# Unanchored Binary Analysis

#### 2025-02-21

# Loading R packages

    # install.packages("maicplus")
    library(maicplus)

Additional R packages for this vignette:

    library(dplyr)

# Illustration using example data

This example reads in `centered_ipd_sat` data that was created in `calculating_weights` vignette and uses `adrs_sat` dataset to run binary outcome analysis using the `maic_unanchored` function by specifying `endpoint_type = "binary"`.

Note that parameters `ipd` and `pseudo_ipd` in the `maic_unanchored` function for binary data analysis needs to have the following columns: USUBJID, ARM, RESPONSE. USUBJID in `ipd` needs to match USUBJID in `weights_object`. `pseudo_ipd` for binary data can be conveniently generated using `get_pseudo_ipd_binary` function.

Robust standard error for the adjusted result are calculated by sandwich variance estimator in `sandwich` package with the function `vcovHC`. Default type of variance estimator (specified by parameter `binary_robust_cov_type`) is `HC3`, but other types can be specified. For more information on different types, see `vcovHC`.

    data(centered_ipd_sat)
    data(adrs_sat)

    centered_colnames <- c("AGE", "AGE_SQUARED", "SEX_MALE", "ECOG0", "SMOKE", "N_PR_THER_MEDIAN")
    centered_colnames <- paste0(centered_colnames, "_CENTERED")

    weighted_data <- estimate_weights(
      data = centered_ipd_sat,
      centered_colnames = centered_colnames
    )

    # get dummy binary pseudo IPD
    pseudo_adrs <- get_pseudo_ipd_binary(
      binary_agd = data.frame(
        ARM = "B",
        RESPONSE = c("YES", "NO"),
        COUNT = c(280, 120)
      ),
      format = "stacked"
    )

    result <- maic_unanchored(
      weights_object = weighted_data,
      ipd = adrs_sat,
      pseudo_ipd = pseudo_adrs,
      trt_ipd = "A",
      trt_agd = "B",
      normalize_weight = FALSE,
      endpoint_type = "binary",
      endpoint_name = "Binary Endpoint",
      eff_measure = "OR",
      # binary specific args
      binary_robust_cov_type = "HC3"
    )

There are two summaries available in the result: descriptive and inferential. In the descriptive section, we have summaries of events.

    result$descriptive

    ## $summary
    ##   trt_ind treatment            type        n   events events_pct
    ## 1       B         B Before matching 400.0000 280.0000   70.00000
    ## 2       A         A Before matching 500.0000 390.0000   78.00000
    ## 3       B         B  After matching 400.0000 280.0000   70.00000
    ## 4       A         A  After matching 199.4265 142.8968   71.65386

In the inferential section, we have the fitted models stored (i.e. logistic regression) and the results from the `glm` models (i.e. odds ratios and CI). If other effect measures are needed besides odds ratios, we have an option to fit risk ratios or risk differences via `eff_measure` parameter. Here is the overall summary.

    result$inferential$summary

    ##          case       OR       LCL      UCL        pval
    ## 1          AB 1.519481 1.1247154 2.052805 0.006417064
    ## 2 adjusted_AB 1.083350 0.7268601 1.614683 0.694183560

Here are model and results before adjustment.

    result$inferential$fit$model_before

    ##
    ## Call:  glm(formula = RESPONSE ~ ARM, family = binomial(link = glm_link),
    ##     data = dat)
    ##
    ## Coefficients:
    ## (Intercept)         ARMA
    ##      0.8473       0.4184
    ##
    ## Degrees of Freedom: 899 Total (i.e. Null);  898 Residual
    ## Null Deviance:       1023
    ## Residual Deviance: 1016  AIC: 1020

    result$inferential$fit$res_AB_unadj

    ## $est
    ## [1] 1.519481
    ##
    ## $se
    ## [1] 0.2373883
    ##
    ## $ci_l
    ## [1] 1.124715
    ##
    ## $ci_u
    ## [1] 2.052805
    ##
    ## $pval
    ## [1] 0.006417064

Here are model and results after adjustment.

    result$inferential$fit$model_after

    ##
    ## Call:  glm(formula = RESPONSE ~ ARM, family = binomial(link = glm_link),
    ##     data = dat, weights = weights)
    ##
    ## Coefficients:
    ## (Intercept)         ARMA
    ##     0.84730      0.08006
    ##
    ## Degrees of Freedom: 899 Total (i.e. Null);  898 Residual
    ## Null Deviance:       726.7
    ## Residual Deviance: 726.5     AIC: 712.5

    result$inferential$fit$res_AB

    ## $est
    ## [1] 1.08335
    ##
    ## $se
    ## [1] 0.2275624
    ##
    ## $ci_l
    ## [1] 0.7268601
    ##
    ## $ci_u
    ## [1] 1.614683
    ##
    ## $pval
    ## [1] 0.6941836

# Using bootstrap to calculate standard errors

If bootstrap standard errors are preferred, we need to specify the number of bootstrap iteration (`n_boot_iteration`) in `estimate_weights` function and proceed fitting `maic_unanchored` function. Then, the outputs include bootstrapped CI. Different types of bootstrap CI can be found by using parameter `boot_ci_type`. See `boot.ci` in `boot` package for more details.

    weighted_data2 <- estimate_weights(
      data = centered_ipd_sat,
      centered_colnames = centered_colnames,
      n_boot_iteration = 100,
      set_seed_boot = 1234
    )

    result_boot <- maic_unanchored(
      weights_object = weighted_data2,
      ipd = adrs_sat,
      pseudo_ipd = pseudo_adrs,
      trt_ipd = "A",
      trt_agd = "B",
      normalize_weight = FALSE,
      endpoint_type = "binary",
      endpoint_name = "Binary Endpoint",
      eff_measure = "OR",
      boot_ci_type = "perc",
      # binary specific args
      binary_robust_cov_type = "HC3"
    )

    result_boot$inferential$fit$boot_res_AB

    ## $est
    ## [1] 1.08335
    ##
    ## $se
    ## [1] NA
    ##
    ## $ci_l
    ## [1] 0.846157
    ##
    ## $ci_u
    ## [1] 1.796863
    ##
    ## $pval
    ## [1] NA

Note that the bootstrap in unanchored analysis only uses resampling of internal IPD trial population and assumes there is no uncertainty in the comparator trial population (i.e. estimated mean outcomes). [1] Therefore, we recommend the use of sandwich estimators for the variance calculation in the unanchored analysis.

# References

[1]
Chandler CO, Proskorovsky I. Uncertain about uncertainty in matching-adjusted indirect comparisons? A simulation study to compare methods for variance estimation. Research Synthesis Methods 2024;15:1094–110. https://doi.org/https://doi.org/10.1002/jrsm.1759.