retinal: Intraocular Gas Decay in Retinal Surgery

In gkwreg: Generalized Kumaraswamy Regression Models for Bounded Data

Intraocular Gas Decay in Retinal Surgery

Description

Longitudinal data on the recorded decay of intraocular gas (perfluoropropane) in complex retinal surgeries. The dataset tracks the proportion of gas remaining over time following vitrectomy procedures.

Usage

retinal

Format

A data frame with 40 observations on 7 variables:

ID

integer. Patient identification number for longitudinal tracking.

Gas

numeric. Proportion of intraocular gas remaining (0-1 scale). Response variable measuring the fraction of perfluoropropane gas still present in the vitreous cavity.

Time

numeric. Time point of measurement (days or weeks post-surgery).

LogT

numeric. Logarithm of time, log(Time). Used to linearize the exponential decay pattern.

LogT2

numeric. Squared logarithm of time, (log(Time))^2. Captures nonlinear decay patterns.

Level

factor. Initial gas concentration level at the time of injection. Different starting concentrations affect decay kinetics.

Details

This longitudinal dataset comes from a study of gas decay following vitreoretinal surgery. Perfluoropropane (C3F8) is commonly used as a temporary tamponade agent in retinal detachment repair and other complex vitreoretinal procedures.

Clinical background: During vitrectomy for retinal detachment, gas bubbles are injected into the vitreous cavity to help reattach the retina by providing internal tamponade. The gas gradually absorbs and dissipates over time. Understanding the decay rate is important for:

• Predicting when patients can resume normal activities (esp. air travel)

• Assessing treatment efficacy

• Planning follow-up examinations

Decay kinetics: Gas decay typically follows a nonlinear pattern that can be approximated by exponential or power-law functions. The log transformation (LogT, LogT2) helps linearize these relationships for regression modeling.

Data structure: This is a longitudinal/panel dataset with repeated measurements on the same patients over time. Correlation structures (exchangeable, AR(1), etc.) should be considered when modeling.

The proportional nature of the gas variable (bounded between 0 and 1) makes this dataset ideal for:

• Simplex marginal models (original application by Song & Tan 2000)

• Beta regression with longitudinal correlation structures

• Kumaraswamy regression with heteroscedastic errors

Source

Based on clinical data from vitreoretinal surgery patients. Originally analyzed in Song and Tan (2000).

References

Meyers, S.M., Ambler, J.S., Tan, M., Werner, J.C., and Huang, S.S. (1992). Variation of Perfluoropropane Disappearance After Vitrectomy. Retina, 12, 359–363.

Song, P.X.-K., and Tan, M. (2000). Marginal Models for Longitudinal Continuous Proportional Data. Biometrics, 56, 496–502. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.0006-341x.2000.00496.x")}

Song, P.X.-K., Qiu, Z., and Tan, M. (2004). Modelling Heterogeneous Dispersion in Marginal Models for Longitudinal Proportional Data. Biometrical Journal, 46, 540–553.

Qiu, Z., Song, P.X.-K., and Tan, M. (2008). Simplex Mixed-Effects Models for Longitudinal Proportional Data. Scandinavian Journal of Statistics, 35, 577–596. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.1467-9469.2008.00603.x")}

Zhang, P., Qiu, Z., and Shi, C. (2016). simplexreg: An R Package for Regression Analysis of Proportional Data Using the Simplex Distribution. Journal of Statistical Software, 71(11), 1–21. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v071.i11")}

Examples

require(gkwreg)
require(gkwdist)

data(retinal)

# Example 1: Nonlinear time decay with level effects
# Model gas decay as quadratic function of log-time
# Allow precision to vary by initial gas concentration
fit_kw <- gkwreg(
  Gas ~ LogT + LogT2 + Level |
    Level,
  data = retinal,
  family = "kw"
)
summary(fit_kw)

# Interpretation:
# - Alpha: Decay curve shape varies by initial gas concentration
#   LogT + LogT2 capture nonlinear exponential-like decay
# - Beta: Precision differs by concentration level
#   Higher concentration may produce more/less variable decay

# Example 2: Heteroscedastic model
# Variability in gas proportion may change over time
fit_kw_hetero <- gkwreg(
  Gas ~ LogT + LogT2 + Level |
    Level + LogT,
  data = retinal,
  family = "kw"
)
summary(fit_kw_hetero)

# Interpretation:
# - Beta: Precision varies with both level and time
#   Early measurements may be more variable than late measurements

# Test heteroscedasticity
anova(fit_kw, fit_kw_hetero)

# Example 3: Exponentiated Kumaraswamy for decay tails
# Gas decay may show different tail behavior at extreme time points
# (very fast initial decay or very slow residual decay)
fit_ekw <- gkwreg(
  Gas ~ LogT + LogT2 + Level | # alpha: decay curve
    Level + LogT | # beta: heteroscedasticity
    Level, # lambda: tail heaviness by level
  data = retinal,
  family = "ekw"
)
summary(fit_ekw)

# Interpretation:
# - Lambda varies by level: Different initial concentrations may have
#   different rates of extreme decay (very fast or very slow residual gas)
# - Important for predicting complete absorption time

# Example 4: McDonald distribution for asymmetric decay
# Alternative parameterization for skewed decay patterns
fit_mc <- gkwreg(
  Gas ~ LogT + LogT2 + Level | # gamma
    LogT + Level | # delta
    Level, # lambda
  data = retinal,
  family = "mc",
  control = gkw_control(
    method = "BFGS",
    maxit = 1500,
    reltol = 1e-8
  )
)
summary(fit_mc)

# Model comparison
AIC(fit_kw, fit_kw_hetero, fit_ekw, fit_mc)

gkwreg documentation built on Nov. 27, 2025, 5:06 p.m.