Estimate 6 min Walk Distance with Single Breath Counts

Guiding Questions

1. SBC as an alternative for 6MW?
   1. Which evidence are needed?
      correlation predictive power SBC predicts 6MW
   2. What is the clinical relevance ?
      people who can’t walk estimating cardio-respiratory fitness improves and declines < 20 see doctor, not improving
2. What is of public interest and can be published?
   
3. Diagnosis of the patients in the trial?
   
4. What could be the overall story line?

Action Items

• review papers: https://uofi.box.com/s/x8y56q1t16imts4c68qz2z2srh79zvlg
  
• make list with evidences needed to demonstrate that SBC can replace 6 min for a specific patient group.
  
• paper draft; overleaf https://www.overleaf.com/2976872196cpdwpqtbcfqy#91d60f

Introduction

When two methods such as 6min walk (MW) and Single Breath Count (SBC) are compared neither provides an unequivocally correct measurement. Here we investigate 2 directions: we estimate the correlation between 6min walk distance [m] and SBC counts, and assess the degree of agreement of those two methods. Finally we discuss if SBC is an alternative to the 6min walk for patients impaired mobility, or no access to instruments to measure V02 update via work. Since

Step 1 Plotting Data: Plot data and draw the line of equality on which all points would lie if the two meters gave exactly the same reading every time. Helpful for gauging the degree of agreement between measurements.

Step 2 Pearson Coefficient: The product-moment correlation coefficient (r) or Pearson’s Coefficient between the results of the two measurement methods and apply the t-test. However, a high correlation does not mean that the two methods agree. Why ?

• 1. r measures the strength of a relation between two variables, not the agreement between them. We have perfect agreement only if the points lie along the line of equality (45 degrees), but we will have perfect correlation if the points lie along any straight line.
     
• 2. measurements can be uncorrelated but in agreement. Thats why a test of significance of correlation is not a test of agreement

Step 3 Measuring Agreement: We want to know by how much the new method is likely to differ from the old: if this is not enough to cause problems in clinical interpretation we can replace the old method by the new or use the two interchangeably. A plot of the difference between the methods against their mean is more informative. Scaling

Improvement, changes in breathcoun. walking same direction, - hypothesis: correlation exist yes, no, test improvement (done) - patient: description of cohort. cardiac, no heartfailure, patient vascular surgery, diabetes,

Dataset Statistics

Dataset: wk1 to wk6 seperate

ID	Age	G	E	SBC_W1	SBC_W3	SBC_W6	MWTD_W1	MWTD_W3	MWTD_W6	BMI_W1	BMI_W3	BMI_W6	P_W1	P_W3	P_W6	BBP_W1_SYS	BBP_W1_DIA	BBP_W3_SYS	BBP_W3_DIA	BBP_W6_SYS	BBP_W6_DIA
1	62	F	W	23	28	27	518	555	549	33.1	32.3	32.0	72	65	75	132	76	138	80	126	72
2	64	M	W	23	22	29	422	477	480	34.6	34.6	34.7	86	82	80	132	60	128	74	146	82
3	56	M	W	24	30	26	439	512	516	31.6	31.0	31.0	82	65	55	112	64	124	68	112	60
4	66	F	W	21	22	33	501	578	607	22.3	21.8	21.6	108	102	92	122	70	106	60	114	66
5	60	M	W	38	33	38	641	594	669	23.0	23.0	23.0	64	77	89	122	60	120	62	120	66
6	54	F	W	21	21	24	419	401	427	32.0	32.1	24.0	65	77	64	122	60	124	72	128	62
7	50	M	W	38	45	49	645	687	710	28.7	28.0	27.4	76	64	87	128	72	118	80	114	62
8	69	M	W	23	31	26	344	415	438	36.8	36.3	34.7	92	92	82	142	84	138	70	122	70
9	73	M	W	24	23	23	373	380	379	30.2	29.9	29.7	110	108	114	114	62	120	64	126	70
10	69	M	W	28	33	37	554	587	614	30.9	31.7	31.6	82	81	102	126	74	120	80	114	64
11	64	F	W	12	17	19	283	293	305	34.8	34.4	34.6	77	84	84	118	62	124	60	122	66
12	61	M	W	20	30	32	624	640	636	19.0	18.9	18.6	70	70	65	112	64	116	62	118	62
13	69	M	W	24	28	24	387	440	419	39.2	39.2	39.3	79	77	77	132	70	130	70	138	82
14	69	F	W	24	24	31	436	457	480	27.2	26.3	25.9	81	73	84	126	68	122	66	118	64
15	65	F	W	25	28	31	349	366	374	35.3	35.5	36.0	93	86	81	106	68	118	66	122	74
16	67	F	W	27	32	30	479	448	466	32.6	30.2	30.2	76	72	62	124	76	132	68	118	70
17	66	M	W	16	19	19	358	360	351	27.3	25.9	25.4	66	75	84	124	68	118	70	118	66
18	55	M	W	23	22	34	480	533	546	25.5	25.3	26.1	83	88	68	132	68	180	82	114	68
20	74	F	W	17	30	28	278	344	376	34.9	33.9	34.5	72	73	69	118	62	114	60	130	62
21**	74	F	W	24	24	20	229	264	204	43.8	44.0	44.7	73	90	89	142	77	116	62	118	64
22	50	M	W	29	28	30	486	507	564	31.4	31.4	30.7	85	97	98	128	78	126	82	110	78
23	71	M	W	12	16	19	282	329	336	33.7	33.4	34.7	93	79	98	132	66	138	82	128	78
25	74	F	W	17	31	31	414	554	524	25.3	25.2	24.9	62	64	60	118	66	110	64	122	66
26	76	M	W	30	29	27	536	577	607	30.5	29.4	29.6	65	68	78	122	66	112	66	128	86
27	49	F	W	23	27	26	477	476	460	31.4	31.7	31.0	93	89	78	104	72	112	78	118	68
29	64	M	W	31	37	36	417	454	518	26.7	27.2	27.2	67	76	65	144	68	152	76	124	70
30	49	M	W	20	39	35	333	411	457	36.5	36.3	36.3	77	72	76	124	68	124	68	138	82
31	74	M	W	26	26	30	402	419	451	26.6	26.5	25.9	75	64	66	118	66	124	60	110	60
32	66	F	W	20	27	37	274	401	575	31.0	30.6	30.8	60	56	53	116	68	118	66	116	74
33	56	M	W	23	25	26	490	503	536	28.9	28.4	28.7	88	86	82	118	74	112	68	114	66
34	63	F	W	22	22	21	434	480	482	32.4	32.1	32.4	85	94	89	114	78	122	80	118	72
35	74	F	AA	24	19	17	360	368	390	23.8	23.9	23.9	79	77	73	126	64	108	72	122	80
D1	78	M	W	25	23	17	344	338	333	43.8	43.8	43.3	76	77	72	120	62	122	62	126	72
36	68	M	W	18	20	22	430	475	482	32.5	32.1	32.2	70	74	73	122	66	120	70	128	82
37	71	M	W	33	37	35	373	410	454	27.4	28.1	27.5	64	72	73	136	80	126	80	122	64
D4	55	M	W	20	21	24	387	469	457	33.1	35.0	35.0	63	76	65	138	64	132	64	138	82
38	55	M	AA	20	23	22	396	408	421	31.7	32.9	32.1	72	91	72	136	84	126	74	148	86
39	71	F	AA	19	20	21	347	395	366	35.7	37.1	35.7	77	86	80	136	88	128	76	136	92
40	61	F	W	20	26	26	470	518	539	25.6	26.0	25.9	72	66	66	122	72	124	66	126	74
41	41	M	W	23	27	30	425	508	540	28.9	27.8	27.4	71	58	64	122	66	156	72	124	74
42	74	M	W	13	20	25	419	479	488	28.0	28.0	27.7	90	72	74	120	82	136	80	128	74
43	56	M	Hisp	25	35	35	450	510	533	26.6	26.6	27.2	80	83	79	134	82	128	82	124	70
44	61	M	W	28	42	32	466	521	545	25.5	25.4	26.7	70	67	77	124	76	136	62	160	82

