Transcript 1249-Law-_b
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
Objectives Discuss two longitudinal methods
– Interrupted Time Series – Survival analysis
For each, I will briefly cover
– The data required – Modeling techniques and software
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
90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 2010 Higher Drug Co-payment 2011
90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Higher Drug Co-payment
90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Higher Drug Co-payment 2010 Region 1 Region 2 2011
90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Higher Drug Co-payment 2010 Region 1 Region 2 2011
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
Intervention Slope Change Level Change
Observed
Pre-intervention Post-intervention Time Adapted from Schneeweiss et al, Health Policy 2001
Source: Tamblyn et al. JAMA 2001;285:421-429.
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.
60% 50% 40% 30% 20% 10% 0% 20 01 , 2 20 01 , 3 20 01 , 4 20 02 , 1 20 02 , 2 20 02 , 3 20 02 , 4 20 03 , 1 20 03 , 2 20 03 , 3 20 03 , 4 20 04 , 1 20 04 , 2 20 04 , 3 20 04 , 4 20 05 , 1 20 05 , 2 20 05 , 3 20 05 , 4
Quarter
West Virginia Control States (n=38) Source: Law et al. Psychiatric Services. 2008
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
Problems with Time Series
• • • • Requires reasonably stable data Can be biased by co-interventions Need longer-term data Linear trend might not be realistic
Data setup for ITS
• Need: Time, population-level outcomes 7 8 4 5 6 2 3
Observation
1 7 8 4 5 6 2 3
Time
1
Outcome
45.3
54.2
47.5
56.3
52.3
48.6
50.2
46.2
1 1 0 1 1 0 0
Post
0 3 4 0 1 2 0 0
Post_Time
0
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
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
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
When to use SA
• • • Time to event outcomes Data at the patient-level Time to anything (death, expenditure threshold, etc.)
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
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
2 1 4 3 0 X 1 2 3 2
Person
4 1 3 4 5 4
Survival Time
3 6 5 0 1
Event
1 1 6 X 7 X 8 O
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
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
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
Thank you
Questions?
Michael R. Law
@Michael_R_Law
•
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
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;
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; run; strata variable;
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 run; /rl ties=exact;