Interrupted Time Series:
What, Why and How
An Example From Suicide Research
Karen Smith
Acknowledgement
Motivated by consultancy work with the
Centre for Suicide Research, University of
Oxford
 All analyses and graphs produced by
Helen Bergen, Centre for Suicide
Research

Motivating example
 What is Interrupted Time Series?
 Why use it?
 Design issues
 Analysis issues
 Guidelines on use

Motivating Example






Between 1997 and 1999 the analgesic co-proxamol was
the single drug used most frequently for suicide by selfpoisoning in England and Wales, with 766 over the 3
year period
There is a relatively narrow margin between therapeutic
and potentially lethal levels
Death occurs largely because of the toxic effects of
dextropropoxyphene on respiration and cardiac
conduction
MHRA conducted a review of the efficacy/safety profile
Committee on Safety of Medicines advised withdrawal
from use in the UK, the final date being 31 December
2007
Patients who find it difficult to move to an alternative
drug can still be prescribed co-proxamol
The Problem

How to evaluate the impact of the
announcement to withdraw co-proxamol
on
◦ Prescribing of analgesics
◦ Mortality involving co-proxamol
◦ Mortality involving other analgesics
(substitution of method is of concern)
Available Data
Quarterly data on prescriptions of co-proxamol,
cocodamol, codeine, codydramol, dihydrocodeine,
NSAIDs, paracetamol and tramadol (from Prescription
Statistics department of the Information Centre for
Health and Social Care, England, and Prescribing Service
Unit, Health Solutions Wales)
 Quarterly data on drug poisoning deaths (suicides, open
verdicts and accidental poisonings) involving coproxamol alone, cocodamol, codeine, codydramol,
dihydrocodeine, NSAIDs, paracetamol and tramadol,
based on death registrations in England and Wales (from
ONS) – single drug, with and without alcohol
 Quarterly data for overall drug poisoning deaths and for
all deaths receiving suicide and undetermined verdicts

Simple Analysis
Compare the proportion of deaths involving coproxamol prior to the legislation with
proportion following legislation
 Compare total number of poisoning deaths
before and after legislation
 Time series plots of prescriptions and deaths
 Co-proxamol withdrawal has reduced suicide
from drugs in Scotland, E. A. Sandilands & D. N.
Bateman, British Journal of Clinical
Pharmacology, 2008.

What’s Wrong With This?







Ignores any trends, both before and after change in
legislation (or intervention in a more general setting)
Ignores any possible cyclical effects
Doesn’t pick up on any discontinuity
Variances around the means before and after the
intervention may be different
Effects may drift back toward the pre-intervention level
and/or slope over time if the effect wears off
Effects may be immediate or delayed
Doesn’t take account of any possible autocorrelation
A Solution – Interrupted Time Series
A special kind of time series in which we
know the specific point in the series at
which an intervention occurred
 Causal hypothesis is that observations
after treatment will have a different level
or slope from those before intervention –
the interruption
 Strong quasi-experimental alternative to
randomised design if this is not feasible

Ramsay et al, 2003
The Model
Use segmented regression analysis (Wagner et al, 2002):
Ŷt = β0 + β1 x timet + β2 x interventiont + β3 x time_after_interventiont + et
Yt is the outcome
time indicates the number of quarters from the start of the series
intervention is a dummy variable taking the values 0 in the pre-intervention
segment and 1 in the post-intervention segment
time_after_intervention is 0 in the pre-intervention segment and counts the
quarters in the post-intervention segment at time t
β0 estimates the base level of the outcome at the beginning of the series
β1 estimates the base trend, i.e. the change in outcome per quarter in the
pre-intervention segment
β2 estimates the change in level in the post-intervention segment
β3 estimates the change in trend in the post-intervention segment
et estimates the error
Threats to Validity
Forces other than the intervention under investigation
influenced the dependent variable
◦ Could add a no-treatment time series from a control
group
◦ Use qualitative or quantitative means to examine
plausible effect-causing events
 Instrumentation – how was data collected/recorded
 Selection – did the composition of the experimental
group change at the time of intervention?
 Poorly specified intervention point; diffusion
 Choice of outcome – usually have only routinely
collected data
 Power, violated test assumptions, unreliability of
measurements, reactivity etc.

