Table of content

1 Descriptive analysis of the participants

1.1 Overview

targets::tar_read(analysis_INCLUSION)

1.2 Sex (1 = men; 2 = women)

targets::tar_read(analysis_sex)

1.3 Age

targets::tar_read(analysis_age)

1.4 Height

targets::tar_read(analysis_height)

1.5 Weight

targets::tar_read(analysis_weight)

1.6 Body mass index

targets::tar_read(analysis_bmi)

1.7 Angioplasty (0 = no angioplasty; 1 = with angioplasty)

targets::tar_read(analysis_angioplasty)[, c(1:2)]

1.8 Bypass (0 = no bypass; 1 = with bypass)

targets::tar_read(analysis_bypass)[, c(1:2)]

2 Change in 6MWT distance between 0 and 12 months

2.1 Descriptive statistics

targets::tar_read(DB_6MWT_0_12) |> 
  dplyr::select(-n_visits) |>   
  dplyr::group_by(MONTH) |> 
  skimr::skim()

Data summary
Name	dplyr::group_by(�)
Number of rows	150
Number of columns	3
_______________________
Column type frequency:
factor	1
numeric	1
________________________
Group variables	MONTH

Variable type: factor

skim_variable	MONTH	n_missing	complete_rate	ordered	n_unique	top_counts
patient	0	0	1	FALSE	75	1: 1, 2: 1, 3: 1, 4: 1
patient	12	0	1	FALSE	75	1: 1, 2: 1, 3: 1, 4: 1

Variable type: numeric

skim_variable	MONTH	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
DIST_M	0	0	1	605.44	71.96	411	559	603	636	816	?????
DIST_M	12	0	1	618.00	81.49	400	574	622	652	880	?????

2.2 T-test

targets::tar_read(t_test_results_6MWT)

## 
##  Paired t-test
## 
## data:  DIST_M by MONTH
## t = 2.8614, df = 74, p-value = 0.005481
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##   3.813784 21.306216
## sample estimates:
## mean difference 
##           12.56

2.3 Pearson correlation

# Rearrange data
data_6MWT <- 
  targets::tar_read(DB_6MWT_0_12) |> 
  tidyr::pivot_wider(names_from = MONTH, values_from = DIST_M)

# Compute Pearson correlation
cor.test(data_6MWT$`0`, data_6MWT$`12`)

## 
##  Pearson's product-moment correlation
## 
## data:  data_6MWT$`0` and data_6MWT$`12`
## t = 16.202, df = 73, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.8227583 0.9256709
## sample estimates:
##       cor 
## 0.8845449

2.4 Effect size (dav)

mean_diff <- mean(data_6MWT$`12` - data_6MWT$`0`)
sd1 <- sd(data_6MWT$`0`)
sd2 <- sd(data_6MWT$`12`)
dav <- mean_diff / sqrt(((sd1^2 + sd2^2) / 2))
round(dav, 2)

## [1] 0.16

2.5 Estimate of the median of the individual changes

tar_read(change_6MWT)$hd_pbci_diff |> 
  dplyr::filter(q == 0.5)  |> 
  dplyr::mutate(dplyr::across(estimate:ci_u, ~round(.x, digits = 2)))

2.6 Shift and difference asymmetry functions

targets::tar_read(change_6MWT)$p

Change in 6-min walking test (6MWT) distance between 0 and 12 months (N = 75). On panel A, the errors bars over the points are the standard deviations around the means, while on panel D it is the percentile bootstrap 95% confidence interval around the median estimate. On panels E and F, the error bars are percentile bootstrap 95% confidence intervals not corrected for multiple comparisons. On panels B, C and D, the horizontal and/or vertical segments are the estimates of the deciles (panels B and C) or the quantiles (panel D, step of 0.05) of the distributions; the thickest segments are the median estimates. On panel B, the diagonal black line depicts the identity line. If any, significant results (based on adjusted p-values) in the shift (panel E) and difference asymmetry (panel F) functions are highlighted using thick red circles. A small pseudo-random movement has been added horizontally and vertically to the raw data displayed on panel B to minimize the presence of points fully overlapped. The estimates of the deciles of the marginal distributions (panels B, C and D), the quantiles of the individual differences (panel D), the decile differences (panel E) and the quantile sums (panel F) have been computed using the Harrell-Davis estimator.

3 Change in IPAQ-SF MET-min/week between 6 and 12 months

3.1 Descriptive statistics

targets::tar_read(DB_IPAQ_6_12) |>
  dplyr::select(-n_visits) |>  
  dplyr::group_by(MONTH) |> 
  skimr::skim()

Data summary
Name	dplyr::group_by(�)
Number of rows	154
Number of columns	3
_______________________
Column type frequency:
factor	1
numeric	1
________________________
Group variables	MONTH

Variable type: factor

skim_variable	MONTH	n_missing	complete_rate	ordered	n_unique	top_counts
patient	6	0	1	FALSE	77	1: 1, 2: 1, 3: 1, 4: 1
patient	12	0	1	FALSE	77	1: 1, 2: 1, 3: 1, 4: 1

Variable type: numeric

skim_variable	MONTH	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
MET_MIN_WK	6	0	1	3999.91	3588.04	0	1680	3318	4914	20040	?????
MET_MIN_WK	12	0	1	4192.22	4722.84	0	1551	2796	5502	23106	?????

3.2 Estimate of the median of the individual changes

tar_read(change_IPAQ_6_12)$hd_pbci_diff |> 
  dplyr::filter(q == 0.5) |> 
  dplyr::mutate(dplyr::across(estimate:ci_u, ~round(.x, digits = 2)))

3.3 Shift and difference asymmetry functions

targets::tar_read(change_IPAQ_6_12)$p

Change in IPAQ-SF MET-min/week between 6 and 12 months (N = 77). On panel A, the errors bars over the points are the standard deviations around the means, while on panel D it is the percentile bootstrap 95% confidence interval around the median estimate. On panels E and F, the error bars are percentile bootstrap 95% confidence intervals not corrected for multiple comparisons. On panels B, C and D, the horizontal and/or vertical segments are the estimates of the deciles (panels B and C) or the quantiles (panel D, step of 0.05) of the distributions; the thickest segments are the median estimates. On panel B, the diagonal black line depicts the identity line. If any, significant results (based on adjusted p-values) in the shift (panel E) and difference asymmetry (panel F) functions are highlighted using thick red circles. A small pseudo-random movement has been added horizontally and vertically to the raw data displayed on panel B to minimize the presence of points fully overlapped. The estimates of the deciles of the marginal distributions (panels B, C and D), the quantiles of the individual differences (panel D), the decile differences (panel E) and the quantile sums (panel F) have been computed using the Harrell-Davis estimator.

