Augmented Inverse Probability of Treatment Weighted Survival Curves using Pseudo-Values

This page explains the details of estimating augmented inverse probability of treatment weighted survival curves using Pseudo-Values for single event time-to-event data (method="aiptw_pseudo" in the adjustedsurv function). All regular arguments of the adjustedsurv function can be used. Additionally, the outcome_vars argument and the treatment_model argument have to be specified in the adjustedsurv call. Further arguments specific to this method are listed below.

Arguments

outcome_vars: [required] A character vector of column names specifying variables to be used when modeling the outcome mechanism using geese. See details and examples.
treatment_model: [required] Must be a glm or multinom model object with variable as response variable. Alternatively you can supply a numeric vector of propensity scores directly. See details and examples.
type_time: A character string specifying how the time should be modeled. Possible values are "factor" (modeling each point in time as a separate variable, the default), "bs" (modeling time using B-Splines) or "ns" (modeling time using natural splines).
spline_df: The number of degrees of freedom used for the natural-spline or B-spline function. Ignored if type_time="factor". Defaults to 5.
censoring_vars: An optional character vector specifying variables in data. Those are used in the calculation of inverse probability of censoring weighted pseudo observations. See ?pseudo_aareg for more information. Set to NULL (default) to use standard pseudo-values without corrections for dependent censoring instead.
ipcw_method: The specific method used in the calculation of inverse probability of censoring weighted pseudo observations. Can be either "binder" (default) or "hajek". See ?pseudo_aareg for more information. Ignored if censoring_vars=NULL.

Details

Type of Adjustment: Requires a treatment assignment model (glm or multinom) and a character vector of variable names used to model the outcome mechanism (internally uses geese). Covariate-Dependent censoring can be corrected for using inverse probability of censoring weighted pseudo-values (Binder et al. 2014)
Doubly-Robust: Estimates are Doubly-Robust.
Categorical groups: Any number of levels in variable are allowed. Must be a factor variable.
Approximate Variance: Calculations to approximate the variance and confidence intervals are available.
Allowed Time Values: Allows both continuous and integer time.
Bounded Estimates: Estimates are not guaranteed to be bounded in the 0 to 1 probability range.
Monotone Function: Estimates are not guaranteed to be monotone.
Dependencies: This method relies on the geepack and prodlim packages. Additionally requires the eventglm package if censoring_vars is specified.

Instead of only modeling the outcome mechanism or the treatment assignment mechanism, both kind of models are required to use this method. If either of those models are correctly specified, unbiased estimates will be obtained. In contrast to the "aiptw" method, the "aiptw_pseudo" method uses a generalized estimation equation (geese) approach to model the outcome mechanism. The model is fit in the same way as described in the "direct_pseudo" method. Those Direct Standardization based estimates are then transformed using the previously estimated propensity score. This results in the doubly-robust property of the method. More information on this particular method can be found in the original article by Wang (2018), more information on Pseudo-Values is available in Andersen et al. (2017) and Andersen and Perme (2010).

When estimating the geese model the ev_time variable is used as a factor by default. This results in one coefficient being estimated for each unique point in time, which can be very slow computationally if there are a lot of unique points in time and/or the dataset has many rows. In these cases it is recommended to use type_time="bs" or type_time="ns", which results in the ev_time being modeled using B-Splines or Natural Splines. Simulation studies indicate that there is little difference in the estimates when an appropriately large number of spline_df is used.

Additionally, covariate-dependent censoring can be accounted for by using inverse probability of censoring weighted pseudo-values (Binder et al. 2014) instead of regular pseudo-values (specified using the censoring_vars and ipcw_method arguments).

Value

Adds the following additional objects to the output of the adjustedsurv function:

pseudo_values: The matrix of estimated pseudo-values.
geese_model: The geese model used to make the predictions.

References

Jixian Wang (2018). "A Simple, Doubly Robust, Efficient Estimator for Survival Functions Using Pseudo Observations". In: Pharmaceutical Statistics 17.38-48

James M. Robins and Andrea Rotnitzky (1992). "Recovery of Information and Adjustment for Dependent Censoring Using Surrogate Markers". In: AIDS Epidemiology: Methodological Issues. Ed. by Nicholas P. Jewell, Klaus Dietz, and Vernon T. Farewell. New York: Springer Science + Business Media, pp. 297-331

Per Kragh Andersen, Elisavet Syriopoulou, and Erik T. Parner (2017). "Causal Inference in Survival Analysis using Pseudo-Observations". In: Statistics in Medicine 36, pp. 2669-2681

Per Kragh Andersen and Maja Pohar Perme (2010). "Pseudo-Observations in Survival Analysis". In: Statistical Methods in Medical Research 19, pp. 71-99

Aris Perperoglou, Willi Sauerbrei, Michal Abrahamowicz, and Matthias Schmid (2019). "A Review of Spline Function Procedures in R". in: BMC Medical Research Methodology 19.46, pp. 1-16

Nadine Binder, Thomas A. Gerds, and Per Kragh Andersen (2014). "Pseudo- Observations for Competing Risks with Covariate Dependent Censoring". In: Lifetime Data Analysis 20, pp. 303-315

Author

Jixian Wang supplied the R source code used in the original article, which was used by Robin Denz to create a generalized version of this method with additional functionality and improved performance.

Examples

library(adjustedCurves)

if (requireNamespace("geepack") & requireNamespace("prodlim")) {

set.seed(42)

# simulate some data as example
sim_dat <- sim_confounded_surv(n=50, max_t=1.2)
sim_dat$group <- as.factor(sim_dat$group)

# estimate a treatment assignment model
glm_mod <- glm(group ~ x1 + x3 + x5 + x6, data=sim_dat, family="binomial")

# use it + pseudo values + geese model to calculate adjusted survival curves
adjsurv <- adjustedsurv(data=sim_dat,
                        variable="group",
                        ev_time="time",
                        event="event",
                        method="aiptw_pseudo",
                        outcome_vars=c("x1", "x2", "x3", "x4", "x5", "x6"),
                        treatment_model=glm_mod,
                        conf_int=TRUE,
                        iso_reg=TRUE,
                        force_bounds=TRUE)

# plot the curves
plot(adjsurv, conf_int=TRUE)
}