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 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 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 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 co proxamol 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):

Ŷ t = β 0 + β 1

x time

t + β 2

x intervention

t + β 3

x time_after_intervention

t + e t

Y t 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

β 0 β 1

estimates the base level of the outcome at the beginning of the series estimates the base trend, i.e. the change in outcome per quarter in the pre-intervention segment

β 2

estimates the change in level in the post-intervention segment

β 3 e t

estimates the change in trend in the post-intervention segment 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 5000

Co-proxam ol w ithdraw al announced

4000 3000 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

Year (quarters)

2004 2005 2006 2007 co-proxamol NSAIDs paracetamol co-codamol tramadol co-dydramol codeine dihydrocodeine * 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)

50 40 30 20 10 90 80 70 60

Co-proxamol withdrawal announced

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)

co-proxamol other analgesics co-proxamol best fit without announcement co-proxamol best fit with announcement

Prescriptions

Co-proxamol Cocodamol Codeine Pre-intervention Base level, β 0 (SE) 3050.1 (139.9) Post-intervention p <0.001

Base trend, β 1 (SE) -45.9 (7.7) p Change in level, β 2 (SE) <0.001

-554.8 (74.9) p <0.001

Change in trend, β 3 (SE) -46.8 (16.8) p 0.01

1349 (12.4) 204.8 (4.2) Codrydamol 1055.2 (6.1) Dihydrocodeine 686.4 (31.1) <0.001

0.007

34.1 (0.8) 9.6 (0.2) <0.001

<0.001

0.004

0.291

300.5 (53.6) 20.5 (11.6) 148.7 (35.8) -29.7 (2.4) <0.001

0.089

<0.001

<0.001

30.7 (6.4) 3.5 (1.2) -4.2 (4.1) -0.8 (2.4) <0.001

-622.9 (70.2) <0.001

-66.2 (8.5) <0.001

0.007

0.316

0.731

<0.001

NSAIDs Paracetamol Tramadol 4652.4 (47.2) 1493.4 (56.1) 47.2 (51.4) <0.001

-1.1 (0.3) <0.001

-1.5 (1.4) <0.001

28.4 (3) <0.001

0.365

42.1 (3.0) 31.4 (2.7) <0.001

<0.001

232 (66.6) -41.9 (6.8) 0.001

<0.001

23 (8.2) 16.3 (5.2) 0.01

0.004

Prescriptions

Co-proxamol Cocodamol Codeine Pre-intervention Base level, β 0 (SE) 3050.1 (139.9) p Base trend, β 1 (SE) <0.001

-45.9 (7.7) Post-intervention p <0.001

Change in level, β 2 (SE) -554.8 (74.9) p <0.001

Change in trend, β 3 (SE) -46.8 (16.8) p 0.01

1349 (12.4) 204.8 (4.2) Codrydamol 1055.2 (6.1) Dihydrocodeine 686.4 (31.1) <0.001

0.007

34.1 (0.8) 9.6 (0.2) <0.001

<0.001

0.004

0.291

300.5 (53.6) 20.5 (11.6) 148.7 (35.8) -29.7 (2.4) <0.001

0.089

<0.001

<0.001

30.7 (6.4) 3.5 (1.2) -4.2 (4.1) -0.8 (2.4) <0.001

-622.9 (70.2) <0.001

-66.2 (8.5) <0.001

0.007

0.316

0.731

<0.001

NSAIDs Paracetamol Tramadol 4652.4 (47.2) 1493.4 (56.1) 47.2 (51.4) <0.001

-1.1 (0.3) <0.001

-1.5 (1.4) <0.001

28.4 (3) <0.001

0.365

42.1 (3.0) 31.4 (2.7) <0.001

<0.001

232 (66.6) -41.9 (6.8) 0.001

<0.001

23 (8.2) 16.3 (5.2) 0.01

0.004

Prescriptions

Co-proxamol Cocodamol Codeine Pre-intervention Base level, β 0 (SE) 3050.1 (139.9) p Base trend, β 1 (SE) <0.001