4 Change in EMAPS scores between 0 and 12 months

4.1 Descriptive statistics

targets::tar_read(DB_EMAPS_0_12) |> 
  dplyr::select(-n_visits) |>  
  dplyr::group_by(MONTH) |> 
  skimr::skim()

Data summary
Name	dplyr::group_by(�)
Number of rows	152
Number of columns	8
_______________________
Column type frequency:
factor	1
numeric	6
________________________
Group variables	MONTH

Variable type: factor

skim_variable	MONTH	n_missing	complete_rate	ordered	n_unique	top_counts
patient	0	0	1	FALSE	76	1: 1, 2: 1, 3: 1, 4: 1
patient	12	0	1	FALSE	76	1: 1, 2: 1, 3: 1, 4: 1

Variable type: numeric

skim_variable	MONTH	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
INTRINSIC	0	1	5.61	0.87	3.00	5.00	5.67	6.00	7.00	?????
INTRINSIC	12	1	5.60	1.29	2.00	5.25	6.00	6.33	7.00	?????
INTEGRATED	0	1	4.95	1.46	1.33	4.00	5.33	6.00	7.00	?????
INTEGRATED	12	1	5.24	1.58	1.00	4.58	5.67	6.33	7.00	?????
IDENTIFIED	0	1	6.02	0.76	3.67	5.67	6.00	6.67	7.00	?????
IDENTIFIED	12	1	6.00	1.09	2.33	5.67	6.33	6.75	7.00	?????
INTROJECTED	0	1	4.39	1.24	2.00	3.58	4.17	5.33	7.00	?????
INTROJECTED	12	1	4.67	1.54	1.00	3.33	5.00	5.75	7.00	?????
EXTERNAL	0	1	1.49	0.77	1.00	1.00	1.00	1.67	5.33	?????
EXTERNAL	12	1	1.34	0.66	1.00	1.00	1.00	1.33	3.67	?????
AMOTIVATION	0	1	1.48	1.00	1.00	1.00	1.00	1.33	6.00	?????
AMOTIVATION	12	1	1.17	0.55	1.00	1.00	1.00	1.00	4.00	?????

4.2 Estimates of the medians of the individual changes

targets::tar_load(change_EMAPS)
res <-
  purrr::map(change_EMAPS, function(x) {
  
  knitr::knit_child(text = c(
                    
                    "\n",
                    "### `r x$variable`",
                    "\n",
                    "```{r, echo = FALSE}",
                    "x$hd_pbci_diff |>  
                     dplyr::filter(q == 0.5) |> 
                     dplyr::mutate(dplyr::across(estimate:ci_u, ~round(.x, digits = 2)))",
                    "```"
  ),
  envir = environment(),
  quiet  = TRUE
  )
})

cat(unlist(res), sep = "\n")

4.2.1 Intrinsic motivation score

4.2.2 Integrated regulation score

4.2.3 Identified regulation score

4.2.4 Introjected regulation score

4.2.5 External regulation score

4.2.6 Amotivation score

5 Change in the motivational profile for physical activity

5.1 Assess cluster tendency

5.1.1 Graphically inspect data using principal component analysis

targets::tar_read(p_pca)

5.1.2 Confirm cluser tendency using graphical method

targets::tar_read(cluster_tendency)

Red: high similarity (ie: low dissimilarity) | Blue: low similarity

5.1.3 Confirm cluser tendency using the Hopkins statistic

5.1.3.1 Hopkins statistic for the dataset at month 0

h_vec <- vector("double", 100)
set.seed(123)
seeds <- round(sample(rnorm(10000, 1000, 500), 100), 0)
for (i in 1:100) {
  set.seed(seeds[i])
  h_vec[i] <- hopkins(DB_EMAPS_0_12_M0_scaled)
}
mean(h_vec)

## [1] 0.9053554

Comment: Data seem clustered (Hopkins statistic >0.7).

5.1.3.2 Hopkins statistic for the dataset at month 12

h_vec <- vector("double", 100)
set.seed(123)
seeds <- round(sample(rnorm(10000, 1000, 500), 100), 0)
for (i in 1:100) {
  set.seed(seeds[i])
  h_vec[i] <- hopkins(DB_EMAPS_0_12_M12_scaled)
  
}
mean(h_vec)

## [1] 0.8935322

Comment: Data seem clustered (Hopkins statistic >0.7).

5.2 Check outliers related to a multivariate analysis

5.2.1 Month 0

check_outliers(DB_EMAPS_0_12_M0_scaled, method = "mcd")

## 18 outliers detected: cases 4, 12, 13, 17, 20, 32, 41, 44, 53, 56, 60,
##   61, 64, 65, 67, 71, 75, 76.
## - Based on the following method and threshold: mcd (22.458).
## - For variables: INTRINSIC, INTEGRATED, IDENTIFIED, INTROJECTED,
##   EXTERNAL, AMOTIVATION.

5.2.2 Month 12

check_outliers(DB_EMAPS_0_12_M12_scaled[, c(names(DB_EMAPS_0_12_M12_scaled)[1:5])], method = "mcd")

## 20 outliers detected: cases 5, 13, 15, 16, 17, 19, 20, 21, 23, 27, 30,
##   31, 40, 48, 50, 55, 58, 61, 70, 74.
## - Based on the following method and threshold: mcd (20.515).
## - For variables: INTRINSIC, INTEGRATED, IDENTIFIED, INTROJECTED,
##   EXTERNAL.

Comment: We removed AMOTIVATION variable that caused an error due to an IQR of 0.

5.3 Determine the optimal number of clusters related to a K-Medoid approach using the silhouette method

targets::tar_read(optim_n_clusters)

Comment: The optimal number of clusters related to the K-Medoid approach is 2 at both 0 and 12 months post-program (according to the silhouette method).

5.4 Visualize the final clusters from K-Medoid approach

targets::tar_read(final_clusters_emaps_viz)

5.5 Visualize the descriptive statistics of the EMAPS scores related to the motivational profiles

targets::tar_read(p_emaps_clust)

AU = Autonomous; IR = Introjected regulation.

targets::tar_read(table_stats_clusters_emaps)

5.6 Compare the motivational profiles

5.6.1 Comparison at Month 0

5.6.1.1 Global analysis

targets::tar_read(nonpartest_global_month0)

## $results
##                                                   Test Statistic   df1      df2
## ANOVA type test p-value                                   39.282 4.316 310.9785
## McKeon approx. for the Lawley Hotelling Test                  NA    NA       NA
## Muller approx. for the Bartlett-Nanda-Pillai Test             NA    NA       NA
## Wilks Lambda                                                  NA    NA       NA
##                                                   P-value
## ANOVA type test p-value                                 0
## McKeon approx. for the Lawley Hotelling Test           NA
## Muller approx. for the Bartlett-Nanda-Pillai Test      NA
## Wilks Lambda                                           NA
##                                                   Permutation Test p-value
## ANOVA type test p-value                                                  0
## McKeon approx. for the Lawley Hotelling Test                            NA
## Muller approx. for the Bartlett-Nanda-Pillai Test                       NA
## Wilks Lambda                                                            NA
## 
## $twogroupreleffects
##                      INTRINSIC INTEGRATED IDENTIFIED INTROJECTED EXTERNAL
## High AU-Mod IR         0.11257    0.08062    0.09233     0.12713  0.52522
## Very High AU-High IR   0.88743    0.91938    0.90767     0.87287  0.47478
##                      AMOTIVATION
## High AU-Mod IR           0.52983
## Very High AU-High IR     0.47017

5.6.1.2 Localisation of the difference(s)

ssnonpartest(INTRINSIC | INTEGRATED | IDENTIFIED | INTROJECTED | EXTERNAL | AMOTIVATION ~ cluster, data = tar_read(DB_EMAPS_0_12_clust) |> filter(MONTH == "0"), test = c(1, 0, 0, 0), alpha = 0.05, factors.and.variables = TRUE)

