Covariate Dependent Random Partitions

author: Peter Mueller, University of Texas M.D. Anderson Cancer Center, The University of Texas at Austin

Description

We propose a model for covariate-dependent clustering, i.e., we develop a probability model for random partitions that is indexed by covariates. The motivating application is inference for a clinical trial. As part of the desired inference we wish to define clusters of patients. Defining a prior probability model for cluster memberships should include a regression on patient baseline covariates. We build on product partition models (PPM). We define an extension of the PPM to include the desired regression. This is achieved by including in the cohesion function a new factor that increases the probability of experimental units with similar covariates to be included in the same cluster.

We discuss implementations suitable for continuous, categorical, count and ordinal covariates.

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*Slides*
0:00	Covariate-Dependent Bayesian Clustering
1:00	Outline
1:27	Intro - Motivating Example (1)
1:35	Intro - Motivating Example (2)
2:17	Intro - Motivating Example (3)
2:35	Intro - Motivating Example (4)
2:47	Intro - Motivating Example (5)
3:19	Intro - Motivating Example (6)
3:48	Intro - Motivating Example (7)
4:21	Intro - Motivating Example (8)
4:50	Intro - Motivating Example (9)
4:58	Random Partition Models - Notation (1)
5:05	Random Partition Models - Notation (2)
5:21	Random Partition Models - Notation (3)
5:43	Random Partition Models - Notation (4)
6:19	Random Partition Models - Data (1)
6:24	Random Partition Models - Data (2)
6:27	Random Partition Models - Data (3)
7:07	Random Partition Models w/o Covariates (1)
8:20	Random Partition Models w/o Covariates (2)
8:30	Random Partition Models w/o Covariates (3)
9:02	Random Partition Models (1)
10:25	Random Partition Models (2)
10:58	Random Partition Models (3)
11:29	Random Partition Models (4)
11:45	Random Partition Models (5)
11:49	Random Partition Models (ctd.) (1)
12:20	Random Partition Models (ctd.) (2)
15:09	Random Partition Models (ctd.) (3)
15:51	Random Partition Models (ctd.) (4)
16:10	Random Partition Models (ctd.) (5)
16:23	Random Partition Models (ctd.) (6)
16:25	Random Partition Models (ctd.) (7)
16:38	Covariate-dependent PPM (1)
18:04	Covariate-dependent PPM (2)
19:24	Covariate-dependent PPM (3)
19:31	Covariate-dependent PPM (4)
21:21	Covariate-dependent PPM: Desiderata (1)
21:46	Covariate-dependent PPM: Desiderata (2)
22:22	Covariate-dependent PPM: Desiderata (3)
22:44	Covariate-dependent PPM: Desiderata (4)
23:29	Covariate-dependent PPM: Desiderata (5)
24:33	Covariate-dependent PPM (ctd.) (1)
25:17	Covariate-dependent PPM (ctd.) (2)
25:21	Covariate-dependent PPM (ctd.) (3)
25:50	Alternative Constructions (1)
26:40	Alternative Constructions (2)
26:56	Alternative Constructions (3)
27:01	Alternative Constructions (4)
27:53	Alternative Constructions (5)
30:58	Alternative Constructions (6)
31:09	Alternative Constructions (7)
31:13	Alternative Constructions (8)
31:25	Alternative Constructions (9)
31:29	Alternative Constructions (10)
31:33	Alternative Constructions (11)
32:17	Alternative Constructions (12)
32:22	Alternative Constructions (13)
32:26	Alternative Constructions (14)
32:43	Posterior Inference - w/o Covariates (1)
33:38	Posterior Inference - w/o Covariates (2)
33:40	Posterior Inference - w/o Covariates (3)
33:42	Posterior Inference - w/o Covariates (4)
33:50	Posterior Inference w. Covariates (1)
34:24	Posterior Inference w. Covariates (2)
34:24	Posterior Inference w. Covariates (3)
34:45	Example: Mixed Effects Model (1)
35:01	Example: Mixed Effects Model (2)
35:12	Example: Mixed Effects Model (3)
35:30	Example: Mixed Effects Model (4)
35:32	Example: Mixed Effects Model (5)
35:35	Example: Mixed Effects Model (6)
35:37	Example: Mixed Effects Model (7)
36:20	Example: Mixed Effects Model (8)
38:49	Example: Mixed Effects Model (9)
38:55	Example: Mixed Effects Model (10)
38:55	Example: Survival Time Model with Clustering (1)
39:14	Example: Survival Time Model with Clustering (2)
39:15	Example: Survival Time Model with Clustering (3)
39:46	Example: Survival Time Model with Clustering (4)
39:47	Summary

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