Using dynamic prediction to inform the optimal intervention time for an abdominal aortic aneurysm screening programme

Transcription

1 Using dynamic prediction to inform the optimal intervention time for an abdominal aortic aneurysm screening programme Michael Sweeting Cardiovascular Epidemiology Unit, University of Cambridge Friday 15th April 1/41

2 Outline Abdominal Aortic Aneurysms (AAAs) A joint AAA growth and rupture model Building a decision model based on expected life-years Application to Multicentre Aneurysm Screening Study 2/41

3 Abdominal Aortic Aneurysms An Abdominal Aortic Aneurysm (AAA) is a swelling of the aorta that can grow over time If left untreated the aorta can rupture, which is associated with a high mortality rate ( 80%) Detection via a simple ultrasound, measuring the aortic diameter Diagnosis: Diameter 3.0cm Surgical intervention: Considered when AAA reaches 5.5cm in diameter 3/41

4 The UK National AAA Screening Programme Set up in 2009, rolled-out nationally across the UK All men aged 65 invited for a one-off ultrasound scan Majority (98.7%) screened normal (< 3.0cm) 0.1% considered immediately for elective surgery ( 5.5cm) 1.2% enrolled into continued surveillance Annual ultrasound scan if 3.0cm and < 4.5cm 3-monthly ultrasound scan if 4.5cm and < 5.5cm 4/41

5 When is the best time to intervene? The intervention threshold is not universally agreed Guidelines use either 5.0 or 5.5cm In the USA nearly half of AAA interventions are under 5.5cm The UK Small Aneurysm Trial and ADAM trial assessed early elective surgery ( cm) versus surveillance until 5.5cm No advantage for early surgery and continued surveillance more cost-effective 1 Could thresholds be patient-specific based on personalised criteria? 2 Should the time of intervention be based on a single measurement above or below a defined criteria? 3 Could the proposed time of intervention be updated dynamically as more information accrues (e.g. on the growth rate of an aneurysm?) 5/41

6 AAA trajectories from the Multicentre Aneurysm Screening Study AAA diameter (mm) Years since screening 6/41

7 Joint growth and rupture model For individual i, let T i = min(ti, C i ) denote the observed time of rupture, which is the minimum of the true event time Ti and the censoring time C i. δ i = I (Ti C i ): the event indicator A set of observed AAA diameter measurements, y ij = {y i (t ij ), j = 1,..., n i } 7/41

8 Joint growth and rupture model We consider the joint longitudinal and time-to-event model Longitudinal sub-model y i (t) = m i (t) + ɛ i (t) = x T i (t)β + z T i (t)b i + ɛ i (t), ɛ i (t) N(0, σ 2 ) Survival sub-model: Three possible structures h i (t) = h 0 (t) exp(γ T w i + αm i (t)) (1) h i (t) = h 0 (t) exp(γ T w i + α 1 m i (t) + α 2 m i(t)) (2) t h i (t) = h 0 (t) exp(γ T w i + α 1 m i (t) + α 2 m i (u) du) (3) where m i (t) = d dt m i(t) 0 8/41

9 Predicted Rupture Probabilities For an individual i with longitudinal measurements Y i (t) = {y i (s); 0 s t} Conditional probability of rupture by time u given no rupture by t is F R,i (u t) = P(Ti = 1 P(Ti = 1 < u T i > t, Y i (t); θ) < u T i > t, b i ; θ)p(b i T i > t, Y i (t); θ)db i Si (u M i (u, b i ; θ)) S i (t M i (t, b i ; θ)) p(b i Ti > t, Y i (t); θ)db i This can be calculated easily using the survfitjm function in the R package JM, where the empirical Bayes estimates of the random-effects and the maximum likelihood estimates of θ are used, or using a Monte Carlo simulation scheme 1 1 Rizopoulos, D. Biometrics 2011;67: /41

10 Building a decision model for AAA intervention Objective: Build a decision model to inform when to intervene for an individual 1 Joint model provides conditional probabilities of rupture 2 Obtain external estimates of mortality following rupture Assume 50% do not reach hospital alive 2 Assume 37% do not survive emergency operation (in-hospital) 3 p(d R) = Obtain external estimates of mortality following elective surgery Assume 3.7% do not survive elective operation (30-days) 4 p(d E) Lindholt et al. Clin Epidemiol. 2012; 4: IMPROVE trial investigators. BMJ 2014;348:f661 4 EVAR trial investigators. N Engl J Med 2010;362: /41

