11-14 May 2014, London
Dr. Vladimir Anisimov
Sr Strategic Biostatistics Director
Predictive Analytics, Innovation
Vladimir.Anisimov@quintiles.com
Copyright © 2013 Quintiles

Stochastic behaviour and complexity of trial operation require developing predictive analytic techniques accounting for
• major uncertainties in input information
• stochasticity of basic processes: enrolment, trial start-up, various events (clinical & non-clinical)
Most of trial operational characteristics are driven by patient enrolment which is stochastic by nature.
Inefficient enrolment forecast is one of the main reasons of trial failure:
- more than 60-70% of trials fail to recruit in time
The majority of existing tools in pharma companies still use ad-hoc simplified or deterministic models.
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• Patient enrolment modelling
• Predicting trial/site enrolment performance and risk-based monitoring
• Forecasting trial operational characteristics
- follow-up patients, visits, events, costs
• Event predictive modelling in event-driven trials
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Analytic data-driven statistical methodology is developed *
Stochastic modelling technique:
• Patients arrive at sites according to Poisson processes
• Variation in enrolment rates is modelled using a gamma distribution
• Delays in site initiation also be random (uniform, beta, gamma)
In site i, n i
(t) = π
λi
(t – v i
) χ(v i
≤t ≤ b i
)
λ i
= γ(α,β) rate , v i
– delay in site initiation, b i
- closure time.
Start-up predictions are created using expected or historical data.
Interim re-forecasting uses real data and Bayesian re-estimation.
Closed-form expressions for mean and predictive bounds are derived ( no need in Monte Carlo simulation).
Methodology is world-wide accepted, validated on tens of real trials.
Basic version is implemented in some pharma companies.
* Anisimov & Fedorov, 2005, 2007; Anisimov, 2009-2011, presented at DIA, JSM (invited sessions), ISCB, PSI,...
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• Compute mean and credibility bounds for the predictive number of patients recruited over time and for time to complete trial at any stage of the trial
• Realize a new paradigm: Plan with confidence e.g.
“70% chance that trial will complete enrolment in time”
• Evaluate the optimal number of sites needed to complete in time
• Advise on adaptive adjustment: o Evaluate Probability to recruit in time; o If study is likely to go late, calculate the number of additional sites needed to complete in time with a given confidence
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Scenario: 400 pts, 70 sites, time = 365 days. Sites initiated in 5-month period, half of sites will be closed in two months before the end of enrolment.
Initial design: to complete with 90% confidence.
Predictive area: mean and confidence bounds.
Interim analysis after 150 days: 88 pts recruited.
Enrolment is slower than predicted.
Interim adjustment: to complete with 90% confidence:
22 new sites to add.
Adjusted prediction is going on time.
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Technique/tools * for forecasting site/trial performance:
 Triggers for detecting unusual behavior
• Low and High-enrolling sites,
• Late-start, inactive, high number of AE, etc.
 Predictive triggers (interim time, data-driven):
• Predict performance
• Create dynamic forecasts in future periods
Opportunity for optimal decision-making: choose the optimal # of sites and allocation accounting for study costs, completion time and risks per delays
Current triggers usually use assumptions of normality and detect unusual behaviour of sites within cohort using Mean and SD:
X > Mean(cohort) + K*SD(cohort), K=1,2,3
However, many of variables describing operation of clinical trials are rather far from the normal distribution .
Thus, using triggers based on Mean and SD will lead to biased results.
Predictive Analytics Team, Quintiles
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Histogram of the enrolment rate
(# of patients)/(site enrolment duration) far from normal distribution,
Red dot – 0.004: Mean + 3*SD, heavy tailed.
Adequate model
– Poisson mixed with gamma
Histogram Time from Last Patient Enrolled till current time
– red line – fitted Pareto distribution far from normal distribution, heavy tailed.
Adequate model
– Exponential mixed with gamma
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Classification of Low-High enrolling sites using Probability Quantile trigger.
Different dots – different sites - 332. Each site is defined by (# of patients, exposure time)
Twodimensional site’s characterization.
Probability Quantiles: 95% - red line , 90% - magenta , 80% - brown .
Adequate model - Poisson process with gamma rate.
Thresholds based on normal approximation:
Black linear lines: Mean + SD; Mean + 2*SD; Mean + 3*SD – current trigger
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Interim analysis, real study,
330 active sites.
Sites:
1006 and 1017
– low enrollers
Sites:
1901 and 1906
–good enrollers
Predictive probabilities to enrol:
| zero | <= one | <= two | <= three | at least one patient |
ML estimation and Bayesian re-estimation.
In particular, if at time t
0 site i recruited zero patients during time interval v i
, then
Prob (zero patients at time t) =
( α,β) – estimated by ML model parameters
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66
67
68
69
61
62
63
64
SID 15 days 30 days 45 days
57 2 2 3
58
59
60
7
8
2
12
13
2
15
17
3
70
71
72
9
2
9
9
26
8
2
7
7
2
5
14
2
14
14
45
13
2
10
10
2
8
14
3
10
63
18
3
14
19
3
19
19
Real trial, interim look,
544 sites active;
1790 patients screened
Predictive 90%-upper bounds for the number of recruited patients in the future.
