From Surveys to SurveillanceFrom Surveys to Surveillance

Time Series AnalysisTime Series Analysis

Eric Holowaty,

Sr. Scientist, Informatics Unit, CCO

Michael Spinks,

Sr. Res. Assoc., CCO.

Under Construction !

BackgroundBackground

1980s and 1990s - occasional surveys precise estimates of rates, proportions, means, nos.

affected detecting important differences in estimates within

survey

2000s - surveillance systems continuous, or at least frequent sampling monitoring and assessing temporal patterns, incl.

change point detection and sub-group differences over time

BackgroundBackground

What is desired periodicity of sampling? Depends on:

how rapidly variables actually change how important it is to detect changes quickly desired precision in describing temporal

patterns, changes and differences

DefinitionsDefinitions Time series

sequence of data points, measured at successive times, and spaced apart at uniform time intervals

Time series analysis methods and models that describe and explain temporal

patterns, and forecast future patterns

Trend long-term movement in an ordered series; may be

temporal or just ordered strata

Typical Time Series for Typical Time Series for One Participating PHUOne Participating PHU

19 25 31 37 43

0.6

0.8

1.0

LCL

CL

UCL

PHU #1 - Restaurants

Proportion Supporting Smoking Bylaws

Pro

po

rtio

n s

upp

ort

ing

Byla

w

Months from Jan 2001

Uncoordinated Fragmented Lack of smaller area data Poorly analysed Poor dissemination Not timely Difficult to access

Risk Factor Surveillance in Risk Factor Surveillance in OntarioOntariopre-RRFSSpre-RRFSS

Pilot tested in Durham Region in 1999

Available for Individual PHUs in Jan 2001

22 PHUs participating as of Dec 2004

?Province-wide coverage in 2005/06

RRFSS Population CoverageRRFSS Population Coverage

RRFSS Start-up by PHU

0

2,000,000

4,000,000

6,000,000

8,000,000

10,000,000

12,000,000

Jan-01 May-01 Sep-01 Jan-02 May-02 Sep-02 Jan-03 May-03 Sep-03

Date of Start-up

Po

pu

lati

on

Co

vera

ge

PHU popn

Cum Coverage

RRFSS (2003) respondents : 25,600 CCHS (2003) resp. : 37,000

87% of pop’n22/37 PHUs

Monthly data more suitable for detecting temporal changes More flexibility re. aggregation - before / after comparisons;

geographic areas; demographic groups Seasonal effects can be better described and analysed (Robust SPC procedures permit timely detection of stat. signif.

changes) LARGE sample size permits more precise analysis Standard CORE of questions helps ensure comparability over

time and with other geo. areas. Flexible MODULES permit targetted sampling and invest. of

local concerns

Benefits of RRFSSBenefits of RRFSS

Fundamental Statistical Issues Fundamental Statistical Issues in Time Series Analysisin Time Series Analysis

Accuracy and precision of estimates precision ~ sample size and survey design bias

differential access and response reporting/measurement bias changes in the measurement tool, incl. wording

importance of bias in time series analysis depends on size and consistency

Statistical power probability of detecting an important change in time

series - slope; seasonality; change points

Estimating the rate of change Estimating the rate of change over timeover time

Estimating that slope differs from the null i.e., zero change

assumption of monotonic relationship e.g., linear or log-linear model or logistic

assumption of no change points in time series

Statistical Power to Detect Statistical Power to Detect Slope > Null Slope > Null

Power influenced by: length of time series (k) size of each sample (n) measurement of interest (p or x or x) and its

variance alpha (Type I error) underlying rate of change/slope (b)

Statistical Power of Trend Statistical Power of Trend TestsTests

p=0.20; b=0.005; alpha=0.05

0.0

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 7 8 9 10

Length of sampling series

Po

we

r o

f tr

en

d t

es

t

50

100

500

1000

10000

Sample Size

From: MacNeill and Umphrey, 1997.

Statistical Power of Trend Statistical Power of Trend TestsTests

p=0.20; b=0.010; alpha=0.05

0.0

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 7 8 9 10

Length of sampling series

Po

we

r o

f tr

en

d t

es

t

50

100

500

1000

10000

Sample Size

From: MacNeill and Umphrey, 1997.

Statistical Power of Trend Statistical Power of Trend TestsTests

p=0.20; b=0.050; alpha=0.05

0.0

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 7 8 9 10

Length of sampling series

Po

we

r o

f tr

en

d t

es

t

50

100

500

1000

10000

Sample Size

From: MacNeill and Umphrey, 1997.

