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ANALYSIS OF INTERRUPTED TIME
SERIES
PRESENTER: THJ
OVERVIEW
• Introduction• The Situation• The Model• Examples• Methodological issues• Stata Syntax
INTRODUCTION
• The interrupted time series (ITS) study design is being used for evaluating the interventions which particularly suits for interventions introduced at apopulation level over a clearly defined time periodand that target population‐level health outcomes.
• In an ITS study, a time series of a particular outcome of interest is used to establish an underlying trend, which is ‘interrupted’ by an intervention at a known point in time.
THE SITUATION OF USING ITS ANALYSIS
• A continuous sequence of observations on a population, taken repeatedly over time.
• The intervention : ITS requires a clear differentiation of the pre‐intervention period and the post‐intervention period
• The Outcome : ITS works best with short‐term outcomes.• Data requirements :
• Sequential measures of the outcome should be available both before and after the intervention.
• equally spaced intervals on variables over time.
THE ITS MODEL:SEGMENTED REGRESSION
Yt=β0 +β1T+β2 Xt + β3TXt +et
• T : the time elapsed since the start of the study in with the unit representing the frequency.
• Xt : a dummy variable indicating the pre‐ or the post‐intervention period.
• Yt : the outcome at time t.• et : estimates the error.
g(μt)
Yt=β0 +β1T+β2 Xt + β3TXt +et
• β0 : estimates the base level of the outcome at the beginning of the series.
• β1 : estimates the base trend.
• β2 : estimates the change in level in the post‐intervention segment.
• β3 : estimates the change in trend in the post‐intervention segment.
EXAMPLES OF IMPACT MODELS USED IN ITS
EXAMPLE• In January 2005, Italy introduced
regulations to ban smoking in all indoor public places, with the aim of limiting the adverse health effects of second‐hand smoke.
• The Italian smoking ban in public places on hospital admissions for acute coronary events (ACEs, ICD10 410‐411)
• Dataset: ACEs in the Sicily region between 2002 and 2006 among those aged 0‐69 years.
THE STATA SYNTAX & OUTPUT• glm aces smokban time smokban#c.time, family(poisson) link(log)
offset(logstdpop) eform
0
50
100
150
200
250
Std
rate
/100
000
pers
on-y
ear
2002 2003 2004 2005 2006
year
rate predicting trend
Sicily, 2002-2006
METHODOLOGICAL ISSUES
• Seasonality• Autocorrelation eg. AR(1) εt = ρεt−1+ut
• Over‐dispersion• Time‐varying confounders
EXAMPLE :
METHODOLOGICAL ISSUES
• Use of controls and other more complex ITS designs.• Yt=β0 +β1T+β2Xt+β3TXt +β4 Z+β5 ZT+β6 ZXt +β7 ZTXt +et
• Z : dummy variable for group• β0 : mean value at the baseline• β1 : trend prior to intervention• β2 : change in level• β3 : change in trend post intervention• β4 : difference between the groups at the beginning time point• β5 : difference between the groups in prior trend• β6 : difference between the groups in change in level• β7 : difference between the groups in change in trend
STATA COMMAND: ITSA• itsa “performs interrupted time‐series analysis using two ordinary least‐squares (OLS) regression‐based approaches
• Syntax : itsa depvar [indepvars] [if] [in] [weight] , trperiod(numlist) single treatid(#) contid(numlist) praislag(#) figure posttrend replace prefix(string) model options.
DATA EXAMPLE
THE SYNTAX & OUTPUT
GENERATED DATA & GRAPH40
4550
5560
65sm
okin
g_p
0 2 4 6 8 10T
1: Actual PredictedControls average: Actual Predicted
Regression with Newey-West standard errors - lag(0)
Intervention starts: 71 and average of controls
4045
5055
6065
smok
ing_
p
0 2 4 6 8 10T
1: Actual PredictedControls average: Actual Predicted
Regression with Newey-West standard errors - lag(0)
Intervention starts: 71 and average of controls
REFERENCE
• JL Bernal, S Cummins, A Gasparrini. Interrupted time series regression for the evaluation of public health interventions: a tutorial. International journal of epidemiology,2017; 46 (1), 348‐355.
• Barone‐Adesi F, Gasparrini A, Vizzini L, Merletti F, Richiardi L. Effects of Italian smoking regulation on rates of hospital admission for acute coronary events: a country‐wide study. PLoS One, 2011; 6:e17419.
• Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐and multiple‐group comparisons. The Stata Journal, 2015; 15(2),480–500.
• Edward L. Hannan et al. Changes in Percutaneous Coronary Interventions Deemed “Inappropriate” by Appropriate Use Criteria. Journal of the American College Of Cardiology,2017; 69(10) ,1234‐1242.