OverLapWght_SurgeonEfect_Tutorial

Simulate Data with Surgeon IDs

set.seed(123)
n <- 1000

# Patient covariates
mydata <- data.frame(
  age = rnorm(n, 60, 10),
  bmi = rnorm(n, 27, 4),
  comorbidity = rpois(n, 2)
)

# Surgeon assignment (e.g., 40 surgeons, some imbalance)
mydata$surgeon_id <- factor(sample(1:40, size = n, replace = TRUE,
                                   prob = runif(40, 0.5, 2)))

# Biased treatment based on covariates
mydata$treat_num <- rbinom(n, 1, plogis(
  -1 + 0.03 * mydata$age - 0.1 * mydata$bmi +
  0.4 * mydata$comorbidity +
  0.3 * as.numeric(mydata$surgeon_id) %% 2  # subtle surgeon effect
))

# Outcome (complication)
mydata$complication <- rbinom(n, 1, plogis(
  -2 + 0.5 * mydata$treat_num +
  0.02 * mydata$age +
  0.05 * mydata$comorbidity
))

# Factor treatment
mydata$surgical_approach <- factor(mydata$treat_num,
                                   labels = c("Approach 0", "Approach 1"))
kbl(cbind(mydata)) %>%
  kable_paper() %>%
  scroll_box(width = "500px", height = "200px")