Design Considerations
Add a non-equivalent no-treatment
control group
 Add non-equivalent dependent variables

◦ Intervention should not affect but would
respond in the same way as primary variable
to validity threat
Remove intervention at a known time
 Add multiple replications
 Add switching replications

Problems







Interventions implemented slowly and diffuse
Effects may occur with unpredictable time
delays
Many data series much shorter than the 100
observations recommended for analysis
Difficult to locate or retrieve data
Time intervals between each data point in
archive may be longer than needed
Missing data
Undocumented definitional shifts
Applied to the Co-Proxamol Data
28 quarters in the pre-intervention
period and 12 in post-intervention
 Examined a number of common
analgesics

◦ Prescriptions
◦ Deaths


Examined overall suicides
Some evidence of autocorrelation in the
data, hence Cochrane-Orcutt
autoregression used (Durbin Watson
statistic of final models close to 2)
Prescriptions* for analgesics dispensed in England and Wales, 1998-2007
6000
Prescription items dispensed per quarter (thousands)
Co-proxam ol w ithdraw al
announced
5000
co-proxamol
4000
NSAIDs
paracetamol
co-codamol
tramadol
3000
co-dydramol
codeine
dihydrocodeine
2000
1000
0
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
Year (quarters)
* excluding liquids, suppositories, granules, powders and effervescent preparations
Mortality in England and Wales from analgesic poisoning (suicide and open
verdicts), 1998-2007, for persons aged 10 years and over (substances taken
alone, +/- alcohol)
90
Co-proxamol withdrawal
announced
80
Number of deaths
70
co-proxamol
60
other
analgesics
50
co-proxamol
best fit without
announcement
40
co-proxamol
best fit with
announcement
30
20
10
0
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1998
1999
2000
2001
2002
2003
Year (quarters)
2004
2005
2006
2007
Prescriptions
Pre-intervention
Post-intervention
Base level, β0
(SE)
p
Base trend,
β1 (SE)
p
Change in
level, β2 (SE)
p
Change in
trend, β3
(SE)
p
Co-proxamol
3050.1 (139.9)
<0.001
-45.9 (7.7)
<0.001
-554.8 (74.9)
<0.001
-46.8 (16.8)
0.01
Cocodamol
1349 (12.4)
<0.001
34.1 (0.8)
<0.001
300.5 (53.6)
<0.001
30.7 (6.4)
<0.001
Codeine
204.8 (4.2)
0.007
9.6 (0.2)
<0.001
20.5 (11.6)
0.089
3.5 (1.2)
0.007
Codrydamol
1055.2 (6.1)
<0.001
-1.1 (0.3)
0.004
148.7 (35.8)
<0.001
-4.2 (4.1)
0.316
Dihydrocodeine
686.4 (31.1)
<0.001
-1.5 (1.4)
0.291
-29.7 (2.4)
<0.001
-0.8 (2.4)
0.731
NSAIDs
4652.4 (47.2)