## 
## The ANOVA type statistic will be used in the following test 
## The Global Hypothesis is significant, subset algorithm will continue 
## 
## ~Performing the Subset Algorithm based on Factor levels~
## The Hypothesis of equality between factor levels  High AU-Mod IR Very High AU-High IR is rejected 
## All appropriate subsets using factor levels have been checked using a closed multiple testing procedure, which controls the maximum overall type I error rate at alpha= 0.05 
## 
## ~Performing the Subset Algorithm based on Response Variables~ 
##  The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED INTROJECTED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED INTROJECTED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED INTROJECTED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED INTROJECTED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED INTROJECTED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED INTROJECTED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED INTROJECTED EXTERNAL AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTEGRATED INTROJECTED EXTERNAL AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED EXTERNAL AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED INTROJECTED AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED INTROJECTED EXTERNAL is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTROJECTED EXTERNAL AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED EXTERNAL AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED INTROJECTED AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED INTROJECTED EXTERNAL is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED EXTERNAL AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED INTROJECTED AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED INTROJECTED EXTERNAL is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED EXTERNAL is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED INTROJECTED is rejected  
## The Hypothesis of equality using response variables  INTROJECTED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED INTROJECTED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED INTROJECTED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTEGRATED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTEGRATED INTROJECTED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTEGRATED INTROJECTED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED INTROJECTED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTROJECTED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTROJECTED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED INTROJECTED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED INTROJECTED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED is rejected 
## The Hypothesis of equality using response variables  INTROJECTED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTROJECTED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED INTROJECTED is rejected 
## The Hypothesis of equality using response variables  INTEGRATED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTEGRATED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTEGRATED INTROJECTED is rejected 
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTROJECTED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED is rejected 
## The Hypothesis of equality using response variables  INTROJECTED is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED is rejected 
## The Hypothesis of equality using response variables  INTEGRATED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC is rejected 
## All appropriate subsets using response variables have been checked using a multiple testing procedure, which controls the maximum overall type I error rate at alpha= 0.05

5.6.2 Comparison at Month 12

5.6.2.1 Global analysis

targets::tar_read(nonpartest_global_month12)

## $results
##                                                   Test Statistic   df1      df2
## ANOVA type test p-value                                   52.305 4.353 298.6204
## McKeon approx. for the Lawley Hotelling Test              32.769 6.000  69.0000
## Muller approx. for the Bartlett-Nanda-Pillai Test         32.337 6.074  68.9316
## Wilks Lambda                                              32.769 6.000  69.0000
##                                                   P-value
## ANOVA type test p-value                                 0
## McKeon approx. for the Lawley Hotelling Test            0
## Muller approx. for the Bartlett-Nanda-Pillai Test       0
## Wilks Lambda                                            0
##                                                   Permutation Test p-value
## ANOVA type test p-value                                                  0
## McKeon approx. for the Lawley Hotelling Test                             0
## Muller approx. for the Bartlett-Nanda-Pillai Test                        0
## Wilks Lambda                                                             0
## 
## $twogroupreleffects
##                      INTRINSIC INTEGRATED IDENTIFIED INTROJECTED EXTERNAL
## High AU-Mod IR         0.08445    0.06436     0.0997     0.07776  0.59561
## Very High AU-High IR   0.91555    0.93564     0.9003     0.92224  0.40439
##                      AMOTIVATION
## High AU-Mod IR           0.66666
## Very High AU-High IR     0.33334

5.6.2.2 Localisation of the difference(s)

ssnonpartest(INTRINSIC | INTEGRATED | IDENTIFIED | INTROJECTED | EXTERNAL | AMOTIVATION ~ cluster, data = tar_read(DB_EMAPS_0_12_clust) |> filter(MONTH == "12"), test = c(1, 0, 0, 0), alpha = 0.05, factors.and.variables = TRUE)

## 
## The ANOVA type statistic will be used in the following test 
## The Global Hypothesis is significant, subset algorithm will continue 
## 
## ~Performing the Subset Algorithm based on Factor levels~
## The Hypothesis of equality between factor levels  High AU-Mod IR Very High AU-High IR is rejected 
## All appropriate subsets using factor levels have been checked using a closed multiple testing procedure, which controls the maximum overall type I error rate at alpha= 0.05 
## 
## ~Performing the Subset Algorithm based on Response Variables~ 
##  The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED INTROJECTED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED INTROJECTED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED INTROJECTED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED INTROJECTED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED INTROJECTED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED INTROJECTED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED INTROJECTED EXTERNAL AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTEGRATED INTROJECTED EXTERNAL AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED EXTERNAL AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED INTROJECTED AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED INTROJECTED EXTERNAL is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTROJECTED EXTERNAL AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED EXTERNAL AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED INTROJECTED AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED INTROJECTED EXTERNAL is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED EXTERNAL AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED INTROJECTED AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED INTROJECTED EXTERNAL is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED AMOTIVATION is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED EXTERNAL is rejected  
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED INTROJECTED is rejected  
## The Hypothesis of equality using response variables  INTROJECTED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED INTROJECTED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED INTROJECTED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTEGRATED EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTEGRATED INTROJECTED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTEGRATED INTROJECTED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED INTROJECTED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC EXTERNAL AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTROJECTED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTROJECTED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED INTROJECTED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED INTROJECTED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED IDENTIFIED is rejected 
## The Hypothesis of equality using response variables  INTROJECTED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTROJECTED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED INTROJECTED is rejected 
## The Hypothesis of equality using response variables  INTEGRATED AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTEGRATED EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTEGRATED INTROJECTED is rejected 
## The Hypothesis of equality using response variables  INTEGRATED IDENTIFIED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC AMOTIVATION is rejected 
## The Hypothesis of equality using response variables  INTRINSIC EXTERNAL is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTROJECTED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC IDENTIFIED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC INTEGRATED is rejected 
## The Hypothesis of equality using response variables  INTROJECTED is rejected 
## The Hypothesis of equality using response variables  IDENTIFIED is rejected 
## The Hypothesis of equality using response variables  INTEGRATED is rejected 
## The Hypothesis of equality using response variables  INTRINSIC is rejected 
## All appropriate subsets using response variables have been checked using a multiple testing procedure, which controls the maximum overall type I error rate at alpha= 0.05

5.7 Characterize the change in the motivational profile

5.7.1 Visualize the change in the motivational profile

targets::tar_read(p_change_emaps_profile_alluvial)

5.7.2 Compute the proportions of patients per profile transition scenario

tar_read(prop_trans_prof_motiv)

6 Barriers to physical activity at 12 months

targets::tar_read(p_BARRIERS)

Barriers to physical activity (N = 77). Answers have been translated from French to English for the reader�s understanding of the figure. The most frequently evocated barriers have been highlighted with darker colours.

