Ruth Keogh

Transcript

1. Flexible modelling of personalised dynamic prediction curves using landmarking, with a case-study in cystic fibrosis Ruth Keogh Department of Medical Statistics London School of Hygiene & Tropical Medicine Improving health worldwide www.lshtm.ac.uk
2. UK Cystic Fibrosis Registry Cystic Fibrosis (CF) • An inherited, chronic, progressive condition • Affects ~10,000 people in the UK • 1 in 2500 live births affected • Estimated median survival age in the UK is 47
3. UK Cystic Fibrosis Registry Cystic Fibrosis (CF) • An inherited, chronic, progressive condition • Affects ~10,000 people in the UK • 1 in 2500 live births affected • Estimated median survival age in the UK is 47 The UK CF Registry • Established 1995, web-based since 2007 • Longitudinal data obtained at annual visits - clinical measurements - hospital stays - treatments used
4. Information on survival for people with CF • Currently quite limited • Median survival age • Little information on conditional survival
5. Information on survival for people with CF • Currently quite limited • Median survival age • Little information on conditional survival Aims • To develop more personalised information on long-term survival via dynamic prediction models from each age which account for current health status
6. Dynamic prediction using landmarking
7. Dynamic prediction using landmarking
8. Dynamic prediction using landmarking
9. Dynamic prediction using landmarking
10. Dynamic prediction using landmarking
11. Dynamic prediction using landmarking
12. Dynamic prediction using landmarking
13. Models used in landmarking 1. Cox model fitted from each landmark using predictors observed at the landmark (“last observation carried forward”) 2. A Cox “supermodel” fitted across landmarks Van Houwelingen & Putter. Dynamic Prediction in Clinical Survival Analysis. CRC Press 2012.
14. Models used in landmarking 1. Cox model fitted from each landmark using predictors observed at the landmark (“last observation carried forward”) 2. A Cox “supermodel” fitted across landmarks Van Houwelingen & Putter. Dynamic Prediction in Clinical Survival Analysis. CRC Press 2012. Accounting for measurement error in predictors by fitting a mixed model to measures up to the landmark. Paige et al. Estimating cardiovascular disease risk using repeated measurements of risk factors in electronic health records.
15. • Estimates are typically in terms of survival to a single time horizon • But we are often interested in several time horizons - 1 year, 5 years, 10 years • Fitting several models for a series of time horizons is inefficient and could lead to inconsistent estimates Dynamic prediction curves
16. • Estimates are typically in terms of survival to a single time horizon • But we are often interested in several time horizons - 1 year, 5 years, 10 years • Fitting several models for a series of time horizons is inefficient and could lead to inconsistent estimates Use of flexible parametric models (Royston & Parmar 2002) • Cox models are typically used in landmarking • Smooth curves are desirable for prediction • A fully parametric model is easier to report Dynamic prediction curves
17. Dynamic prediction curves
18. Dynamic prediction curves
19. Dynamic prediction curves
20. Dynamic prediction curves log | = log 0 + () A flexible model fitted separately from each landmark
21. Dynamic prediction curves log | = log 0 + () A flexible model fitted separately from each landmark Modelled using a restricted cubic spline
22. Dynamic prediction curves log | = log 0 + () A flexible model fitted separately from each landmark Modelled using a restricted cubic spline Predictors at the landmark
23. Dynamic prediction curves log | = log 0 + () A flexible model fitted separately from each landmark A flexible supermodel fitted using a single stacked data set log | = log 0 + ()() + , + () Modelled using a restricted cubic spline Predictors at the landmark
24. Dynamic prediction curves log | = log 0 + () A flexible model fitted separately from each landmark A flexible supermodel fitted using a single stacked data set Covariate effects can depend on the landmark log | = log 0 + ()() + , + () Modelled using a restricted cubic spline Predictors at the landmark
25. Dynamic prediction curves log | = log 0 + () A flexible model fitted separately from each landmark A flexible supermodel fitted using a single stacked data set Covariate effects can depend on the landmark log | = log 0 + ()() + , + () Modelled using a restricted cubic spline Predictors at the landmark Baseline cumulative hazard depends on the landmark