Goal: to predict supply in advance, prepare staff in hospitals,..
Site 66 is highly enrolling ; sites 57, 60, 68, 71 – low enrolling
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Artificial case study: number of patients =450; number of clinical sites =175; time to complete enrolment =9 months; all centres initiated uniformly in 3-month period.
Blue curve: site’s start-up green curve: mean # of empty sites red curves- 90% predictive bounds
At the end: mean 55, low bound = 45, upper bound = 67
Proportion of empty sites at study completion ~ 30%
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Predicted number of sites recruited more than 8 pts each.
The same case study: number of patients =450; number of clinical sites =175; time to complete enrolment =9 months; all centres initiated at start up.
Green curve: mean # of sites recruited > 8 pts red curves- 90% predictive bounds
At the end of enrolment: mean = 8, low bound = 4, upper bound = 13
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Next stage: Predictive modelling operational processes.
A new technique using hierarchic evolving processes is developed.
In centre i recruited at time t ki
• follow-up visits, related events patient k generates some follow-up evolving process with random life time ξ ki
(t- t ki
), t ki
≤ t ≤ t ki
+ τ ki
, e.g.:
(clinical or operational, e.g. - AE, CRF, monitoring visits,...)
• associated costs (visits, maintenance, supply)
Z i
(t) = Σ k
ξ ki
(t – t ki
) - sum of evolving processes in centre i,
Statistical technique for forecasting evolving processes is developed.
Closed-form solutions are derived for many practical scenarios.
Tools in C#, R and RExcel are created
* Predictive Analytics Team, Quintiles
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Monthly cost of trial operation
Mean and 90% credibility intervals.
Input – tables:
• Site’s initiation data
• # of sites
• Costs per sites/patient visits
Input: Costs per patient visits
Visit No Time # of visits
1 1 600
2 30 450
3
4
5
58
87
114
400
350
304
9
10
6
7
8
143
172
198
282
366
297
290
283
276
269
Cost
100
50
40
40
50
40
30
40
45
40
Input: Operational costs:
• Opening site = $10,000
• Maintenance cost per site/day = $100
• Site closing cost = $1,000
• Monitoring cost per patient/day = $20
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Study design: Sites – 200, patient’s target – 800, enrolment duration – 1 year
Predictive number of follow-up patients
Mean, Low and Upper 90% bounds
Region with 100 sites,
μ – drop-out rate,
Follow-up period L= 180 days.
At some conditions – stable regime: for L < t <T, n(t) ~ n stat
–
Poisson with rate
λ(1 – e -
μL ) /μ
Predictive number of Visits No. 3
Visits time-schedule:
4 visits in total, each after 60 days
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Patients are followed-up.
Analytic technique * is developed for predicting over time the number of events together with ongoing enrolment and time to stop trial
Assumptions:
• Enrolment follows a Poisson-gamma model
• Can be different types of events
• For multiple events Markov evolving processes are used.
Predictive process: and - transition probabilities of Markov chain,
- global posterior rate (using Bayesian re-estimation in sites).
Predictive characteristics are derived in a closed form
(no need in Monte Carlo simulation)
Opportunity: to combine prediction of the # of events with predictive power.
* Anisimov, Pharma Stats, 2011
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B
A
Scenario.
Enrolment completion target time 21 months,
Trial completion target time 70 months
Other 150 sites ( with 0.4 pts/month/site) are added after interim look
P
A
= 100% (enrolment complete in time)
P
B
= 95% (events complete in time)
Hazard ratio – 0.8, test on non-inferiority.
Power depends on the # of events - random
P
C
= 97.5% Prob( Power >0.9)
C
Trial completion target time
Trial completion target time
Target number of events
Acknowledgment: Val Fedorov, Xiaoqiang Xue
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The advanced statistical techniques for predictive analytic modelling of trial operation are developed:
• Predict and adaptively adjust patient enrolment
• Forecast trial operational characteristics trial/site performance, visits, follow-up patients, operational costs...
• Provide risk-based monitoring of the main characteristics
• Forecast of different event’s
We are not aware about similar tools used by other pharma companies and CRO.
Supporting software tools are created and in use by
Predictive Analytics Team, Innovation, Quintiles.
Tools open wide opportunities for improving the efficiency and quality of CT prediction, additional benefits and cost savings.
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1. Anisimov V., Fedorov V., Modelling, prediction and adaptive adjustment of recruitment in multicentre trials, Statistics in Medicine , 26, 2007, 4958 –
4975.
2. Anisimov V., Predictive modelling of recruitment and drug supply in multicentre clinical trials, Proc. of JSM , Washington, August, 2009, 1248-
1259.
3. Anisimov V., Predictive event modelling in multicentre clinical trials with waiting time to response, Pharmaceutical Statistics , 10, iss. 6, 2011, 517-
522.
4. Anisimov V., Statistical modelling of clinical trials (recruitment and randomization), Communications in Statistics – Theory and Methods, 40:
19-20, 2011, 3684-3699.
5. Anisimov V., Predictive hierarchic modelling of operational characteristics in clinical trials, Communications in Statistics - Simulation and
Computation (submitted)
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