age	bmi	comorbidity	surgeon_id	treat_num	complication	surgical_approach
54.39524	23.01681	1	26	0	0	Approach 0
57.69823	22.84018	3	14	1	0	Approach 1
75.58708	26.92808	2	17	0	1	Approach 0
60.70508	26.47130	3	1	0	0	Approach 0
61.29288	16.80263	1	40	1	0	Approach 1
77.15065	31.16229	1	26	0	1	Approach 0
64.60916	27.99890	4	27	0	1	Approach 0
47.34939	36.66483	0	9	0	0	Approach 0
53.13147	29.74079	2	21	0	0	Approach 0
55.54338	25.21216	5	7	1	1	Approach 1
72.24082	38.18956	1	15	0	0	Approach 0
63.59814	38.32890	6	19	1	0	Approach 1
64.00771	22.12515	0	27	0	0	Approach 0
61.10683	28.87613	1	38	0	0	Approach 0
54.44159	26.15501	1	19	0	0	Approach 0
77.86913	27.74820	5	21	1	1	Approach 1
64.97850	27.91017	5	4	1	1	Approach 1
40.33383	21.95240	3	7	0	0	Approach 0
67.01356	28.14236	1	12	0	1	Approach 0
55.27209	33.99699	2	23	1	0	Approach 1
49.32176	26.34364	1	28	0	1	Approach 0
57.82025	26.34829	3	27	1	0	Approach 1
49.73996	32.59429	3	39	0	0	Approach 0
52.71109	30.59359	2	19	0	0	Approach 0
53.74961	20.40602	2	40	0	1	Approach 0
43.13307	27.91423	3	27	0	0	Approach 0
68.37787	33.61419	3	2	0	0	Approach 0
61.53373	32.66111	2	37	0	1	Approach 0
48.61863	28.67981	1	25	0	1	Approach 0
72.53815	29.88488	2	3	0	0	Approach 0
64.26464	22.21226	4	20	0	0	Approach 0
57.04929	28.20053	2	23	0	0	Approach 0
68.95126	23.18220	0	3	0	0	Approach 0
68.78133	25.16793	2	31	1	1	Approach 1
68.21581	30.74241	2	36	0	1	Approach 0
66.88640	22.45243	4	2	1	0	Approach 1
65.53918	28.06767	1	18	1	0	Approach 1
59.38088	28.71333	3	24	0	1	Approach 0
56.94037	27.21965	3	7	0	0	Approach 0
56.19529	34.28876	2	16	0	0	Approach 0
53.05293	22.91061	2	2	0	0	Approach 0
57.92083	29.42452	2	25	1	0	Approach 1
47.34604	26.64428	4	7	1	1	Approach 1
81.68956	25.95667	2	30	1	0	Approach 1
72.07962	28.85636	5	16	0	0	Approach 0
48.76891	22.91840	0	9	0	0	Approach 0
55.97115	21.74620	2	28	1	0	Approach 1
55.33345	25.02208	1	39	0	0	Approach 0
67.79965	34.00703	1	14	0	0	Approach 0
59.16631	27.22306	3	39	0	0	Approach 0
62.53319	28.32574	1	40	0	1	Approach 0
59.71453	26.24061	2	39	0	0	Approach 0
59.57130	28.88197	1	1	0	1	Approach 0
73.68602	23.19328	1	23	0	1	Approach 0
57.74229	31.63164	2	33	0	1	Approach 0
75.16471	29.33882	3	16	0	0	Approach 0
44.51247	23.77419	5	20	0	1	Approach 0
65.84614	27.21821	1	11	0	1	Approach 0
61.23854	29.86533	0	2	0	0	Approach 0
62.15942	29.23092	2	16	0	0	Approach 0
63.79639	32.92774	1	29	0	1	Approach 0
54.97677	24.54805	1	11	0	0	Approach 0
56.66793	31.46455	1	8	0	1	Approach 0
49.81425	31.14619	1	40	0	1	Approach 0
49.28209	26.35007	3	18	0	0	Approach 0
63.03529	23.09629	3	9	0	0	Approach 0
64.48210	22.64342	3	22	0	0	Approach 0
60.53004	28.83115	1	25	0	0	Approach 0
69.22267	26.71549	1	27	0	0	Approach 0
80.50085	34.11641	2	24	1	0	Approach 1
55.08969	29.14055	2	21	0	0	Approach 0
36.90831	25.51222	2	16	0	0	Approach 0
70.05739	22.89783	2	34	1	0	Approach 1
52.90799	24.67039	0	21	0	0	Approach 0
53.11991	28.37155	4	12	1	0	Approach 1
70.25571	25.19626	6	9	1	1	Approach 1
57.15227	29.05692	4	24	0	0	Approach 0
47.79282	25.66265	3	31	0	0	Approach 0
61.81303	26.57776	1	4	0	0	Approach 0
58.61109	24.07796	2	37	0	0	Approach 0
60.05764	34.62017	2	22	0	0	Approach 0
63.85280	28.33049	0	10	0	0	Approach 0
56.29340	27.92253	3	10	0	0	Approach 0
66.44377	20.23255	3	15	1	0	Approach 1
57.79513	29.63917	0	23	0	1	Approach 0
63.31782	22.90551	4	39	0	0	Approach 0
70.96839	23.43391	1	11	0	0	Approach 0
64.35181	30.67336	3	1	0	1	Approach 0
56.74068	25.18920	3	25	1	0	Approach 1
71.48808	20.00651	3	27	1	1	Approach 1
69.93504	34.07962	1	18	0	1	Approach 0
65.48397	17.49037	1	40	0	0	Approach 0
62.38732	29.29125	2	23	1	0	Approach 1
53.72094	31.06900	0	36	0	1	Approach 0
73.60652	24.47613	2	7	1	0	Approach 1
53.99740	28.77715	2	33	1	1	Approach 1
81.87333	28.75652	1	28	1	0	Approach 1
75.32611	31.16249	5	38	0	0	Approach 0
57.64300	28.93640	1	33	0	1	Approach 0
49.73579	26.02046	2	19	0	0	Approach 0
52.89593	30.66397	2	32	0	0	Approach 0
62.56884	30.20249	0	15	0	1	Approach 0
57.53308	23.25372	1	11	1	0	Approach 1
56.52457	21.39685	7	15	1	1	Approach 1
50.48381	27.64111	3	40	0	0	Approach 0
59.54972	25.90415	1	16	0	1	Approach 0
52.15096	23.05784	4	29	0	1	Approach 0
43.32058	27.33572	3	2	0	1	Approach 0
56.19773	21.72001	2	40	0	1	Approach 0
69.18997	27.64491	3	40	1	1	Approach 1
54.24653	24.50029	2	18	1	1	Approach 1
66.07964	30.82866	1	14	0	0	Approach 0
43.82117	36.69796	2	40	0	0	Approach 0
59.44438	23.33608	2	9	1	0	Approach 1
65.19407	31.23066	3	34	0	0	Approach 0
63.01153	30.30060	1	15	1	0	Approach 1
61.05676	26.71922	2	11	0	1	Approach 0
53.59294	25.18541	2	14	0	0	Approach 0
51.50296	33.30123	2	39	0	1	Approach 0
49.75871	18.97817	4	23	1	0	Approach 1
61.17647	24.42722	4	10	1	0	Approach 1
50.52525	21.25263	3	28	1	0	Approach 1
55.09443	32.58125	1	30	0	0	Approach 0
57.43908	26.23719	1	30	1	1	Approach 1
78.43862	24.90132	4	33	1	0	Approach 1
53.48050	39.73618	4	16	0	0	Approach 0
62.35387	26.79985	2	33	1	1	Approach 1
60.77961	25.22500	3	32	0	0	Approach 0
50.38143	28.19946	2	32	0	0	Approach 0
59.28692	20.72630	0	23	0	0	Approach 0
74.44551	28.96121	1	40	1	1	Approach 1
64.51504	26.61535	2	28	1	0	Approach 1
60.41233	28.87410	2	21	0	0	Approach 0
55.77503	23.07052	4	40	1	0	Approach 1
39.46753	22.90806	2	16	0	1	Approach 0
71.31337	24.22634	0	30	0	1	Approach 0
45.39360	23.92804	0	15	0	1	Approach 0
67.39948	32.19620	1	12	0	0	Approach 0
79.09104	33.31658	1	13	0	0	Approach 0
45.56107	26.37243	3	19	1	0	Approach 1
67.01784	25.56425	3	37	0	0	Approach 0
57.37803	25.68384	3	33	0	0	Approach 0
44.27856	27.27695	1	14	0	0	Approach 0
44.85332	27.38762	1	14	0	1	Approach 0
43.98464	28.16014	1	6	0	0	Approach 0
54.69093	24.01328	3	17	1	0	Approach 1
45.38244	23.61241	1	13	0	0	Approach 0
66.87917	31.78831	1	2	0	0	Approach 0
81.00109	24.80549	2	17	1	0	Approach 1
47.12970	28.21218	1	13	1	1	Approach 1
67.87739	26.77212	0	10	0	1	Approach 0
67.69042	23.16860	0	19	0	0	Approach 0
63.32203	29.36425	3	40	0	0	Approach 0
49.91623	27.69242	3	25	1	1	Approach 1
58.80547	32.59913	0	15	0	1	Approach 0
57.19605	27.46984	2	13	0	0	Approach 0
65.62990	25.67382	1	21	1	1	Approach 1
56.27561	28.11318	2	26	0	1	Approach 0
69.76973	22.25763	1	24	1	1	Approach 1
56.25419	23.65642	5	10	0	0	Approach 0
70.52711	29.04109	0	5	1	0	Approach 1
49.50823	25.66752	0	15	0	0	Approach 0
47.39845	26.73616	1	22	0	1	Approach 0
92.41040	26.53911	1	22	0	1	Approach 0
55.83142	24.39795	2	14	1	1	Approach 1
