rctglm_with_prognosticscore.md
In postcard: Estimating Marginal Effects with Prognostic Covariate Adjustment

`rctglm_with_prognosticscore` snapshot tests

Code
  ate <- withr::with_seed(42, {
    rctglm_with_prognosticscore(formula = Y ~ ., exposure_indicator = A,
    exposure_prob = exposure_prob, data = dat_treat, family = gaussian(),
    estimand_fun = "ate", data_hist = dat_notreat, learners = learners,
    cv_variance = TRUE, verbose = 2)
  })
Message

  -- Fitting prognostic model --

  i Created formula for fitting prognostic model as: Y ~ .
  i Fitting learners
  * mod_mars
  * mod_lm
  i No tuning parameters. `fit_resamples()` will be attempted
  i 1 of 2 resampling: mod_mars
  v 1 of 2 resampling: mod_mars ()
  i No tuning parameters. `fit_resamples()` will be attempted
  i 2 of 2 resampling: mod_lm
  v 2 of 2 resampling: mod_lm ()
  i Model with lowest RMSE: mod_mars
  i Investigate trained learners and fitted model in `prognostic_info` list element

  -- Symbolic differentiation of estimand function --

  i Symbolically deriving partial derivative of the function 'psi1 - psi0' with respect to 'psi0' as: '-1'.
  * Alternatively, specify the derivative through the argument
  `estimand_fun_deriv0`
  i Symbolically deriving partial derivative of the function 'psi1 - psi0' with respect to 'psi1' as: '1'.
  * Alternatively, specify the derivative through the argument
  `estimand_fun_deriv1`

Code
  ate_wo_cvvariance <- withr::with_seed(42, {
    rctglm_with_prognosticscore(formula = Y ~ ., exposure_indicator = A,
    exposure_prob = exposure_prob, data = dat_treat, family = gaussian(),
    estimand_fun = "ate", data_hist = dat_notreat, learners = learners,
    cv_variance = FALSE, verbose = 0)
  })

Code
  rr_pois_wo_cvvariance
Output

  Object of class rctglm_prog

  Call:  rctglm_with_prognosticscore(formula = Y ~ ., exposure_indicator = A, 
      exposure_prob = exposure_prob, data = dat_treat_pois, family = poisson(), 
      estimand_fun = "rate_ratio", cv_variance = FALSE, data_hist = dat_notreat_pois, 
      learners = learners, verbose = 0)

  Counterfactual control mean (psi_0=E[Y|X, A=0]) estimate: 7.981
  Counterfactual control mean (psi_1=E[Y|X, A=1]) estimate: 58.48
  Estimand function r: psi1/psi0
  Estimand (r(psi_1, psi_0)) estimate (SE): 7.327 (0.518)

Code
  rr_pois_with_cvvariance
Output

  Object of class rctglm_prog

  Call:  rctglm_with_prognosticscore(formula = Y ~ ., exposure_indicator = A, 
      exposure_prob = exposure_prob, data = dat_treat_pois, family = poisson(), 
      estimand_fun = "rate_ratio", cv_variance = TRUE, data_hist = dat_notreat_pois, 
      learners = learners, verbose = 0)

  Counterfactual control mean (psi_0=E[Y|X, A=0]) estimate: 7.981
  Counterfactual control mean (psi_1=E[Y|X, A=1]) estimate: 58.48
  Estimand function r: psi1/psi0
  Estimand (r(psi_1, psi_0)) estimate (SE): 7.327 (0.5271)

Code
  rr_nb_wo_cvvariance
Output

  Object of class rctglm_prog

  Call:  rctglm_with_prognosticscore(formula = Y ~ ., exposure_indicator = A, 
      exposure_prob = exposure_prob, data = dat_treat_pois, family = MASS::negative.binomial(2), 
      estimand_fun = "rate_ratio", cv_variance = FALSE, data_hist = dat_notreat_pois, 
      learners = learners, verbose = 0)

  Counterfactual control mean (psi_0=E[Y|X, A=0]) estimate: 8.067
  Counterfactual control mean (psi_1=E[Y|X, A=1]) estimate: 57.7
  Estimand function r: psi1/psi0
  Estimand (r(psi_1, psi_0)) estimate (SE): 7.153 (0.5005)

Code
  rr_nb_with_cvvariance
Output

  Object of class rctglm_prog

  Call:  rctglm_with_prognosticscore(formula = Y ~ ., exposure_indicator = A, 
      exposure_prob = exposure_prob, data = dat_treat_pois, family = MASS::negative.binomial(2), 
      estimand_fun = "rate_ratio", cv_variance = TRUE, data_hist = dat_notreat_pois, 
      learners = learners, verbose = 0)

  Counterfactual control mean (psi_0=E[Y|X, A=0]) estimate: 8.067
  Counterfactual control mean (psi_1=E[Y|X, A=1]) estimate: 57.7
  Estimand function r: psi1/psi0
  Estimand (r(psi_1, psi_0)) estimate (SE): 7.153 (0.5114)