Interrupted Time Series

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Presentation by Karen Smith

Transcript of Interrupted Time Series

Interrupted Time Series: What, Why and How

Karen Smith

Acknowledgement Motivated by consultancy work with the Centre for Suicide Research 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 coproxamol was the single drug used most frequently for suicide by self-poisoning 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 coproxamol

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 co-proxamol 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.

Whats 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 Doesnt 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 Doesnt 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 ModelUse segmented regression analysis (Wagner et al, 2002): t = 0 + 1 x timet + 2 x interventiont + 3 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 preintervention 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 0 estimates the base level of the outcome at the beginning of the series 1 estimates the base trend, i.e. the change in outcome per quarter in the pre-intervention segment 2 estimates the change in level in the post-intervention segment 3 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

Co-proxam ol w ithdraw al announced

Prescription items dispensed per quarter (thousands)

5000

co-proxam 4000 NSAIDs

paracetam tramadol codeine

co-codam 3000

co-dydram

dihydroco 2000

1000

01 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

80

Co-proxamol withdrawal announced

70

co-proxa

Number of deaths

60

other analges

50

40

co-proxa best fit w announc

30

co-proxa best fit w announc

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

2004

2005

2006

2007

Year (quarters)

PrescriptionsPre-intervention Base level, 0 (SE) p Base trend, 1 (SE) -45.9 (7.7) 34.1 (0.8) 9.6 (0.2) -1.1 (0.3) -1.5 (1.4) 28.4 (3) 42.1 (3.0) 31.4 (2.7) p Post-intervention Change in level, 2 (SE) -554.8 (74.9) 300.5 (53.6) 20.5 (11.6) 148.7 (35.8) -29.7 (2.4) -622.9 (70.2) 232 (66.6) -41.9 (6.8) p Change in trend, 3 (SE) -46.8 (16.8) 30.7 (6.4) 3.5 (1.2) -4.2 (4.1) -0.8 (2.4) -66.2 (8.5) 23 (8.2) 16.3 (5.2) p

Co-proxamol Cocodamol Codeine Codrydamol Dihydrocodeine NSAIDs Paracetamol Tramadol

3050.1 (139.9) 1349 (12.4) 204.8 (4.2) 1055.2 (6.1) 686.4 (31.1) 4652.4 (47.2) 1493.4 (56.1) 47.2 (51.4)