RHRVEasy automates all steps of a Heart Rate Variability (HRV) analysis, including data processing, indices calculation, and statistical analysis. It takes as input a list of folders, each containing the recordings of a same population. It calculates time, frequency, and nonlinear domain HRV indices, and then it applies hypothesis test, and corrects the significance levels. If there are more than two experimental groups and statistically significant differences are found, it performs a post-hoc analysis to find out which groups have the differences.

This tutorial uses the recordings of the Normal Sinus Rhythm RR Interval Database (hereinafter referred to as NSR_DB), a subset of the RR interval time series from healthy subjects (referred to as HEALTHY_DB), and the Congestive Heart Failure RR Interval Database (referred to as CHF_DB). The former two databases comprise data from healthy individuals, while the latter consists of recordings from patients with severe cardiac pathology. Consequently, significant disparities in numerous HRV indices are anticipated between the healthy databases and the CHF_DB.

The three databases are available in the GitHub repository
for the book “Heart Rate Variability Analysis with the R package
RHRV”, under the `data/Chapter8`

folder, within the
`data/Chapter8`

directory. To execute this tutorial, download
this folder to your local machine and define the following
variables:

```
library("RHRV")
basePath <- "book_data" # adjust as needed
NSR_DB <- file.path(basePath, "normal")
CHF_DB <- file.path(basePath, "chf")
HEALTHY_DB <- file.path(basePath, "healthy")
```

RHRVEasy permits creating an Excel spreadsheet with all the HRV indices calculated for each recording. The following variable must contain the folder on the local machine where the Excel spreadsheet is to be saved:

`RHRVEasy`

enables the user to carry out a full HRV
analysis by just invoking a function with a single mandatory parameter:
a list with the folders containing the recordings of the experimental
groups. This list must have at least two folders. Each folder must
contain all the RR recordings of the same experimental group and no
additional files, as `RHRVEasy`

will try to open all the
files within these folders. The name that will be used to refer to each
experimental group within `RHRVEasy`

will be the name of the
folder in which its recordings are located.

The following function call computes the time and frequency indices
for the NSR_DB and CHF_DB databases, and performs a statistical
comparison of each index correcting the significance level with the
Bonferroni method. Note the use of the `nJobs`

to use several
cores and parallelize the computations. With `nJobs = -1`

, it
uses all available cores; if an integer greater than 0 is indicated, it
uses the number of cores indicated by the integer.

When the returned object is displayed in the console, it shows which indices present statistically significant differences:

```
## Significant differences in SDNN (Kruskal-Wallis rank sum test, bonferroni p-value = 1.117154e-07):
## chf's mean95% CI: (61.91503, 94.0085) [Bootstrap CI without adjustment]
## normal's mean95% CI: (131.1187, 148.1985) [Bootstrap CI without adjustment]
##
## Significant differences in SDANN (Kruskal-Wallis rank sum test, bonferroni p-value = 3.799696e-07):
## chf's mean95% CI: (48.19527, 80.0444) [Bootstrap CI without adjustment]
## normal's mean95% CI: (122.0759, 139.05) [Bootstrap CI without adjustment]
##
## Significant differences in SDNNIDX (Kruskal-Wallis rank sum test, bonferroni p-value = 0.01426098):
## chf's mean95% CI: (29.96821, 47.6446) [Bootstrap CI without adjustment]
## normal's mean95% CI: (47.0144, 54.5201) [Bootstrap CI without adjustment]
##
## Significant differences in IRRR (Kruskal-Wallis rank sum test, bonferroni p-value = 1.492754e-07):
## chf's mean95% CI: (78.67064, 124.1918) [Bootstrap CI without adjustment]
## normal's mean95% CI: (189.5291, 215.7118) [Bootstrap CI without adjustment]
##
## Significant differences in TINN (Kruskal-Wallis rank sum test, bonferroni p-value = 1.452872e-06):
## chf's mean95% CI: (243.1949, 373.8965) [Bootstrap CI without adjustment]
## normal's mean95% CI: (511.0544, 586.6332) [Bootstrap CI without adjustment]
##
## Significant differences in HRVi (Kruskal-Wallis rank sum test, bonferroni p-value = 1.452872e-06):
## chf's mean95% CI: (15.96148, 23.78737) [Bootstrap CI without adjustment]
## normal's mean95% CI: (32.80169, 37.58583) [Bootstrap CI without adjustment]
##
## Significant differences in ULF (Kruskal-Wallis rank sum test, bonferroni p-value = 1.74099e-08):
## chf's mean95% CI: (1182.117, 4410.562) [Bootstrap CI without adjustment]
## normal's mean95% CI: (7215.618, 9824.658) [Bootstrap CI without adjustment]
##
## Significant differences in VLF (Kruskal-Wallis rank sum test, bonferroni p-value = 0.002535127):
## chf's mean95% CI: (52.21509, 135.5065) [Bootstrap CI without adjustment]
## normal's mean95% CI: (131.5723, 175.2834) [Bootstrap CI without adjustment]
```