Dataset: wk1 to wk6 merged

	ID	PID	Age	G	E	SBC	MWTD	BMI	P	SYSBP	DIABP	WK	BMI_classes	AGE_classes	BPSYS_classes	BPDIA_classes
1	1	1	62	F	W	23	518	33.1	72	132	76	0	Obesity I	50-64	Prehypertension	Normal
2	2	2	64	M	W	23	422	34.6	86	132	60	0	Obesity I	50-64	Prehypertension	Normal
3	3	3	56	M	W	24	439	31.6	82	112	64	0	Obesity I	50-64	Normal	Normal
4	4	4	66	F	W	21	501	22.3	108	122	70	0	Normal	>64	Prehypertension	Normal
5	5	5	60	M	W	38	641	23.0	64	122	60	0	Normal	50-64	Prehypertension	Normal
6	6	6	54	F	W	21	419	32.0	65	122	60	0	Obesity I	50-64	Prehypertension	Normal
7	7	7	50	M	W	38	645	28.7	76	128	72	0	Overweight	<50	Prehypertension	Normal
8	8	8	69	M	W	23	344	36.8	92	142	84	0	Obesity II	>64	Stage 1 Hypertension	Prehypertension
9	9	9	73	M	W	24	373	30.2	110	114	62	0	Obesity I	>64	Normal	Normal
10	10	10	69	M	W	28	554	30.9	82	126	74	0	Obesity I	>64	Prehypertension	Normal
11	11	11	64	F	W	12	283	34.8	77	118	62	0	Obesity I	50-64	Normal	Normal
12	12	12	61	M	W	20	624	19.0	70	112	64	0	Normal	50-64	Normal	Normal
13	13	13	69	M	W	24	387	39.2	79	132	70	0	Obesity II	>64	Prehypertension	Normal
14	14	14	69	F	W	24	436	27.2	81	126	68	0	Overweight	>64	Prehypertension	Normal
15	15	15	65	F	W	25	349	35.3	93	106	68	0	Obesity II	>64	Normal	Normal
16	16	16	67	F	W	27	479	32.6	76	124	76	0	Obesity I	>64	Prehypertension	Normal
17	17	17	66	M	W	16	358	27.3	66	124	68	0	Overweight	>64	Prehypertension	Normal
18	18	18	55	M	W	23	480	25.5	83	132	68	0	Overweight	50-64	Prehypertension	Normal
20	20	20	74	F	W	17	278	34.9	72	118	62	0	Obesity I	>64	Normal	Normal
21	21	21**	74	F	W	24	229	43.8	73	142	77	0	Obesity III	>64	Stage 1 Hypertension	Normal
22	22	22	50	M	W	29	486	31.4	85	128	78	0	Obesity I	<50	Prehypertension	Normal
23	23	23	71	M	W	12	282	33.7	93	132	66	0	Obesity I	>64	Prehypertension	Normal
25	25	25	74	F	W	17	414	25.3	62	118	66	0	Overweight	>64	Normal	Normal
26	26	26	76	M	W	30	536	30.5	65	122	66	0	Obesity I	>64	Prehypertension	Normal
27	27	27	49	F	W	23	477	31.4	93	104	72	0	Obesity I	<50	Normal	Normal
29	29	29	64	M	W	31	417	26.7	67	144	68	0	Overweight	50-64	Stage 1 Hypertension	Normal
30	30	30	49	M	W	20	333	36.5	77	124	68	0	Obesity II	<50	Prehypertension	Normal
31	31	31	74	M	W	26	402	26.6	75	118	66	0	Overweight	>64	Normal	Normal
32	32	32	66	F	W	20	274	31.0	60	116	68	0	Obesity I	>64	Normal	Normal
33	33	33	56	M	W	23	490	28.9	88	118	74	0	Overweight	50-64	Normal	Normal
34	34	34	63	F	W	22	434	32.4	85	114	78	0	Obesity I	50-64	Normal	Normal
35	35	35	74	F	AA	24	360	23.8	79	126	64	0	Normal	>64	Prehypertension	Normal
36	36	D1	78	M	W	25	344	43.8	76	120	62	0	Obesity III	>64	Normal	Normal
39	39	36	68	M	W	18	430	32.5	70	122	66	0	Obesity I	>64	Prehypertension	Normal
40	40	37	71	M	W	33	373	27.4	64	136	80	0	Overweight	>64	Prehypertension	Normal
41	41	D4	55	M	W	20	387	33.1	63	138	64	0	Obesity I	50-64	Prehypertension	Normal
42	42	38	55	M	AA	20	396	31.7	72	136	84	0	Obesity I	50-64	Prehypertension	Prehypertension
43	43	39	71	F	AA	19	347	35.7	77	136	88	0	Obesity II	>64	Prehypertension	Prehypertension
44	44	40	61	F	W	20	470	25.6	72	122	72	0	Overweight	50-64	Prehypertension	Normal
45	45	41	41	M	W	23	425	28.9	71	122	66	0	Overweight	<50	Prehypertension	Normal
46	46	42	74	M	W	13	419	28.0	90	120	82	0	Overweight	>64	Normal	Prehypertension
47	47	43	56	M	Hisp	25	450	26.6	80	134	82	0	Overweight	50-64	Prehypertension	Prehypertension
