Fits a specified time-to-dropout model to the dropout data.
fitDropout(
df,
dropout_model = "exponential",
piecewiseDropoutTime = 0,
k_dropout = 0,
scale_dropout = "hazard",
m_dropout = 5,
showplot = TRUE,
by_treatment = FALSE,
covariates = NULL
)A list of results from the model fit including key information
such as the dropout model, model, the estimated model parameters,
theta, the covariance matrix, vtheta, as well as the
Akaike Information Criterion, aic, and
Bayesian Information Criterion, bic.
If the piecewise exponential model is used, the location
of knots used in the model, piecewiseDropoutTime, will
be included in the list of results.
If the model averaging option is chosen, the weight assigned
to the Weibull component is indicated by the w1 variable.
If the spline option is chosen, the knots and scale
will be included in the list of results.
If the cox model option is chosen, the list of results will include
model, theta, vtheta, aic, bic, and
piecewiseDropoutTime. Here
$$\theta = (\log(\lambda_1), \ldots, \log(\lambda_M), \beta^T)^T,$$
\(M\) denotes the number of distinct observed dropout times,
\(t_1 < \cdots < t_M\),
\(\lambda_j\) denotes the estimated hazard rate in the \(j\)th
dropout time interval, \((t_{j-1}, t_j]\), and
\(\beta\) represents the regression
coefficients (log hazard ratios) from the Cox model.
For a fair comparison, the estimation of baseline hazards is
incorporated into the aic and bic values.
In addition, \(\mbox{piecewiseDropoutTime} = (0, t_1, \ldots, t_M)\).
To extend the survival curve
beyond the last observed dropout time, a weighted average of the hazard
rates from the final m_dropout dropout time intervals is used.
The weights are proportional to the lengths of those intervals, i.e.,
$$\lambda_{M+1} = \sum_{j=M-m_{\rm{dropout}}+1}^{M} w_j \lambda_j,$$
where \(w_j = (t_j - t_{j-1})/(t_M - t_{M-m_{\rm{dropout}}})\) for \(j=M-m_{\rm{dropout}}+1,\ldots,M\).
When fitting the dropout model by treatment, the outcome is presented as a list of lists, where each list element corresponds to a specific treatment group.
The fitted time-to-dropout survival curve is also returned.
The subject-level dropout data, including time and
dropout. The data should also include treatment
coded as 1, 2, and so on, and treatment_description
for fitting the dropout model by treatment.
The dropout model used to analyze the dropout data
which can be set to one of the following options:
"exponential", "Weibull", "log-logistic", "log-normal",
"piecewise exponential", "model averaging", "spline", or "cox model".
The model averaging uses the exp(-bic/2) weighting and
combines Weibull and log-normal models. The spline model of
Royston and Parmar (2002) assumes that a transformation of
the survival function is modeled as a natural cubic spline
function of log time. By default, it is set to "exponential".
A vector that specifies the time intervals for the piecewise exponential dropout distribution. Must start with 0, e.g., c(0, 60) breaks the time axis into 2 event intervals: [0, 60) and [60, Inf). By default, it is set to 0.
The number of inner knots of the spline. The default
k_dropout=0 gives a Weibull, log-logistic or log-normal model,
if scale_dropout is "hazard", "odds", or "normal", respectively.
The knots are chosen as equally-spaced quantiles of the log
uncensored survival times. The boundary knots are chosen as the
minimum and maximum log uncensored survival times.
If "hazard", the log cumulative hazard is modeled as a spline function. If "odds", the log cumulative odds is modeled as a spline function. If "normal", -qnorm(S(t)) is modeled as a spline function.
The number of dropout time intervals to extrapolate the hazard function beyond the last observed dropout time.
A Boolean variable to control whether or not to
show the fitted time-to-dropout survival curve. By default, it is
set to TRUE.
A Boolean variable to control whether or not to
fit the time-to-dropout data by treatment group. By default,
it is set to FALSE.
The names of baseline covariates from the input data frame to include in the dropout model, e.g., c("age", "sex"). Factor variables need to be declared in the input data frame.
Kaifeng Lu, kaifenglu@gmail.com
Patrick Royston and Mahesh K. B. Parmar. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Stat in Med. 2002; 21:2175-2197.
dropout_fit <- fitDropout(
df = interimData2,
dropout_model = "exponential")
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