All computed indices, as well as all p-values resulting from all
comparisons, are stored in `data.frames`

contained in the
object. Two different sets of p-values are available; the ones obtained
before (`p.value`

) and after (`adj.p.value`

)
applying the significance level correction:

```
## # A tibble: 6 × 16
## file group SDNN SDANN SDNNIDX pNN50 SDSD rMSSD IRRR MADRR TINN HRVi
## <chr> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 chf201_rr… chf 75.5 52.9 49.6 2.03 20.2 20.2 93.8 7.81 358. 22.9
## 2 chf202_rr… chf 88.5 75.8 39.6 6.13 34.7 34.7 117. 15.6 350. 22.4
## 3 chf203_rr… chf 38.8 30.9 21.7 1.20 17.3 17.3 46.9 7.81 170. 10.9
## 4 chf204_rr… chf 55.1 39.1 36.0 4.84 33.0 33.0 70.3 7.81 237. 15.2
## 5 chf205_rr… chf 34.9 26.1 19.5 1.97 23.7 23.7 46.9 7.81 169. 10.8
## 6 chf206_rr… chf 41.2 34.9 14.8 2.02 18.9 18.9 31.2 7.81 122. 7.79
## # ℹ 4 more variables: ULF <dbl>, VLF <dbl>, LF <dbl>, HF <dbl>
```

```
## # A tibble: 6 × 4
## HRVIndex method p.value adj.p.value
## <chr> <chr> <dbl> <dbl>
## 1 SDNN Kruskal-Wallis rank sum test 0.00000000798 0.000000112
## 2 SDANN Kruskal-Wallis rank sum test 0.0000000271 0.000000380
## 3 SDNNIDX Kruskal-Wallis rank sum test 0.00102 0.0143
## 4 pNN50 Kruskal-Wallis rank sum test 0.774 1
## 5 SDSD Kruskal-Wallis rank sum test 0.0891 1
## 6 rMSSD Kruskal-Wallis rank sum test 0.0891 1
```

The `format`

parameter specifies the format in which the
RR intervals are stored. All formats supported by the RHRV package can
be used: `WFDB`

, `ASCII`

, `RR`

,
`Polar`

, `Suunto`

, `EDFPlus`

or
`Ambit`

(check the RHRV website for more
information). The default format is RR, where the beat distances in
seconds are stored in a single column of an ASCII file. This is the
format of the three databases used in this tutorial.

By default, the frequency analysis is performed using the Fourier
transform. It is also possible to use the Wavelet transform pasing the
value `'wavelet'`

to the `typeAnalysis`

parameter
(check the paper “García, C. A., Otero, A., Vila, X., & Márquez, D.
G. (2013). A new algorithm for wavelet-based heart rate variability
analysis. Biomedical Signal Processing and Control, 8(6), 542-550” for
details):

```
easyAnalysisWavelet <- RHRVEasy(
folders = c(NSR_DB, CHF_DB),
typeAnalysis = 'wavelet',
n_jobs = -1
)
```

Note that the significant indices are the same as the previous ones.

Given that multiple statistical tests are performed on several HRV
indices, a correction of the significance level should be applied. The
Bonferroni method is used by default. This behavior can be overridden
with the parameter `correctionMethod`

of
`RHRVEasy`

. The possible values of this parameter besides
`bonferroni`

are `holm`

, `hochberg`

,
`hommel`

, `BH`

(Benjamini & Hochberg),
`fdr`

(false discovery rate), `BY`

(Benjamini
& Yekutieli), and `none`

(indicating that no correction
is to be made). Furthermore, there is no need to recompute the HRV
indices to apply a different correction method, but the
`RHRVEasyStats`

function can be used to this end. The
confidence level can also be changed using the `significance`

parameter (in both `RHRVEasy`

and `RHRVEasyStats`

functions).

```
easyAnalysisFDR <- RHRVEasyStats(easyAnalysis, correctionMethod = 'fdr')
pValues <- merge(
easyAnalysis$stats,
easyAnalysisFDR$stats,
by = setdiff(names(easyAnalysis$stats), "adj.p.value"),
suffixes = c(".bonf", ".fdr")
)
#Let us compare the p-values obtained with different correction methods
print(
head(
pValues[, c("HRVIndex", "p.value", "adj.p.value.bonf", "adj.p.value.fdr")]
)
)
```

```
## HRVIndex p.value adj.p.value.bonf adj.p.value.fdr
## 1 HF 5.601495e-01 1.000000e+00 6.032380e-01
## 2 HRVi 1.037766e-07 1.452872e-06 2.421454e-07
## 3 IRRR 1.066253e-08 1.492754e-07 4.975847e-08
## 4 LF 1.651479e-02 2.312071e-01 2.568968e-02
## 5 MADRR 6.319903e-02 8.847864e-01 8.847864e-02
## 6 pNN50 7.744691e-01 1.000000e+00 7.744691e-01
```