48	48	44	61	M	W	28	466	25.5	70	124	76	0	Overweight	50-64	Prehypertension	Normal
49	49	1	62	F	W	28	555	32.3	65	138	80	3	Obesity I	50-64	Prehypertension	Normal
50	50	2	64	M	W	22	477	34.6	82	128	74	3	Obesity I	50-64	Prehypertension	Normal
51	51	3	56	M	W	30	512	31.0	65	124	68	3	Obesity I	50-64	Prehypertension	Normal
52	52	4	66	F	W	22	578	21.8	102	106	60	3	Normal	>64	Normal	Normal
53	53	5	60	M	W	33	594	23.0	77	120	62	3	Normal	50-64	Normal	Normal
54	54	6	54	F	W	21	401	32.1	77	124	72	3	Obesity I	50-64	Prehypertension	Normal
55	55	7	50	M	W	45	687	28.0	64	118	80	3	Overweight	<50	Normal	Normal
56	56	8	69	M	W	31	415	36.3	92	138	70	3	Obesity II	>64	Prehypertension	Normal
57	57	9	73	M	W	23	380	29.9	108	120	64	3	Overweight	>64	Normal	Normal
58	58	10	69	M	W	33	587	31.7	81	120	80	3	Obesity I	>64	Normal	Normal
59	59	11	64	F	W	17	293	34.4	84	124	60	3	Obesity I	50-64	Prehypertension	Normal
60	60	12	61	M	W	30	640	18.9	70	116	62	3	Normal	50-64	Normal	Normal
61	61	13	69	M	W	28	440	39.2	77	130	70	3	Obesity II	>64	Prehypertension	Normal
62	62	14	69	F	W	24	457	26.3	73	122	66	3	Overweight	>64	Prehypertension	Normal
63	63	15	65	F	W	28	366	35.5	86	118	66	3	Obesity II	>64	Normal	Normal
64	64	16	67	F	W	32	448	30.2	72	132	68	3	Obesity I	>64	Prehypertension	Normal
65	65	17	66	M	W	19	360	25.9	75	118	70	3	Overweight	>64	Normal	Normal
66	66	18	55	M	W	22	533	25.3	88	180	82	3	Overweight	50-64	Stage 2 Hypertension	Prehypertension
68	68	20	74	F	W	30	344	33.9	73	114	60	3	Obesity I	>64	Normal	Normal
69	69	21**	74	F	W	24	264	44.0	90	116	62	3	Obesity III	>64	Normal	Normal
70	70	22	50	M	W	28	507	31.4	97	126	82	3	Obesity I	<50	Prehypertension	Prehypertension
71	71	23	71	M	W	16	329	33.4	79	138	82	3	Obesity I	>64	Prehypertension	Prehypertension
73	73	25	74	F	W	31	554	25.2	64	110	64	3	Overweight	>64	Normal	Normal
74	74	26	76	M	W	29	577	29.4	68	112	66	3	Overweight	>64	Normal	Normal
75	75	27	49	F	W	27	476	31.7	89	112	78	3	Obesity I	<50	Normal	Normal
77	77	29	64	M	W	37	454	27.2	76	152	76	3	Overweight	50-64	Stage 1 Hypertension	Normal
78	78	30	49	M	W	39	411	36.3	72	124	68	3	Obesity II	<50	Prehypertension	Normal
79	79	31	74	M	W	26	419	26.5	64	124	60	3	Overweight	>64	Prehypertension	Normal
80	80	32	66	F	W	27	401	30.6	56	118	66	3	Obesity I	>64	Normal	Normal
81	81	33	56	M	W	25	503	28.4	86	112	68	3	Overweight	50-64	Normal	Normal
82	82	34	63	F	W	22	480	32.1	94	122	80	3	Obesity I	50-64	Prehypertension	Normal
83	83	35	74	F	AA	19	368	23.9	77	108	72	3	Normal	>64	Normal	Normal
84	84	D1	78	M	W	23	338	43.8	77	122	62	3	Obesity III	>64	Prehypertension	Normal
87	87	36	68	M	W	20	475	32.1	74	120	70	3	Obesity I	>64	Normal	Normal
88	88	37	71	M	W	37	410	28.1	72	126	80	3	Overweight	>64	Prehypertension	Normal
89	89	D4	55	M	W	21	469	35.0	76	132	64	3	Obesity II	50-64	Prehypertension	Normal
90	90	38	55	M	AA	23	408	32.9	91	126	74	3	Obesity I	50-64	Prehypertension	Normal
91	91	39	71	F	AA	20	395	37.1	86	128	76	3	Obesity II	>64	Prehypertension	Normal
92	92	40	61	F	W	26	518	26.0	66	124	66	3	Overweight	50-64	Prehypertension	Normal
93	93	41	41	M	W	27	508	27.8	58	156	72	3	Overweight	<50	Stage 1 Hypertension	Normal
94	94	42	74	M	W	20	479	28.0	72	136	80	3	Overweight	>64	Prehypertension	Normal
95	95	43	56	M	Hisp	35	510	26.6	83	128	82	3	Overweight	50-64	Prehypertension	Prehypertension
96	96	44	61	M	W	42	521	25.4	67	136	62	3	Overweight	50-64	Prehypertension	Normal