7 Predict 6WT distance trajectory using latent class mixed modelling

7.1 Build the models

# Load the model summarises
tar_load(model_6MWT_n1)
tar_load(model_6MWT_n2)
tar_load(model_6MWT_n3)
tar_load(model_6MWT_n4)
tar_load(model_6MWT_n5)

7.1.1 1-class model

summary(model_6MWT_n1)

## Heterogenous linear mixed model 
##      fitted by maximum likelihood method 
##  
## hlme(fixed = DIST_6MWT ~ MONTH, random = ~1, subject = "patient", 
##     ng = 1, data = DB_PRED_6MWT_0_12, var.time = "MONTH")
##  
## Statistical Model: 
##      Dataset: DB_PRED_6MWT_0_12 
##      Number of subjects: 75 
##      Number of observations: 150 
##      Number of latent classes: 1 
##      Number of parameters: 4  
##  
## Iteration process: 
##      Convergence criteria satisfied 
##      Number of iterations:  19 
##      Convergence criteria: parameters= 4.7e-10 
##                          : likelihood= 2.6e-12 
##                          : second derivatives= 1.1e-18 
##  
## Goodness-of-fit statistics: 
##      maximum log-likelihood: -807.98  
##      AIC: 1623.96  
##      BIC: 1633.23  
##  
##  
## Maximum Likelihood Estimates: 
##  
## Fixed effects in the longitudinal model:
## 
##                 coef      Se     Wald p-value
## intercept  605.44000 8.81756   68.663 0.00000
## MONTH        1.04667 0.36334    2.881 0.00397
## 
## 
## Variance-covariance matrix of the random-effects:
##           intercept
## intercept  5118.307
## 
##                                coef      Se
## Residual standard error:   26.70012 2.18060

7.1.2 2-class model

summary(model_6MWT_n2)

## Heterogenous linear mixed model 
##      fitted by maximum likelihood method 
##  
## hlme(fixed = DIST_6MWT ~ MONTH, mixture = ~MONTH, random = ~1, 
##     subject = "patient", ng = 2, data = DB_PRED_6MWT_0_12, var.time = "MONTH")
##  
## Statistical Model: 
##      Dataset: DB_PRED_6MWT_0_12 
##      Number of subjects: 75 
##      Number of observations: 150 
##      Number of latent classes: 2 
##      Number of parameters: 7  
##  
## Iteration process: 
##      Convergence criteria satisfied 
##      Number of iterations:  1 
##      Convergence criteria: parameters= 1e-10 
##                          : likelihood= 3.4e-13 
##                          : second derivatives= 3e-14 
##  
## Goodness-of-fit statistics: 
##      maximum log-likelihood: -804.75  
##      AIC: 1623.5  
##      BIC: 1639.72  
##  
##  
## Maximum Likelihood Estimates: 
##  
## Fixed effects in the class-membership model:
## (the class of reference is the last class) 
## 
##                        coef       Se     Wald p-value
## intercept class1    0.92959  0.78224    1.188 0.23469
## 
## Fixed effects in the longitudinal model:
## 
##                        coef       Se     Wald p-value
## intercept class1  618.45200 10.92629   56.602 0.00000
## intercept class2  572.47456 24.12087   23.734 0.00000
## MONTH class1        2.19493  0.64589    3.398 0.00068
## MONTH class2       -1.86242  1.09135   -1.707 0.08791
## 
## 
## Variance-covariance matrix of the random-effects:
##           intercept
## intercept  4235.124
## 
##                                coef       Se
## Residual standard error:   21.73450  2.55354

7.1.3 3-class model

summary(model_6MWT_n3)

## Heterogenous linear mixed model 
##      fitted by maximum likelihood method 
##  
## hlme(fixed = DIST_6MWT ~ MONTH, mixture = ~MONTH, random = ~1, 
##     subject = "patient", ng = 3, data = DB_PRED_6MWT_0_12, var.time = "MONTH")
##  
## Statistical Model: 
##      Dataset: DB_PRED_6MWT_0_12 
##      Number of subjects: 75 
##      Number of observations: 150 
##      Number of latent classes: 3 
##      Number of parameters: 10  
##  
## Iteration process: 
##      Convergence criteria satisfied 
##      Number of iterations:  1 
##      Convergence criteria: parameters= 9.8e-11 
##                          : likelihood= 2.3e-13 
##                          : second derivatives= 9.1e-15 
##  
## Goodness-of-fit statistics: 
##      maximum log-likelihood: -799.71  
##      AIC: 1619.42  
##      BIC: 1642.6  
##  
##  
## Maximum Likelihood Estimates: 
##  
## Fixed effects in the class-membership model:
## (the class of reference is the last class) 
## 
##                        coef       Se     Wald p-value
## intercept class1    2.93787  0.74700    3.933 0.00008
## intercept class2    2.81747  0.75951    3.710 0.00021
## 
## Fixed effects in the longitudinal model:
## 
##                        coef       Se     Wald p-value
## intercept class1  588.73829 12.39353   47.504 0.00000
## intercept class2  617.86859 12.67690   48.740 0.00000
## intercept class3  712.71000 52.53194   13.567 0.00000
## MONTH class1       -0.70141  0.44815   -1.565 0.11756
## MONTH class2        3.56567  0.51972    6.861 0.00000
## MONTH class3       -8.11139  1.32606   -6.117 0.00000
## 
## 
## Variance-covariance matrix of the random-effects:
##           intercept
## intercept   4559.21
## 
##                                coef       Se
## Residual standard error:   15.02270  1.81554

7.1.4 4-class model

summary(model_6MWT_n4)

## Heterogenous linear mixed model 
##      fitted by maximum likelihood method 
##  
## hlme(fixed = DIST_6MWT ~ MONTH, mixture = ~MONTH, random = ~1, 
##     subject = "patient", ng = 4, data = DB_PRED_6MWT_0_12, var.time = "MONTH")
##  
## Statistical Model: 
##      Dataset: DB_PRED_6MWT_0_12 
##      Number of subjects: 75 
##      Number of observations: 150 
##      Number of latent classes: 4 
##      Number of parameters: 13  
##  
## Iteration process: 
##      Convergence criteria satisfied 
##      Number of iterations:  1 
##      Convergence criteria: parameters= 1e-10 
##                          : likelihood= 1.1e-13 
##                          : second derivatives= 2e-14 
##  
## Goodness-of-fit statistics: 
##      maximum log-likelihood: -795.67  
##      AIC: 1617.34  
##      BIC: 1647.47  
##  
##  
## Maximum Likelihood Estimates: 
##  
## Fixed effects in the class-membership model:
## (the class of reference is the last class) 
## 
##                        coef       Se     Wald p-value
## intercept class1    1.67944  0.85377    1.967 0.04917
## intercept class2    1.32031  0.85122    1.551 0.12088
## intercept class3    3.27207  0.73008    4.482 0.00001
## 
## Fixed effects in the longitudinal model:
## 
##                        coef       Se     Wald p-value
## intercept class1  517.47416 21.95123   23.574 0.00000
## intercept class2  736.76149 24.08361   30.592 0.00000
## intercept class3  600.46864  7.75010   77.479 0.00000
## intercept class4  716.48954 32.14137   22.292 0.00000
## MONTH class1       -1.94655  0.81868   -2.378 0.01742
## MONTH class2        2.00029  1.02097    1.959 0.05009
## MONTH class3        1.86415  0.41295    4.514 0.00001
## MONTH class4       -8.02674  1.85553   -4.326 0.00002
## 
## 
## Variance-covariance matrix of the random-effects:
##           intercept
## intercept  1602.019
## 
##                                coef       Se
## Residual standard error:   20.34771  1.89292

7.1.5 5-class model

summary(model_6MWT_n5)