62.98228	18.92525	1	39	0	1	Approach 0
66.36570	28.39534	2	18	0	0	Approach 0
55.16219	30.04656	2	7	0	0	Approach 0
65.16862	21.84514	1	16	0	1	Approach 0
63.68965	32.92961	6	8	0	0	Approach 0
57.84619	28.54062	0	17	0	1	Approach 0
60.65293	32.36656	4	36	1	1	Approach 1
59.65933	23.17132	0	33	0	0	Approach 0
81.28452	27.66713	1	25	1	1	Approach 1
52.58664	26.59994	2	16	0	0	Approach 0
49.04004	30.07403	3	30	1	1	Approach 1
60.37788	24.69656	1	4	0	1	Approach 0
63.10481	26.95961	1	11	1	0	Approach 1
64.36523	19.88536	1	3	1	0	Approach 1
55.41635	23.88951	1	10	1	1	Approach 1
49.36674	27.50014	3	2	0	0	Approach 0
72.63185	24.17471	3	30	0	0	Approach 0
56.50350	26.82572	2	39	0	1	Approach 0
51.34487	25.12830	3	11	1	0	Approach 1
57.63720	29.42772	1	40	0	0	Approach 0
58.02824	31.67395	1	25	0	1	Approach 0
71.09920	23.70999	1	12	0	0	Approach 0
60.84737	25.77185	0	18	1	0	Approach 1
67.54054	32.75905	1	25	0	0	Approach 0
55.00708	18.20431	3	40	1	0	Approach 1
62.14445	25.72065	1	18	0	0	Approach 0
56.75314	35.25882	2	25	0	0	Approach 0
60.94584	35.77436	1	34	0	1	Approach 0
51.04637	27.62638	3	22	0	0	Approach 0
46.89198	23.54556	2	2	0	1	Approach 0
79.97213	27.66183	0	28	1	0	Approach 1
66.00709	24.38890	3	24	0	1	Approach 0
47.48729	32.81127	4	29	0	0	Approach 0
53.88834	23.77407	2	22	0	0	Approach 0
48.14520	28.49165	2	21	0	0	Approach 0
81.98810	29.47940	2	10	0	0	Approach 0
73.12413	23.96996	0	22	0	0	Approach 0
57.34855	30.40610	2	4	0	0	Approach 0
65.43194	24.00828	2	30	0	0	Approach 0
55.85660	29.52096	3	35	0	0	Approach 0
55.23753	31.38665	2	25	0	0	Approach 0
52.11397	23.04623	2	16	0	0	Approach 0
54.05383	31.43198	3	23	0	0	Approach 0
76.50907	25.04187	2	20	1	0	Approach 1
59.45972	28.17741	0	39	0	0	Approach 0
61.19245	27.80735	0	4	0	0	Approach 0
62.43687	25.29121	3	39	1	1	Approach 1
72.32476	28.07241	1	31	0	1	Approach 0
54.83936	22.07828	2	40	0	1	Approach 0
50.07493	26.45545	1	37	0	0	Approach 0
76.75697	30.30316	2	11	0	1	Approach 0
55.58837	18.30350	2	10	0	0	Approach 0
52.76934	21.04830	1	3	0	0	Approach 0
47.63727	22.35225	2	15	0	0	Approach 0
47.15284	20.64364	1	29	0	0	Approach 0
54.26027	28.67833	2	15	0	1	Approach 0
66.17986	23.02829	1	22	0	1	Approach 0
71.09848	18.34181	1	23	1	1	Approach 1
67.07588	24.44972	1	16	0	0	Approach 0
56.36343	25.43746	1	14	0	0	Approach 0
60.59750	30.42714	2	22	0	0	Approach 0
52.95404	22.58499	2	15	0	1	Approach 0
52.82782	31.64516	2	28	0	0	Approach 0
68.84650	28.59345	4	7	1	1	Approach 1
49.84407	28.44941	1	28	0	0	Approach 0
79.55294	23.58990	1	5	0	0	Approach 0
59.09680	34.81467	2	39	0	1	Approach 0
62.14539	26.34292	1	7	0	1	Approach 0
52.61472	19.70041	4	15	0	0	Approach 0
54.25611	26.18457	2	15	0	1	Approach 0
46.82984	19.26222	2	22	0	1	Approach 0
58.17075	25.75796	1	4	0	0	Approach 0
64.18982	25.31109	0	12	0	0	Approach 0
63.24304	29.72732	2	3	0	0	Approach 0
52.18464	31.03798	1	12	0	0	Approach 0
52.11378	24.09558	2	21	0	0	Approach 0
54.97801	30.22444	3	15	1	0	Approach 1
74.96061	32.69729	1	25	0	1	Approach 0
48.62696	23.86342	0	20	0	1	Approach 0
58.20948	24.39038	3	12	1	0	Approach 1
79.02362	29.60311	1	9	0	1	Approach 0
58.99025	27.73219	3	22	0	1	Approach 0
46.40159	29.19510	0	12	0	0	Approach 0
53.35231	32.61874	3	24	0	1	Approach 0
64.85460	28.54833	3	39	0	0	Approach 0
56.24397	31.20681	4	19	1	0	Approach 1
54.38124	29.49162	1	11	0	1	Approach 0
56.56083	28.73448	1	30	0	1	Approach 0
60.90497	28.54434	4	22	1	0	Approach 1
75.98509	32.16529	1	22	0	0	Approach 0
59.11435	22.99096	4	17	1	0	Approach 1
70.80800	22.57927	2	23	0	0	Approach 0
66.30754	29.36778	2	23	0	0	Approach 0
58.86360	26.52124	3	20	1	0	Approach 1
44.67098	27.29602	1	11	1	0	Approach 1
54.78883	29.96511	1	33	0	1	Approach 0
55.10130	30.01318	2	10	0	0	Approach 0
60.47154	25.94932	1	14	0	1	Approach 0
73.00199	25.74982	3	40	0	1	Approach 0
82.93079	27.29439	1	26	0	1	Approach 0
75.47581	31.25207	3	28	0	0	Approach 0
58.66849	28.70408	4	35	0	0	Approach 0
42.43473	32.73203	2	15	0	0	Approach 0
56.11220	26.96945	0	32	0	0	Approach 0
60.89207	31.50267	4	23	0	0	Approach 0
68.45013	30.53201	2	29	0	0	Approach 0
69.62528	29.44833	3	39	0	1	Approach 0
66.84309	28.65880	2	3	1	0	Approach 1
46.04726	25.88047	2	37	0	0	Approach 0
68.49643	26.56385	1	25	0	0	Approach 0
55.53443	27.91758	0	40	0	0	Approach 0
61.74803	27.19556	2	32	0	0	Approach 0
60.74551	30.77290	1	20	0	1	Approach 0
64.28167	26.56273	0	3	0	1	Approach 0
60.24675	26.71849	0	36	0	0	Approach 0
43.32525	25.06272	3	13	0	0	Approach 0
67.36496	26.44665	3	31	1	1	Approach 1
63.86027	26.72494	0	28	0	0	Approach 0
57.34348	17.74506	3	30	0	0	Approach 0
61.18145	21.54067	0	7	0	0	Approach 0
61.34039	26.71005	2	37	0	0	Approach 0
62.21019	25.93886	1	39	0	0	Approach 0
76.40846	22.19652	2	23	0	0	Approach 0
57.80950	19.03385	2	16	0	1	Approach 0
61.68065	25.58252	2	37	0	0	Approach 0
71.68384	29.61398	1	30	0	1	Approach 0
70.54181	34.09295	1	3	0	1	Approach 0
71.45263	26.84617	1	20	0	0	Approach 0
54.22532	32.97274	1	20	0	1	Approach 0
80.02483	27.33209	2	26	0	1	Approach 0
60.66701	27.46213	0	20	0	1	Approach 0
78.66852	28.29930	1	23	0	0	Approach 0
46.49097	23.51769	2	36	1	1	Approach 1
60.20984	26.79313	2	2	0	0	Approach 0
72.49915	30.63379	2	14	0	0	Approach 0
52.84758	24.00110	3	23	0	0	Approach 0
52.47311	25.71358	9	23	1	1	Approach 1
50.61461	22.40892	5	14	1	0	Approach 1
49.47487	28.41741	5	40	0	1	Approach 0
55.62840	28.69920	3	22	0	1	Approach 0
63.31179	29.59339	3	40	0	1	Approach 0
39.85789	22.12076	5	22	1	1	Approach 1
62.11980	27.42894	1	9	0	1	Approach 0
72.36675	23.22377	2	12	0	1	Approach 0
80.37574	26.99846	0	21	0	0	Approach 0
73.01176	32.37050	2	10	0	1	Approach 0
67.56775	24.98590	3	19	0	0	Approach 0
42.73270	29.86673	0	12	0	0	Approach 0
53.98493	24.00133	1	15	1	1	Approach 1
56.47954	25.08589	0	15	0	0	Approach 0
67.03524	28.75489	3	24	0	1	Approach 0
58.94329	24.28355	1	29	1	1	Approach 1
47.41351	20.18814	2	22	0	0	Approach 0
76.84436	32.06067	3	18	1	1	Approach 1
69.11391	28.44143	1	35	0	1	Approach 0
62.37430	24.66544	1	40	1	0	Approach 1
72.18109	19.02368	1	13	1	0	Approach 1
46.61226	34.60884	3	12	0	0	Approach 0
66.60820	40.56148	2	27	0	0	Approach 0
54.77088	27.82992	1	36	1	0	Approach 1
66.83746	30.39923	1	24	0	0	Approach 0
59.39178	31.89824	1	14	0	0	Approach 0
66.32961	24.19278	2	31	0	1	Approach 0
73.35518	25.59522	2	27	0	1	Approach 0
60.07290	20.09152	1	31	0	0	Approach 0
70.17559	24.05369	1	2	0	0	Approach 0
48.11566	29.48964	4	16	0	0	Approach 0