11 Expected life-years AAA related survival S AAA,i (t) = 1 F R,i (t)p(d R) Non-AAA related survival Taken from age and sex-specific population mortality statistics S nonaaa,i (t) Overall survival Expected life-years S i (t) = S AAA,i (t)s nonaaa,i (t) Assume that for individual i we intervene (elective surgery) at time x x E[LY I = x] = S i (u) du + (1 p(d E)) S nonaaa,i (v) dv 0 x }{{}}{{} Before intervention After intervention 11/41

12 Optimal intervention time and incorporating uncertainty The optimal intervention time is defined as that which maximises expected life-years Calculations are conducted as follows: 1 Survival probabilities evaluated over a fine grid of time points 2 Expected life-years calculated by a trapezoidal rule 3 Evaluated for any possible future intervention time over the grid 4 The maximum is found and the optimal intervention time and corresponding threshold diameter are recorded 5 A Monte Carlo simulation scheme proposed by Rizopoulos 5 is used to obtain estimates of variability in S AAA,i (t) and hence the optimal intervention time 5 Rizopoulos, D. Biometrics 2011;67: /41

13 Application to Multicentre Aneurysm Screening Study 13/41

14 The Multicentre Aneurysm Screening Study A trial of 67,800 men, randomly allocated to receive an invite for an abdominal ultrasound scan or not. 1,333 AAA detected 166 Large AAA ( 5.5cm): considered immediately for elective surgery 1167 Small AAA: followed-up with annual ( cm) or 3-monthly ( cm) ultrasounds Individuals were followed-up on average for 4.1 years, with an average of 7.5 ultrasound scans; there were 33 ruptures that occurred before 5.5cm 14/41

15 Joint growth and rupture model A joint longitudinal (AAA measurements) and survival (rupture) model was fitted. Note that... in this model we censor for all other events (e.g. non-aaa deaths, referral for elective surgery, drop-out from study) follow-up ends at the first observed AAA diameter 5.5cm Most referred to surgery at this point Those that remain under surveillance are contraindicated and not representative 15/41

16 Joint model Longitudinal model Unstructured variance-covariance matrix for random-effects 1 Linear model (Random-intercept, random-slope) 2 Quadratic model 3 Natural cubic spline Survival model No evidence for non-constant baseline hazard: Wald test for Weibull shape parameter p = Association with current diameter 2 Association with current diameter and rate of growth 3 Association with current diameter and cumulative effects (area under growth curve) 16/41

17 Longitudinal process From linear model From quadratic model Parameter Estimate SE p-value Intercept < Time < Parameter Estimate SE p-value Intercept < Time < Time < /41

18 Predicted average growth trajectory 70 AAA diameter (mm) Model Linear Natural cubic spline Quadratic Time since screening (years) 18/41

19 Survival process Linear Model Quadratic Model Parameter Estimate SE p-value Current diameter < Rate of growth Parameter Estimate SE p-value Current diameter Rate of growth Hazard ratio of rupture is 1.09 (95% CI 1.04, 1.13) for each mm increase in current AAA diameter Hazard ratio of rupture is 1.78 (95% CI 1.22, 2.61) for each mm/year increase in rate of growth 19/41

20 Model Selection Model loglik AIC BIC Current value models Linear trajectory Quadratic trajectory Current value and rate of change models Linear trajectory Quadratic trajectory Current value and cumulative effect models Linear trajectory Quadratic trajectory /41

21 Predictions Consider making predictions of optimal intervention times for different groups of individuals with the following history of AAA measurements: 1 Single diameter at screening (3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5cm) 2 Two measurements taken one year apart Observed 0mm/year growth Observed 5mm/year growth 3 Dynamic prediction for an individual with 1, 2, 3, 4, 5 or 6 previous measurements 21/41

22 1. Single diameter at screening 22/41

23 Expected life-years 15 Expected life years Size 3.0cm baseline 3.5cm baseline 4.0cm baseline 4.5cm baseline 5.0cm baseline 5.5cm baseline 6.0cm baseline 6.5cm baseline Intervention Time (yrs) 23/41

24 Survival curves 3.0cm baseline 3.5cm baseline cm baseline 4.5cm baseline S i (u) 0.50 Survival probability cm baseline 6.0cm baseline 5.5cm baseline 6.5cm baseline Survival curve Overall Survival Survival following elective repair (1 p(d E))S nonaaa (v) Maximum expected life-years occur when two survival curves cross Time (yrs) 24/41

25 Threshold associated with optimal intervention time cm baseline 3.5cm baseline cm baseline 4.5cm baseline AAA diameter (mm) cm baseline 5.5cm baseline cm baseline 6.5cm baseline Time since screening (years) 25/41