97	97	1	62	F	W	27	549	32.0	75	126	72	6	Obesity I	50-64	Prehypertension	Normal
98	98	2	64	M	W	29	480	34.7	80	146	82	6	Obesity I	50-64	Stage 1 Hypertension	Prehypertension
99	99	3	56	M	W	26	516	31.0	55	112	60	6	Obesity I	50-64	Normal	Normal
100	100	4	66	F	W	33	607	21.6	92	114	66	6	Normal	>64	Normal	Normal
101	101	5	60	M	W	38	669	23.0	89	120	66	6	Normal	50-64	Normal	Normal
102	102	6	54	F	W	24	427	24.0	64	128	62	6	Normal	50-64	Prehypertension	Normal
103	103	7	50	M	W	49	710	27.4	87	114	62	6	Overweight	<50	Normal	Normal
104	104	8	69	M	W	26	438	34.7	82	122	70	6	Obesity I	>64	Prehypertension	Normal
105	105	9	73	M	W	23	379	29.7	114	126	70	6	Overweight	>64	Prehypertension	Normal
106	106	10	69	M	W	37	614	31.6	102	114	64	6	Obesity I	>64	Normal	Normal
107	107	11	64	F	W	19	305	34.6	84	122	66	6	Obesity I	50-64	Prehypertension	Normal
108	108	12	61	M	W	32	636	18.6	65	118	62	6	Normal	50-64	Normal	Normal
109	109	13	69	M	W	24	419	39.3	77	138	82	6	Obesity II	>64	Prehypertension	Prehypertension
110	110	14	69	F	W	31	480	25.9	84	118	64	6	Overweight	>64	Normal	Normal
111	111	15	65	F	W	31	374	36.0	81	122	74	6	Obesity II	>64	Prehypertension	Normal
112	112	16	67	F	W	30	466	30.2	62	118	70	6	Obesity I	>64	Normal	Normal
113	113	17	66	M	W	19	351	25.4	84	118	66	6	Overweight	>64	Normal	Normal
114	114	18	55	M	W	34	546	26.1	68	114	68	6	Overweight	50-64	Normal	Normal
116	116	20	74	F	W	28	376	34.5	69	130	62	6	Obesity I	>64	Prehypertension	Normal
117	117	21**	74	F	W	20	204	44.7	89	118	64	6	Obesity III	>64	Normal	Normal
118	118	22	50	M	W	30	564	30.7	98	110	78	6	Obesity I	<50	Normal	Normal
119	119	23	71	M	W	19	336	34.7	98	128	78	6	Obesity I	>64	Prehypertension	Normal
121	121	25	74	F	W	31	524	24.9	60	122	66	6	Normal	>64	Prehypertension	Normal
122	122	26	76	M	W	27	607	29.6	78	128	86	6	Overweight	>64	Prehypertension	Prehypertension
123	123	27	49	F	W	26	460	31.0	78	118	68	6	Obesity I	<50	Normal	Normal
125	125	29	64	M	W	36	518	27.2	65	124	70	6	Overweight	50-64	Prehypertension	Normal
126	126	30	49	M	W	35	457	36.3	76	138	82	6	Obesity II	<50	Prehypertension	Prehypertension
127	127	31	74	M	W	30	451	25.9	66	110	60	6	Overweight	>64	Normal	Normal
128	128	32	66	F	W	37	575	30.8	53	116	74	6	Obesity I	>64	Normal	Normal
129	129	33	56	M	W	26	536	28.7	82	114	66	6	Overweight	50-64	Normal	Normal
130	130	34	63	F	W	21	482	32.4	89	118	72	6	Obesity I	50-64	Normal	Normal
131	131	35	74	F	AA	17	390	23.9	73	122	80	6	Normal	>64	Prehypertension	Normal
132	132	D1	78	M	W	17	333	43.3	72	126	72	6	Obesity III	>64	Prehypertension	Normal
135	135	36	68	M	W	22	482	32.2	73	128	82	6	Obesity I	>64	Prehypertension	Prehypertension
136	136	37	71	M	W	35	454	27.5	73	122	64	6	Overweight	>64	Prehypertension	Normal
137	137	D4	55	M	W	24	457	35.0	65	138	82	6	Obesity II	50-64	Prehypertension	Prehypertension
138	138	38	55	M	AA	22	421	32.1	72	148	86	6	Obesity I	50-64	Stage 1 Hypertension	Prehypertension
139	139	39	71	F	AA	21	366	35.7	80	136	92	6	Obesity II	>64	Prehypertension	Stage 1 Hypertension
140	140	40	61	F	W	26	539	25.9	66	126	74	6	Overweight	50-64	Prehypertension	Normal
141	141	41	41	M	W	30	540	27.4	64	124	74	6	Overweight	<50	Prehypertension	Normal
142	142	42	74	M	W	25	488	27.7	74	128	74	6	Overweight	>64	Prehypertension	Normal
143	143	43	56	M	Hisp	35	533	27.2	79	124	70	6	Overweight	50-64	Prehypertension	Normal
144	144	44	61	M	W	32	545	26.7	77	160	82	6	Overweight	50-64	Stage 2 Hypertension	Prehypertension