If the argument `saveHRVindicesInPath`

is specified when
invoking the function `RHRVEasy`

, an Excel spreadsheet with
all the HRV indices calculated for each recording will be created in the
path specified by this parameter. The name of the spreadsheet generated
is “<group 1 name>*Vs*<group 2 name> .xlsx”:

This spreadsheet can also be generated from the object returned by
`RHRVEasy`

by calling the function
`SaveHRVIndices`

.

If the analysis involves three or more groups, when statistically significant differences are found among them it does not necessarily mean that there are statistically significant differences between all pairs of groups. In such a scenario post-hoc tests are used to find which pairs of groups present differences:

```
#Comparison of the three databases
easyAnalysis3 <- RHRVEasy(
folders = c(NSR_DB, CHF_DB, HEALTHY_DB),
nJobs = -1
)
print(easyAnalysis3)
```

```
## Significant differences in SDNN (Kruskal-Wallis rank sum test, bonferroni p-value = 3.543622e-07):
## Significant differences in the post-hoc tests (Dunn's all-pairs test + bonferroni-p-value adjustment):
## group1 group2 adj.p.value
## 1 healthy chf 0.00799
## 2 normal chf 0.000000282
## ----------------------------
## chf's mean95% CI: (63.20538, 92.2515) [Bootstrap CI without adjustment]
## healthy's mean95% CI: (123.242, 158.269) [Bootstrap CI without adjustment]
## normal's mean95% CI: (131.665, 147.9961) [Bootstrap CI without adjustment]
##
## Significant differences in SDANN (Kruskal-Wallis rank sum test, bonferroni p-value = 1.345688e-06):
## Significant differences in the post-hoc tests (Dunn's all-pairs test + bonferroni-p-value adjustment):
## group1 group2 adj.p.value
## 1 normal chf 0.000000403
## ---------------------------
## chf's mean95% CI: (47.61222, 81.42191) [Bootstrap CI without adjustment]
## healthy's mean95% CI: (105.1872, 134.0331) [Bootstrap CI without adjustment]
## normal's mean95% CI: (120.4753, 138.5329) [Bootstrap CI without adjustment]
##
## Significant differences in SDNNIDX (Kruskal-Wallis rank sum test, bonferroni p-value = 0.001063849):
## Significant differences in the post-hoc tests (Dunn's all-pairs test + bonferroni-p-value adjustment):
## group1 group2 adj.p.value
## 1 healthy chf 0.00111
## ----------------------------
## chf's mean95% CI: (29.1345, 47.73994) [Bootstrap CI without adjustment]
## healthy's mean95% CI: (56.23389, 74.9991) [Bootstrap CI without adjustment]
## normal's mean95% CI: (47.0101, 54.33106) [Bootstrap CI without adjustment]
##
## Significant differences in IRRR (Kruskal-Wallis rank sum test, bonferroni p-value = 3.688167e-07):
## Significant differences in the post-hoc tests (Dunn's all-pairs test + bonferroni-p-value adjustment):
## group1 group2 adj.p.value
## 1 healthy chf 0.00395
## 2 normal chf 0.000000425
## ----------------------------
## chf's mean95% CI: (77.3305, 124.7238) [Bootstrap CI without adjustment]
## healthy's mean95% CI: (179.9086, 234.5556) [Bootstrap CI without adjustment]
## normal's mean95% CI: (187.6484, 215.9975) [Bootstrap CI without adjustment]
##
## Significant differences in MADRR (Kruskal-Wallis rank sum test, bonferroni p-value = 0.006224158):
## Significant differences in the post-hoc tests (Dunn's all-pairs test + bonferroni-p-value adjustment):
## group1 group2 adj.p.value
## 1 healthy chf 0.00237
## ----------------------------
## chf's mean95% CI: (8.62069, 11.85345) [Bootstrap CI without adjustment]
## healthy's mean95% CI: (16.55556, 24.66667) [Bootstrap CI without adjustment]
## normal's mean95% CI: (11.28472, 14.03356) [Bootstrap CI without adjustment]
##
## Significant differences in TINN (Kruskal-Wallis rank sum test, bonferroni p-value = 1.350844e-06):
## Significant differences in the post-hoc tests (Dunn's all-pairs test + bonferroni-p-value adjustment):
## group1 group2 adj.p.value
## 1 healthy chf 0.000933
## 2 normal chf 0.00000519
## ----------------------------
## chf's mean95% CI: (244.0477, 371.3618) [Bootstrap CI without adjustment]
## healthy's mean95% CI: (533.6798, 701.4795) [Bootstrap CI without adjustment]
## normal's mean95% CI: (511.6379, 586.4394) [Bootstrap CI without adjustment]
##
## Significant differences in HRVi (Kruskal-Wallis rank sum test, bonferroni p-value = 1.350844e-06):
## Significant differences in the post-hoc tests (Dunn's all-pairs test + bonferroni-p-value adjustment):
## group1 group2 adj.p.value
## 1 healthy chf 0.000933
## 2 normal chf 0.00000519
## ----------------------------
## chf's mean95% CI: (15.85798, 23.7487) [Bootstrap CI without adjustment]
## healthy's mean95% CI: (34.45, 45.19331) [Bootstrap CI without adjustment]
## normal's mean95% CI: (32.68737, 37.61479) [Bootstrap CI without adjustment]
##
## Significant differences in ULF (Kruskal-Wallis rank sum test, bonferroni p-value = 5.860632e-08):
## Significant differences in the post-hoc tests (Dunn's all-pairs test + bonferroni-p-value adjustment):
## group1 group2 adj.p.value
## 1 normal chf 0.0000000162
## ----------------------------
## chf's mean95% CI: (1075.296, 4358.885) [Bootstrap CI without adjustment]
## healthy's mean95% CI: (4995.594, 8167.694) [Bootstrap CI without adjustment]
## normal's mean95% CI: (7063.468, 9898.164) [Bootstrap CI without adjustment]
##
## Significant differences in VLF (Kruskal-Wallis rank sum test, bonferroni p-value = 0.0005669878):
## Significant differences in the post-hoc tests (Dunn's all-pairs test + bonferroni-p-value adjustment):
## group1 group2 adj.p.value
## 1 healthy chf 0.00239
## 2 normal chf 0.00977
## ----------------------------
## chf's mean95% CI: (54.04686, 134.9712) [Bootstrap CI without adjustment]
## healthy's mean95% CI: (171.6335, 340.8925) [Bootstrap CI without adjustment]
## normal's mean95% CI: (130.0847, 177.0061) [Bootstrap CI without adjustment]
```

