1 Checking dataset / cleaning procedures

The database was initially explored for consistency and coding information.

Três aspectos são fundamentais em qualquer conjunto de dados, que são: comunicabilidade dos nomes das variáveis, confiabilidade e consistência dos dados. A primeira refere-se à nomeação das variáveis, a segunda refere-se às garantias que o processo de coleta foi adequado e a terceira refere-se à condição de análise dos dados. Empiricamente, é possível verificar mais diretamente à consistência da base a partir de técnicas gráficas, tabulares e analíticas.

2 Mixed effects

A linear mixed model was computed to check the effect of the factors on the outcome. This model also included an interaction term (time x group) and included random intercepts for each participant.

Random intercept means that each participant was assigned a different intercept value. Therefore, the individual differences of the participants were accounted for in the model. The computational equation is:

\[acq_6 = group + time + (group \ x \ time) + (1 | participant)\]

The table below reports the results. Since the interaction term was significant (F(2, 87.675) = 5.89, p < 0.01), the main effect of time was not interpreted.

Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
group 0.15 0.15 1 52 0.44 0.511
time 5.73 2.87 2 89 8.20 0.001
group:time 4.12 2.06 2 89 5.90 0.004

To check the differences between all pairwise comparions, a post-hoc procedure was carried-out. It is widely know that risk of Type I errors will be increased by performing comparions. Thus, Bonferroni method was modeled to adjust the p-values derived from all comparisons.

Detailing the results, the interaction between “Treatment x Time” was explored to check the group differences over time and the time differences among the two groups. In the aerobic training group (AG), the ACQ6 score decreased significantly from 2.0 (1.6-2.3 95% confidence interval (CI)) at the baseline to 1.3 (0.9-1.6 95% CI) after the intervention and to 1.2 (0.8 to 1.5 95% CI) at 3 months of follow-up (P < 0.001 for both after the intervention and at 3 months of follow-up versus the baseline). In the breathing exercises group (BG), the ACQ6 score showed no significant change when comparing the baseline score of 1.7 (1.2 to 2.0 95% CI) to 1.5 after the intervention (1.0 to 1.8 95% CI; P = 0.71 vs. baseline)) and to 1.7 at 3 months of follow-up (1.3 to 2.1 95% CI; P =1.0 vs. baseline)).

time group emmean SE df lower.CL upper.CL
Baseline AG 2.0 0.17 89 1.65 2.3
Post-intervention AG 1.3 0.17 96 0.94 1.6
3-month follow-up AG 1.2 0.18 110 0.80 1.5
Baseline BG 1.7 0.18 89 1.31 2.0
Post-intervention BG 1.5 0.18 92 1.10 1.8
3-month follow-up BG 1.7 0.20 111 1.33 2.1
contrast group estimate SE df t.ratio p.value
Baseline - Post-intervention AG 0.69 0.16 88 4.26 0.00
Baseline - 3-month follow-up AG 0.81 0.18 90 4.61 0.00
Post-intervention - 3-month follow-up AG 0.12 0.18 88 0.67 1.00
Baseline - Post-intervention BG 0.21 0.17 86 1.22 0.68
Baseline - 3-month follow-up BG -0.06 0.19 89 -0.32 1.00
Post-intervention - 3-month follow-up BG -0.27 0.19 88 -1.41 0.49

Overall, the main difference between baseline and post-intervention (Δ = .448, p = 0.001), and between the baseline and the follow-up (3 months after) (Δ = .373, p = 0.014) were significant. The comparison between the post-intervention and the 3 months follow-up was not significant (Δ = - 0.075, p = 1).

