Using polytomous logistic regression to find p-value of heterogeneity across 3 nominaloutcome levels

[ak2011]

I would be grateful if someone could help me with the code to find an overall p-value for heterogeneity of association by type of breast cancer bct.

Using polytomous(multinomial) logistic regression I am looking for a single p-value that test for heterogeneity across 3 groups(breast cancer type 1 (bct1)), bct2 and bct3. The variable histo is histological differences among the bc types.

Histo 1=bct1, 2=bct2 and 3=bct3. Under each bct, 1=case 0=control.

My main independent variable is agent_exp(0=unexposed and 1=exposed).

My code, log and results for finding histological differences are found below:

data ht2; 
input id$ 1-7  agents_exp 8-9 histo 10-11  bct1 12-13  bct2 14-15 bct3 16-17; 
datalines; 
OSaa01	0	.	0	0	0
OSaa06	0	.	1	1	1
OSaa11	0	.	0	0	0
OSaa12	0	.	1	1	1
OSaa13	1	1	.	1	.
OSaa14	0	2	1	.	.
OSaa15	0	1	.	1	.
OSaa19	0	.	1	1	1
OSaa21	0	.	0	0	0
OSaa22	0	.	1	1	1
OSaa23	0	.	0	0	0
OSaa24	0	1	.	1	.
OSaa29	1	.	1	1	1
OSaa30	1	2	1	.	.
OSaa31	0	.	1	1	1
OSaa36	0	.	1	1	1
OSaa46	0	1	.	1	.
OSaa52	0	.	0	0	0
OSaa54	0	.	0	0	0
OSaa55	0	.	1	1	1
OSaa56	0	.	.	.	.
OSaa58	0	.	1	1	1
OSaa63	0	2	1	.	.
OSaa69	0	1	.	1	.
OSaa70	0	.	1	1	1
OSaa72	0	.	1	1	1
OSaa73	0	.	0	0	0
OSaa75	0	.	1	1	1
OSaa84	0	.	1	1	1
OSaa86	1	.	1	1	1
OSaa93	1	.	0	0	0
OSaa99	0	.	1	1	1
OSab00	0	.	1	1	1
OSab04	0	.	1	1	1
OSab12	0	.	1	1	1
OSab16	0	3	.	.	1
OSab17	0	1	.	1	.
OSab19	0	.	1	1	1
OSab20	1	1	.	1	.
OSab24	0	.	1	1	1
OSab33	0	.	1	1	1
OSab37	0	.	1	1	1
OSab38	0	.	1	1	1
OSab39	0	.	1	1	1
OSab46	0	.	1	1	1
OSab50	0	.	0	0	0
OSab54	0	.	1	1	1
OSab58	0	.	0	0	0
OSab68	0	.	1	1	1
OSab70	0	.	1	1	1
OSab71	0	1	.	1	.
OSab73	0	1	.	1	.
OSab79	0	.	1	1	1
OSab84	0	.	1	1	1
OSab86	0	.	1	1	1
OSab89	0	.	1	1	1
OSab97	0	.	1	1	1
OSac02	0	.	1	1	1
OSac04	0	.	1	1	1
OSac07	1	.	0	0	0
OSac08	0	.	1	1	1
OSac13	0	.	1	1	1
OSac16	0	.	1	1	1
OSac17	1	.	1	1	1
OSac33	1	1	.	1	.
OSac34	0	.	1	1	1
OSac35	0	2	1	.	.
OSac42	0	.	1	1	1
OSac43	0	.	0	0	0
OSac47	0	.	0	0	0
OSac49	0	2	1	.	.
OSac52	0	.	1	1	1
OSac53	0	.	0	0	0
OSac58	0	.	1	1	1
OSac67	0	.	1	1	1
OSac74	1	1	.	1	.
OSac76	0	1	.	1	.
OSac80	0	.	0	0	0
OSac86	0	.	0	0	0
OSac87	0	.	.	.	.
OSac88	0	.	0	0	0
OSac91	1	3	.	.	1
OSac93	0	.	1	1	1
OSac97	0	.	0	0	0
OSad01	0	.	1	1	1
;

proc print data=ht2;
var id agents_exp  histo  bct1 bct2 bct3;
run;

proc logistic data=ht2;
class histo (ref ='2') /param=ref;
model histo = agents_exp/link=glogit;
run;