52.78396	25.83714	2	36	0	0	Approach 0
75.19218	26.14315	2	15	1	0	Approach 1
63.77388	26.54976	1	21	0	0	Approach 0
39.47777	19.54533	1	33	0	0	Approach 0
46.35963	30.35052	2	2	1	0	Approach 1
57.99219	21.22603	1	27	0	0	Approach 0
68.65779	26.16572	2	23	0	0	Approach 0
58.98117	25.24575	1	24	0	0	Approach 0
66.24187	26.12562	2	5	0	0	Approach 0
69.59005	32.83986	4	3	1	0	Approach 1
76.71055	24.67176	0	5	0	0	Approach 0
60.56017	23.86761	1	15	0	1	Approach 0
59.48018	20.92138	1	36	0	1	Approach 0
42.46763	23.77721	2	17	0	0	Approach 0
60.99328	22.33526	0	19	0	0	Approach 0
54.28150	28.63178	2	11	1	1	Approach 1
50.25990	23.54798	0	36	0	0	Approach 0
58.20094	28.21617	1	33	0	1	Approach 0
70.14943	26.41429	1	13	0	1	Approach 0
40.07252	21.26575	2	40	0	0	Approach 0
55.72721	23.83757	2	2	1	1	Approach 1
61.16637	30.54045	6	9	1	0	Approach 1
51.06792	30.61230	2	25	0	0	Approach 0
63.33903	35.02229	1	30	0	0	Approach 0
64.11430	26.98568	4	15	1	0	Approach 1
59.66964	21.01669	1	23	1	0	Approach 1
35.34102	23.92633	2	19	0	1	Approach 0
85.71458	28.63395	4	36	1	1	Approach 1
57.94701	34.60055	3	2	0	0	Approach 0
66.51193	27.44004	0	23	0	0	Approach 0
62.73766	31.56155	1	9	0	0	Approach 0
70.24673	30.07233	2	17	1	1	Approach 1
68.17659	22.32763	1	16	0	1	Approach 0
57.90207	26.31555	3	4	0	0	Approach 0
63.78168	32.22105	4	39	1	0	Approach 1
50.54591	30.50438	3	2	0	0	Approach 0
68.56923	28.85518	2	12	0	0	Approach 0
55.38962	28.90846	3	4	0	1	Approach 0
84.16773	25.03438	0	23	0	1	Approach 0
43.48951	21.72246	1	26	0	0	Approach 0
55.36013	32.18170	1	20	0	0	Approach 0
68.25380	21.31912	3	23	1	1	Approach 1
65.10133	23.24442	3	36	1	0	Approach 1
54.10519	29.51586	3	37	1	1	Approach 1
50.03219	21.95122	1	22	0	0	Approach 0
61.44476	24.79252	0	37	0	0	Approach 0
59.85693	22.26880	2	40	1	1	Approach 1
42.09719	29.48265	3	5	0	0	Approach 0
60.34551	28.78525	2	40	0	1	Approach 0
61.90230	28.68754	1	8	0	0	Approach 0
61.74726	28.76986	1	16	0	1	Approach 0
49.44983	29.22898	1	28	0	1	Approach 0
64.76133	29.55743	1	19	0	0	Approach 0
73.78570	19.12535	2	10	1	0	Approach 1
64.56236	26.40473	2	9	1	1	Approach 1
48.64412	27.44986	1	15	1	0	Approach 1
55.64355	29.89870	2	9	1	0	Approach 1
63.46104	22.25006	3	22	0	1	Approach 0
53.52954	25.00160	4	4	1	0	Approach 1
38.42354	22.70543	5	24	0	0	Approach 0
68.84251	31.22896	2	26	1	0	Approach 1
51.70522	32.11629	2	25	1	1	Approach 1
54.26440	30.15071	1	4	0	0	Approach 0
75.03901	22.11039	0	32	1	1	Approach 1
52.25855	28.80781	2	35	0	0	Approach 0
68.45732	31.60180	3	38	0	1	Approach 0
47.39317	27.67176	3	40	1	0	Approach 1
56.45458	24.73556	2	36	0	0	Approach 0
59.26444	22.65553	6	1	1	1	Approach 1
48.31349	24.33879	6	28	1	1	Approach 1
53.65252	29.85939	1	8	0	0	Approach 0
59.71158	25.27336	1	31	0	0	Approach 0
66.70696	27.91046	1	14	0	1	Approach 0
43.49453	32.17978	2	31	1	0	Approach 1
56.50246	29.31334	3	32	0	0	Approach 0
67.56406	32.45869	3	2	1	0	Approach 1
54.61191	20.19368	4	14	1	1	Approach 1
62.27292	25.87729	3	9	1	1	Approach 1
64.92229	27.26027	1	27	0	0	Approach 0
62.67835	29.31436	1	15	0	1	Approach 0
66.53258	22.32317	3	36	1	0	Approach 1
58.77291	30.22474	1	1	1	1	Approach 1
55.86323	28.22956	1	37	0	0	Approach 0
33.56851	28.05522	4	29	0	0	Approach 0
59.07059	29.03394	1	19	0	0	Approach 0
64.30285	26.53457	1	14	1	1	Approach 1
65.35399	30.70218	3	12	1	0	Approach 1
54.44722	29.59292	2	3	0	1	Approach 0
77.79503	26.39916	2	34	0	0	Approach 0
62.86424	31.16151	3	9	0	1	Approach 0
61.26316	28.17023	2	31	1	0	Approach 1
72.72267	29.67501	3	21	1	1	Approach 1
52.81534	24.62329	1	13	0	0	Approach 0
55.49661	33.32173	6	40	1	1	Approach 1
83.97452	26.98404	5	3	1	1	Approach 1
60.11129	30.39137	0	16	0	1	Approach 0
76.33568	26.59953	3	24	0	1	Approach 0
45.61493	25.88148	1	1	0	0	Approach 0
58.09483	30.13775	1	13	0	1	Approach 0
63.78424	20.66153	0	21	0	1	Approach 0
63.00039	28.91346	3	5	0	1	Approach 0
49.94364	28.57427	1	22	0	0	Approach 0
60.19259	16.21868	0	18	0	0	Approach 0
49.22579	28.47351	3	20	0	1	Approach 0
67.12703	18.32633	2	9	0	0	Approach 0
70.84775	29.63922	0	13	0	1	Approach 0
37.75012	25.18435	4	9	0	0	Approach 0
72.35693	24.22025	3	25	0	1	Approach 0
47.58955	26.97261	2	15	0	1	Approach 0
64.54769	32.49221	0	32	0	0	Approach 0
66.59903	24.45871	3	28	0	0	Approach 0
58.00110	29.23241	3	10	0	0	Approach 0
53.54886	28.36463	2	37	0	0	Approach 0
61.65321	22.28193	1	30	1	1	Approach 1
64.38819	20.03591	0	26	0	0	Approach 0
68.83303	19.02966	1	32	1	1	Approach 1
39.47663	29.20510	1	2	0	0	Approach 0
43.63621	26.86103	2	32	1	0	Approach 1
74.30402	34.40229	2	19	1	1	Approach 1
70.46629	29.29470	1	34	0	0	Approach 0
64.35289	30.39878	4	30	1	1	Approach 1
67.15178	32.33753	3	20	0	0	Approach 0
69.17175	24.99712	1	21	1	1	Approach 1
33.39077	29.04039	3	12	0	0	Approach 0
71.10277	30.47517	2	5	0	1	Approach 0
55.15012	32.47741	2	29	0	0	Approach 0
62.30617	30.05060	1	37	0	1	Approach 0
57.04842	28.68459	0	29	0	1	Approach 0
68.71965	23.52710	1	14	0	0	Approach 0
56.51528	29.91824	2	39	1	1	Approach 1
65.18504	29.00106	1	12	0	1	Approach 0
56.09315	29.53700	0	19	0	0	Approach 0
49.07213	28.69458	4	18	1	1	Approach 1
72.10011	26.19265	4	20	1	0	Approach 1
67.40900	26.69254	3	17	1	0	Approach 1
77.24262	29.74946	2	14	0	0	Approach 0
60.65154	27.68653	3	30	0	0	Approach 0
71.25003	23.67957	3	39	1	1	Approach 1
79.75419	25.83936	4	3	0	1	Approach 0
57.18518	21.72350	3	30	1	1	Approach 1
46.77049	23.13187	1	22	1	1	Approach 1
57.60648	26.42156	2	33	0	0	Approach 0
57.85959	19.80747	3	1	0	0	Approach 0
61.51680	20.24583	2	36	0	0	Approach 0
77.12305	31.41026	2	24	0	1	Approach 0
56.73856	24.69352	1	35	0	1	Approach 0
63.73005	19.59323	1	2	0	0	Approach 0
57.72316	26.54855	1	23	0	0	Approach 0
60.20451	32.28428	1	40	0	0	Approach 0
63.14058	29.64902	1	30	0	1	Approach 0
73.28215	28.76553	2	37	1	0	Approach 1
61.21318	31.73498	4	27	0	0	Approach 0
67.12842	23.91399	2	14	0	0	Approach 0
67.78860	29.91876	1	7	0	0	Approach 0
69.14773	24.65166	1	37	0	0	Approach 0
54.25605	27.00306	2	4	1	1	Approach 1
76.26881	35.85786	1	14	0	0	Approach 0
56.19043	30.87774	2	10	0	1	Approach 0
58.94216	30.07203	0	32	0	0	Approach 0
74.04050	22.56669	0	23	0	0	Approach 0
72.94084	23.85506	2	4	1	1	Approach 1
49.10008	36.13647	1	34	0	1	Approach 0
51.26929	22.62680	1	11	0	1	Approach 0
46.41921	27.85792	1	5	1	1	Approach 1
61.81847	30.57028	3	32	0	0	Approach 0
61.64841	31.07503	2	30	1	1	Approach 1
63.64115	31.35645	0	5	0	0	Approach 0