## Heterogenous linear mixed model 
##      fitted by maximum likelihood method 
##  
## hlme(fixed = DIST_6MWT ~ MONTH, mixture = ~MONTH, random = ~1, 
##     subject = "patient", ng = 5, data = DB_PRED_6MWT_0_12, var.time = "MONTH")
##  
## Statistical Model: 
##      Dataset: DB_PRED_6MWT_0_12 
##      Number of subjects: 75 
##      Number of observations: 150 
##      Number of latent classes: 5 
##      Number of parameters: 16  
##  
## Iteration process: 
##      Convergence criteria satisfied 
##      Number of iterations:  1 
##      Convergence criteria: parameters= 1.9e-05 
##                          : likelihood= 2.3e-08 
##                          : second derivatives= 1.1e-10 
##  
## Goodness-of-fit statistics: 
##      maximum log-likelihood: -793.24  
##      AIC: 1618.48  
##      BIC: 1655.56  
##  
##  
## Maximum Likelihood Estimates: 
##  
## Fixed effects in the class-membership model:
## (the class of reference is the last class) 
## 
##                        coef       Se     Wald p-value
## intercept class1    1.47921  0.64617    2.289 0.02207
## intercept class2    1.16064  0.72325    1.605 0.10855
## intercept class3   -1.34808  0.90409   -1.491 0.13594
## intercept class4   -0.18085  0.73602   -0.246 0.80590
## 
## Fixed effects in the longitudinal model:
## 
##                        coef       Se     Wald p-value
## intercept class1  596.44041 10.53783   56.600 0.00000
## intercept class2  603.49269 11.01307   54.798 0.00000
## intercept class3  716.99703 31.31971   22.893 0.00000
## intercept class4  748.60884 23.42899   31.952 0.00000
## intercept class5  502.70072 25.53577   19.686 0.00000
## MONTH class1        0.17891  0.59780    0.299 0.76473
## MONTH class2        3.90563  0.71218    5.484 0.00000
## MONTH class3       -8.16887  1.34904   -6.055 0.00000
## MONTH class4        1.53208  0.92494    1.656 0.09764
## MONTH class5       -2.28154  0.78589   -2.903 0.00369
## 
## 
## Variance-covariance matrix of the random-effects:
##           intercept
## intercept  1702.061
## 
##                                coef       Se
## Residual standard error:   15.68832  1.95686

7.2 Compare the models

7.2.1 Analyse the metrics of the models

tar_read(compa_latent_mixed_models_table_6MWT)

##                    AIC      BIC   entropy   %class1   %class2   %class3
## model_6MWT_n1 1623.961 1633.230 1.0000000 100.00000        NA        NA
## model_6MWT_n2 1623.495 1639.718 0.5212070  74.66667 25.333333        NA
## model_6MWT_n3 1619.422 1642.597 0.7691509  52.00000 45.333333  2.666667
## model_6MWT_n4 1617.344 1647.471 0.8647545  13.33333  9.333333 74.666667
## model_6MWT_n5 1618.482 1655.562 0.7620378  48.00000 30.666667  2.666667
##                %class4  %class5
## model_6MWT_n1       NA       NA
## model_6MWT_n2       NA       NA
## model_6MWT_n3       NA       NA
## model_6MWT_n4 2.666667       NA
## model_6MWT_n5 8.000000 10.66667

lcmm::summaryplot(
  model_6MWT_n1,
  model_6MWT_n2,
  model_6MWT_n3,
  model_6MWT_n4,
  model_6MWT_n5,
  which = c("AIC", "BIC", "entropy")
)

7.2.2 Posterior classification of the models

7.2.2.1 2-class model

lcmm::postprob(model_6MWT_n2)

##  
## Posterior classification: 
##   class1 class2
## N  56.00  19.00
## %  74.67  25.33
##  
## Posterior classification table: 
##      --> mean of posterior probabilities in each class 
##         prob1  prob2
## class1 0.8855 0.1145
## class2 0.2202 0.7798
##  
## Posterior probabilities above a threshold (%): 
##          class1 class2
## prob>0.7  92.86  68.42
## prob>0.8  76.79  42.11
## prob>0.9  60.71  26.32
##

7.2.2.2 3-class model

lcmm::postprob(model_6MWT_n3)

##  
## Posterior classification: 
##   class1 class2 class3
## N     39  34.00   2.00
## %     52  45.33   2.67
##  
## Posterior classification table: 
##      --> mean of posterior probabilities in each class 
##         prob1  prob2  prob3
## class1 0.8895 0.1089 0.0016
## class2 0.1166 0.8834 0.0000
## class3 0.0064 0.0000 0.9936
##  
## Posterior probabilities above a threshold (%): 
##          class1 class2 class3
## prob>0.7  84.62  85.29    100
## prob>0.8  76.92  79.41    100
## prob>0.9  66.67  61.76    100
##

7.2.2.3 4-class model

lcmm::postprob(model_6MWT_n4)

##  
## Posterior classification: 
##   class1 class2 class3 class4
## N  10.00   7.00  56.00   2.00
## %  13.33   9.33  74.67   2.67
##  
## Posterior classification table: 
##      --> mean of posterior probabilities in each class 
##         prob1  prob2  prob3  prob4
## class1 0.8703 0.0000 0.1296 0.0001
## class2 0.0000 0.9190 0.0776 0.0034
## class3 0.0415 0.0226 0.9352 0.0007
## class4 0.0002 0.0009 0.0033 0.9957
##  
## Posterior probabilities above a threshold (%): 
##          class1 class2 class3 class4
## prob>0.7     80  85.71  94.64    100
## prob>0.8     80  85.71  87.50    100
## prob>0.9     50  71.43  82.14    100
##

7.2.2.4 5-class model

lcmm::postprob(model_6MWT_n5)

##  
## Posterior classification: 
##   class1 class2 class3 class4 class5
## N     36  23.00   2.00      6   8.00
## %     48  30.67   2.67      8  10.67
##  
## Posterior classification table: 
##      --> mean of posterior probabilities in each class 
##         prob1  prob2  prob3  prob4  prob5
## class1 0.8150 0.1445 0.0002 0.0061 0.0343
## class2 0.1355 0.8385 0.0000 0.0260 0.0000
## class3 0.0006 0.0000 0.9994 0.0000 0.0000
## class4 0.0152 0.0414 0.0013 0.9422 0.0000
## class5 0.1847 0.0007 0.0001 0.0000 0.8145
##  
## Posterior probabilities above a threshold (%): 
##          class1 class2 class3 class4 class5
## prob>0.7  75.00  78.26    100 100.00   62.5
## prob>0.8  61.11  65.22    100 100.00   62.5
## prob>0.9  38.89  47.83    100  83.33   62.5
##

Comment: Based on the metrics shown above, the 4-class model could seem to be the best model but the 3-class model also showed good metrics and had less classes containing very few participants compared to the 4-class model. Thus the 3-class model was chosen.