1 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;

72

73 data ht2;

74 input id$ 1-7 agents_exp 8-9 histo 10-11 bct1 12-13 bct2 14-15 bct3 16-17;

75 datalines;

NOTE: The data set WORK.HT2 has 85 observations and 6 variables.

NOTE: DATA statement used (Total process time):

real time 0.01 seconds

cpu time 0.01 seconds

161 ;

162

163 proc print data=ht2;

164 var id agents_exp histo bct1 bct2 bct3;

165 run;

NOTE: There were 85 observations read from the data set WORK.HT2.

NOTE: PROCEDURE PRINT used (Total process time):

real time 0.75 seconds

cpu time 0.75 seconds

166

167 proc logistic data=ht2;

168 class histo (ref ='2') /param=ref;

169 model histo = agents_exp/link=glogit;

170 run;

NOTE: PROC LOGISTIC is fitting the generalized logit model. The logits modeled contrast each response category against the

reference category (histo=2).

NOTE: Convergence criterion (GCONV=1E-8) satisfied.

NOTE: There were 85 observations read from the data set WORK.HT2.

NOTE: PROCEDURE LOGISTIC used (Total process time):

real time 0.63 seconds

cpu time 0.57 seconds

171

172

173 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;

185

Obs	id	agents_exp	histo	bct1	bct2	bct3
1	OSaa01	0	.	0	0	0
2	OSaa06	0	.	1	1	1
3	OSaa11	0	.	0	0	0
4	OSaa12	0	.	1	1	1
5	OSaa13	1	1	.	1	.
6	OSaa14	0	2	1	.	.
7	OSaa15	0	1	.	1	.
8	OSaa19	0	.	1	1	1
9	OSaa21	0	.	0	0	0
10	OSaa22	0	.	1	1	1
11	OSaa23	0	.	0	0	0
12	OSaa24	0	1	.	1	.
13	OSaa29	1	.	1	1	1
14	OSaa30	1	2	1	.	.
15	OSaa31	0	.	1	1	1
16	OSaa36	0	.	1	1	1
17	OSaa46	0	1	.	1	.
18	OSaa52	0	.	0	0	0
19	OSaa54	0	.	0	0	0
20	OSaa55	0	.	1	1	1
21	OSaa56	0	.	.	.	.
22	OSaa58	0	.	1	1	1
23	OSaa63	0	2	1	.	.
24	OSaa69	0	1	.	1	.
25	OSaa70	0	.	1	1	1
26	OSaa72	0	.	1	1	1
27	OSaa73	0	.	0	0	0
28	OSaa75	0	.	1	1	1
29	OSaa84	0	.	1	1	1
30	OSaa86	1	.	1	1	1
31	OSaa93	1	.	0	0	0
32	OSaa99	0	.	1	1	1
33	OSab00	0	.	1	1	1
34	OSab04	0	.	1	1	1
35	OSab12	0	.	1	1	1
36	OSab16	0	3	.	.	1
37	OSab17	0	1	.	1	.
38	OSab19	0	.	1	1	1
39	OSab20	1	1	.	1	.
40	OSab24	0	.	1	1	1
41	OSab33	0	.	1	1	1
42	OSab37	0	.	1	1	1
43	OSab38	0	.	1	1	1
44	OSab39	0	.	1	1	1
45	OSab46	0	.	1	1	1
46	OSab50	0	.	0	0	0
47	OSab54	0	.	1	1	1
48	OSab58	0	.	0	0	0
49	OSab68	0	.	1	1	1
50	OSab70	0	.	1	1	1
51	OSab71	0	1	.	1	.
52	OSab73	0	1	.	1	.
53	OSab79	0	.	1	1	1
54	OSab84	0	.	1	1	1
55	OSab86	0	.	1	1	1
56	OSab89	0	.	1	1	1
57	OSab97	0	.	1	1	1
58	OSac02	0	.	1	1	1
59	OSac04	0	.	1	1	1
60	OSac07	1	.	0	0	0
61	OSac08	0	.	1	1	1
62	OSac13	0	.	1	1	1
63	OSac16	0	.	1	1	1
64	OSac17	1	.	1	1	1
65	OSac33	1	1	.	1	.
66	OSac34	0	.	1	1	1
67	OSac35	0	2	1	.	.
68	OSac42	0	.	1	1	1
69	OSac43	0	.	0	0	0
70	OSac47	0	.	0	0	0
71	OSac49	0	2	1	.	.
72	OSac52	0	.	1	1	1
73	OSac53	0	.	0	0	0
74	OSac58	0	.	1	1	1
75	OSac67	0	.	1	1	1
76	OSac74	1	1	.	1	.
77	OSac76	0	1	.	1	.
78	OSac80	0	.	0	0	0
79	OSac86	0	.	0	0	0
80	OSac87	0	.	.	.	.
81	OSac88	0	.	0	0	0
82	OSac91	1	3	.	.	1
83	OSac93	0	.	1	1	1
84	OSac97	0	.	0	0	0
85	OSad01	0	.	1	1	1

