100120140

SAO PAULO

-10 0 10 20 30 40

80100120140

SANTIAGO

-10 0 10 20 30 40

80100120140

CAPE TOWN

-10 0 10 20 30 40

80100120140

Daily mortality in relation to mean temperature during preceding two

weeks

(3) ADAPTATION

Th

resh

old

for

heat

imp

act

s

Maximum daily mean temperature

20 25 30 35

-10

0

10

20

30

Thresholds for heat-related mortality: 12 lower- & middle-income cities

Positive slope suggests adaptation

7.0°C

12.5°C

7

8

9

10

11

12

SP01

Ris

k of

death

rela

tive t

o a

nnual m

inim

um

10-w

eek

movin

g a

vera

ge

Day of year 1Jan 1Apr 1Jul 1Oct 31Dec

.75

1

1.25

1.5

1.75

2

High standardized heating costs

Low standardized heating costs

Seasonal variation in deaths from cardiovascular disease by cost of home heating. England, 1986-1996.

CARDIOVASCULAR MORTALITY IN RELATION TO HOME HEATING: ENGLAND, 1986-96

Standardized indoor temp. /deg Celsius

Mortality(deaths/day)

Winter:non-winter ratio*

Winter Non-winter

Unadjusted Adjusted for deprivation

1 <14.8 0.8(1080)

0.6(1568)

1.39(1.28,1.50)

1.38(1.16,1.63)

2 14.8- 0.7(973)

0.6(1580)

1.24(1.15,1.35)

1.24(1.05,1.47)

3 16.6- 0.7(869)

0.5(1442)

1.21(1.11,1.31)

1.21(1.02,1.44)

4 18.4- 0.7(957)

0.6(1569)

1.22(1.13,1.32)

1.23(1.04,1.46)

5 19.4-27.0

0.8(1055)

0.7(1906)

1.11(1.03,1.20)

1.13(0.96,1.34)

* All ratios adjusted for region

(4) EFFECT MODIFICATION

Table. Change in population health and deaths attributable to cold over the 20th century

Percentage of deaths by age & cause:

Period

1900-10 1927-37 1954-64 1986-96

0-14 years15-64 years65+ years

38.5%32.0%29.4%

13.3%40.5%46.1%

4.9%31.4%63.7%

1.5%18.8%79.7%

CardiovascularRespiratoryOther

12.1%18.9%69.0%

27.9%20.0%52.1%

33.3%14.1%52.6%

42.3%14.0%43.7%

Percent of deaths attributable to cold

12.5(10.1, 14.9)

11.2(8.40, 14.0)

8.74(5.93, 11.5)

5.42(4.13, 6.69)

05

01

001

502

002

503

00

1900 1902 1904 1906 1908 1910

1900 to 1910

05

01

001

502

002

503

00

1927 1929 1931 1933 1935 1937

1927 to 1937

05

01

001

502

002

503

00

1954 1956 1958 1960 1962 1964

1954 to 1964

05

01

001

502

002

503

00

1986 1988 1990 1992 1994 1996

1986 to 1996

R

atio

of

obse

rve

d/ex

pect

ed

deat

hs

ALL CAUSE MORTALITY

-20

020

4060

-10 0 10 20 30

1900-1910

-20

020

4060

-10 0 10 20 30

1927-1937

-20

020

4060

-10 0 10 20 30

1954-1964

-20

020

4060

-10 0 10 20 30

1986-1996

All-cause

Temperature (degrees Celsius)

IMPLICATIONS FOR MONITORING HEALTH IMPACTS OF CLIMATE

CHANGE

METHODOLOGICAL ISSUES

• Gradual change• Year to year fluctuation• Secular trends• Modifiers

- physiological acclimatization- structural and behavioural adaptation- specific protection measures

• Attribution

1. Measurement of trend in disease rates

2. Measurement of trend in attributable disease: direct method

3. Application of climate-disease relationships to measured changes in climate: indirect method

Confounded by secular trends: un-interpretable unless v. specific markerBased on analysis of (short-term) climate-disease relationships

Depends on understanding effect modification or assumption of its absence

MONITORING

Deaths in June & July, London, 1986-1996

Death

s in

June &

July

Year

Days

over

27ºC

1986 1988 1990 1992 1994 19960

5000

10000

15000

0

10

20

30

Deaths in June & July

Days over 27 Celsius

Deaths attributable to heat, London, 1986-1996

Perc

en

t att

ributa

ble

to h

eat

year

Days

over

27ºC

1986 1988 1990 1992 1994 19960

.2

.4

.6

.8

1

0

5

10

15

20

25

30Heat deaths

Days over 27 Celsius

Central England mean June & July temperatures, 1900-1999Tem

pera

ture

/degre

es

Cels

ius

Year

1900 1920 1940 1960 1980 2000

6

10

14

18

22

Regression slope, 1986-1996

19

86 1

99

6

Band of historical climatic variability

20

15

1900 21002000

14

16

17

18

13

19Average Global Temperature (OC)

Year205019501860

Low

High

Central estimate = 2.5 oC (+ increased variability)

IPCC (2001) estimatesa 1.4-5.8 oC increase

This presents a rate-of-change problem for many natural systems/processes

NEEDED EVIDENCE

MITIGATION

Evidence for change that benefits health & lowers emissions

• Reduction in greenhouse gas emissions/energy use

• Social, economic and technological changes

ADAPTATION/PREPAREDNESS

Evidence that can influence health in short and longer term

• Understanding of weather-health > climate-health relationships

• Vulnerability in terms of impacts, geographical distribution and population characteristics

• Public protection through:public health system (short-medium term)infrastructure, adaptation

CONTACT DERTAILS

Sari KovatsPaul Wilkinson

Public & Environmental Health Research UnitLondon School of Hygiene & Tropical MedicineKeppel StreetLondonWC1E 7HT(UK)

www.lshtm.ac.ukTel: +44 (0)20 7972 2415Fax: +44 (0)20 7580 4524

sari.kovats@lshtm.ac.ukpaul.wilkinson@lshtm.ac.uk