26 Threshold incorporating uncertainty Medians shown as vertical lines 0.06 Density Size 3.0cm baseline 3.5cm baseline 4.0cm baseline 4.5cm baseline 5.0cm baseline 5.5cm baseline 6.0cm baseline 6.5cm baseline Intervention threshold 26/41

27 Sensitivity analysis to model selection Optimal intervention times 3.0cm baseline 3.5cm baseline Linear, current value Quadratic, current value Quadratic, current value & slope Quadratic, current value & cumulative effect 4.0cm baseline 4.5cm baseline Linear, current value Quadratic, current value Quadratic, current value & slope Quadratic, current value & cumulative effect 5.0cm baseline 5.5cm baseline Linear, current value Quadratic, current value Quadratic, current value & slope Quadratic, current value & cumulative effect 6.0cm baseline 6.5cm baseline Linear, current value Quadratic, current value Quadratic, current value & slope Quadratic, current value & cumulative effect Intervention time 27/41

28 2. Two measurements taken one year apart 28/41

29 Optimal intervention times Median (SD) optimal intervention time according history of previous measurements Average diameter Number of measurements One Two Two No observed growth 5mm/yr growth 3.0cm (6.9) (6.7) 9.75 (5.9) 3.5cm 8.75 (5.7) 9.00 (5.8) 7.25 (4.9) 4.0cm 6.75 (4.7) 7.00 (5.0) 5.75 (4.1) 4.5cm 4.50 (3.4) 4.75 (3.6) 3.75 (3.0) 5.0cm 3.00 (2.9) 3.25 (3.4) 2.25 (2.7) 5.5cm 2.00 (2.2) 2.25 (2.4) 1.75 (2.0) 6.0cm 1.25 (1.5) 1.25 (1.7) 0.75 (1.3) 6.5cm 0.75 (1.2) 0.75 (1.3) 0.50 (1.1) 29/41

30 3. Dynamic prediction 30/41

31 Dynamic prediction Consider a patient with a 45mm aneurysm How would their predicted intervention time change if they had shown previous growth of 1mm/year for the past year? the past two years?... the past 5 years? 31/41

32 Dynamic longitudinal predictions 100 AAA diameter (mm) Time since screening (years) 32/41

33 Dynamic longitudinal predictions 100 AAA diameter (mm) Time since screening (years) 33/41

34 Dynamic longitudinal predictions 100 AAA diameter (mm) Time since screening (years) 34/41

35 Dynamic longitudinal predictions 100 AAA diameter (mm) Time since screening (years) 35/41

36 Dynamic longitudinal predictions 100 AAA diameter (mm) Time since screening (years) 36/41

37 Dynamic longitudinal predictions 100 AAA diameter (mm) Time since screening (years) 37/41

38 But are we improving discriminative power? What is the predictive accuracy of our joint model? How does this change depending on the number of AAA measurements? Using t = 2 years as the landmark time for a future prediction For all individuals still at risk, calculate their 5-year risk of rupture, r i Calculate Harrell s concordance index C = Pr(r i > r j T i < T j ) For the MASS data, only 21 events occur between [2, 2 + 5) years Data from the UK Small Aneurysm Trial provides another validation dataset with 1105 patients and 27 events Calculate concordance based on predictions using only 1 longitudinal measurement (closest to t = 2) 2 longitudinal measurements (at times 2 years) 3 longitudinal measurements (at times 2 years) 4 longitudinal measurements (at times 2 years) 38/41

39 Concordance Index for 5-yr predictions MASS UKSAT 1 2 or less 3 or less 4 or less All Concordance index 39/41

40 Further clinical research questions Should the intervention threshold be different for men and women? Females have approximately 4 times the risk of rupture for the same AAA diameter How might threshold decisions change if based on maximising 1 Quality-adjusted life-years 2 Net Benefit (considering efficacy and costs, at a certain willingness-to-pay) Should the intervention threshold depend on a patient s age? 40/41

41 Summary Joint models can be utilised within a decision simulation model Allow dynamic predictions of expected life-years to be obtained based on conditional survival probabilities Variability of individual predictions will generally be high for most realistic applications Survival extrapolations are used to inform rupture risk in large AAA Is this a robust/sensible thing to do? Are there other data that could be used to inform this relationship? Clinical datasets only continue to follow-up contraindicated patients Further model development and validation needed on larger datasets RESCAN collaboration, 18 studies, 228 rupture events Need to evaluate how much a personalised prediction approach would benefit patients, on average, compared to the current non-personalised approach 41/41