65.52158	26.34748	2	20	0	0	Approach 0
53.98107	23.71605	0	28	0	0	Approach 0
50.06301	25.77097	1	15	1	1	Approach 1
70.26785	23.39161	2	2	0	0	Approach 0
67.51061	29.50828	2	30	1	1	Approach 1
44.90833	31.48142	0	23	0	0	Approach 0
59.04853	35.50885	1	16	0	0	Approach 0
51.04052	28.46446	0	13	0	0	Approach 0
39.29249	23.50087	1	22	0	0	Approach 0
61.50120	31.09790	3	15	0	0	Approach 0
59.20788	30.61904	3	37	1	1	Approach 1
59.02631	26.04701	3	1	0	0	Approach 0
62.16153	20.76858	0	4	0	0	Approach 0
68.82465	30.04524	1	7	1	1	Approach 1
62.05597	31.51658	2	9	1	1	Approach 1
53.83564	25.81957	1	33	0	0	Approach 0
52.65201	29.14497	1	12	0	0	Approach 0
58.68197	25.89644	0	23	0	0	Approach 0
63.10017	29.72926	0	26	0	1	Approach 0
49.60320	26.53084	2	36	0	1	Approach 0
58.15691	25.62130	2	36	0	0	Approach 0
69.67267	27.44648	2	9	0	0	Approach 0
58.91720	25.86638	4	10	0	0	Approach 0
53.01579	24.63593	1	20	0	0	Approach 0
57.24055	25.73625	3	9	0	1	Approach 0
71.14649	26.96739	1	27	0	0	Approach 0
65.50044	27.82998	1	19	0	0	Approach 0
72.36676	33.12969	1	37	0	1	Approach 0
61.39098	21.56801	4	14	0	0	Approach 0
64.10275	26.20152	2	19	0	0	Approach 0
54.41543	29.52609	2	20	0	1	Approach 0
66.05371	34.04808	3	38	1	0	Approach 1
54.93666	28.70406	3	27	1	0	Approach 1
45.79434	26.94499	2	33	1	0	Approach 1
61.27993	25.76977	4	23	0	0	Approach 0
79.45851	28.65723	1	12	1	1	Approach 1
68.00914	30.95623	2	6	0	1	Approach 0
71.65253	26.26457	0	27	1	0	Approach 1
63.58856	27.65505	1	17	0	0	Approach 0
53.91443	27.86775	3	23	0	1	Approach 0
57.97759	29.91711	3	13	1	0	Approach 1
57.26752	31.44552	2	11	0	0	Approach 0
55.31300	28.11664	1	23	0	0	Approach 0
67.04167	26.69532	2	23	0	0	Approach 0
48.02636	32.57865	0	33	0	0	Approach 0
68.66366	27.65814	3	39	0	1	Approach 0
68.64152	33.31141	2	36	0	0	Approach 0
48.01378	26.75231	1	3	1	0	Approach 1
66.39492	29.45569	2	25	0	0	Approach 0
84.30227	20.81565	4	32	0	0	Approach 0
54.42785	26.55043	1	34	0	0	Approach 0
68.44904	26.91282	1	40	1	0	Approach 1
52.17798	23.96662	3	40	0	0	Approach 0
71.10711	22.85643	1	40	0	0	Approach 0
62.49825	30.79264	0	9	0	0	Approach 0
76.51915	30.65663	2	9	0	0	Approach 0
45.41029	21.80507	1	37	0	0	Approach 0
59.48702	28.69752	2	29	0	0	Approach 0
54.73075	22.54982	2	28	0	1	Approach 0
58.02735	22.79571	2	28	0	0	Approach 0
53.70421	29.10165	1	36	0	0	Approach 0
51.66156	24.25590	1	4	0	1	Approach 0
65.78722	30.97392	2	22	0	0	Approach 0
49.12419	27.15409	1	14	1	1	Approach 1
74.84031	29.14460	0	21	0	1	Approach 0
48.13793	24.90549	0	21	0	1	Approach 0
61.01079	22.39511	4	20	0	0	Approach 0
65.32989	30.65901	1	17	0	0	Approach 0
65.86735	27.95229	5	11	0	1	Approach 0
56.98253	26.04373	2	32	0	0	Approach 0
60.79502	27.27694	3	20	1	1	Approach 1
69.61264	32.30363	2	15	0	1	Approach 0
45.43534	24.20733	4	32	0	0	Approach 0
52.18260	24.00237	3	37	1	0	Approach 1
63.20402	24.52154	1	14	0	0	Approach 0
55.55218	20.66003	3	24	1	1	Approach 1
73.70004	30.27851	4	7	1	1	Approach 1
66.73254	27.76948	3	9	1	1	Approach 1
60.72167	27.82869	2	32	1	1	Approach 1
44.92243	26.82661	3	29	1	0	Approach 1
60.26100	24.95936	0	26	1	1	Approach 1
56.83584	23.70633	0	37	0	0	Approach 0
58.97653	30.40743	1	37	1	1	Approach 1
48.18441	21.29526	2	36	0	0	Approach 0
64.98658	28.76120	5	21	1	1	Approach 1
49.61044	23.82955	5	8	1	1	Approach 1
57.73778	28.12924	2	26	0	0	Approach 0
63.81426	24.03724	1	3	1	0	Approach 1
52.16484	24.90663	2	14	0	1	Approach 0
65.82991	34.07746	2	26	0	1	Approach 0
46.83490	29.67313	4	37	0	1	Approach 0
31.90225	18.42041	2	14	1	0	Approach 1
64.64968	27.50565	0	26	0	0	Approach 0
68.40540	25.19275	3	30	0	0	Approach 0
57.14155	22.45350	3	9	0	1	Approach 0
65.04126	27.83914	1	9	0	0	Approach 0
48.44083	27.51986	1	36	1	0	Approach 1
58.72851	25.68597	1	14	0	0	Approach 0
40.58482	34.89081	0	11	0	0	Approach 0
71.81181	18.00524	2	31	0	0	Approach 0
78.59911	30.35288	2	12	0	0	Approach 0
70.74012	25.84391	2	30	0	1	Approach 0
59.72653	29.62605	4	40	1	0	Approach 1
59.66670	25.18401	2	21	0	0	Approach 0
44.83932	24.62454	1	24	0	0	Approach 0
67.90385	20.15848	2	40	0	0	Approach 0
57.89266	26.16221	0	23	0	0	Approach 0
53.43257	36.91498	2	14	0	0	Approach 0
45.87974	30.95881	3	39	1	0	Approach 1
57.00238	33.70229	1	31	0	0	Approach 0
51.50939	30.65986	1	2	1	1	Approach 1
56.02969	31.57705	4	38	0	0	Approach 0
47.82400	30.61151	1	11	0	0	Approach 0
76.87589	28.90157	6	40	0	1	Approach 0
59.83997	24.66988	3	8	0	0	Approach 0
70.74945	24.86826	4	30	1	0	Approach 1
33.98300	20.59664	3	2	1	0	Approach 1
55.46802	26.97673	1	25	0	1	Approach 0
53.24518	30.59742	1	37	1	1	Approach 1
47.77074	31.12769	0	38	0	0	Approach 0
75.46609	27.38053	4	30	0	0	Approach 0
45.84718	24.80949	2	2	0	0	Approach 0
63.18390	40.16207	1	2	0	0	Approach 0
68.46436	29.94674	3	36	0	0	Approach 0
61.78190	32.68230	3	14	0	0	Approach 0
51.24745	25.64928	3	14	0	0	Approach 0
69.41166	26.84817	2	30	0	1	Approach 0
61.70588	28.79443	0	9	1	0	Approach 1
49.36502	33.70609	4	40	0	0	Approach 0
46.11951	25.75410	0	37	1	1	Approach 1
80.86717	30.41446	3	3	0	0	Approach 0
53.21497	18.62074	2	19	0	0	Approach 0
41.44428	24.97098	2	16	0	0	Approach 0
65.33259	21.83196	3	17	0	1	Approach 0
63.10230	31.45345	1	22	0	0	Approach 0
46.46166	26.34219	3	25	0	0	Approach 0
40.57044	25.43850	3	5	1	0	Approach 1
58.83697	32.47640	3	38	0	0	Approach 0
71.39396	31.46509	2	25	1	1	Approach 1
66.36124	23.40792	1	11	0	0	Approach 0
55.07063	28.71147	3	21	0	0	Approach 0
51.65812	22.08622	0	21	0	0	Approach 0
62.71067	25.09754	0	14	0	0	Approach 0
61.57353	33.46631	0	19	0	0	Approach 0
66.29712	32.80051	2	15	0	0	Approach 0
56.04202	31.43607	3	25	1	0	Approach 1
68.99354	24.71638	1	12	0	0	Approach 0
51.69188	19.47427	3	40	1	1	Approach 1
56.69455	22.29721	3	21	1	0	Approach 1
67.40815	30.81023	2	4	0	0	Approach 0
69.89972	25.83773	5	7	1	1	Approach 1
40.61495	18.34957	1	24	0	0	Approach 0
61.07190	26.27925	0	25	0	0	Approach 0
66.08779	32.64096	4	32	0	1	Approach 0
45.49176	29.57387	3	13	0	1	Approach 0
64.80626	23.71497	1	30	0	1	Approach 0
51.71826	20.81633	1	12	0	1	Approach 0
70.20253	23.69381	5	40	0	1	Approach 0
65.38482	27.13811	0	9	0	0	Approach 0
67.69052	30.55229	3	21	1	1	Approach 1
61.20719	19.24024	2	2	1	1	Approach 1
68.63648	31.09281	4	4	1	1	Approach 1
73.80515	27.02183	3	3	0	0	Approach 0
79.66248	29.27912	2	27	1	0	Approach 1
59.71605	20.38698	1	32	0	0	Approach 0
37.50949	24.33338	2	30	0	0	Approach 0
60.31526	25.20706	2	7	1	0	Approach 1