-45.9 (7.7) Post-intervention p <0.001

Change in level, β 2 (SE) -554.8 (74.9) p <0.001

Change in trend, β 3 (SE) -46.8 (16.8) p 0.01

1349 (12.4) 204.8 (4.2) Codrydamol 1055.2 (6.1) Dihydrocodeine 686.4 (31.1) <0.001

0.007

34.1 (0.8) 9.6 (0.2) <0.001

<0.001

0.004

0.291

300.5 (53.6) 20.5 (11.6) 148.7 (35.8) -29.7 (2.4) <0.001

0.089

<0.001

<0.001

30.7 (6.4) 3.5 (1.2) -4.2 (4.1) -0.8 (2.4) <0.001

-622.9 (70.2) <0.001

-66.2 (8.5) <0.001

0.007

0.316

0.731

<0.001

NSAIDs Paracetamol Tramadol 4652.4 (47.2) 1493.4 (56.1) 47.2 (51.4) <0.001

-1.1 (0.3) <0.001

-1.5 (1.4) <0.001

28.4 (3) <0.001

0.365

42.1 (3.0) 31.4 (2.7) <0.001

<0.001

232 (66.6) -41.9 (6.8) 0.001

<0.001

23 (8.2) 16.3 (5.2) 0.01

0.004

Suicides

Pre-intervention Post-intervention Co-proxamol Base level, β 0 (SE) 81.0 (4.5) Other analgesics All drugs except co-proxamol and other analgesics All drugs 51.3 (2.8) 221.2 (7.3) 353.7 (10.2) p <0.001

Base trend, β 1 (SE) -1.194 (0.3) <0.001

<0.001

<0.001

-0.3 (0.2) -0.5 (0.5) -2.0 (0.7) p <0.001

Change in level, β 2 (SE) -28.3 (4.9) p <0.001

Change in trend, β 3 (SE) 0.6 (0.6) p 0.355

0.095

0.299

0.008

6.4 (6.0) 21.6 (12.8) 0.004 (18.1) 0.297

0.100

1.000

-0.3 (0.6) -5.4 (1.4) -4.9 (1.7) 0.724

<0.001

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

Ŷ 34.5

= β 0 + β 1

x 34.5

Ŷ 34.5

= β 0 + β 1

x 34.5 +

β 2 + β 3

x 6.5

without intervention with intervention

   Thus, the absolute effect of the intervention is

β 2 + β 3

x 6.5 Standard errors calculated using method of Zhang et al

σ 2 2 + 6.5

2 x σ 3 2 + 2 x 6.5 x σ 23

Non-significant terms included due to correlation between slope and level terms

Results - Prescriptions

Prescriptions (x1000)

Co-proxamol Cocodamol Codeine Codrydamol Dihydrocodeine NSAIDs Paracetamol Tramadol

Estimates of absolute effect during 2005 to 2007 Mean quarterly estimated number pre announcement Mean quarterly number post announcement Mean quarterly change (95% CI)

1465.1

2524.7

534.6

1018.2

634.6

5633.8

2947.0

1130.1

605.7

3024.6

578 1140.0

600.0

4581.0

3330.0

1193.9

-859 (-1065 to -653) 500 (459 to 540) 43 (31 to 55) 122 (99 to 145) -35 (-68 to -2) -1053 (-1186 to -920) 382 (268 to 497) 64 (-5 to 133)

Results - Deaths

Suicides, Open

Co-proxamol

Estimates of absolute effect during 2005 to 2007 Mean quarterly estimated number pre announcement Mean quarterly number post announcement Mean quarterly change (95% CI)

Other analgesics All drugs except co-proxamol and other analgesics 39 39 204 15 44 191 -24 (-37 to -12) 5 (-5 to 15) -13 (-34 to 8) All drugs All causes 283 1152 252 1130 -31 (-66 to 3) -22 (-89 to 45)

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 post intervention 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 co proxamol 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 post estimation 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 co proxamol 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 non equivalent 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