<0.001
28.4 (3)
<0.001
-622.9 (70.2)
<0.001
-66.2 (8.5)
<0.001
Paracetamol
1493.4 (56.1)
<0.001
42.1 (3.0)
<0.001
232 (66.6)
0.001
23 (8.2)
0.01
Tramadol
47.2 (51.4)
0.365
31.4 (2.7)
<0.001
-41.9 (6.8)
<0.001
16.3 (5.2)
0.004
Prescriptions
Pre-intervention
Post-intervention
Base level, β0
(SE)
p
Base trend,
β1 (SE)
p
Change in
level, β2 (SE)
p
Change in
trend, β3
(SE)
p
Co-proxamol
3050.1 (139.9)
<0.001
-45.9 (7.7)
<0.001
-554.8 (74.9)
<0.001
-46.8 (16.8)
0.01
Cocodamol
1349 (12.4)
<0.001
34.1 (0.8)
<0.001
300.5 (53.6)
<0.001
30.7 (6.4)
<0.001
Codeine
204.8 (4.2)
0.007
9.6 (0.2)
<0.001
20.5 (11.6)
0.089
3.5 (1.2)
0.007
Codrydamol
1055.2 (6.1)
<0.001
-1.1 (0.3)
0.004
148.7 (35.8)
<0.001
-4.2 (4.1)
0.316
Dihydrocodeine
686.4 (31.1)
<0.001
-1.5 (1.4)
0.291
-29.7 (2.4)
<0.001
-0.8 (2.4)
0.731
NSAIDs
4652.4 (47.2)
<0.001
28.4 (3)
<0.001
-622.9 (70.2)
<0.001
-66.2 (8.5)
<0.001
Paracetamol
1493.4 (56.1)
<0.001
42.1 (3.0)
<0.001
232 (66.6)
0.001
23 (8.2)
0.01
Tramadol
47.2 (51.4)
0.365
31.4 (2.7)
<0.001
-41.9 (6.8)
<0.001
16.3 (5.2)
0.004
Prescriptions
Pre-intervention
Post-intervention
Base level, β0
(SE)
p
Base trend,
β1 (SE)
p
Change in
level, β2 (SE)
p
Change in
trend, β3
(SE)
p
Co-proxamol
3050.1 (139.9)
<0.001
-45.9 (7.7)
<0.001
-554.8 (74.9)
<0.001
-46.8 (16.8)
0.01
Cocodamol
1349 (12.4)
<0.001
34.1 (0.8)
<0.001
300.5 (53.6)
<0.001
30.7 (6.4)
<0.001
Codeine
204.8 (4.2)
0.007
9.6 (0.2)
<0.001
20.5 (11.6)
0.089
3.5 (1.2)
0.007
Codrydamol
1055.2 (6.1)
<0.001
-1.1 (0.3)
0.004
148.7 (35.8)
<0.001
-4.2 (4.1)
0.316
Dihydrocodeine
686.4 (31.1)
<0.001
-1.5 (1.4)
0.291
-29.7 (2.4)
<0.001
-0.8 (2.4)
0.731
NSAIDs
4652.4 (47.2)
<0.001
28.4 (3)
<0.001
-622.9 (70.2)
<0.001
-66.2 (8.5)
<0.001
Paracetamol
1493.4 (56.1)
<0.001
42.1 (3.0)
<0.001
232 (66.6)
0.001
23 (8.2)
0.01
Tramadol
47.2 (51.4)
0.365
31.4 (2.7)
<0.001
-41.9 (6.8)
<0.001
16.3 (5.2)
0.004
Suicides
Pre-intervention
Post-intervention
Base level, β0
(SE)
p
Base trend,
β1 (SE)
p
Change in
level, β2 (SE)
p
Change in
trend, β3 (SE)
p
Co-proxamol
81.0 (4.5)
<0.001
-1.194 (0.3)
<0.001
-28.3 (4.9)
<0.001
0.6 (0.6)
0.355
Other
analgesics
51.3 (2.8)
<0.001
-0.3 (0.2)
0.095
6.4 (6.0)
0.297
-0.3 (0.6)
0.724
All drugs except
co-proxamol
and other
analgesics
221.2 (7.3)
<0.001
-0.5 (0.5)
0.299
21.6 (12.8)
0.100
-5.4 (1.4)
<0.001
All drugs
353.7 (10.2)
<0.001
-2.0 (0.7)
0.008
0.004 (18.1)
1.000
-4.9 (1.7)
0.007
All causes
1319.0 (22.5)
<0.001
-4.8 (1.4)
0.002
12.8 (34.8)
0.716
-5.4 (4.1)
0.192
Estimating Absolute Effect