time emmean SE df lower.CL upper.CL
Baseline 1.8 0.12 89 1.6 2.1
Post-intervention 1.4 0.12 94 1.1 1.6
3-month follow-up 1.4 0.14 110 1.2 1.7
contrast estimate SE df t.ratio p.value
Baseline - Post-intervention 0.45 0.12 87 3.82 0.00
Baseline - 3-month follow-up 0.37 0.13 90 2.91 0.01
Post-intervention - 3-month follow-up -0.07 0.13 88 -0.58 1.00
group time emmean SE df lower.CL upper.CL
AG Baseline 2.0 0.17 89 1.65 2.3
BG Baseline 1.7 0.18 89 1.31 2.0
AG Post-intervention 1.3 0.17 96 0.94 1.6
BG Post-intervention 1.5 0.18 92 1.10 1.8
AG 3-month follow-up 1.2 0.18 110 0.80 1.5
BG 3-month follow-up 1.7 0.20 111 1.33 2.1
contrast time estimate SE df t.ratio p.value
AG - BG Baseline 0.31 0.24 89 1.26 0.209
AG - BG Post-intervention -0.18 0.25 94 -0.71 0.481
AG - BG 3-month follow-up -0.56 0.27 110 -2.07 0.041

Fifty-eight percentage of participants from the AG and 28% of BG participants showed a clinically significant improvement in the ACQ6 score (≥0.5 points)

group mean(imp_acq6)
AG 0.59
BG 0.28
group mean(imp_acq6)
AG 0.38
BG 0.08

3 Asma day-free [GEE]

## Analysis of 'Wald statistic' Table
## Model: poisson, link: log
## Response: dias_sintomas
## Terms added sequentially (first to last)
## 
##                   Df    X2 P(>|Chi|)   
## grupo_15           1  0.15    0.6960   
## tempo_16           3 15.81    0.0012 **
## grupo_15:tempo_16  3  4.10    0.2509   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
term estimate std.error statistic p.value conf.low conf.high
(Intercept) 2.28 0.21 122.32 0.00 1.87 2.68
grupo_15 -0.25 0.31 0.63 0.43 -0.86 0.36
tempo_162meses 0.21 0.11 3.75 0.05 0.00 0.42
tempo_163meses 0.20 0.08 5.87 0.02 0.04 0.36
tempo_16PRE -0.44 0.18 5.77 0.02 -0.81 -0.08
grupo_15:tempo_162meses 0.05 0.19 0.07 0.80 -0.32 0.42
grupo_15:tempo_163meses 0.13 0.19 0.47 0.49 -0.24 0.51
grupo_15:tempo_16PRE 0.46 0.23 3.97 0.05 0.01 0.92

4 Activity

Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
group 0.28 0.28 1 50 0.43 0.51
time 10.45 5.23 2 88 8.01 0.00
group:time 4.48 2.24 2 88 3.44 0.04

5 Score total

Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
group 0.03 0.03 1 49 0.05 0.82
time 11.14 5.57 2 88 8.52 0.00
group:time 1.58 0.79 2 88 1.21 0.30
time group emmean SE df lower.CL upper.CL
Baseline AG 3.9 0.21 98 3.4 4.3
Post-intervention AG 4.6 0.21 98 4.2 5.1
3-month follow-up AG 4.6 0.24 115 4.2 5.1
Baseline BG 4.2 0.22 98 3.7 4.6
Post-intervention BG 4.4 0.22 100 4.0 4.9
3-month follow-up BG 4.7 0.24 115 4.2 5.2
contrast group estimate SE df t.ratio p.value
Baseline - Post-intervention AG -0.78 0.22 85 -3.46 0.00
Baseline - 3-month follow-up AG -0.79 0.25 89 -3.21 0.01
Post-intervention - 3-month follow-up AG -0.01 0.25 89 -0.05 1.00
Baseline - Post-intervention BG -0.27 0.23 86 -1.18 0.72
Baseline - 3-month follow-up BG -0.53 0.25 90 -2.09 0.12
Post-intervention - 3-month follow-up BG -0.25 0.25 89 -1.00 0.96

6 Shuttel Distance

Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
group_shuttle 4.1e-01 4.1e-01 1 52 0.0 0.99
time_shuttle 1.2e+05 1.2e+05 1 48 71.1 0.00
group_shuttle:time_shuttle 7.4e+03 7.4e+03 1 48 4.4 0.04