62.05561	31.17557	1	24	0	1	Approach 0
58.44655	31.11270	3	37	1	0	Approach 1
65.68289	28.74036	1	6	0	0	Approach 0
70.10678	33.41685	2	19	0	0	Approach 0
54.82018	24.93836	2	17	0	0	Approach 0
57.05905	31.05015	2	30	0	0	Approach 0
63.97842	26.85624	2	36	0	1	Approach 0
54.49776	24.33063	0	7	1	1	Approach 1
60.91267	30.69352	2	33	0	0	Approach 0
40.38292	32.52440	1	3	0	0	Approach 0
48.80100	30.51300	2	19	0	1	Approach 0
46.72245	24.96239	2	23	0	0	Approach 0
51.46376	25.12085	2	13	0	0	Approach 0
53.06695	32.51070	1	23	0	0	Approach 0
63.82305	28.41131	1	39	0	0	Approach 0
69.82113	30.31830	0	23	0	0	Approach 0
52.72616	25.64519	1	25	0	0	Approach 0
50.03161	32.04414	3	39	1	0	Approach 1
49.58311	23.76498	0	12	0	0	Approach 0
55.85411	29.50141	5	23	0	0	Approach 0
57.60971	23.73130	3	10	0	0	Approach 0
64.83618	17.14970	4	21	0	0	Approach 0
56.78675	21.62817	2	30	0	1	Approach 0
39.21511	27.54518	1	7	0	0	Approach 0
59.08566	30.53169	2	15	1	0	Approach 1
71.87187	19.99479	0	25	0	0	Approach 0
71.91601	21.99430	1	30	0	0	Approach 0
52.11037	34.05818	1	13	0	0	Approach 0
44.52223	25.26440	1	3	0	0	Approach 0
84.58060	29.02280	2	17	1	0	Approach 1
58.37578	24.89226	1	5	1	1	Approach 1
59.02549	25.80567	2	29	0	0	Approach 0
64.20574	27.34898	1	14	0	0	Approach 0
43.85961	27.04385	2	40	0	0	Approach 0
52.71781	26.22976	0	38	0	1	Approach 0
44.59558	25.12081	3	37	0	0	Approach 0
53.06905	14.80856	3	19	1	0	Approach 1
61.18849	34.47462	1	28	0	1	Approach 0
46.35291	34.16170	2	29	0	1	Approach 0
65.89983	22.59567	2	2	0	0	Approach 0
62.89344	26.32757	0	2	0	1	Approach 0
50.95785	32.50110	3	15	0	0	Approach 0
62.26325	30.99316	4	40	0	1	Approach 0
67.48081	32.10641	5	2	0	1	Approach 0
70.61095	22.71301	3	24	1	0	Approach 1
57.87152	37.30907	0	24	0	0	Approach 0
59.06363	22.46616	3	33	0	0	Approach 0
59.13286	30.01567	1	16	0	0	Approach 0
74.41462	27.56510	2	32	0	0	Approach 0
71.25072	25.38516	0	13	0	1	Approach 0
68.34402	25.48234	1	15	1	1	Approach 1
57.12659	23.03441	1	37	0	0	Approach 0
63.73241	33.49064	2	2	1	0	Approach 1
64.03290	27.35805	3	39	0	0	Approach 0
49.58327	28.03687	2	14	0	0	Approach 0
42.71695	27.83853	1	11	0	1	Approach 0
66.41830	25.49932	3	37	0	0	Approach 0
44.70689	22.46392	1	5	0	0	Approach 0
60.01684	28.01491	4	8	0	0	Approach 0
62.50248	18.62544	3	9	0	0	Approach 0
65.63867	21.32573	1	11	0	0	Approach 0
61.89426	22.69441	1	28	0	1	Approach 0
52.67146	22.68528	1	37	0	0	Approach 0
69.86366	27.42876	4	20	0	1	Approach 0
77.38634	33.39395	2	9	1	1	Approach 1
68.81179	20.93870	4	33	0	1	Approach 0
40.56349	28.73470	7	9	1	1	Approach 1
73.99576	30.59818	2	32	0	0	Approach 0
59.43944	23.04187	1	23	0	0	Approach 0
65.24914	26.78880	2	26	0	0	Approach 0
66.22033	30.29444	4	5	0	0	Approach 0
59.03314	25.97796	5	34	0	1	Approach 0
59.24737	26.11726	1	19	0	0	Approach 0
70.19157	28.23091	3	9	1	1	Approach 1
67.11602	26.75995	1	9	0	1	Approach 0
69.90262	24.77739	2	22	1	1	Approach 1
83.82927	26.44554	1	3	0	0	Approach 0
66.64416	34.53136	3	35	1	0	Approach 1
62.07381	30.49467	2	21	1	0	Approach 1
37.89367	23.34161	3	32	0	0	Approach 0
86.91714	22.02033	5	22	1	0	Approach 1
55.17323	25.56007	0	40	0	0	Approach 0
83.74735	32.31510	2	29	0	1	Approach 0
63.74644	28.17072	3	21	0	0	Approach 0
75.38430	24.19398	3	32	1	0	Approach 1
58.90290	30.52894	4	4	0	0	Approach 0
65.11471	26.46652	3	10	0	0	Approach 0
62.13958	22.51729	4	12	0	0	Approach 0
58.13879	28.84477	5	15	0	0	Approach 0
58.79606	33.09657	2	9	0	1	Approach 0
70.12834	28.73787	3	35	1	0	Approach 1
57.98542	27.76800	2	16	0	1	Approach 0
39.62318	24.37503	0	12	0	0	Approach 0
58.04111	29.27359	2	8	1	0	Approach 1
65.39791	22.71772	1	16	0	0	Approach 0
66.16456	20.38740	2	6	0	0	Approach 0
66.16568	26.82659	0	2	0	0	Approach 0
43.07898	26.86163	3	23	1	1	Approach 1
63.68742	36.46022	0	7	0	1	Approach 0
69.67859	22.13461	0	36	0	0	Approach 0
72.76579	27.68363	4	4	1	0	Approach 1
57.75039	30.22021	5	29	1	0	Approach 1
56.78107	31.20237	1	30	0	0	Approach 0
74.87838	26.95710	2	5	1	1	Approach 1
43.32072	24.02698	2	37	0	1	Approach 0
55.63170	26.73686	2	15	0	1	Approach 0
64.57462	34.75902	4	5	0	0	Approach 0
43.82226	28.93096	3	21	0	1	Approach 0
62.79628	18.82209	1	10	0	0	Approach 0
78.77864	32.69384	0	36	0	0	Approach 0
59.95939	29.16201	2	22	0	1	Approach 0
57.21546	26.86571	2	14	0	1	Approach 0
64.74912	26.92855	2	21	1	1	Approach 1
57.20928	26.40084	3	19	0	0	Approach 0
68.13400	28.02624	2	7	1	0	Approach 1
69.04435	24.98453	2	9	0	0	Approach 0
60.02692	28.10805	1	33	0	1	Approach 0
48.23308	23.27458	2	35	0	1	Approach 0
46.81779	27.80059	3	36	1	1	Approach 1
54.07003	31.42735	1	8	0	0	Approach 0
67.97380	29.03682	3	32	0	0	Approach 0
40.41795	31.13500	3	36	0	0	Approach 0
41.13675	22.63652	1	2	0	0	Approach 0
53.46220	27.21917	1	37	0	0	Approach 0
63.94395	29.46900	0	40	0	1	Approach 0
50.86434	22.72798	2	3	1	0	Approach 1
68.86749	33.26326	3	20	0	0	Approach 0
63.33370	22.86077	2	36	0	0	Approach 0
58.29360	27.65807	4	39	1	0	Approach 1
68.18828	27.60733	0	37	0	0	Approach 0
63.88365	27.48668	4	21	0	0	Approach 0
55.54065	26.15830	2	22	0	0	Approach 0
62.31115	28.79975	3	31	1	1	Approach 1
66.47513	22.87534	2	39	0	1	Approach 0
63.56283	21.84254	1	10	1	0	Approach 1
53.41990	24.38173	2	31	0	0	Approach 0
68.55202	26.77070	1	22	0	0	Approach 0
71.52936	32.02699	0	8	0	0	Approach 0
62.76275	33.34982	1	9	0	1	Approach 0
61.44105	28.27793	1	25	0	0	Approach 0
59.24375	28.52637	1	24	0	0	Approach 0
81.61416	26.02542	0	35	0	0	Approach 0
62.76316	27.19221	3	18	0	1	Approach 0
58.41706	21.38182	2	5	1	1	Approach 1
34.92082	28.15973	2	36	0	1	Approach 0
44.34718	24.85779	0	2	0	1	Approach 0
59.22327	28.33872	0	12	0	1	Approach 0
62.06294	25.61607	1	13	0	0	Approach 0
62.76872	24.35354	0	4	0	1	Approach 0
68.21507	26.12355	4	23	1	0	Approach 1
58.05848	25.53238	2	2	0	1	Approach 0
72.14589	31.37831	3	16	0	0	Approach 0
50.78484	27.83683	2	22	0	0	Approach 0
47.91557	28.72997	0	38	0	0	Approach 0
47.71014	22.03659	0	24	1	1	Approach 1
67.42297	32.98729	2	23	0	1	Approach 0
59.17080	27.63748	1	16	1	1	Approach 1
67.89818	23.57487	3	40	0	1	Approach 0
57.32294	28.23619	2	14	0	0	Approach 0
54.08108	30.48174	2	8	0	0	Approach 0
56.31647	21.46529	4	37	0	0	Approach 0
41.47383	33.76043	0	10	1	0	Approach 1
48.30385	26.36788	0	37	0	0	Approach 0
45.57965	31.48468	2	9	0	0	Approach 0
70.54322	27.28905	0	16	0	0	Approach 0
54.02670	25.67031	1	30	1	1	Approach 1
67.89460	19.66032	1	33	0	1	Approach 0