The model may be used to estimate the absolute effect of the
intervention. This is the difference between the estimated outcome
at a certain time after the intervention and the outcome at that time
if the intervention not taken place.
For example, to estimate the effect of the intervention at the
midpoint of the post-intervention period (when time = 34.5 and
time_after_intervention = 6.5), we have
Ŷ34.5 = β0 + β1 x 34.5
without intervention
Ŷ34.5 = β0 + β1 x 34.5 + β2 + β3 x 6.5



with intervention
Thus, the absolute effect of the intervention is
β2 + β3 x 6.5
Standard errors calculated using method of Zhang et al
σ22 + 6.52 x σ32 + 2 x 6.5 x σ23
Non-significant terms included due to correlation between slope and
level terms
Results - Prescriptions
Estimates of absolute effect during 2005 to 2007
Mean quarterly
estimated
number pre
announcement
Mean quarterly
number post
announcement
Mean quarterly
change (95% CI)
Prescriptions
(x1000)
Co-proxamol
1465.1
605.7
-859 (-1065 to -653)
Cocodamol
2524.7
3024.6
500 (459 to 540)
534.6
578
43 (31 to 55)
1018.2
1140.0
122 (99 to 145)
634.6
600.0
-35 (-68 to -2)
NSAIDs
5633.8
4581.0
-1053 (-1186 to -920)
Paracetamol
2947.0
3330.0
382 (268 to 497)
Tramadol
1130.1
1193.9
64 (-5 to 133)
Codeine
Codrydamol
Dihydrocodeine
Results - Deaths
Estimates of absolute effect during 2005 to 2007
Mean quarterly
estimated
number pre
announcement
Mean quarterly
number post
announcement
Mean quarterly
change (95% CI)
Suicides, Open
Co-proxamol
39
15
-24 (-37 to -12)
Other analgesics
39
44
5 (-5 to 15)
All drugs except
co-proxamol and
other analgesics
204
191
-13 (-34 to 8)
All drugs
283
252
-31 (-66 to 3)
1152
1130
-22 (-89 to 45)
All causes
Co-Proxamol Prescriptions
Prescription data for England and Wales showed a
steep reduction in prescribing of co-proxamol in the
first two quarters of 2005, with further reductions
thereafter.
 Regression analyses indicated a significant decrease in
both level and slope in prescribing of co-proxamol - the
number of prescriptions decreased by an average of
859 (95% confidence interval (CI) = 653 to 1065)
thousand per quarter in the post-intervention period.
 This equates to an overall decrease of approximately
59% in the three year post-intervention period, 2005 to
2007.

Other Analgesic Prescriptions
There were also significant decreases in prescribing of
NSAIDS of an average of 1053 (95% CI = 920 to 1186)
thousand per quarter, equating to an approximate 19%
decrease overall for 2005 to 2007; and for
dihydrocodeine of an average of 35 (95% CI = 2 to 68)
thousand per quarter, or approximately 6% overall for
2005 to 2007.
 Prescriptions for the other analgesics increased
significantly in the post-intervention period, apart from
tramadol. Based on mean quarterly estimates this
equated to percentage increases over the 2005 to 2007
period of approximately 20% for cocodamol, 13% for
paracetamol, 12% for codydramol, and 8% for codeine.

26
Co-Proxamol Deaths





Marked reduction in suicide and open verdicts involving co-proxamol
in the first quarter of 2005, which persisted until the end of 2007.
Prior to 2005 deaths due to co-proxamol alone were 19.5% (95% CI
= 16.9 to 22.2) of all drug poisoning suicides, whereas between 2005
and 2007 they constituted just 6.4% (95% CI = 5.2 to 7.5).
Regression analyses indicated a significant decrease in both level and
slope for deaths involving co-proxamol which received a suicide or
open verdict - decreased by on average 24 (95% CI = 12 to 37) per
quarter in the post-intervention period.
This equates to an estimated overall decrease of 295 (95% CI = 251
to 338) deaths, approximately 62%, in the three year postintervention period 2005 to 2007.
When accidental poisoning deaths involving co-proxamol were
included, there was a mean quarterly decrease of 29 (95% CI = 17 to
42) deaths, equating to an overall decrease of 349 (95% CI = 306 to
392) deaths, approximately 61%, in the three year post-intervention
period 2005 to 2007.
Other Deaths