Description:
* 48 participated, and observed over 6 weeks.
* 19, 24, 28, D2, D3 dropped out, which leaves 43 unique patents and dataset of 129, 16.
At week 0, 3 and 6 week a set of 6 min walk distance, SBC, BP, HR, BMI were taken.
* 5 didn’t finish the trial.
* Classes have been introduced for BMI, BP, and Age.

Dataset Stats

## [1] "Variables: ID, Age, G, E, SBC_W1, SBC_W3, SBC_W6, MWTD_W1, MWTD_W3, MWTD_W6, BMI_W1, BMI_W3, BMI_W6, P_W1, P_W3, P_W6, BBP_W1_SYS, BBP_W1_DIA, BBP_W3_SYS, BBP_W3_DIA, BBP_W6_SYS, BBP_W6_DIA"

## [1] "Enrolled Patients: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19*, 20, 21**, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, D1, D2, D3, 36, 37, D4, 38, 39, 40, 41, 42, 43, 44"

## [1] "Drop outs: 19*, 24, 28, D2, D3"

## [1] "Dataset: 43 patients completed the trial."

## 
##  F  M 
## 16 27

## 
##   AA Hisp    W 
##    3    1   39

## 
## 41 49 50 54 55 56 60 61 62 63 64 65 66 67 68 69 71 73 74 76 78 
##  1  2  2  1  3  3  1  3  1  1  3  1  3  1  1  4  3  1  6  1  1

## Warning in plot_theme(plot): The `size` theme element is not defined in the
## element hierarchy.

	SBC	MWTD	Age	BMI	P	SYSBP	DIABP
mean	26.10	454.0	63.80	30.50	77.5	125.0	70.80
sd	6.65	98.8	8.74	5.28	11.8	11.1	7.57

## $BMI
## 
##       Under      Normal  Overweight   Obesity I  Obesity II Obesity III 
##           0          14          45          48          16           6 
## 
## $BPDIA
## 
##               Normal      Prehypertension Stage 1 Hypertension 
##                  111                   17                    1 
## Stage 2 Hypertension 
##                    0 
## 
## $BPSYS
## 
##               Normal      Prehypertension Stage 1 Hypertension 
##                   48                   72                    7 
## Stage 2 Hypertension 
##                    2 
## 
## $Age
## 
##   <50 50-64   >64 
##    15    48    66

##      PID BMI_classes
## 1      1   Obesity I
## 49     1   Obesity I
## 97     1   Obesity I
## 10    10   Obesity I
## 58    10   Obesity I
## 106   10   Obesity I
## 11    11   Obesity I
## 59    11   Obesity I
## 107   11   Obesity I
## 12    12      Normal
## 60    12      Normal
## 108   12      Normal
## 13    13  Obesity II
## 61    13  Obesity II
## 109   13  Obesity II
## 14    14  Overweight
## 62    14  Overweight
## 110   14  Overweight
## 15    15  Obesity II
## 63    15  Obesity II
## 111   15  Obesity II
## 16    16   Obesity I
## 64    16   Obesity I
## 112   16   Obesity I
## 17    17  Overweight
## 65    17  Overweight
## 113   17  Overweight
## 18    18  Overweight
## 66    18  Overweight
## 114   18  Overweight
## 2      2   Obesity I
## 50     2   Obesity I
## 98     2   Obesity I
## 20    20   Obesity I
## 68    20   Obesity I
## 116   20   Obesity I
## 21  21** Obesity III
## 69  21** Obesity III
## 117 21** Obesity III
## 22    22   Obesity I
## 70    22   Obesity I
## 118   22   Obesity I
## 23    23   Obesity I
## 71    23   Obesity I
## 119   23   Obesity I
## 25    25  Overweight
## 73    25  Overweight
## 121   25      Normal
## 26    26   Obesity I
## 74    26  Overweight
## 122   26  Overweight
## 27    27   Obesity I
## 75    27   Obesity I
## 123   27   Obesity I
## 29    29  Overweight
## 77    29  Overweight
## 125   29  Overweight
## 3      3   Obesity I
## 51     3   Obesity I
## 99     3   Obesity I
## 30    30  Obesity II
## 78    30  Obesity II
## 126   30  Obesity II
## 31    31  Overweight
## 79    31  Overweight
## 127   31  Overweight
## 32    32   Obesity I
## 80    32   Obesity I
## 128   32   Obesity I
## 33    33  Overweight
## 81    33  Overweight
## 129   33  Overweight
## 34    34   Obesity I
## 82    34   Obesity I
## 130   34   Obesity I
## 35    35      Normal
## 83    35      Normal
## 131   35      Normal
## 39    36   Obesity I
## 87    36   Obesity I
## 135   36   Obesity I
## 40    37  Overweight
## 88    37  Overweight
## 136   37  Overweight
## 42    38   Obesity I
## 90    38   Obesity I
## 138   38   Obesity I
## 43    39  Obesity II
## 91    39  Obesity II
## 139   39  Obesity II
## 4      4      Normal
## 52     4      Normal
## 100    4      Normal
## 44    40  Overweight
## 92    40  Overweight
## 140   40  Overweight
## 45    41  Overweight
## 93    41  Overweight
## 141   41  Overweight
## 46    42  Overweight
## 94    42  Overweight
## 142   42  Overweight
## 47    43  Overweight
## 95    43  Overweight
## 143   43  Overweight
## 48    44  Overweight
## 96    44  Overweight
## 144   44  Overweight
## 5      5      Normal
## 53     5      Normal
## 101    5      Normal
## 6      6   Obesity I
## 54     6   Obesity I
## 102    6      Normal
## 7      7  Overweight
## 55     7  Overweight
## 103    7  Overweight
## 8      8  Obesity II
## 56     8  Obesity II
## 104    8   Obesity I
## 9      9   Obesity I
## 57     9  Overweight
## 105    9  Overweight
## 36    D1 Obesity III
## 84    D1 Obesity III
## 132   D1 Obesity III
## 41    D4   Obesity I
## 89    D4  Obesity II
## 137   D4  Obesity II