7.3 Permut the classes of the chosen model

tar_load(model_6MWT_n3_permut)
summary(model_6MWT_n3_permut)

## Heterogenous linear mixed model 
##      fitted by maximum likelihood method 
##  
## hlme(fixed = DIST_6MWT ~ MONTH, mixture = ~MONTH, random = ~1, 
##     subject = "patient", ng = 3, data = DB_PRED_6MWT_0_12, var.time = "MONTH")
##  
## Statistical Model: 
##      Dataset: DB_PRED_6MWT_0_12 
##      Number of subjects: 75 
##      Number of observations: 150 
##      Number of latent classes: 3 
##      Number of parameters: 10  
##  
## Iteration process: 
##      Convergence criteria satisfied 
##      Number of iterations:  1 
##      Convergence criteria: parameters= 2.7e-11 
##                          : likelihood= 3.4e-13 
##                          : second derivatives= 6.8e-16 
##  
## Goodness-of-fit statistics: 
##      maximum log-likelihood: -799.71  
##      AIC: 1619.42  
##      BIC: 1642.6  
##  
##  
## Maximum Likelihood Estimates: 
##  
## Fixed effects in the class-membership model:
## (the class of reference is the last class) 
## 
##                        coef       Se     Wald p-value
## intercept class1   -2.81747  0.75945   -3.710 0.00021
## intercept class2    0.12040  0.40895    0.294 0.76843
## 
## Fixed effects in the longitudinal model:
## 
##                        coef       Se     Wald p-value
## intercept class1  712.71000 52.53197   13.567 0.00000
## intercept class2  588.73829 12.39370   47.503 0.00000
## intercept class3  617.86859 12.67692   48.740 0.00000
## MONTH class1       -8.11139  1.32607   -6.117 0.00000
## MONTH class2       -0.70141  0.44820   -1.565 0.11760
## MONTH class3        3.56567  0.51977    6.860 0.00000
## 
## 
## Variance-covariance matrix of the random-effects:
##           intercept
## intercept   4559.21
## 
##                                coef       Se
## Residual standard error:   15.02270  1.81553

lcmm::postprob(model_6MWT_n3_permut)

##  
## Posterior classification: 
##   class1 class2 class3
## N   2.00     39  34.00
## %   2.67     52  45.33
##  
## Posterior classification table: 
##      --> mean of posterior probabilities in each class 
##         prob1  prob2  prob3
## class1 0.9936 0.0064 0.0000
## class2 0.0016 0.8895 0.1089
## class3 0.0000 0.1166 0.8834
##  
## Posterior probabilities above a threshold (%): 
##          class1 class2 class3
## prob>0.7    100  84.62  85.29
## prob>0.8    100  76.92  79.41
## prob>0.9    100  66.67  61.76
##

7.4 Assess the chosen model

plot(model_6MWT_n3_permut)

7.5 Visualize the fixed effetcs of the model

tar_read(plot_preds_6MWT)

7.6 Analyse the predictors of the latent classes of the model

tar_load(predictors_6MWT_classes)
summary(predictors_6MWT_classes)

## Secondary multinomial model for external class predictor 
##      fitted by maximum likelihood method 
##  
## externVar(model = model_6MWT_n3_permut, subject = "patient", 
##     classmb = ~DIST_6MWT_M0 + MET_MIN_WK_M0 + MOTIVATION_CLUSTER_M0 + 
##         meteo_defavorable + manque_temps, data = DB_PRED_6MWT_0_12, 
##     method = "twoStageJoint")
##  
## Statistical Model: 
##      Dataset: DB_PRED_6MWT_0_12 
##      Number of subjects: 74 
##      Number of latent classes: 3 
##      Number of parameters: 12  
##  
## Iteration process: 
##      Convergence criteria satisfied 
##      Number of iterations:  65 
##      Convergence criteria: parameters= 9.9e-05 
##                          : likelihood= 2.6e-06 
##                          : second derivatives= 4.3e-05 
##  
## Goodness-of-fit statistics: 
##      maximum log-likelihood: -780.17  
##      AIC: 1584.34  
##      BIC: 1611.99  
##  
##  
##  
## Maximum Likelihood Estimates: 
##  
## Fixed effects in the class-membership model:
## (the class of reference is the last class) 
## 
##                                                       coef     Se**   Wald
## intercept class1                                 -17.20337 62.36430 -0.276
## intercept class2                                   7.60341  7.74625  0.982
## DIST_6MWT_M0 class1                                0.01139  0.01428  0.798
## DIST_6MWT_M0 class2                               -0.01481  0.01463 -1.012
## MET_MIN_WK_M0 class1                              -0.00024  0.00101 -0.235
## MET_MIN_WK_M0 class2                               0.00012  0.00013  0.909
## MOTIVATION_CLUSTER_M0Very High AU-High IR class1   9.12534 61.89733  0.147
## MOTIVATION_CLUSTER_M0Very High AU-High IR class2   0.40474  0.73971  0.547
## meteo_defavorable1 class1                         -7.54157 88.84566 -0.085
## meteo_defavorable1 class2                          0.46055  0.91156  0.505
## manque_temps1 class1                              -7.17773 89.33639 -0.080
## manque_temps1 class2                               1.25477  1.31232  0.956
##                                                  p-value
## intercept class1                                 0.78266
## intercept class2                                 0.32632
## DIST_6MWT_M0 class1                              0.42501
## DIST_6MWT_M0 class2                              0.31145
## MET_MIN_WK_M0 class1                             0.81434
## MET_MIN_WK_M0 class2                             0.36331
## MOTIVATION_CLUSTER_M0Very High AU-High IR class1 0.88279
## MOTIVATION_CLUSTER_M0Very High AU-High IR class2 0.58427
## meteo_defavorable1 class1                        0.93235
## meteo_defavorable1 class2                        0.61339
## manque_temps1 class1                             0.93596
## manque_temps1 class2                             0.33900
## 
##  ** total variance estimated through the Hessian of the joint likelihood 
##

8 Predict IPAQ-SF MET-min/week trajectory using latent class mixed modelling

8.1 Build the models

# Load the model summarises
tar_load(model_IPAQ_n1)
tar_load(model_IPAQ_n2)
tar_load(model_IPAQ_n3)
tar_load(model_IPAQ_n4)
tar_load(model_IPAQ_n5)

8.1.1 1-class model

summary(model_IPAQ_n1)

## Heterogenous linear mixed model 
##      fitted by maximum likelihood method 
##  
## hlme(fixed = MET_MIN_WK ~ MONTH, random = ~1, subject = "patient", 
##     ng = 1, data = DB_PRED_IPAQ_6_12, var.time = "MONTH")
##  
## Statistical Model: 
##      Dataset: DB_PRED_IPAQ_6_12 
##      Number of subjects: 77 
##      Number of observations: 154 
##      Number of latent classes: 1 
##      Number of parameters: 4  
##  
## Iteration process: 
##      Convergence criteria satisfied 
##      Number of iterations:  34 
##      Convergence criteria: parameters= 1.5e-10 
##                          : likelihood= 4.5e-13 
##                          : second derivatives= 3.5e-17 
##  
## Goodness-of-fit statistics: 
##      maximum log-likelihood: -1488.88  
##      AIC: 2985.76  
##      BIC: 2995.14  
##  
##  
## Maximum Likelihood Estimates: 
##  
## Fixed effects in the longitudinal model:
## 
##                    coef        Se        Wald p-value
## intercept    3807.59740 800.89659       4.754 0.00000
## MONTH          32.05195  76.00845       0.422 0.67325
## 
## 
## Variance-covariance matrix of the random-effects:
##           intercept
## intercept   9355385
## 
##                                   coef        Se
## Residual standard error:    2829.45253 228.05682

8.1.2 2-class model

summary(model_IPAQ_n2)