There were no statistically significant changes in level or slope in
the post-intervention period for deaths involving other analgesics
(cocodamol, codeine, codydramol, dihydrocodeine, NSAIDs,
paracetamol and tramadol) which received a suicide or open
verdict (both including and excluding accidental deaths).
There was a substantial though not statistically significant reduction
during the post-intervention period in deaths (suicide and open
verdicts) involving all drugs (including co-proxamol and other
analgesics), with the mean quarterly change between 2005 and
2007 being -31 (95% CI = -66 to 3) deaths.
The overall suicide rate (including open verdicts) during this period
also decreased, though to a lesser extent, and the mean quarterly
change of -22 (95% CI = -89 to 45) deaths was not statistically
significant.
28
Substitution of Method of Suicide

Possible substitution of method must be considered in
estimating the effect of changing availability of a specific
method of suicide.
◦ Research evidence on failed suicide attempts suggests that it’s
unusual for completely different method to be used.

Withdrawal of co-proxamol was associated with
changes in prescribing of other analgesics.
◦ Significant increases in prescribing of co-codamol, paracetamol,
and codydramol occurred during 2005-2007.

Analyses of suicide and open verdict deaths involving
other analgesics combined indicated little evidence of
substitution.
29
NSAIDs
An abrupt reduction in prescribing of NSAIDs
occurred shortly before the announcement of
the withdrawal of co-proxamol due to concerns
about Cox 2 inhibitors.
 However, NSAIDs are rarely a direct acute
cause of death, especially by suicide.

30
Interpretation



Following the announcement of the withdrawal of coproxamol in January 2005 there was an immediate large
reduction in prescriptions. This was associated with a 62%
reduction in suicide deaths (including open verdicts), or an
estimated 295 fewer deaths.
Inclusion of accidental deaths, some of which were likely
to have been suicides increased the estimated reduction in
number of deaths to approximately 349 over 3 years.
Overall suicide and open verdict deaths decreased in
England and Wales during 2005 to 2007. Thus underlying
downward trends in suicide cannot explain the full extent
of the decrease in co-proxamol related deaths following
the MHRA announcement to withdraw co-proxamol.
Limitations





Interrupted time series autoregression controls for baseline level
and trend when estimating expected changes in the number of
prescriptions (or deaths) due to the intervention.
The estimates of the overall effect on prescriptions and mortality
involved extrapolation, which is inevitably associated with
uncertainty.
The regression method assumes linear trends over time, and the
co-proxamol prescribing data, in particular, had a poor fit, resulting
in large standard errors in the post-intervention period.
Estimates of the standard errors for absolute mean quarterly
changes in number of prescriptions or deaths were determined
exactly, including the covariance of level and slope terms.
Estimates of percentage changes over the three year postestimation period are point estimates and were not determined
with standard error calculations.
Threats to Validity





Co-proxamol prescription only drug, often given to
elderly patients suffering arthritis
Most poisoning suicides are in younger people, so coproxamol use considered to be opportunistic
Recording of suicide may be coroner dependent
Open verdict may be given when there is lack of suicide
note
Prescriptions numbers were reducing as GPs tried to
move patients to alternative analgesics prior to
withdrawal so some diffusion of intervention
33
Design Considerations
Post-hoc analysis
 Very difficult to identify suitable nonequivalent no treatment control group
 Inclusion of overall suicide rates goes
some way towards examination of validity
threat