## [1] "1"
## [1] "2"
## [1] "3"
## [1] "4"
## [1] "5"
## [1] "6"
## [1] "7"
## [1] "8"
## [1] "9"
## [1] "10"
## [1] "11"
## [1] "12"
## [1] "13"
## [1] "14"
## [1] "15"
## [1] "16"
## [1] "17"
## [1] "18"
## [1] "20"
## [1] "21**"
## [1] "22"
## [1] "23"
## [1] "25"
## [1] "26"
## [1] "27"
## [1] "29"
## [1] "30"
## [1] "31"
## [1] "32"
## [1] "33"
## [1] "34"
## [1] "35"
## [1] "D1"
## [1] "36"
## [1] "37"
## [1] "D4"
## [1] "38"
## [1] "39"
## [1] "40"
## [1] "41"
## [1] "42"
## [1] "43"
## [1] "44"

Patient Recovery

Cohort level

	term	estimate	std.error	statistic	p.value
MWTD Intercept	(Intercept)	426.0969	13.41804	31.7555	0.0000
MWTD Slope	WK	9.4302	3.46452	2.7219	0.0074
SBC Intercept	(Intercept)	23.6434	0.88671	26.6643	0.0000
SBC Slope	WK	0.8062	0.22895	3.5213	0.0006

On average the 6MW and SBC recognized an improvement over the 6 weeks trial.

• SBC: +0.8 counts improvement, p<0.05
• 6MW: +9.4 meter improvement, p<0.05

Patient level

ID	SBC_SLP_16	SBC_SLP_16_pvalue	SBC_SLP_16_std_error	MW_SLP_16	MW_SLP_16_pvalue	MW_SLP_16_std_error
1	0.667	0.45437	0.57735	5.167	0.42988	4.13768
10	1.500	0.41766	0.76980	10.000	0.30408	5.00370
11	1.167	0.78770	0.96225	3.667	0.30395	6.63953
12	2.000	0.28548	0.96225	2.000	0.16280	4.61880
13	0.000	1.00000	0.96225	5.333	0.75912	11.73946
14	1.167	0.33333	0.28868	7.333	0.80578	4.23390
15	1.000	0.09943	0.28868	4.167	0.10644	1.82828
16	0.500	0.75792	1.25093	-2.167	0.18252	4.61880
17	0.500	0.33333	0.09623	-1.167	0.41766	0.76980
18	1.833	0.04078	0.09623	11.000	0.03671	0.57735
2	1.000	0.15442	0.28868	9.667	0.03338	0.19245
20	1.833	0.23391	0.76980	16.333	0.48775	1.92450
21**	-0.667	1.00000	0.76980	-4.167	0.59074	7.12065
22	0.167	0.33333	0.67358	13.000	0.01670	0.19245
23	1.167	0.00000	0.00000	9.000	0.13046	0.86603
25	2.333	0.59348	0.67358	18.333	0.72578	4.71503
26	-0.500	0.33333	0.28868	11.833	0.46907	1.05848
27	0.500	0.38118	1.25093	-2.833	0.21428	3.84900
29	0.833	0.42459	1.44338	16.833	0.12585	3.27165
3	0.333	0.33333	0.38490	12.833	0.72774	9.14138
30	2.500	0.66667	0.28868	20.667	0.16579	3.46410
31	0.667	0.05239	0.09623	8.167	0.25728	3.84900
32	2.833	0.33333	1.34715	50.167	0.46379	16.35826
33	0.500	0.12104	0.09623	7.667	0.05679	1.05848
34	-0.167	0.48775	0.48113	8.000	0.29995	1.44338
35	-1.167	0.43276	0.67358	5.000	0.09749	2.59808
36	0.667	0.46131	2.21318	8.667	0.09416	3.07920
37	0.333	0.33333	0.38490	13.500	0.11137	1.44338
38	0.333	0.06464	0.28868	4.167	0.05724	4.52258
39	0.333	0.12104	0.09623	3.167	0.15657	1.92450
4	2.000	0.33333	0.09623	17.667	0.30988	4.23390
40	1.000	0.15442	0.28868	11.500	0.16755	1.34715
41	1.167	0.17891	0.38490	19.167	0.03338	0.09623
42	2.000	0.00000	0.00000	11.500	0.25417	3.65655
43	1.667	0.66667	0.57735	13.833	0.03174	0.67358
44	0.667	0.17891	0.19245	13.167	0.41985	9.04515
5	0.000	0.54563	0.38490	4.667	0.01470	0.09623
6	0.500	0.00000	0.00000	1.333	0.74287	7.40933
7	1.833	0.33333	0.57735	10.833	0.14145	2.59808
8	0.500	0.05239	0.09623	15.667	0.15957	4.90748
9	-0.167	0.06107	0.19245	1.000	0.25677	4.90748
D1	-1.333	0.33333	0.96225	-1.833	0.16037	3.56033
D4	0.667	0.82109	2.30940	11.667	0.14184	2.98298

Histograms

Taking a look a the individual patients the distributions negative but mostly positive improvements. No

Patients, that got worse

	ID	SBC_SLP_16	SBC_SLP_16_pvalue	MW_SLP_16	MW_SLP_16_pvalue
8	16	0.500	0.75792	-2.167	0.18252
9	17	0.500	0.33333	-1.167	0.41766
13	21**	-0.667	1.00000	-4.167	0.59074
17	26	-0.500	0.33333	11.833	0.46907
18	27	0.500	0.38118	-2.833	0.21428
25	34	-0.167	0.48775	8.000	0.29995
26	35	-1.167	0.43276	5.000	0.09749
41	9	-0.167	0.06107	1.000	0.25677
42	D1	-1.333	0.33333	-1.833	0.16037

Table: 6MW or SBC indicated diseaess progression, patients didn’t recover, or measurement fails indicate correct status. All p-values are > 0.05, no statistical significance.
. std_err_MWTD = 3.46
. std_err_SBC = 0.887

	ID	SBC_SLP_16	MW_SLP_16
13	21**	-0.667	-4.167
17	26	-0.500	11.833
25	34	-0.167	8.000
26	35	-1.167	5.000

Table: Patients for which SBC or 6MW indicated no recovery, negative slope was greater than standard error.