26. Dynamic prediction curves log | = log 0 + () A flexible model fitted separately from each landmark A flexible supermodel fitted using a single stacked data set Covariate effects can depend on the landmark log | = log 0 + ()() + , + () Modelled using a restricted cubic spline Predictors at the landmark Baseline cumulative hazard depends on the landmark Time-varying effects
27. Application to UK CF Registry data Baseline variables • Sex, genotype Time-dependent variables • Lung function (FEV1%) • BMI • Number of days treated with IV antibiotics in past year • CF-related diabetes • Presence of 4 airway infections • Pancreatic insufficiency
28. Application to UK CF Registry data Baseline variables • Sex, genotype Time-dependent variables • Lung function (FEV1%) • BMI • Number of days treated with IV antibiotics in past year • CF-related diabetes • Presence of 4 airway infections • Pancreatic insufficiency • Bivariate mixed model • Fitted value and slope used as predictors • Modelled using restricted cubic splines
29. Application to UK CF Registry data Baseline variables • Sex, genotype Time-dependent variables • Lung function (FEV1%) • BMI • Number of days treated with IV antibiotics in past year • CF-related diabetes • Presence of 4 airway infections • Pancreatic insufficiency “Period” approach There are up to 20 years of follow-up in this registry, but survival has improved over time. I restricted to deaths during 2011-2015.
30. Application to UK CF Registry data Baseline variables • Sex, genotype Time-dependent variables • Lung function (FEV1%) • BMI • Number of days treated with IV antibiotics in past year • CF-related diabetes • Presence of 4 airway infections • Pancreatic insufficiency “Period” approach There are up to 20 years of follow-up in this registry, but survival has improved over time. I restricted to deaths during 2011-2015. 6236 individuals alive during 2011-2015 Total of 704 deaths Supermodel fitted using landmarks at ages 18-45
31. Why use landmarking for this application? Lung transplants At each landmark we restrict to those who have not received a transplant.
32. Why use landmarking for this application? Lung transplants At each landmark we restrict to those who have not received a transplant. Multivariate mixed models fitted up to each landmark. Multiple predictors measured with error: Lung function and BMI
33. Why use landmarking for this application? Lung transplants At each landmark we restrict to those who have not received a transplant. Left-truncation due to the period analysis approach Flexible modelling of associations, including time-dependent associations, is easy Multivariate mixed models fitted up to each landmark. Multiple predictors measured with error: Lung function and BMI Keogh et al. Landmarking as a flexible approach to dynamic prediction of survival. To appear!
34. Model assessment Models were developed on a 50% random sample and model assessment based on the remaining 50%
35. Model assessment Models were developed on a 50% random sample and model assessment based on the remaining 50% C-Index • Measure of discrimination • C-Index for time-dependent effects: Antolini et al (Stat. Med. 2005)
36. Model assessment Models were developed on a 50% random sample and model assessment based on the remaining 50% C-Index • Measure of discrimination • C-Index for time-dependent effects: Antolini et al (Stat. Med. 2005) Calibration plots • Divided people into deciles based on survival probability • Obtain Kaplan-Meier estimate of x-year survival within the deciles
37. C-Index
38. C-Index
39. C-Index
40. Calibration
41. Calibration
42. Dynamic prediction curves
43. Dynamic prediction curves
44. Dynamic prediction curves
45. Ongoing and future work Settle on a final model for this application
46. Ongoing and future work Handling missing data on predictors Keogh & Morris. Multiple imputation in Cox regression when there are time-varying effects of exposures. http://arxiv.org/abs/1706.09187 Settle on a final model for this application
47. Ongoing and future work Handling missing data on predictors Keogh & Morris. Multiple imputation in Cox regression when there are time-varying effects of exposures. http://arxiv.org/abs/1706.09187 Settle on a final model for this application Develop a user-friendly way of presenting this information
48. Ongoing and future work
49. Thanks… For data and data preparation • UK Cystic Fibrosis Registry • The CF Epi-Net data group (Cystic Fibrosis Trust, Strategic Research Centre Grant) For helpful discussions • Shaun Seaman, Rhonda Szczesniak, Jessica Barrett, Angela Wood For funding • MRC Methodology Fellowship