Nested and longitudinal data

Long format, natively

Repeated-measures and nested designs are the reason flexsynth works in long format. You never pivot to wide: the structure formula declares the hierarchy, for example ~ id / visit (patients, each with a sequence of visits).

We simulate a longitudinal cohort. Each patient has a fixed baseline (age, sex) and a time-varying systolic blood pressure that drifts over visits — an autocorrelated series with an unequal number of visits per patient.

n_pat <- 120
base <- data.frame(
  id  = seq_len(n_pat),
  age = round(rnorm(n_pat, 60, 10)),
  sex = sample(c("F", "M"), n_pat, replace = TRUE)
)
n_visits <- 1 + rpois(n_pat, 2)                 # unequal length units

rows <- lapply(seq_len(n_pat), function(i) {
  k <- n_visits[i]
  sbp <- numeric(k)
  sbp[1] <- 0.6 * base$age[i] + rnorm(1, 95, 8)
  for (t in seq_len(k)[-1]) sbp[t] <- 0.8 * sbp[t - 1] + rnorm(1, 26, 6)
  data.frame(id = base$id[i], visit = seq_len(k),
             age = base$age[i], sex = base$sex[i],
             sbp = round(sbp))
})
real <- do.call(rbind, rows)
head(real, 8)

id	visit	age	sex	sbp
1	1	54	M	133
2	1	62	M	140
2	2	62	M	140
3	1	52	F	119
3	2	52	F	128
3	3	52	F	117
3	4	52	F	116
4	1	76	M	139

Synthesising the hierarchy

res <- synth(real, structure = ~ id / visit, seed = 1)
res

#> <synth_result>
#>   track        : A (high-utility; NOT differentially private)
#>   datasets (m) : 1 
#>   rows each    : 358  (input: 366 )
#>   synthesised  : age, sex, sbp 
#>   unit-level   : age, sex (once per unit)
#>   carried      : visit 
#>   method       : cart 
#> 
#> Get the data with as.data.frame(x)  

The engine detects that age and sex are constant within a patient (subject-invariant) and synthesises them once per unit, broadcasting them across that unit’s visits, so a synthetic patient stays internally consistent. The number of visits per patient is drawn from the learned count distribution, and sbp is synthesised with an initial-state model plus a Markov transition that conditions on the previous visit — so the within-patient autocorrelation survives.

syn <- as.data.frame(res)

# unequal-length units are reproduced, not fixed-width
table(table(syn$id))

#> 
#>  1  2  3  4  5  6  7 
#> 19 34 29 14 19  2  3 

# baseline stays constant within each synthetic patient
all(tapply(syn$age, syn$id, function(a) length(unique(a)) == 1))

#> [1] TRUE

Within-unit temporal constraints

rule() with scope = "unit" evaluates a rule per unit, which is how you express temporal logic. Suppose visits must be numbered consecutively from 1 and sbp must stay in a plausible range on every visit:

res_c <- synth(
  real, ~ id / visit,
  constraints = list(
    rule(sbp >= 60 & sbp <= 260),                       # row scope (default)
    rule(all(diff(visit) == 1), scope = "unit")         # consecutive visits
  ),
  seed = 1
)
syn_c <- as.data.frame(res_c)

# every synthetic unit's visits are 1, 2, 3, ...
all(tapply(syn_c$visit, syn_c$id,
           function(v) identical(v, seq_along(v))))

#> [1] TRUE

Units that violate any rule are regenerated (bounded by constraint_max_tries in synth_control()), so the nested structure is never broken to satisfy a constraint.

Diagnostics

The utility and risk diagnostics work unchanged on long data.

diagnose(real, res, vars = c("age", "sex", "sbp"))

#> <flexsynth_diagnostics>
#>   rows        : real 366  synthetic 358 
#>   variables   : 3 
#> 
#> Univariate fit (smaller = closer):
#>  variable        type metric distance
#>       age     numeric     ks   0.1345
#>       sex categorical    tvd   0.0082
#>       sbp     numeric     ks   0.0924
#>   mean distance: 0.0784   worst: age (0.1345)
#> 
#> Correlation structure (2 numeric vars):
#>   Frobenius diff: 0.0555   mean |diff|: 0.0392   max |diff|: 0.0392
#> 
#> Propensity utility (pMSE, logistic; descriptive, in-sample):
#>   pMSE: 0.00035   expected: 0.00052   ratio: 0.68 (1 = indistinguishable)

Because visits share a patient, treat the diagnostics as descriptive: the pMSE here mixes baseline and time-varying columns rather than modelling the dependence explicitly.