ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted...
Transcript of ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted...
![Page 1: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/1.jpg)
ANALYSIS OF INTERRUPTED TIME
SERIES
PRESENTER: THJ
![Page 2: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/2.jpg)
OVERVIEW
• Introduction• The Situation• The Model• Examples• Methodological issues• Stata Syntax
![Page 3: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/3.jpg)
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.
![Page 4: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/4.jpg)
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.
![Page 5: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/5.jpg)
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)
![Page 6: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/6.jpg)
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.
![Page 7: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/7.jpg)
EXAMPLES OF IMPACT MODELS USED IN ITS
![Page 8: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/8.jpg)
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.
![Page 9: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/9.jpg)
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
![Page 10: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/10.jpg)
METHODOLOGICAL ISSUES
• Seasonality• Autocorrelation eg. AR(1) εt = ρεt−1+ut
• Over‐dispersion• Time‐varying confounders
![Page 11: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/11.jpg)
EXAMPLE :
![Page 12: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/12.jpg)
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
![Page 13: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/13.jpg)
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.
![Page 14: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/14.jpg)
DATA EXAMPLE
![Page 15: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/15.jpg)
THE SYNTAX & OUTPUT
![Page 16: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/16.jpg)
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
![Page 17: ANALYSIS OF INTERRUPTED TIME SERIES · • Ariel Linden, Ann Arbor. Conducting interrupted time‐series analysis for single‐ and multiple‐group comparisons. The Stata Journal,](https://reader030.fdocuments.us/reader030/viewer/2022040205/5ed92bd16714ca7f4769474b/html5/thumbnails/17.jpg)
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.