The results show the interaction effect was significant (F(1, 47.89) = 4.37, p = 0.042), and also the main effect of time (F(1, 47.98) = 59.02, p < 0.01). Group was not significant (F(1, 52.27) = 0.01, p = 0.98). For participants in the AG, the mean ISWT distance improved from baseline 342 (from 302 to 382 95% CI) to 429 meters (389 to 470 95% CI (P < 0.01, post hoc pairwised comparision after vs baseline). In the breathing exercise group (BG), from 360 to 412 (369 to 456 95% CI) after the intervention (P < 0.01, post hoc pairwised comparision after vs baseline).

The adjusted mean difference in the walking distance between the AG and the BG was 17.8 meters at the baseline and 17 after intervention.

time_shuttle group_shuttle emmean SE df lower.CL upper.CL
Baseline AG 342 20 59 302 382
Post-intervention AG 429 20 62 389 470
Baseline BG 360 22 59 317 403
Post-intervention BG 412 22 62 369 456
contrast group_shuttle estimate SE df t.ratio p.value
Baseline - Post-intervention AG -88 11 48 -7.7 0
Baseline - Post-intervention BG -53 12 48 -4.3 0
group_shuttle time_shuttle emmean SE df lower.CL upper.CL
AG Baseline 342 20 59 302 382
BG Baseline 360 22 59 317 403
AG Post-intervention 429 20 62 389 470
BG Post-intervention 412 22 62 369 456
contrast time_shuttle estimate SE df t.ratio p.value
AG - BG Baseline -18 29 59 -0.61 0.55
AG - BG Post-intervention 17 30 62 0.57 0.57

7 Hospital Anxiety and Depression Scale (HADS):

Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
group 1.0 1 1 52 0.18 0.67
time 28.9 14 2 81 2.57 0.08
group:time 7.9 4 2 81 0.70 0.50

There were no interactions nor difference between the groups in both domains (Table 2). Pairwise comparision over time revealed a significant decrease after intervention and follow up for both groups with regard to depression.

group time emmean SE df lower.CL upper.CL
AG Baseline 8.7 0.76 75 7.2 10.2
BG Baseline 8.6 0.83 75 6.9 10.2
AG Post-intervention 7.5 0.79 84 5.9 9.0
BG Post-intervention 7.7 0.85 80 6.0 9.4
AG 3-month follow-up 7.8 0.87 102 6.1 9.5
BG 3-month follow-up 9.0 0.93 98 7.2 10.8
contrast time estimate SE df t.ratio p.value
AG - BG Baseline 0.11 1.1 75 0.09 0.92
AG - BG Post-intervention -0.23 1.2 82 -0.20 0.84
AG - BG 3-month follow-up -1.18 1.3 100 -0.93 0.36
time group emmean SE df lower.CL upper.CL
Baseline AG 8.7 0.76 75 7.2 10.2
Post-intervention AG 7.5 0.79 84 5.9 9.0
3-month follow-up AG 7.8 0.87 102 6.1 9.5
Baseline BG 8.6 0.83 75 6.9 10.2
Post-intervention BG 7.7 0.85 80 6.0 9.4
3-month follow-up BG 9.0 0.93 98 7.2 10.8
contrast group estimate SE df t.ratio p.value
Baseline - Post-intervention AG 1.23 0.66 80 1.85 0.20
Baseline - 3-month follow-up AG 0.86 0.75 82 1.15 0.76
Post-intervention - 3-month follow-up AG -0.37 0.76 80 -0.49 1.00
Baseline - Post-intervention BG 0.89 0.71 79 1.26 0.64
Baseline - 3-month follow-up BG -0.42 0.80 81 -0.53 1.00
Post-intervention - 3-month follow-up BG -1.31 0.80 80 -1.64 0.32

Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
group 4.945 4.945 1 52 1.100 0.299
time 60.160 30.080 2 80 6.692 0.002
group:time 0.019 0.009 2 80 0.002 0.998
group time emmean SE df lower.CL upper.CL
AG Baseline 7.2 0.77 69 5.6 8.7
BG Baseline 8.2 0.84 69 6.6 9.9
AG Post-intervention 5.6 0.80 76 4.0 7.1
BG Post-intervention 6.7 0.86 73 5.0 8.4
AG 3-month follow-up 6.3 0.86 93 4.6 8.0
BG 3-month follow-up 7.4 0.92 89 5.6 9.2
contrast time estimate SE df t.ratio p.value
AG - BG Baseline -1.1 1.1 69 -0.94 0.35
AG - BG Post-intervention -1.1 1.2 74 -0.96 0.34
AG - BG 3-month follow-up -1.1 1.3 90 -0.89 0.37
time group emmean SE df lower.CL upper.CL
Baseline AG 7.2 0.77 69 5.6 8.7
Post-intervention AG 5.6 0.80 76 4.0 7.1
3-month follow-up AG 6.3 0.86 93 4.6 8.0
Baseline BG 8.2 0.84 69 6.6 9.9
Post-intervention BG 6.7 0.86 73 5.0 8.4
3-month follow-up BG 7.4 0.92 89 5.6 9.2
contrast group estimate SE df t.ratio p.value
Baseline - Post-intervention AG 1.62 0.59 80 2.7 0.02
Baseline - 3-month follow-up AG 0.89 0.67 81 1.3 0.57
Post-intervention - 3-month follow-up AG -0.72 0.68 79 -1.1 0.87
Baseline - Post-intervention BG 1.56 0.64 79 2.5 0.05
Baseline - 3-month follow-up BG 0.84 0.72 80 1.2 0.73
Post-intervention - 3-month follow-up BG -0.72 0.72 79 -1.0 0.96

8 Modeling data with imputate data

This study is being conceived with 53 participants and the following graph display the proportion of missing cases.

## # A tibble: 1 x 1
##   `sum(is.na(.))`
##             <int>
## 1               0

9 LMM with complete dataset (ater MI procedures)

9.1 ACQ6

9.1.1 LMM using complete dataset

Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
group 0.031 0.031 1 52 0.073 0.788
time 5.902 2.951 2 104 6.916 0.002
group:time 3.186 1.593 2 104 3.734 0.027

9.2 Symptoms

9.3 Total Score

9.3.1 LMM using complete dataset

Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
group 0.01 0.01 1 52 0.01 0.92
time 11.05 5.53 2 104 7.12 0.00
group:time 1.19 0.59 2 104 0.76 0.47

9.4 HADS

9.4.1 LMM using complete dataset

Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
group 0.07 0.07 1 52 0.01 0.93
time 51.33 25.67 2 104 3.05 0.05
group:time 13.78 6.89 2 104 0.82 0.44

9.4.2 LMM using complete dataset

Df X2 P(>|Chi|)
grupo_15 1 0.13 0.72
tempo_16 3 14.21 0.00
grupo_15:tempo_16 3 3.89 0.27
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
grupo_20 0.24 0.24 1 52 0.0 0.99
tempo_21 91985.79 91985.79 1 52 48.1 0.00
grupo_20:tempo_21 8234.79 8234.79 1 52 4.3 0.04

10 Lasts variables

Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
grupo1 2606574 2606574 1 52 0.32 0.58
tempo1 13817149 13817149 1 52 1.68 0.20
grupo1:tempo1 201 201 1 52 0.00 1.00
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
grupo 2807340 2807340 1 73 0.29 0.59
tempo 38637068 38637068 1 73 4.03 0.05
grupo:tempo 1743 1743 1 73 0.00 0.99

Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
grupo1 0.60 0.60 1 52 0.12 0.73
tempo1 2.05 2.05 1 52 0.40 0.53
grupo1:tempo1 0.95 0.95 1 52 0.18 0.67
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
grupo 0.03 0.03 1 43 0.01 0.92
tempo 18.05 18.05 1 38 5.32 0.03
grupo:tempo 10.58 10.58 1 37 3.12 0.09