. Standard Error MWTD = 3.46
. Standard Error SBC = 0.887

• 21** SBC and MWTD contradiction. Did this patient not react to treatment?
• 26, 34, 35 SBC below standard error, but MW above standard error.

Mixed Effect Model

## 'data.frame':    129 obs. of  16 variables:
##  $ ID           : num  1 2 3 4 5 6 7 8 9 10 ...
##  $ PID          : chr  "1" "2" "3" "4" ...
##  $ Age          : num  62 64 56 66 60 54 50 69 73 69 ...
##  $ G            : chr  "F" "M" "M" "F" ...
##  $ E            : chr  "W" "W" "W" "W" ...
##  $ SBC          : num  23 23 24 21 38 21 38 23 24 28 ...
##  $ MWTD         : num  518 422 439 501 641 419 645 344 373 554 ...
##  $ BMI          : num  33.1 34.6 31.6 22.3 23 32 28.7 36.8 30.2 30.9 ...
##  $ P            : num  72 86 82 108 64 65 76 92 110 82 ...
##  $ SYSBP        : num  132 132 112 122 122 122 128 142 114 126 ...
##  $ DIABP        : num  76 60 64 70 60 60 72 84 62 74 ...
##  $ WK           : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ BMI_classes  : Factor w/ 6 levels "Under","Normal",..: 4 4 4 2 2 4 3 5 4 4 ...
##  $ AGE_classes  : Factor w/ 3 levels "<50","50-64",..: 2 2 2 3 2 2 1 3 3 3 ...
##  $ BPSYS_classes: Factor w/ 4 levels "Normal","Prehypertension",..: 2 2 1 2 2 2 2 3 1 2 ...
##  $ BPDIA_classes: Factor w/ 4 levels "Normal","Prehypertension",..: 1 1 1 1 1 1 1 2 1 1 ...

## boundary (singular) fit: see help('isSingular')

## Linear mixed model fit by REML ['lmerMod']
## Formula: 
## MWTD ~ SBC + (1 + SBC | PID) + (1 + SBC | WK) + (1 + SBC | BMI_classes) +  
##     (1 + SBC | AGE_classes)
##    Data: dfm
## REML criterion at convergence: 1320.7
## Random effects:
##  Groups      Name        Std.Dev. Corr 
##  PID         (Intercept) 126.500       
##              SBC           3.263  -0.82
##  BMI_classes (Intercept)   6.013       
##              SBC           0.462  -1.00
##  AGE_classes (Intercept)  47.356       
##              SBC           0.565  -1.00
##  WK          (Intercept)  24.067       
##              SBC           1.038  -0.77
##  Residual                 18.973       
## Number of obs: 129, groups:  PID, 43; BMI_classes, 5; AGE_classes, 3; WK, 3
## Fixed Effects:
## (Intercept)          SBC  
##      357.23         3.98  
## optimizer (nloptwrap) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings

Relationship SBC and 6MW (Linear Regression)

Overall impression

Findings:
The graphic shows the means (wk1 & wk3 & wk6) of MW (red) and SBC (blk) per patient, see annoation. The mean differences per SBC and MW per among patient are large and infuence the prediction and increase the variabiliy. . For predicting MW using SBC I remove the mean of SBC and MW of each patient for better predictability.

6MW| SBC, WK, BP, BMI, AGE, ETHN, G

Showing relationship 6MW and SBC conditioned on WK, BP, BMI, AGE, ETHN, G.

WK: The slopes of wk0 to wk3 are similar, which indicates that correlation between 6MW and SBC doesn’t change over time.
BMI: With increasing BMI intercept and slope changes. The higher the BMI the smaller the intercept, and slope. As the distance remains almost constant for patients in obesity class 3 the SBC might be a better choice. Patients with obesity III dont exhibit a correlation between SBC and 6MW. Remark: A few patients (PID 6, 8, 9, 25, 26, D4) changed the BMI during the 6 week period.
AGE: The slope, or correlation doesnt change between SBC and 6MW. The intercept decreases with age class.
Ethnicity: The trial population is too homogenous white to infer conclustions.
Gender: F and M perform similarly. Highest counts and distances were achieved my male. Whereby female patients showed on average a faster recover, slightly steeper slope.
BP Systolic:: With higher BP the slope and intercept are smaller compared to patients with normal BP. Exception are patient with Stage 2 hyptertension. Higher intercept, but smaller slope.
BP Diastolic: Patient with normal BP DIA greater slope, stronger correlation to 6MW.
Last Diagram Shows all fitted lines for patients over 6 weeks

Predicting 6MW via SBC

Prediction Models

• \(6MW = SBC + BMI + Age + G + P + SYSBP + DIABP + WK + \epsilon\)
  
• \(6MW = SBC + \epsilon\)
  
• \(6MW = SBC + BMI + DIABP + \epsilon\)

