Treatment coding and interpretation • PDRobust

Choose treatment coding before analysis

Treatment 1 must represent the survival-favorable arm: the causal survival-monotonicity assumption is $S^1(t_*) \ge S^0(t_*)$ , where $t_*$ is the selected cutoff. The always-survivor population comprises subjects who would survive to that cutoff under either treatment. The implementation uses the survival probability under arm 0 as its principal score.

This is a scientific assumption about potential survival for each subject. Higher observed survival in one group does not establish it. Mapping() names columns and DataCheck() validates the observed panel; neither infers the appropriate treatment direction or verifies causal identification.

The main estimator in Zhang et al. (2026) uses the opposite treatment labels. To adapt data coded according to that convention, reverse the binary treatment in the raw data before calling Mapping(), DataCheck(), and DataStandard(). Apply the recoding consistently to the treatment used by every model. Do not simply relabel a fitted object’s output.

paper_treatment <- c(0L, 1L, 1L, 0L)
package_treatment <- 1L - paper_treatment
data.frame(paper_treatment, package_treatment)
#>   paper_treatment package_treatment
#> 1               0                 1
#> 2               1                 0
#> 3               1                 0
#> 4               0                 1

For character or factor treatment columns, first explicitly identify the two levels and their intended numeric codes. The built-in datasets already follow the package convention and should not be reversed for their example analyses.

Report the intended effect direction

The package estimates arm 1 minus arm 0. Reversing input treatment labels therefore reverses the contrast relative to the original labels. Negate an effect estimate and map an interval [lower, upper] to [-upper, -lower]; its standard error is unchanged. For example, using illustrative numbers:

package_result <- data.frame(estimate = 2, lower = 1, upper = 3, SD = 0.5)
original_contrast <- data.frame(
  estimate = -package_result$estimate,
  lower = -package_result$upper,
  upper = -package_result$lower,
  SD = package_result$SD
)
original_contrast
#>   estimate lower upper  SD
#> 1       -2    -3    -1 0.5

For HTESepT() the estimate column is summary$estimate and the interval columns are summary$LowerBound and summary$UpperBound; HTEAllT() uses the same column names. The sign transformation applies to effect-model coefficients and their intervals. It does not instruct users to negate survival odds ratios returned by ORCI().

Interpret the working effect model

For a continuous outcome, the working treatment effect is the intercept plus the linear combination of the mapped baseline effect modifiers. For a binary outcome, that linear predictor eta is transformed by 2 * plogis(eta) - 1 to obtain the working risk difference. Binary coefficients are consequently not direct risk differences or log odds ratios. The link is odd about zero, so reversing all coefficients reverses the modeled effect.

HTESepT() fits separate coefficients for the requested standardized times. HTEAllT() uses every observed time from baseline through cutoff and includes a linear time term when multiple times are present. DataStandard() maps raw visits to consecutive integers. A pooled time coefficient is therefore per standardized visit, not automatically per month or year; irregular raw visit spacing is not retained as a continuous time covariate by that coefficient.

The target principal stratum remains defined at the cutoff, including when reporting effects at earlier times. Observed survivors are not individually identified as always-survivors by this analysis.

Assumptions, numerical safeguards, and scope

Consult the package overview and the methodological reference for causal assumptions. The fitted models do not resolve unmeasured confounding, interference, violations of survival monotonicity, or violations of principal ignorability. Covariate balance and successful optimization are diagnostic evidence, not proof of those assumptions.

The implementation clips propensity scores to [0.01, 0.99] and the product of propensity and treatment-1 survival probability to [0.005, 0.995] in the HTE equations. Clipping changes the equation when active. The coding conversion explains the contrast but is not a guarantee of exact numerical reproduction of the paper’s unmodified formulas. The package fits parametric nuisance models internally; it does not expose arbitrary machine-learning or cross-fitting interfaces.

SA() adds random outcome noise. It does not implement the paper’s principal-ignorability sensitivity ratio. Label this output as outcome-noise sensitivity, and set a seed for reproducibility. The small bootstrap counts in example vignettes demonstrate the interface; increase them and assess inference stability before using confidence intervals substantively.

Use citation("PDRobust") to obtain the software and methodological references.