## Heterogenous linear mixed model 
##      fitted by maximum likelihood method 
##  
## hlme(fixed = MET_MIN_WK ~ MONTH, mixture = ~MONTH, random = ~1, 
##     subject = "patient", ng = 2, data = DB_PRED_IPAQ_6_12, var.time = "MONTH")
##  
## Statistical Model: 
##      Dataset: DB_PRED_IPAQ_6_12 
##      Number of subjects: 77 
##      Number of observations: 154 
##      Number of latent classes: 2 
##      Number of parameters: 7  
##  
## Iteration process: 
##      Convergence criteria satisfied 
##      Number of iterations:  1 
##      Convergence criteria: parameters= 2.3e-10 
##                          : likelihood= 9.1e-13 
##                          : second derivatives= 7.2e-15 
##  
## Goodness-of-fit statistics: 
##      maximum log-likelihood: -1452.14  
##      AIC: 2918.28  
##      BIC: 2934.69  
##  
##  
## Maximum Likelihood Estimates: 
##  
## Fixed effects in the class-membership model:
## (the class of reference is the last class) 
## 
##                           coef         Se        Wald p-value
## intercept class1       2.67999    0.46854       5.720 0.00000
## 
## Fixed effects in the longitudinal model:
## 
##                           coef         Se        Wald p-value
## intercept class1    3840.89686  652.94808       5.882 0.00000
## intercept class2    3321.92590 2508.72561       1.324 0.18545
## MONTH class1         -58.71239   67.13797      -0.875 0.38184
## MONTH class2        1355.84623  261.80607       5.179 0.00000
## 
## 
## Variance-covariance matrix of the random-effects:
##           intercept
## intercept   1481643
## 
##                                   coef         Se
## Residual standard error:    2417.23850  195.11440

8.1.3 3-class model

summary(model_IPAQ_n3)

## Heterogenous linear mixed model 
##      fitted by maximum likelihood method 
##  
## hlme(fixed = MET_MIN_WK ~ MONTH, mixture = ~MONTH, random = ~1, 
##     subject = "patient", ng = 3, data = DB_PRED_IPAQ_6_12, var.time = "MONTH")
##  
## Statistical Model: 
##      Dataset: DB_PRED_IPAQ_6_12 
##      Number of subjects: 77 
##      Number of observations: 154 
##      Number of latent classes: 3 
##      Number of parameters: 10  
##  
## Iteration process: 
##      Convergence criteria satisfied 
##      Number of iterations:  10 
##      Convergence criteria: parameters= 1e-09 
##                          : likelihood= 2.3e-13 
##                          : second derivatives= 1.3e-17 
##  
## Goodness-of-fit statistics: 
##      maximum log-likelihood: -1448.61  
##      AIC: 2917.21  
##      BIC: 2940.65  
##  
##  
## Maximum Likelihood Estimates: 
##  
## Fixed effects in the class-membership model:
## (the class of reference is the last class) 
## 
##                          coef         Se       Wald p-value
## intercept class1      2.48601    0.69032      3.601 0.00032
## intercept class2     -0.32362    0.82697     -0.391 0.69556
## 
## Fixed effects in the longitudinal model:
## 
##                          coef         Se       Wald p-value
## intercept class1   3175.94038  668.19712      4.753 0.00000
## intercept class2   2157.01113 2630.67708      0.820 0.41225
## intercept class3  12590.06427 3862.36130      3.260 0.00112
## MONTH class1        -18.25823   68.29452     -0.267 0.78920
## MONTH class2       1574.66656  282.80923      5.568 0.00000
## MONTH class3       -479.68502  375.03154     -1.279 0.20088
## 
## 
## Variance-covariance matrix of the random-effects:
##           intercept
## intercept  494489.9
## 
##                                  coef         Se
## Residual standard error:   2316.61529  194.50568

8.1.4 4-class model

summary(model_IPAQ_n4)

## Heterogenous linear mixed model 
##      fitted by maximum likelihood method 
##  
## hlme(fixed = MET_MIN_WK ~ MONTH, mixture = ~MONTH, random = ~1, 
##     subject = "patient", ng = 4, data = DB_PRED_IPAQ_6_12, var.time = "MONTH")
##  
## Statistical Model: 
##      Dataset: DB_PRED_IPAQ_6_12 
##      Number of subjects: 77 
##      Number of observations: 154 
##      Number of latent classes: 4 
##      Number of parameters: 13  
##  
## Iteration process: 
##      The program stopped abnormally. No results can be displayed.

8.1.5 5-class model

summary(model_IPAQ_n5)

## Heterogenous linear mixed model 
##      fitted by maximum likelihood method 
##  
## hlme(fixed = MET_MIN_WK ~ MONTH, mixture = ~MONTH, random = ~1, 
##     subject = "patient", ng = 5, data = DB_PRED_IPAQ_6_12, var.time = "MONTH")
##  
## Statistical Model: 
##      Dataset: DB_PRED_IPAQ_6_12 
##      Number of subjects: 77 
##      Number of observations: 154 
##      Number of latent classes: 5 
##      Number of parameters: 16  
##  
## Iteration process: 
##      The program stopped abnormally. No results can be displayed.

8.2 Compare the models

8.2.1 Analyse the metrics of the models

tar_read(compa_latent_mixed_models_table_IPAQ)

##                        AIC          BIC   entropy   %class1  %class2  %class3
## model_IPAQ_n1 2.985761e+03 2.995137e+03 1.0000000 100.00000       NA       NA
## model_IPAQ_n2 2.918285e+03 2.934691e+03 0.9956238  93.50649 6.493506       NA
## model_IPAQ_n3 2.917214e+03 2.940652e+03 0.9379943  88.31169 5.194805 6.493506
## model_IPAQ_n4 2.000000e+09 2.000000e+09 1.0000000   0.00000 0.000000 0.000000
## model_IPAQ_n5 2.000000e+09 2.000000e+09 1.0000000   0.00000 0.000000 0.000000
##               %class4 %class5
## model_IPAQ_n1      NA      NA
## model_IPAQ_n2      NA      NA
## model_IPAQ_n3      NA      NA
## model_IPAQ_n4       0      NA
## model_IPAQ_n5       0       0

lcmm::summaryplot(
  model_IPAQ_n1,
  model_IPAQ_n2,
  model_IPAQ_n3,
  model_IPAQ_n4,
  model_IPAQ_n5,
  which = c("AIC", "BIC", "entropy")
)

8.2.2 Posterior classification of the models

8.2.2.1 2-class model

lcmm::postprob(model_IPAQ_n2)

##  
## Posterior classification: 
##   class1 class2
## N  72.00   5.00
## %  93.51   6.49
##  
## Posterior classification table: 
##      --> mean of posterior probabilities in each class 
##        prob1 prob2
## class1 1.000 0.000
## class2 0.012 0.988
##  
## Posterior probabilities above a threshold (%): 
##          class1 class2
## prob>0.7    100    100
## prob>0.8    100    100
## prob>0.9    100    100
##

8.2.2.2 3-class model

lcmm::postprob(model_IPAQ_n3)

##  
## Posterior classification: 
##   class1 class2 class3
## N  68.00   4.00   5.00
## %  88.31   5.19   6.49
##  
## Posterior classification table: 
##      --> mean of posterior probabilities in each class 
##         prob1  prob2  prob3
## class1 0.9805 0.0000 0.0195
## class2 0.0000 1.0000 0.0000
## class3 0.1326 0.0111 0.8563
##  
## Posterior probabilities above a threshold (%): 
##          class1 class2 class3
## prob>0.7  97.06    100     80
## prob>0.8  97.06    100     80
## prob>0.9  92.65    100     60
##

8.2.2.3 4-class model

lcmm::postprob(model_IPAQ_n4)

