1. Longitudinal Methods for Pharmaceutical Policy Evaluation Common Analytic Approaches Michael Law The Centre for Health Services and Policy Research The University of British Columbia Vancouver, Canada

2. Objectives Discuss two longitudinal methods –Interrupted Time Series –Survival analysis For each, I will briefly cover –The data required –Modeling techniques and software

3. The key messages If you plan in advance, you can collect the right data There are multiple data sources that work –includes sales data, insurance claims data, hospital data and sample-based data Statistical methods are more sophisticated, but not impossible

4. Higher Drug Co-payment

8. Interrupted Time Series Basic Design –Compare longitudinal trends before and after the policy change –Good for sharply-defined interventions Major Assumption –The trend in the outcome among those exposed to the policy would have been the same absent the policy

9. Level Change Slope Change Pre-intervention Post-intervention Time Outcome of Interest Intervention Adapted from Schneeweiss et al, Health Policy 2001 Counterfactual Observed

10. Source: Tamblyn et al. JAMA 2001;285:421-429.

11. ITS with Control Series Estimate of counterfactual becomes the observation of what happened in the control group Control group adds further legitimacy by limiting effect of possible history threats Can be an unaffected group, another jurisdiction, etc.

12. Effect of Policy Source: Law et al. Psychiatric Services. 2008

13. Strengths of Time Series Easy to show results graphically More robust to secular trends Less difficult to estimate and communicate than other methods –E.g. propensity score matching, instrumental variables estimates Null results are more convincing

14. Problems with Time Series Requires reasonably stable data Can be biased by co-interventions Need longer-term data Linear trend might not be realistic

15. Data setup for ITS Need: Time, population-level outcomes ObservationTimeOutcomePostPost_Time 1145.300 2254.200 3347.500 4456.300 5552.311 6648.612 7750.213 8846.214

16. Statistical Modeling Statistical Model: segmented regression Outcome t =β 1 +β 1 time t +β 1 policy t +β 1 time t  policy t +ε Should Account for autocorrelation –The tendency for subsequent values to be related

17. Individual-level ITS You can use data at the individual level –Means collecting each outcome for each person at each time Requires using more sophisticated mixed model (e.g. logistic or poisson type GEE) Provides more power, requires more statistical skill

18. Survival Analysis Method of studying longitudinal data on the occurrence of events Also known as “time to event” studies For example: –time until discontinuation –time until drug dispensing

19. When to use SA Time to event outcomes Data at the patient-level Time to anything (death, expenditure threshold, etc.)

20. Who to compare to? Two basic options: –Pre-post analysis of the same population For example, people who initiate a particular class of medication –Concurrent analysis of those subject to and not subject to a policy For example, individuals in another jurisdiction Be wary of potential biases

21. Data setup You need the following variables to perform a survival analysis: –Censoring: 0 if event did not occur, 1 if the event did occur –Time to event: the number of time periods (e.g. days) before the event or censoring took place –Any control variables

22. O X X X PersonSurvival TimeEvent 431 350 241 161

23. Kaplan-Meier Analysis Non-parametric estimate of survival function Commonly used as descriptive statistic and for figures in manuscripts Requires categorical variables for including other variables

25. Cox Proportional Hazards Method for fitting a survival model Compares hazard rates (the instantaneous probability of failure) between different groups Assumes hazard functions are proportional to one another

26. Key Points Longitudinal designs make your study –More convincing –More publishable –You can do this based on your data However, you need to plan for data collection from the start to ensure you get the necessary data

27. Thank you Questions? Michael R. Law mlaw@chspr.ubc.ca @Michael_R_Law

28. Further Reading Interrupted Time Series –A.K. Wagner et al., “Segmented regression analysis of interrupted time series studies in medication use research,” Journal of Clinical Pharmacy and Therapeutics 27, no. 4 (2002): 299-309. Survival Analysis –Paul Alison. Survival Analysis Using SAS: A Practical Guide. 2010. Cary, NC: The SAS Institute. –John Fox. Introduction to Survival Analysis. http://socserv.mcmaster.ca/jfox/Courses/soc761/survi val-analysis.pdf http://socserv.mcmaster.ca/jfox/Courses/soc761/survi val-analysis.pdf

29. Time Series Example Code R library (nlme) itsmodel <- gls(model=outcome ~ trend + post + post_time, data=timeseries, correlation=corARMA(p=1, form=~trend), method=“ML”) SAS proc autoreg data=timeseries; model outcome = time post post_time / method=ml nlag=(1 2 3) backstep; run;

30. Example code: Kaplan-Meier R fit<-survfit(formula = Surv(time, censor)~variable, data = survivaldata) plot(fit, xlab="Time", ylab="Survival Probability", col = c("blue","red")) SAS Proc lifetest data=survivaldata plots=(s); time time*censor; strata variable; run;

31. Example code: Cox P-H R library(survival) survmodel <- coxph(Surv(time,censor) ~ variable, data=survivaldata) summary(survmodel) SAS Proc phreg data=survivaldata; model time*censor(0) = variable /rl ties=exact; run;