Antolini Galimberti Valsecchi

Views:
 
Category: Education
     
 

Presentation Description

No description available.

Comments

Presentation Transcript

Slide1: 

NONPARAMETRIC APPROACH TO INFERENCE ON COMPETING RISKS FOR TREATMENT COMPARISON IN THE ABSENCE OF RANDOMIZATION Laura Antolini, Stefania Galimberti and Maria Grazia Valsecchi 28th Annual ISCB Conference 29th July-2 August 2007, Thraki Palace Hotel, Alexandroupolis, Greece Dipartimento di Medicina Clinica e Prevenzione Università Milano-Bicocca, Italy 1

INTRODUCTION : 

INTRODUCTION General context In the absence of randomization : samples in different treatment groups are possibly selected due to confounding variables Survival function estimates should be adjusted by: Matching (Galimberti et al 2002) Stratification (Nieto FJ, Coresh 1996) Propensity (Xie and Liu 2005) SIB 2007, Pisa Propensity : subjects are weigthed by the inverse probability of being in a certain group conditional on covariates Specific context 28th ISCB Conference 2

Slide3: 

T : time to failure X : confounder (0, 1) G : treatment group (‘a’, ‘b’) Propensity score Randomised Not randomised treatment assignment The distribution of the confounder within the treament groups is different from the one in the overall population POPULATION : NOTATION e : type of failure (1, 2) 28th ISCB Conference 3

Slide4: 

conditional marginal Overall cumulative incidence of failure conditional marginal Crude Cumulative incidence of failure type 2 POPULATION : QUANTITIES IN GROUP g 4

Slide5: 

is not that we would instead estimate if Kaplan-Meier is applied on group g Note that… the cumulative incidence of failure we wish to estimate 28th ISCB Conference 5

Slide6: 

The weighted KM estimator correct for is OVERALL INCIDENCE ACCOUNTING FOR CONFOUNDING weighted n. of failures Contribution to the estimate of subject i having confounder xi is weigthed by Inverse-probabilty-of-treatment weighting (IPTW) n. at risk 6

Slide7: 

OVERALL INCIDENCE ACCOUNTING FOR CONFOUNDING : VARIANCE Factor accounting for the variability of the propensity scores Greenwood-type expression 7

Slide8: 

OVERALL INCIDENCE ACCOUNTING FOR CONFOUNDING : VARIANCE = Greenwood variance Factor accounting for the variability of the propensity scores Greenwood-type expression 7

Slide9: 

OVERALL INCIDENCE ACCOUNTING FOR CONFOUNDING : VARIANCE = Greenwood variance > Greenwood variance Factor accounting for the variability of the propensity scores Greenwood-type expression 7

Slide10: 

We need to express the estimator of the crude incidence How can we deal with propensity adjustment in the presence of competing risks? in a Kaplan Meier form with a Greenwood type variance in order to extend it to include IPTW 8

Slide11: 

Estimate in the ABSENCE of censoring The subjects who had the competing event are added to the risk set KM VERSION OF THE CRUDE INCIDENCE T : time to failure e : type of failure (1, 2) The estimator of the crude incidence can be expressed in a KM form observing that 9

Slide12: 

The estimator of the crude incidence can be expressed in a KM form observing that Estimate in the PRESENCE of censoring KM VERSION OF THE CRUDE INCIDENCE T : time to failure e : type of failure (1, 2) The contribution to the risk set is weighted by the probabilty of being free from censoring 10

Slide13: 

standard KM type Delta method Delta method awkward easy Greenwood-type variance KM VERSION OF THE CRUDE INCIDENCE : VARIANCE 11

Slide14: 

SIMULATIONS a : Bias x 103 (variance x 103) Gray b : Bias x 103 (variance x 103) Greenwood a / b : ratio between MSE B=1000 n=50 12

Slide15: 

CRUDE INCIDENCE ACCOUNTING FOR CONFOUNDING The IPTW applies to : the contribution of subjects who had the competing event the subjects at risk (free from failure) the failures of type 2 13

Slide16: 

CRUDE INCIDENCE ACCOUNTING FOR CONFOUNDING The IPTW applies to : the contribution of subjects who had the competing event the subjects at risk (free from failure) the failures of type 2 The weighted KM estimator correct for is 14

Slide17: 

Propensity score in group g Over-represented Under-represented SIMULATION STRATEGY 15 X = 0 X = 1 Crude incidence of event type 2 in group g

Slide18: 

20% uniform censoring 30% uniform censoring B=2 n=1000 NO ADJUSTMENT for confounding ADJUSTMENT for confounding SIMULATION RESULTS 16

Slide19: 

CRUDE INCIDENCE ACCOUNTING FOR CONFOUNDING : VARIANCE Factor accounting for the variability of the propensity scores Greenwood-type expression 17

Slide20: 

CRUDE INCIDENCE ACCOUNTING FOR CONFOUNDING : VARIANCE Factor accounting for the variability of the propensity scores Greenwood-type expression 18

Slide21: 

B=1000 n=100 t = 0.75 SIMULATION RESULTS Results espressed x 103 19

Slide22: 

FUTURE DEVELOPMENTS Assess the performance of the test for comparing crude incidences adjusted for confounding Estend the approach based on matching to the case of crude incidence 28th ISCB Conference 20

Slide23: 

REFERENCES L. Antolini, E. Biganzoli and P. Boracchi (2006) – Crude Cumulative Incidence in the form of a Horvitz-Thompson like and Kaplan-Meier like Estimator - COBRA Preprint Series. Article 10. S. Galimberti, P. Sasieni, M.G. Valsecchi (2002) - A Weighted Kaplan-Meier Estimator for Matched Data with Application to the Comparison of Chemotherapy and Bone-Marrow Transplant in Leukemia Statistics in Medicine, 21:3847-3864. J. Xie, L. Chaofeng (2005) - Adjusted Kaplan-Meier estimator and log-rank test with inverse probability of treatment weigthing for survival data - Statistics in Medicine, 24:3089-3110. Nieto FJ, Coresh J. (1996) Adjusting survival curves for confounders: a review and a new method. Am J Epidemiology, 143(10):1059-68 28th ISCB Conference 21

authorStream Live Help