75.16491	22.59931	1	18	0	1	Approach 0
58.08225	26.83464	2	22	0	0	Approach 0
62.83879	30.31141	0	3	0	1	Approach 0
42.48932	19.47329	2	9	0	0	Approach 0
51.81330	32.50176	3	8	1	1	Approach 1
60.56215	32.59596	1	9	0	1	Approach 0
62.99087	22.42674	3	30	0	0	Approach 0
52.40602	28.88920	0	13	0	0	Approach 0
86.84859	22.86544	2	19	1	1	Approach 1
55.41610	26.49920	1	39	0	1	Approach 0
60.64244	30.71465	1	19	0	0	Approach 0
66.49792	30.47336	1	30	0	1	Approach 0
59.73981	23.60330	2	26	0	0	Approach 0
53.56433	25.45345	2	5	1	1	Approach 1
70.45306	23.09535	2	25	1	0	Approach 1
76.15545	28.35817	5	32	1	1	Approach 1
59.70306	20.76370	2	5	0	0	Approach 0
65.62267	16.48270	1	8	1	0	Approach 1
59.02587	32.87925	3	5	0	0	Approach 0
70.16455	36.09389	2	20	0	1	Approach 0
48.43833	25.17987	1	40	0	0	Approach 0
83.20860	30.04441	1	33	1	0	Approach 1
53.96469	26.96999	0	39	1	0	Approach 1
45.41151	32.89726	0	1	0	0	Approach 0
56.49082	29.21658	2	35	0	1	Approach 0
61.46708	27.81466	3	39	0	0	Approach 0
76.23621	19.80345	2	30	1	0	Approach 1
69.11210	31.33182	1	25	1	1	Approach 1
61.42458	25.59659	3	33	0	0	Approach 0
46.10516	21.38604	7	17	0	0	Approach 0
51.33962	26.19281	0	30	0	0	Approach 0
58.36715	26.49289	2	36	1	1	Approach 1
85.53026	31.23683	3	27	0	0	Approach 0
41.39772	22.33042	2	26	0	0	Approach 0
71.31055	24.76943	1	4	0	0	Approach 0
54.72766	32.95248	2	40	1	0	Approach 1
76.65991	32.43466	1	9	0	0	Approach 0
48.60799	31.65286	5	34	0	1	Approach 0
61.43623	33.64610	3	23	0	1	Approach 0
49.00449	27.81612	3	40	1	0	Approach 1
69.03516	24.67247	0	9	0	0	Approach 0
74.83779	29.22082	1	12	1	0	Approach 1
79.50721	31.23489	2	23	1	1	Approach 1
67.97601	36.65453	0	31	0	1	Approach 0
78.43266	19.14007	1	2	1	1	Approach 1
72.46424	28.09294	1	27	1	1	Approach 1
58.68125	29.61918	2	40	1	0	Approach 1
64.77037	26.78161	1	33	0	1	Approach 0
50.28006	20.76871	2	32	0	1	Approach 0
58.14798	29.96600	4	25	1	0	Approach 1
72.20964	23.88366	2	4	0	0	Approach 0
65.41284	29.02345	2	25	0	1	Approach 0
64.57357	30.63021	1	20	0	0	Approach 0
49.61869	32.13583	1	6	0	1	Approach 0
53.95487	20.76854	0	31	0	0	Approach 0
52.35394	31.32697	3	21	0	0	Approach 0
63.95296	23.97207	5	23	0	1	Approach 0
50.09492	21.84392	4	22	1	0	Approach 1
65.62041	32.25728	1	9	0	1	Approach 0
48.83584	31.58504	1	21	0	0	Approach 0
78.28530	26.02967	1	21	0	1	Approach 0
64.60591	30.03816	1	27	0	1	Approach 0
52.98996	23.55870	2	34	0	0	Approach 0
62.41046	26.39587	2	37	0	1	Approach 0
56.47547	26.62511	0	28	0	0	Approach 0
63.71148	25.87704	2	30	0	0	Approach 0
62.43533	29.93639	0	9	0	1	Approach 0
49.85886	33.14931	2	34	0	0	Approach 0
52.08686	25.17692	5	8	1	1	Approach 1
62.99594	26.86937	5	40	1	1	Approach 1
76.39052	33.54703	4	39	0	0	Approach 0
70.84617	25.68383	2	17	0	0	Approach 0
53.75433	16.58385	1	29	0	0	Approach 0
68.25923	29.05594	1	21	1	0	Approach 1
59.51432	23.45413	4	16	0	0	Approach 0
63.01314	23.00585	3	1	1	0	Approach 1
62.60361	32.68327	2	27	0	1	Approach 0
85.75450	36.79199	2	4	0	1	Approach 0
48.14711	22.84087	3	19	0	1	Approach 0
61.00920	31.12410	3	28	1	0	Approach 1
42.20023	26.62341	2	14	0	0	Approach 0
65.89836	27.56723	2	9	0	1	Approach 0
70.96608	31.88895	1	24	0	0	Approach 0
74.45662	27.85470	2	1	0	1	Approach 0
40.74855	23.59454	3	27	0	0	Approach 0
64.12770	25.11836	0	34	1	0	Approach 1
75.93370	29.74454	2	28	0	0	Approach 0
55.85984	17.65621	2	16	0	0	Approach 0
57.87849	31.38098	1	36	0	0	Approach 0
59.63463	20.73140	1	38	0	0	Approach 0
63.65019	27.08772	1	30	0	0	Approach 0
66.65160	26.23856	0	38	0	1	Approach 0
73.17821	32.17228	3	33	0	0	Approach 0
59.04512	27.75540	1	36	0	0	Approach 0
61.96278	27.40776	0	1	0	1	Approach 0
84.87998	29.79254	2	39	0	0	Approach 0
64.31099	23.69194	3	18	0	0	Approach 0
61.88753	26.21640	2	40	0	0	Approach 0
46.57757	31.71034	2	34	0	0	Approach 0
60.02856	29.73389	3	30	0	0	Approach 0
57.78674	21.89801	4	14	1	0	Approach 1
59.88954	29.55183	3	24	0	0	Approach 0
54.24582	21.48964	2	14	0	1	Approach 0
53.13184	24.60676	3	3	1	1	Approach 1
52.79226	31.84368	1	32	1	0	Approach 1
57.85495	17.99582	1	29	0	0	Approach 0
73.68133	19.88394	2	23	0	0	Approach 0
70.49087	32.20549	0	35	0	0	Approach 0
56.40025	23.74083	0	19	1	1	Approach 1
43.14084	31.97483	1	2	0	0	Approach 0
51.55417	26.32700	1	40	0	1	Approach 0
55.42239	28.71110	4	36	1	0	Approach 1
61.03638	30.25312	2	26	0	0	Approach 0
53.37393	24.39515	2	29	1	0	Approach 1
80.06681	25.78164	2	14	1	1	Approach 1
57.27732	25.33961	0	19	0	0	Approach 0
47.86056	38.26434	3	21	0	0	Approach 0
58.58738	27.50459	3	7	0	0	Approach 0
49.94622	28.89120	0	16	0	0	Approach 0
61.56156	25.63699	2	15	0	1	Approach 0
62.33634	26.03284	2	23	1	0	Approach 1
63.55588	32.51502	1	15	0	1	Approach 0
43.78142	25.64447	3	10	0	0	Approach 0
62.20711	27.08055	2	10	0	0	Approach 0
63.10450	28.50785	1	26	0	1	Approach 0
45.78892	25.27311	4	11	1	1	Approach 1
69.55366	34.83626	0	26	0	0	Approach 0
67.84171	21.28616	4	30	0	0	Approach 0
82.99619	35.04517	3	37	0	0	Approach 0
61.56703	25.59363	1	28	0	1	Approach 0
60.46734	32.42848	2	3	1	0	Approach 1
60.96586	19.00329	2	21	1	1	Approach 1
60.69766	30.82432	2	33	1	1	Approach 1
41.51527	30.50573	0	19	0	0	Approach 0
43.28873	21.91513	1	31	0	0	Approach 0
59.22461	23.92670	1	38	0	0	Approach 0
54.18933	27.77410	0	21	0	0	Approach 0
60.54737	31.57534	5	39	0	1	Approach 0
38.88792	23.93600	1	20	0	1	Approach 0
45.01302	26.10350	4	27	1	0	Approach 1
48.98517	33.28539	3	24	1	0	Approach 1
69.86058	22.49061	2	9	0	1	Approach 0
49.01510	30.79118	3	5	0	0	Approach 0
52.00486	28.79507	1	8	0	0	Approach 0
60.79874	22.57674	3	15	0	0	Approach 0
56.77254	24.32853	0	39	1	1	Approach 1
61.46417	30.13311	1	34	1	0	Approach 1
83.05062	27.99584	5	1	1	0	Approach 1
48.75396	32.70039	0	19	0	1	Approach 0
56.94530	24.59286	2	36	0	1	Approach 0
54.83241	20.14205	2	15	0	1	Approach 0
75.12395	31.19131	1	16	0	0	Approach 0
52.30515	24.56551	2	34	1	0	Approach 1
59.17913	27.48136	4	18	0	0	Approach 0
67.87134	33.87617	2	20	0	0	Approach 0
49.41409	25.99834	1	37	0	0	Approach 0
76.55176	33.19822	1	40	0	1	Approach 0
66.75762	22.61144	3	35	0	1	Approach 0
49.25793	30.70204	0	28	0	1	Approach 0
64.54578	27.98720	4	3	0	0	Approach 0
57.86693	24.05291	3	23	1	1	Approach 1
63.13229	21.87996	2	35	1	0	Approach 1
59.10025	27.30657	0	23	0	1	Approach 0
70.70516	28.02066	4	4	0	0	Approach 0
46.48900	28.10979	1	19	0	0	Approach 0
54.77383	29.14742	3	28	0	0	Approach 0
57.50809	25.15806	0	26	1	1	Approach 1