## $`################ 6MW = SBC + BMI + Age + G  + P + SYSBP + DIABP + WK ####################`
## 
## Call:
## lm(formula = MWTD ~ SBC + BMI + Age + G + P + SYSBP + DIABP + 
##     WK, data = dfm)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -147.63  -44.81    4.12   44.28  124.23 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 646.4089    98.7077    6.55  1.5e-09 ***
## SBC           6.4224     0.9197    6.98  1.7e-10 ***
## BMI          -8.2740     1.0742   -7.70  4.2e-12 ***
## Age          -1.7942     0.6445   -2.78   0.0062 ** 
## GM           23.3427    11.8102    1.98   0.0504 .  
## P             0.0168     0.4724    0.04   0.9716    
## SYSBP        -1.3075     0.5787   -2.26   0.0257 *  
## DIABP         2.0543     0.8255    2.49   0.0142 *  
## WK            3.1044     2.2904    1.36   0.1778    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 60 on 120 degrees of freedom
## Multiple R-squared:  0.654,  Adjusted R-squared:  0.631 
## F-statistic: 28.4 on 8 and 120 DF,  p-value: <2e-16
## 
## 
## $`################6MW = SBC + BMI + Age + SYSBP + DIABP ################`
## 
## Call:
## lm(formula = MWTD ~ SBC + BMI + Age + SYSBP + DIABP, data = dfm)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -151.15  -42.10   -0.85   46.79  131.40 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  622.607     90.055    6.91  2.3e-10 ***
## SBC            7.129      0.854    8.35  1.2e-13 ***
## BMI           -8.307      1.076   -7.72  3.5e-12 ***
## Age           -1.848      0.646   -2.86   0.0050 ** 
## SYSBP         -1.091      0.555   -1.97   0.0515 .  
## DIABP          2.169      0.818    2.65   0.0091 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 60.6 on 123 degrees of freedom
## Multiple R-squared:  0.638,  Adjusted R-squared:  0.624 
## F-statistic: 43.4 on 5 and 123 DF,  p-value: <2e-16
## 
## 
## $`################ 6MW = SBC ################`
## 
## Call:
## lm(formula = MWTD ~ SBC, data = dfm)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -206.22  -46.93    0.78   60.36  225.95 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   212.17      27.66    7.67  3.9e-12 ***
## SBC             9.29       1.03    9.03  2.3e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 77.4 on 127 degrees of freedom
## Multiple R-squared:  0.391,  Adjusted R-squared:  0.386 
## F-statistic: 81.6 on 1 and 127 DF,  p-value: 2.3e-15

Prediction Error

	predict_err	unit	R_squared	coeff_slope_error_pval
SBC + BMI + Age + G + P + SYSBP + DIABP + WK	59.994	m	0.39120	7.12922513195007, -1.84777153741858, 0.853565507110138
SBC + BMI + Age + SYSBP + DIABP	60.603	m	0.65411	6.42237473843453, -1.79415351282887, 2.05432353766545
SBC	77.368	m	0.63822	9.29376062284116, 1.0287934540631, 2.30178689685541e-15

Summary

SBC Model: SBD is very significantly (< 0.001) associated with 6 min walk. On average 1 count translates to about 7.6 meters on min walk distance. The predictive error +- 77.4 m.

SBC FULL Model: Show strong association with SBC, BMI, AGE,and DiaBP. The predictability improves with BMI and AGE, and DiaBP. Interesting and expected is the effect of Age, BMI on the predictabilty of 6 min walk distance. The WK doesn’t play role, interestingly. SBD MIN Model: Show strong association with SBC, BMI, AGE,and DiaBP. The predictability improves with BMI and AGE, and DiaBP. Interesting and expected is the effect of Age, BMI on the predictabilty of 6 min walk distance.

Correlation Pearson Coefficient

\[\begin{aligned} \text{Pearson correlation}&\\ r &= \frac{\sum(x-\bar x)(y-\bar y)}{\sum(x-\bar x)^2 \sum(y-\bar y)^2} \\ \\ \text{t-test}&\\ &H0: r = 0 \\ &H1: r \neq 0 \\ \\ &t = \frac{r}{\sqrt{1-r^2}} \sqrt{n-2}\\ \\ &\text{if p-value < 0.05 we reject H0}&\\ \end{aligned}\]

Normal Distribution Test | Shapiro Wilk Test

\[\begin{aligned} &H0: \text{normally distributed}\\ &H1: \text{not normally distributed}\\ \end{aligned}\]

	p-values
SBC_W1	0.07347
SBC_W3	0.12332
SBC_W6	0.18625
MWTD_W1	0.35083
MWTD_W3	0.99487
MWTD_W6	0.98317

Result: All p-values are > 0.05, H0 can’t be rejected, this indicates that the data for both the 6-minute walk distance and the single breath count are normally distributed in our study population. Pearson correlation analysis becomes appropriate and reliable.

Linear Covariance Test

Visual inspection of the data normality using Q-Q plots (quantile-quantile plots).

Remark: The qq-plot shows are linear relationship between the theoretical normally distributed values and the data distribution.

Correlation week 1, 3, 6

	r
wk1	0.553
wk2	0.469
wk3	0.751

Strength of correlation:
Week 1: The correlation coefficient of 0.562 indicates a moderate positive correlation between the 6-minute walk distance and the single breath count during week 1.
Week 2: The correlation coefficient of 0.489 also indicates a moderate positive correlation between the variables during week 2.
Week 3: The correlation coefficient of 0.749 suggests a strong positive correlation between the variables during week 3.

Direction of correlation: Positive correlation coefficients, counts increase with distance of 6-minute walk.

Correlation Significance

	p.value
wk1	0.00012
wk2	0.00151
wk3	0.00000

Result: All p-values are < 0.05, which allows us to reject the H0, and conclude that the correlation is different from 0. The value of wk3 is 6.61341^{-9}

Actionability:

1. Is the SBC an alternative to 6min given specific conditions?
   
2. When could it be used, and would provide a value add in managing a patient’s recovery?

Next Steps

• Literature research: studying how 6min walk was established as a proxy for C02 uptake measurement.
  
• Start outlining paper
  
• List clinical decisions that are made based on 6min walk data. How likely does the error result in a wrong clinical decision?
  
• Bland-Altman Plot: A Bland-Altman plot is used to visualize the differences in measurements between two different instruments or two different measurement techniques. Used for determining how similar the two techniques are at measuring the same construct.

Work in Progress

##           s1      w1      s3      w3      s6     w6
## mean 23.1628 422.581 27.0233 461.419 28.0000 479.16
## sd    5.6859  94.449  6.6565  92.271  6.6797 102.87

The Bland-Altman shows the agreement between SBC and 6min walk. If they are measuring the same. That means, even if the pearson correlation is 0 you can still have high agreement.

Slopes

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