---

The LOGISTIC Procedure

Model Information
Data Set	WORK.HT2
Response Variable	histo
Number of Response Levels	3
Model	generalized logit
Optimization Technique	Newton-Raphson

Number of Observations Read	85
Number of Observations Used	19

Response Profile
Ordered Value	histo	Total Frequency
1	1	12
2	2	5
3	3	2

Logits modeled use histo=2 as the reference category.

Note:66 observations were deleted due to missing values for the response or explanatory variables.

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics
Criterion	Intercept Only	Intercept and Covariates
AIC	37.384	40.738
SC	39.273	44.516
-2 Log L	33.384	32.738

Testing Global Null Hypothesis: BETA=0
Test	Chi-Square	DF	Pr > ChiSq
Likelihood Ratio	0.6459	2	0.7240
Score	0.6415	2	0.7256
Wald	0.6137	2	0.7358

Type 3 Analysis of Effects
Effect	DF	Wald Chi-Square	Pr > ChiSq
agents_exp	2	0.6137	0.7358

Analysis of Maximum Likelihood Estimates
Parameter	histo	DF	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
Intercept	1	1	0.6931	0.6124	1.2812	0.2577
Intercept	3	1	-1.3863	1.1180	1.5374	0.2150
agents_exp	1	1	0.6931	1.2748	0.2957	0.5866
agents_exp	3	1	1.3863	1.8028	0.5913	0.4419

Odds Ratio Estimates
Effect	histo	Point Estimate	95% Wald Confidence Limits
agents_exp	1	2.000	0.164	24.328
agents_exp	3	4.000	0.117	136.958

Finding a single p-value for heterogeneity is where I am stuck at:

I checked the solution on "Heterogeneity test for multinomial logistic regression' posted on 04-09-2012 but I am still stuck on my question.

Please help. Thanks.

ak.

[StatDave · Accepted solution]

I would hate to try to answer this without better understanding these unusual looking data. Avoiding any subject matter terminology which will only further obfuscate, why is it that any observation with a nonmissing HISTO value has exactly 1 nonmissing value in the BCT variables? And why does any observation with missing HISTO have all three nonmissing BCT values... and why are they always the all the same - either all 0 or all 1 or all missing? How do the three values of HISTO relate to the BCT values and what do they mean - again, without subject matter terminology. Note that with so few usable observations (only 19 with nonmissing HISTO), any analysis results might be considered unreliable.