Monthly Estimates of ETS Exposure Monthly Estimates of ETS Exposure TrendsTrends - - RRFSS GTA Aug01-Dec03RRFSS GTA Aug01-Dec03

0 5 10 20 30

0.15

0.20

0.25

0.30

0.35

0.40

0.45

ETS Exposure

PHU= 1 , Sex = 5

0 5 10 20 30

0.1

0.2

0.3

0.4

0.5

ETS Exposure

PHU= 6 , Sex = 5

0 5 10 15 20 25 30 35

0.15

0.20

0.25

0.30

0.35

0.40

0.45

ETS Exposure

PHU= 7 , Sex = 5

0 5 10 15 20 25 30 35

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

ETS Exposure

PHU= 9 , Sex = 5

0 5 10 15 20 25 30

0.1

0.2

0.3

0.4

0.5

ETS Exposure

PHU= 11 , Sex = 5

0 5 10 20 30

0.20

0.25

0.30

0.35

0.40

ETS Exposure

PHU= 99 , Sex = 5

Quarterly Estimates of ETS Exposure Quarterly Estimates of ETS Exposure TrendsTrends - - RRFSS GTA Aug01-Dec03RRFSS GTA Aug01-Dec03

2 4 6 8 10 12

0.20

0.25

0.30

0.35

ETS Exposure

PHU= 1 , Sex = 5

2 4 6 8 10 12

0.20

0.25

0.30

0.35

0.40

ETS Exposure

PHU= 6 , Sex = 5

2 4 6 8 10 12

0.20

0.25

0.30

0.35

ETS Exposure

PHU= 7 , Sex = 5

2 4 6 8 10 12

0.15

0.20

0.25

0.30

0.35

ETS Exposure

PHU= 9 , Sex = 5

2 4 6 8 10

0.24

0.26

0.28

0.30

0.32

0.34

0.36

ETS Exposure

PHU= 11 , Sex = 5

2 4 6 8 10 12

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

ETS Exposure

PHU= 99 , Sex = 5

Estimates of ETS Exposure Estimates of ETS Exposure Trends - Trends - RRFSS GTA Aug01-Dec03RRFSS GTA Aug01-Dec03

Month Quarter Semi

-0.0

6-0

.04

-0.0

20.

000.

02

Exposure to ETS Bootstrap Estimates of Slopes

Durham, Ages 20-44

Slo

pe

Month Quarter Semi

-0.0

6-0

.04

-0.0

20.

000.

02

Exposure to ETS Bootstrap Estimates of Slopes

Durham, Females

Slo

pe

Month Quarter Semi

-0.0

6-0

.04

-0.0

20.

000.

02

Exposure to ETS Bootstrap Estimates of Slopes

GTA, Females

Slo

pe

Detecting abrupt changes in Detecting abrupt changes in lengthy time serieslengthy time series

Change-point methods e.g. JoinPoint

Control Charts conventional p-charts CUSUM charts EWMA charts, with residuals

Monthly Estimates of Support for Monthly Estimates of Support for BylawsBylaws - - RRFSS GTA Jan02-Dec04RRFSS GTA Jan02-Dec04

19 25 31 37 430.0

0.2

0.4

0.6

0.8

1.0

LCL

CL

UCL

PHU #1 - Restaurants

Proportion Supporting Smoking Bylaws

Pro

port

ion s

upport

ing

Byl

aw

Months from Jan 2001

19 25 31 37 43

0.6

0.8

1.0

LCL

CL

UCL

PHU #1 - Restaurants

Proportion Supporting Smoking Bylaws

Pro

po

rtio

n s

up

port

ing

Byla

w

Months from Jan 2001

Monthly Estimates of Support for Monthly Estimates of Support for BylawsBylaws - - RRFSS GTA Jan02-Dec04RRFSS GTA Jan02-Dec04

15/35 point estimates

in violation of Western

Electric rules

Monthly Estimates of Support for Monthly Estimates of Support for BylawsBylaws - - RRFSS GTA Jan02-Dec04RRFSS GTA Jan02-Dec04

19 25 31 37 430.75

0.80

0.85

0.90

.

EW

MA

Re

sid

ua

ls

PHU #1 - RestaurantsProportion Supporting Smoking Bylaws

EW

MA

Pre

dic

t (r

= 0

.37

1)

Months from Jan 200119 25 31 37 43

-0.15

-0.10

-0.05

0.00

0.05

0.10

Monthly Estimates of Support for Monthly Estimates of Support for BylawsBylaws - - RRFSS GTA Jan02-Dec04RRFSS GTA Jan02-Dec04

-1.0

-0.5

0.0

0.5

1.0

5 10 15 20 25 30

Correlogram of EWMA Residuals (Prediction Errors)

Corr

ela

tion

Lag Number

PlanPlan

Complete analysis of definitions, incl. temporal consistency and CCHS consistency

Assign final sample weights Production of point estimates for 2003

and 2004 Age-standardized comparisons Time series analysis