Note that the `stats`

`data.frame`

now contains
a column named `pairwise`

storing the results of the post-hoc
analysis for those indices where the omnibus test has been
significant:

```
## # A tibble: 6 × 5
## HRVIndex method p.value adj.p.value pairwise
## <chr> <chr> <dbl> <dbl> <list>
## 1 SDNN Kruskal-Wallis rank sum test 0.0000000253 0.000000354 <tibble>
## 2 SDANN Kruskal-Wallis rank sum test 0.0000000961 0.00000135 <tibble>
## 3 SDNNIDX Kruskal-Wallis rank sum test 0.0000760 0.00106 <tibble>
## 4 pNN50 Kruskal-Wallis rank sum test 0.0186 0.260 <NULL>
## 5 SDSD Kruskal-Wallis rank sum test 0.0301 0.421 <NULL>
## 6 rMSSD Kruskal-Wallis rank sum test 0.0301 0.421 <NULL>
```

```
## # A tibble: 3 × 6
## HRVIndex group1 group2 method p.value adj.p.value
## <chr> <chr> <chr> <chr> <dbl> <dbl>
## 1 SDNN healthy chf Dunn's all-pairs test 0.000296 0.00799
## 2 SDNN normal chf Dunn's all-pairs test 0.0000000104 0.000000282
## 3 SDNN normal healthy Dunn's all-pairs test 0.861 1
```

Any parameter of any RHRV function can be specified as an additional
parameter of the `RHRVEasy`

function; in this case, the
default value used for that parameter will be overwritten by the one
specified for the user. The default values used in the
`RHRVEasy`

package are the same as those used in the RHRV
package. For more information about the parameters available you can
consult the RHRV
website. For example, the following analysis modifies the the limits
of the ULF, VLF, LF and HF spectral bands, and uses an interpolation
frequency (`freqhr`

) of 2 Hz:

The calculation of the nonlinear indices requires considerable
computational resources, specially the Recurrence Quantification
Analysis (RQA). Whereas in a typical HRV analysis the computation of all
the time and frequency domain indices for a few dozens of recordings
often completes within a few minutes, the computation of the nonlinear
indices could last many hours. That’s why the boolean parameters
`nonLinear`

and `doRQA`

are set to
`FALSE`

by default. If these parameters are not changed, only
time and frequency indices will be calculated, as in the previous
sections.

**Warning**: the following sentence, will take several
hours to execute on a medium to high performance PC. You may reproduce
the results of the paper by running this chunk of code.