Longitudinal Methods for Pharmaceutical Policy Evaluation

Common Analytic Approaches

Michael LawThe Centre for Health Services and Policy Research

The University of British Columbia

Vancouver, Canada

ObjectivesDiscuss 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

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Interrupted Time SeriesBasic 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

Level Change

Slope Change

Pre-intervention Post-intervention Time

Ou

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Inte

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Intervention

Adapted from Schneeweiss et al, Health Policy 2001

Counterfactual

Observed

Observed

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.

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West Virginia Control States (n=38)

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Effect of Policy

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

Observation Time Outcome Post Post_Time

1 1 45.3 0 0

2 2 54.2 0 0

3 3 47.5 0 0

4 4 56.3 0 0

5 5 52.3 1 1

6 6 48.6 1 2

7 7 50.2 1 3

8 8 46.2 1 4

Statistical Modeling• Statistical Model: segmented regression

Outcomet=β1+β1timet+β1policyt+β1timetpolicyt+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

O

X

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Person Survival Time Event

4 3 1

3 5 0

2 4 1

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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. Lawmlaw@chspr.ubc.ca@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/survival-analysis.pdf

Time Series Example CodeR

library (nlme)

itsmodel <- gls(model=outcome ~ trend + post + post_time, data=timeseries, correlation=corARMA(p=1, form=~trend),method=“ML”)

SASproc autoreg data=timeseries;

model outcome = time post post_time / method=ml nlag=(1 2 3) backstep;

run;

Example code: Kaplan-MeierR

fit<-survfit(formula = Surv(time, censor)~variable,data = survivaldata)

plot(fit, xlab="Time", ylab="Survival Probability",

col = c("blue","red"))

SASProc lifetest data=survivaldata plots=(s);

time time*censor;

strata variable;

run;

Example code: Cox P-HR

library(survival)

survmodel <- coxph(Surv(time,censor) ~ variable,

data=survivaldata)

summary(survmodel)

SASProc phreg data=survivaldata;

model time*censor(0) = variable

/rl ties=exact;

run;