##  
## Posterior classification: 
##   class1 class2 class3 class4
## N      0      0      0      0
## %      0      0      0      0
##  
## Posterior classification table: 
##      --> mean of posterior probabilities in each class 
##        prob1 prob2 prob3 prob4
## class1   NaN   NaN   NaN   NaN
## class2   NaN   NaN   NaN   NaN
## class3   NaN   NaN   NaN   NaN
## class4   NaN   NaN   NaN   NaN
##  
## Posterior probabilities above a threshold (%): 
##          class1 class2 class3 class4
## prob>0.7    NaN    NaN    NaN    NaN
## prob>0.8    NaN    NaN    NaN    NaN
## prob>0.9    NaN    NaN    NaN    NaN
##

8.2.2.4 5-class model

lcmm::postprob(model_IPAQ_n5)

##  
## Posterior classification: 
##   class1 class2 class3 class4 class5
## N      0      0      0      0      0
## %      0      0      0      0      0
##  
## Posterior classification table: 
##      --> mean of posterior probabilities in each class 
##        prob1 prob2 prob3 prob4 prob5
## class1   NaN   NaN   NaN   NaN   NaN
## class2   NaN   NaN   NaN   NaN   NaN
## class3   NaN   NaN   NaN   NaN   NaN
## class4   NaN   NaN   NaN   NaN   NaN
## class5   NaN   NaN   NaN   NaN   NaN
##  
## Posterior probabilities above a threshold (%): 
##          class1 class2 class3 class4 class5
## prob>0.7    NaN    NaN    NaN    NaN    NaN
## prob>0.8    NaN    NaN    NaN    NaN    NaN
## prob>0.9    NaN    NaN    NaN    NaN    NaN
##

Comment: The 4-class and the 5-class models did not converge. The 2-class model seemed to be a reasonable choice.

8.2.3 Assess the chosen model

plot(model_IPAQ_n2)

8.2.4 Visualize the fixed effetcs of the model

tar_read(plot_preds_IPAQ)

8.3 Analyse the predictors of the latent classes of the model

tar_load(predictors_IPAQ_classes)
summary(predictors_IPAQ_classes)

## Secondary multinomial model for external class predictor 
##      fitted by maximum likelihood method 
##  
## externVar(model = model_IPAQ_n2, subject = "patient", classmb = ~DIST_6MWT_M0 + 
##     MET_MIN_WK_M0 + MOTIVATION_CLUSTER_M0 + meteo_defavorable + 
##     manque_temps, data = DB_PRED_IPAQ_6_12, method = "twoStageJoint")
##  
## Statistical Model: 
##      Dataset: DB_PRED_IPAQ_6_12 
##      Number of subjects: 76 
##      Number of latent classes: 2 
##      Number of parameters: 6  
##  
## Iteration process: 
##      Convergence criteria satisfied 
##      Number of iterations:  11 
##      Convergence criteria: parameters= 2.2e-07 
##                          : likelihood= 1.3e-08 
##                          : second derivatives= 1.4e-10 
##  
## Goodness-of-fit statistics: 
##      maximum log-likelihood: -1433.2  
##      AIC: 2878.4  
##      BIC: 2892.38  
##  
##  
##  
## Maximum Likelihood Estimates: 
##  
## Fixed effects in the class-membership model:
## (the class of reference is the last class) 
## 
##                                                      coef    Se**   Wald
## intercept class1                                  1.29289 4.05010  0.319
## DIST_6MWT_M0 class1                               0.00047 0.00636  0.074
## MET_MIN_WK_M0 class1                              0.00024 0.00024  1.004
## MOTIVATION_CLUSTER_M0Very High AU-High IR class1  0.02629 0.99719  0.026
## meteo_defavorable1 class1                        -0.30177 0.97011 -0.311
## manque_temps1 class1                              0.52264 1.16166  0.450
##                                                  p-value
## intercept class1                                 0.74956
## DIST_6MWT_M0 class1                              0.94087
## MET_MIN_WK_M0 class1                             0.31554
## MOTIVATION_CLUSTER_M0Very High AU-High IR class1 0.97897
## meteo_defavorable1 class1                        0.75574
## manque_temps1 class1                             0.65278
## 
##  ** total variance estimated through the Hessian of the joint likelihood 
##

Table of content

APA&Co project | Results shown in the manuscript

1 Descriptive analysis of the participants

1.1 Overview

1.2 Sex (1 = men; 2 = women)

1.3 Age

1.4 Height

1.5 Weight

1.6 Body mass index

1.7 Angioplasty (0 = no angioplasty; 1 = with angioplasty)

1.8 Bypass (0 = no bypass; 1 = with bypass)

2 Change in 6MWT distance between 0 and 12 months

2.1 Descriptive statistics

2.2 T-test

2.3 Pearson correlation

2.4 Effect size (dav)

2.5 Estimate of the median of the individual changes

2.6 Shift and difference asymmetry functions

3 Change in IPAQ-SF MET-min/week between 6 and 12 months

3.1 Descriptive statistics

3.2 Estimate of the median of the individual changes

3.3 Shift and difference asymmetry functions

4 Change in EMAPS scores between 0 and 12 months

4.1 Descriptive statistics

4.2 Estimates of the medians of the individual changes

4.2.1 Intrinsic motivation score

4.2.2 Integrated regulation score

4.2.3 Identified regulation score

4.2.4 Introjected regulation score

4.2.5 External regulation score

4.2.6 Amotivation score

5 Change in the motivational profile for physical activity

5.1 Assess cluster tendency

5.1.1 Graphically inspect data using principal component analysis

5.1.2 Confirm cluser tendency using graphical method

5.1.3 Confirm cluser tendency using the Hopkins statistic

5.1.3.1 Hopkins statistic for the dataset at month 0

5.1.3.2 Hopkins statistic for the dataset at month 12

5.2 Check outliers related to a multivariate analysis

5.2.1 Month 0

5.2.2 Month 12

5.3 Determine the optimal number of clusters related to a K-Medoid approach using the silhouette method

5.4 Visualize the final clusters from K-Medoid approach

5.5 Visualize the descriptive statistics of the EMAPS scores related to the motivational profiles

5.6 Compare the motivational profiles

5.6.1 Comparison at Month 0

5.6.1.1 Global analysis

5.6.1.2 Localisation of the difference(s)

5.6.2 Comparison at Month 12

5.6.2.1 Global analysis

5.6.2.2 Localisation of the difference(s)

5.7 Characterize the change in the motivational profile

5.7.1 Visualize the change in the motivational profile

5.7.2 Compute the proportions of patients per profile transition scenario

6 Barriers to physical activity at 12 months

7 Predict 6WT distance trajectory using latent class mixed modelling

7.1 Build the models

7.1.1 1-class model

7.1.2 2-class model

7.1.3 3-class model

7.1.4 4-class model

7.1.5 5-class model

7.2 Compare the models

7.2.1 Analyse the metrics of the models

7.2.2 Posterior classification of the models

7.2.2.1 2-class model

7.2.2.2 3-class model

7.2.2.3 4-class model

7.2.2.4 5-class model

7.3 Permut the classes of the chosen model

7.4 Assess the chosen model

7.5 Visualize the fixed effetcs of the model

7.6 Analyse the predictors of the latent classes of the model

8 Predict IPAQ-SF MET-min/week trajectory using latent class mixed modelling

8.1 Build the models

8.1.1 1-class model

8.1.2 2-class model

8.1.3 3-class model

8.1.4 4-class model

8.1.5 5-class model