Considering non linear modelling as a primary analysis – an example and some challenges

1. Considering non linear modelling as a primary analysis – an example and some challenges Kimberley Stephens 8th June 2011

2. Contents Overview of study Explanation of Data Issues Results Learnings Further work

3. The Academic Discovery Performance Unit is a specialist team within GSK that works specifically with academics on a portfolio of novel targets. We give our academic partners the freedom to make their ideas a reality by providing the unique capabilities and expertise of a large scale pharmaceutical company.

4. Study Details • Double-blind • Single centre • Parallel Group • Randomized • Placebo controlled • Single dose • Active drug or placebo (2:1 ratio) • Phase II study • Male and females • Critically ill patients: - with enteral feed intolerance - on mechanical ventilation - expected to survive for at least 24 hrs post dose • Ongoing study – Interim Analysis data (N=23)

5. Study Objectives and Endpoints • In ICU patients, investigate; • Pharmacodynamic effect of single doses on gastric emptying • Safety and tolerability of single doses • Pharmacokinetics of single doses • Primary endpoint: • Gastric emptying measured by 13C octanoic acid breath test • Gastric half emptying time (T1/2) • Primary comparison: • Day 1 vs Baseline (within subject) GSK Drug • Day 1 vs Baseline (within subject) Placebo • Exploratory comparison: • GSK Drug vs Placebo Mortality Ventilator Dependence Infections LOS Improve Outcomes GE EN

6. What is Gastric Emptying? • How fast the meal is emptied from the stomach • In this study it was measured by 13C-octanoic acid breath test • Reliable indirect method of measuring gastric emptying • Test meal marked with 13C-octanoic acid • Marked meal empties gradually through pylorus to duodenum,where 13C-octonoic acid is absorbed and metabolized in liver to 13CO2 • 13CO2 is expelled via the lungs • Breath samples collected at baseline and regular intervals after meal ingestion out to 240mins • The isotope (13C) is stable; technique is nonradioactive

7. Typical Gastric Emptying Curve Non Linear model fitted through data points Percent of Dose Recovered Time (mins)

8. Non Linear Models • Model “B” • Model “W” Corrected for scintigraphy Keller etal, Neurogastroenterology and Motility,21, 1039-e83, (2009). Kocelaketal, J Gastroenterol, 43, 609-617, (2008).

9. Previous Study in Healthy Volunteers Comparing T1/2 from Models Pearson’s correlation 0.9995 (p value <0.0001) T1/2w(mins) Best fitting model (B or W) chosen based on smallest sums of squares T1/2b(mins)

10. Issue with Gastric Emptying Curve in some ICU Patients Curve hasn’t started to come down by end of sampling Curve has started to come down Percent of Dose Recovered Time (mins)

11. Difference between Models and T1/2 in some ICU Patients Up until 240mins models fit similarly Model B Model W Extrapolation of models beyond 240mins can lead to very different curves T1/2b = 413.38 mins T1/2w = 677.35 mins Percent of Dose Recovered Time (mins) Model B Model W

12. Had little confidencein T1/2 values which are extrapolated beyond sampling time of 240 mins. • Six T1/2 values were > 240 mins (Total of 13% of data).This was found in 5 out of the 23 subjects. • Investigated different approaches to dealing with this data. Loge Transformed Analysis Nonparametric Imputed 240 mins PROC QLIM TOBIT Analysis (Censored) PROC NLMIXED

13. Analysis Loge Transformed Analysis • Assuming we have confidence in the T1/2 values extrapolated beyond 240 mins. • Analysis carried out separately for each treatment. • Mixed model fitting visit (Baseline/Day 1) as fixed effect and subject as random. • For each treatment the difference “Day 1 – Baseline” were constructed and then back transformed onto a ratio scale. • On GSK, there was approximately a 35% decrease in T1/2 compared to Baseline BL = Baseline; GLS = Geometric Least Squares; CI = Confidence Interval

14. Analysis Nonparametric • Nonparametric analysis using normal order scores (by treatment) instead of raw data (Distribution free). • Analysis carried out separately for each treatment. • Mixed model fitting visit (Baseline/Day 1) as fixed effect and subject as random. • For each treatment the p value of the difference “Day 1 – Baseline” were constructed. • On GSK, there was approximately a 35mins decrease in T1/2 compared to Baseline. BL = Baseline

15. Analysis Imputed 240 mins • All values >240mins imputed to be 240 • Analysis carried out separately for each treatment. • Mixed model fitting visit (Baseline/Day 1) as fixed effect and subject as random. • For each treatment the difference “Day 1 – Baseline” were constructed. • On GSK, there was approximately a 36mins decrease in T1/2 compared to Baseline. BL = Baseline; LS = Least Squares; CI = Confidence Interval

16. TOBIT Analysis • All right-censored data are assumed to follow the same normal distribution that is indicated by the real observed truncated distribution up to 240mins. • Assume a latent (unobservable) variable yi* • Indicator • Likelihood function: Probabilities that an observation is censored Likelihood from observed

17. TOBIT Analysis Few observations >240mins, then mean estimation from TOBIT not too different More observations >240mins, then mean estimation from TOBIT is different

18. Analysis PROC QLIM TOBIT Analysis (Censored) • Analysis carried out separately for each treatment. • Intercept and difference between Day 1 and Baseline was estimated. • On GSK, there was approximately a 40 minsdecrease in T1/2 compared to baseline. • Output and flexibility of PROC QLIM in SAS can be limiting. BL = Baseline

19. Analysis PROC NLMIXED TOBIT Analysis (Censored) • Analysis carried out separately for each treatment. Subject was fitted as a random effect. • Intercept, random subject level and difference between Day 1 and Baseline was estimated. • On GSK, there was approximately a 40 minsdecrease in T1/2 compared to baseline. • Still investigating how to obtain within subject SD from the models. • Sensitive to starting values for parameter estimates. • Need SAS V9.2 for analysis. BL = Baseline; CI = Confidence Interval

20. Comparison of Results 35% decrease from baseline Loge Transformed Analysis Nonparametric 35mins decrease from baseline Imputed 240 mins 36 minsdecrease from baseline 40 mins decrease from baseline PROC QLIM TOBIT Analysis (Censored) PROC NLMIXED All p values were approximately the same. TOBIT methods point estimate agreement to 2dp.

21. Conclusions • All methods give similar answers in this case, maybe due to relatively few values >240mins. • PROC QLIM is designed for TOBIT analysis, output is meaningful but can be limiting with regards to the flexibility in models fitted. • More work to get PROC NLMIXED reproducing output for PROC QLIM. • PROC NLMIXED can be sensitive to starting values for parameters so use PROC QLIM to do analysis first to get estimates then can use NLMIXED to extend model if required.

22. Further Work • Working with modelling and simulation group to look at modelling the curves from original data to estimate population T1/2 (Manchester group) • Final reporting may have more >240mins so methods may vary a little more. • Further modelling using NLMIXED to fully understand covariate structure and also build upon model to may be include both treatments in one model. • Extension of the TOBIT analysis for GSK vs Placebo comparison via regression model in groups (although this would not censor baseline values correctly).

23. Acknowledgements • David Shaw (GSK) • Aiden Flynn (GSK) • Kristen Verbeke (Leuven)