Module 4: Analysis and Summaries

Weekend Warrior

From Shiroma et al. (2019)

Within each MVPA category

• inactive: <37.5 minutes
• insufficiently active: 37.5-<150 minutes
• sufficiently active: ≥150 minutes per week

Weekend warriors: accrued ≥ 50% of their weekly MVPA on only one or two days, and “regularly active” participants who spread their activity over the entire week.

Population Data

Subset of 100 people, multiple days from NHANES AC data

wide = readr::read_rds(here::here("data/ac_subset_wide.rds"))
head(wide)

# A tibble: 6 × 1,443
   SEQN PAXDAYM PAXDAYWM min_1 min_2 min_3 min_4 min_5 min_6 min_7 min_8 min_9
  <dbl>   <dbl>    <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 73557       1        3    NA    NA    NA    NA    NA    NA    NA    NA    NA
2 73557       2        4    NA    NA    NA    NA    NA    NA    NA    NA    NA
3 73557       3        5    NA    NA    NA    NA    NA    NA    NA    NA    NA
4 73557       4        6    NA    NA    NA    NA    NA    NA    NA    NA    NA
5 73557       5        7    NA    NA    NA    NA    NA    NA    NA    NA    NA
6 73557       6        1    NA    NA    NA    NA    NA    NA    NA    NA    NA
# ℹ 1,431 more variables: min_10 <dbl>, min_11 <dbl>, min_12 <dbl>,
#   min_13 <dbl>, min_14 <dbl>, min_15 <dbl>, min_16 <dbl>, min_17 <dbl>,
#   min_18 <dbl>, min_19 <dbl>, min_20 <dbl>, min_21 <dbl>, min_22 <dbl>,
#   min_23 <dbl>, min_24 <dbl>, min_25 <dbl>, min_26 <dbl>, min_27 <dbl>,
#   min_28 <dbl>, min_29 <dbl>, min_30 <dbl>, min_31 <dbl>, min_32 <dbl>,
#   min_33 <dbl>, min_34 <dbl>, min_35 <dbl>, min_36 <dbl>, min_37 <dbl>,
#   min_38 <dbl>, min_39 <dbl>, min_40 <dbl>, min_41 <dbl>, min_42 <dbl>, …

Average Day per Person

We reshaped it so each time is a minute and then thresholded average minute (not really “correct”):

df = wide |>
  pivot_longer(starts_with("min_"), names_prefix = "min_", names_to = "minute")
df = df |>
  group_by(SEQN, minute) |>
  summarise(value = mean(value, na.rm = TRUE)) |>
  ungroup() |>
  mutate(minute = as.numeric(minute) - 1,
         minute = hms::hms(minutes = minute),
         time = ymd_hms(paste0("2000-01-01", " ", as.character(minute)),
                        tz = "UTC"))

df = df |>
  select(SEQN, time, value)
df = df |>
  arrange(SEQN, time)
df = df |> 
  mutate(mvpa = cut(value, breaks = c(0, 2860, 3940, Inf),
                    include.lowest = FALSE, 
                    labels = c("sedentary", "light", "mvpa")))
head(df)

# A tibble: 6 × 4
   SEQN minute time                    value
  <dbl> <time> <dttm>                  <dbl>
1 73557 00'00" 2000-01-01 00:00:00.000   NaN
2 73557 01'00" 2000-01-01 00:01:00.000   NaN
3 73557 02'00" 2000-01-01 00:02:00.000   NaN
4 73557 03'00" 2000-01-01 00:03:00.000   NaN
5 73557 04'00" 2000-01-01 00:04:00.000   NaN
6 73557 05'00" 2000-01-01 00:05:00.000   NaN

Plotting Population

Plotting one row per person (100 people):

df |> 
  mutate(SEQN = as.numeric(factor(SEQN))) |> 
  ggplot(aes(x = minute, y = SEQN)) + 
  geom_tile(aes(fill = mvpa)) + 
  ylab(NULL) + 
  theme(axis.ticks.y = element_blank(),
        axis.text.y = element_blank())

Lasagna Plot

Swihart et al. (2009) stacks the data into layers

res = ggplot2::resolution(df$minute)
df |> 
  ggplot(aes(x = minute)) + 
  geom_bar(aes(fill = mvpa), position = "stack", width = res) + 
  guides()