34
Problems






Diffusion of intervention but in this case prior to identified
intervention point as demonstrated by decrease in prescriptions
prior to announcement
Data series rather shorter than the ideal of 100 observations, but
minimum of 12 before and after intervention point considered not
unreasonable
Quarterly figures give reasonable time intervals
There’s no concrete evidence of a definitional shift in suicides in
this time interval although this cannot be ruled out
Open verdicts were included as a sensitivity check as one way of
addressing potential missing data
Almost impossible to consider impact of missing data on agent
used in self-poisoning
35
Guidelines on Use

Ramsay et al, 2003
◦ Quality criteria
 Intervention occurred independently of other changes over time
 Intervention was unlikely to affect data collection
 The primary outcome was assessed blindly or was measured
objectively
 The primary outcome was reliable or was measured objectively
 The composition of the data set at each time point covered at least
80% of the total number of participants in the study
 The shape of the intervention effect was prespecified
 A rationale for the number and spacing of data points was described
 The study was analyzed appropriately using time series techniques
Findings of the Systematic Reviews

Mass media review of 20 studies, Guideline dissemination and
implementation review of 38 studies
◦ Most studies had short time series




Standard errors increased
Reduced power
Type I error increased
Failure to detect autocorrelation or secular trends
◦ Over 65% analysed inappropriately
 Of the 37 re-analysed, 8 had significant pre-intervention trends
◦ Most were underpowered
 Rule of thumb: with 10 pre- and 10 post-intervention time points the
study would have at least 80% power to detect a change in level of
five standard deviations of the pre-data if the autocorrelation >0.4
 Long pre-intervention phase increases power to detect secular
trends
References
Shadish, Cook and Campbell, 2002, Experimental and quasi-experimental
designs for generalised causal inference, Houghton Mifflin.
 Ramsay CR, Matowe L, Grilli R, Grimshaw JM, Thomas RE. Interrupted time
series designs in health technology assessment: Lessons from two
systematic reviews of behavior change strategies. Int.J.Technol.Assess.Health
Care 2003;19:613-23
 Wagner AK, Soumerai SB, Zhang F, Ross-Degnan D. Segmented regression
analysis of interrupted time series studies in medication use research.
J.Clin.Pharm.Ther. 2002;27:299-309
 Zhang, F, Wagner, A, Soumerai, S. B., and Ross-Degnan, D. Estimating
confidence intervals around relative changes in outcomes in segmented
regression analyses of time series data. 15th Annual NESUG (NorthEast
SAS Users Group Inc) Conference Last update 2002.
http://www.nesug.info/Proceedings/nesug02/st/st005.pdf. Accessed 22
October 2008.

Examples of Use




Matowe, L, Ramsay, C. R., Grimshaw, J. M., Gilbert F. J., MacLeod, M.-J.
and Needham, G. Effects of mailed dissemination of the Royal
College of Radiologists’ Guidelines on general practitioner referrals
for radiography: a time series analysis. Clinical Radiology 2002, 57,
575-578
Neustrom, M. W. and Norton, W. M. The impact of drunk driving
legislation in Louisiana. Journal of Safety Research, 1993, 24, 107-121
Ansari, F, Gray, K, Nathwani, D, Phillips, G, Ogston, S, Ramsay, C and
Davey, P. Outcomes of an intervention to improve hospital
antibiotic prescribing: interrupted time series with segmented
regression analysis. Journal of Antimicrobial Chemotherapy, 2003, 52,
842-848
Morgan, O. W., Griffiths, C and Majeed, A. Interrupted time-series
analysis of regulations to reduce paracetamol (acetaminophen)
poisoning. PLoS Medicine, 2007, 4, 0654-0659

K. Hawton, H. Bergen, S. Simkin, A. Brock,
C. Griffiths, E. Romeri, K. L. Smith, N.
Kapur, D. Gunnell (2009). Effect of
withdrawal of co-proxamol on prescribing
and deaths from drug poisoning in
England and Wales: time series analysis.
BMJ, 338:b2270