Estimate Overlap Weights Using WeightIt Package

# Propensity score overlap weights
w.ato <- weightit(surgical_approach ~ age + bmi + comorbidity,
                  data = mydata,
                  method = "ps",
                  estimand = "ATO")

## Assuming "Approach 1" is the treated level. If not, recode the
## treatment so that 1 is treated and 0 is control.
## Assuming "Approach 1" is the treated level. If not, recode the
## treatment so that 1 is treated and 0 is control.

mydata$w_ato <- w.ato$weights

Overlap Weights diagnostics: Balance Table and Love Plot

# Balance table (weighted standardized mean differences)
bal_tab <- bal.tab(w.ato, un = TRUE, m.threshold = 0.1)  # 'un=TRUE' shows unweighted and weighted balance
#print(bal_tab)

## Cleaner Balance Table

bal_df <- as.data.frame(bal_tab$Balance)


kable(bal_df, format = "html", digits = 3, caption = "Weighted Balance Table") %>%
  kable_styling(full_width = FALSE, bootstrap_options = c("striped", "hover", "condensed"))

Weighted Balance Table

	Type	Diff.Un	Diff.Adj	M.Threshold
prop.score	Distance	0.619	-0.008	Balanced, <0.1
age	Contin.	0.157	0.000	Balanced, <0.1
bmi	Contin.	-0.204	0.000	Balanced, <0.1
comorbidity	Contin.	0.566	0.000	Balanced, <0.1

# Love plot to visualize balance before/after weighting
love.plot(bal_tab, stats = "mean.diffs", thresholds = c(m = 0.1), abs = TRUE)

Unadjusted Baseline Characteristic Tables

# Add weights to your data frame for convenience
mydata$weights_ato <- w.ato$weights


# Define variables to summarize
vars <- c("age", "bmi", "comorbidity")

# Unadjusted table (no weights)
table_unadj <- tableby(surgical_approach ~ age + bmi + comorbidity, data = mydata)
summary(table_unadj, text = TRUE, title = "Unadjusted Baseline Characteristics by Surgical Approach")

Unadjusted Baseline Characteristics by Surgical Approach

	Approach 0 (N=730)	Approach 1 (N=270)	Total (N=1000)	p value
age				0.026
- Mean (SD)	59.738 (9.721)	61.306 (10.359)	60.161 (9.917)
- Range	33.391 - 92.410	31.902 - 86.917	31.902 - 92.410
bmi				0.005
- Mean (SD)	27.388 (4.074)	26.581 (3.889)	27.170 (4.039)
- Range	16.219 - 40.561	14.809 - 38.329	14.809 - 40.561
comorbidity				< 0.001
- Mean (SD)	1.736 (1.239)	2.489 (1.475)	1.939 (1.349)
- Range	0.000 - 7.000	0.000 - 9.000	0.000 - 9.000

Adjusted (overlap weight) Baseline Characteristic Tables

Statistical tests (like t-tests, chi-squared tests) for group differences usually assume unweighted, independent samples.When we apply weights (especially overlap or propensity score weights), the data are effectively a pseudo-population, and standard test statistics and p-values are not straightforward to calculate. tableby() is cautious and does not provide p-values by default for weighted data, because naive tests would be invalid.

table_adj <- tableby(surgical_approach ~ age + bmi + comorbidity, 
                     data = mydata,
                     weights = mydata$weights_ato)

summary(table_adj, text = TRUE, title = "Weighted (Overlap Weights) Baseline Characteristics by Surgical Approach ")

Weighted (Overlap Weights) Baseline Characteristics by Surgical Approach

	Approach 0 (N=182)	Approach 1 (N=182)	Total (N=364)
age
- Mean (SD)	60.845 (9.782)	60.845 (10.205)	60.845 (9.989)
- Range	33.391 - 92.410	31.902 - 86.917	31.902 - 92.410
bmi
- Mean (SD)	26.788 (4.054)	26.788 (3.846)	26.788 (3.949)
- Range	16.219 - 40.561	14.809 - 38.329	14.809 - 40.561
comorbidity
- Mean (SD)	2.217 (1.340)	2.217 (1.326)	2.217 (1.332)
- Range	0.000 - 7.000	0.000 - 9.000	0.000 - 9.000

Overlap Weight with sandwich variance and quasi binomial Model for wieghted logistic regression

# 1. Fit weighted logistic regression using survey package, as it naturally handles fractional weights


design <- svydesign(ids = ~1, weights = ~w_ato, data = mydata)
model_ato <- svyglm(complication ~ surgical_approach, design = design, family = quasibinomial())
#summary(model_ato)

#model_ato <- glm(complication ~ surgical_approach,data = mydata,family = binomial,weights = w_ato)

# 2. Create cluster-robust vcov matrix
vcov_clust <- vcovCR(model_ato, cluster = mydata$surgeon_id, type = "CR2")

# Coefficients with clustered SEs
#coeftest(model_ato, vcov. = vcov_clust)

# 3. Create tidy summary using broom with cluster robust SEs
tidy_clust <- broom::tidy(model_ato, conf.int = TRUE, exponentiate = TRUE)
# But tidy() uses default SEs; instead, we override SEs and CIs below:

# Manually calculate robust SEs and CIs
coefs <- coef(model_ato)
ses <- sqrt(diag(vcov_clust))
est <- exp(coefs)
lower_ci <- exp(coefs - 1.96 * ses)
upper_ci <- exp(coefs + 1.96 * ses)
p_values <- 2 * pnorm(abs(coefs / ses), lower.tail = FALSE)

# Create a data frame in tidy format
df_tidy_clust <- data.frame(
  term = names(coefs),
  estimate = coefs,
  std.error = ses,
  statistic = coefs / ses,
  p.value = p_values,
  conf.low = lower_ci,
  conf.high = upper_ci
)

# 4. Pass this to tbl_regression, telling it to use tidy data frame
tbl <- tbl_regression(
  model_ato,
  tidy_fun = function(x, ...) df_tidy_clust,
  exponentiate = TRUE,
  estimate_fun = function(x) style_ratio(x, digits = 2)
)

# 5. Print publication-ready table
tbl

Characteristic	OR	95% CI	p-value
surgical_approach
Approach 0	—	—
Approach 1	0.61	1.04, 3.30	0.038
Abbreviations: CI = Confidence Interval, OR = Odds Ratio

Acknowledgment

The simulationof data and debugging of the above code were facilitated with assistance from OpenAI’s ChatGPT (GPT-4) language model. Reference: OpenAI. (2023). ChatGPT (GPT-4) [Large language model]. Retrieved from https://chat.openai.com/