Lasagna Plot

General Lasagna Function

geom_lasagna = function(data, x, ..., position = "stack") {
  xvar = rlang::enquo(x)
  x_string = rlang::as_label(xvar)
  xvalues = data[[x_string]]
  if (hms::is_hms(xvalues)) {
    xvalues = as.numeric(xvalues)
  }
  res = ggplot2::resolution(xvalues)
  data %>%
    ggplot2::ggplot(aes(..., x = !!xvar)) +
    ggplot2::geom_bar(position = position, width = res)
}

Quantile Mapping

• actiquantiles
• Map your data into NHANES quantiles (and by age/sex)

library(actiquantiles)
example_data <- data.frame(
  id = 1:2,
  age = c(25, 62),
  sex = c("Female", "Male"),
  measure = c("mims", "ssl_steps"),
  value = c(15000, 7500)
)

acti_map_nhanes(example_data)

  id age    sex   measure value acti_pa_quantile
1  1  25 Female      mims 15000        0.5349443
2  2  62   Male ssl_steps  7500        0.3527381

Analysis

Mean Analysis

• Inclusion criteria per day
• Person inclusion by number of days
• Mean over days - one measure per person
• Standard statistical framework

FUI Analysis

• FUI - Fast univariate inference for longitudinal functional models Cui et al. (2022)
• fastFMM package

1. fit massively univariate pointwise mixed effects models
2. apply a smoother along the functional domain
3. obtain joint confidence bands (usually bootstrap)

FUI Analysis

library(fastFMM)
wide = readr::read_rds(here::here("data/ac_subset_wide.rds"))
head(wide)
wide = wide[rowSums(is.na(wide |> select(starts_with("min")))) == 0,]
# does not like tibbles
wide = as.data.frame(wide)
fit_data <- fastFMM::fui(
  min ~ PAXDAYWM + (1 | SEQN),
  data = wide
)

FDA Packages

• refund package
• tidyfun
• fda

Function on Scalar Regression

Large generalized additive model (mgcv)

• y - scalar outcome
• functional effect for minute, by age, sex

fit <- bam(
  y ~
    s(minute, bs = "cc", k = 24) +             # population mean 24-hour curve
    s(minute, by = age_category, bs = "cc", k = 24) + # age effect varies over day
    s(minute, by = sex, bs = "cc", k = 24) +# female–male difference over day
    s(SEQN, bs = "re"),                        # participant random intercept
  data = minute_data,
  method = "fREML",
  discrete = TRUE,
  knots = list(minute = c(0.5, 1440.5))
)

Survey Weighting

• Smirnova et al. (2024) surveySoFR - scalar on function
• Koffman et al. (2025) svyfosr - function on scalar
  • FUI with survey package

FDA Book

Functional Data Analysis with R

Modules

https://jhuwit.github.io/wearabler/modules

References

Cui, Erjia, Andrew Leroux, Ekaterina Smirnova, and Ciprian M Crainiceanu. 2022. “Fast Univariate Inference for Longitudinal Functional Models.” Journal of Computational and Graphical Statistics 31 (1): 219–30.

Koffman, Lily, Sunan Gao, Xinkai Zhou, Andrew Leroux, Ciprian Crainiceanu, and John Muschelli III. 2025. “Function on Scalar Regression with Complex Survey Designs.” arXiv Preprint arXiv:2511.05487.

Shiroma, Eric J, I-Min Lee, Mitchell A Schepps, Masamitsu Kamada, and Tamara B Harris. 2019. “Physical Activity Patterns and Mortality: The Weekend Warrior and Activity Bouts.” Medicine and Science in Sports and Exercise 51 (1): 35.

Smirnova, Ekaterina, Erjia Cui, Lucia Tabacu, and Andrew Leroux. 2024. “Scalar-on-Function Regression: Estimation and Inference Under Complex Survey Designs.” Statistics in Medicine 43 (23): 4559–74.

Swihart, Bruce, Brian Caffo, Bryan D James, Matthew Strand, Brian S Schwartz, and Naresh M Punjabi. 2009. Lasagna Plots: A Saucy Alternative to Spaghetti Plots.