Output Language Revision Trial

Summary

1. Output Language Update

The function is working in the pkonfound() command, available in the GitHub repository.
Revisions have been made for the RIR in Linear / Non-linear Model

2. Several Notes with Examples

* Citation link has been added in the “Viewer” Pane See here

* Handling of Rare Cases:

Specific language has been added for the rare case where needtworows = TRUE, particularly when switch_trm is either TRUE or FALSE.See here

* Updates on RIR percentage and p-value

Update in reporting RIR_pi and p-value See here
A specific note has been added for instances when RIR_pi (percentage) exceeds 100% See here

* Example using tkonfound (2by2 table) See here

Language updated

* Newly Added Functions that need review See here

* Quick Question

For tailoring sentence before user-entered/implied table by estimates,
it seems that user-entered table is generated by tkonfound() and implied table by estimates is generated by test_sensitivity_ln()
Would it be okay to change “The table you entered or is implied by your effect size:” in test_sensitivity_ln()
to “The table implied by the parameter estimates and sample sizes you entered is”?

0) install `konfound` from github repository

library(tidyverse)
library(htmltools)
library(evaluate)
library(githubinstall)
suppressMessages(gh_install_packages("konfound", ref = "newitcv_output", force = TRUE))

## Warning in fread(download_url, sep = "\t", header = FALSE, stringsAsFactors =
## FALSE, : Found and resolved improper quoting out-of-sample. First healed line
## 4848: <<Puriney honfleuR "Evening, honfleuR" by Seurat>>. If the fields are not
## quoted (e.g. field separator does not appear within any field), try quote="" to
## avoid this warning.

## Do you want to install the package (Y/n)?  
## future (1.33.0 -> 1.33.1) [CRAN]
## 
## The downloaded binary packages are in
##  /var/folders/52/my2sfsnn1qs78nfvl14zyynh0000gn/T//Rtmpzv4Ct5/downloaded_packages
## ── R CMD build ─────────────────────────────────────────────────────────────────
##   
   checking for file ‘/private/var/folders/52/my2sfsnn1qs78nfvl14zyynh0000gn/T/Rtmpzv4Ct5/remotesac323f008e28/konfound-project-konfound-d93cbc3/DESCRIPTION’ ...
  
✔  checking for file ‘/private/var/folders/52/my2sfsnn1qs78nfvl14zyynh0000gn/T/Rtmpzv4Ct5/remotesac323f008e28/konfound-project-konfound-d93cbc3/DESCRIPTION’
## 
  
─  preparing ‘konfound’:
## 
  
   checking DESCRIPTION meta-information ...
  
✔  checking DESCRIPTION meta-information
## 
  
─  checking for LF line-endings in source and make files and shell scripts
## 
  
─  checking for empty or unneeded directories
## 
  
─  building ‘konfound_0.4.0.tar.gz’
## 
  
   
##

library(konfound)

1) Output Language for RIR in Linear Model

1.1) Invalidate, `eff_thr = NA`

# Case 1: Linear
### invalidate
## eff_thr = NA
pkonfound(est_eff = -0.3, std_err = 0.01, n_obs = 5000, n_covariates = 10, alpha = .05, tails = 2, index = "RIR", nu = 0, model_type = "ols", eff_thr = NA, to_return = "print")

## Robustness of Inference to Replacement (RIR):
## TO INVALIDATE:
## 
## RIR = 4673
## 
## You entered an estimated effect of -0.3. To invalidate
## the inference of an effect using the threshold of -0.02 for
## statistical significance with alpha = 0.05, 93.465% of the
## (-0.3) estimate would have to be due to bias. This implies
## that to invalidate the inference one would expect to have to
## replace 4673 (93.465%) observations with cases for which the
## treatment effect is 0 (RIR = 4673).
## 
## See Frank et al. (2013) for a description of the method.
## 
## Citation: Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. (2013).
## What would it take to change an inference?
## Using Rubin's causal model to interpret the robustness of causal inferences.
## Education, Evaluation and Policy Analysis, 35 437-460.

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

* Example image of citation hyperlink (automatically poped-up in viewer pane)

It appears that R might not directly support adding hyperlinks in the Console pane (where output language is displayed), so I suggest alternative method.

1.2) Invalidate, `eff_thr != NA` (user-entered threshold)

## eff_thr != NA (user entered)
pkonfound(est_eff = -0.3, std_err = 0.01, n_obs = 5000, n_covariates = 10, alpha = .05, tails = 2, index = "RIR", nu = 0, model_type = "ols", eff_thr = 0.2, to_return = "print")

## Robustness of Inference to Replacement (RIR):
## TO INVALIDATE:
## 
## RIR = 4673
## 
## You entered an effect of -0.3, and specified a threshold
## for inference of 0.2. To invalidate the inference based on your
## estimate, 93.465% of the (-0.3) estimate would have to be due to
## bias. This implies that to invalidate the inference one would
## expect to have to replace 4673 (93.465%) observations with
## cases for which the treatment effect is 0 (RIR = 4673).
## 
## See Frank et al. (2013) for a description of the method.
## 
## Citation: Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. (2013).
## What would it take to change an inference?
## Using Rubin's causal model to interpret the robustness of causal inferences.
## Education, Evaluation and Policy Analysis, 35 437-460.

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

1.3) Sustain, `eff_thr = NA`

### sustain
## eff_thr = NA
pkonfound(est_eff = 0.003, std_err = 0.1, n_obs = 5000, n_covariates = 10, alpha = .05, tails = 2, index = "RIR", nu = 0, model_type = "ols", eff_thr = NA, to_return = "print")

## Robustness of Inference to Replacement (RIR):
## TO SUSTAIN:
## 
## RIR = 4923
## 
## You entered an estimated effect of 0.003. The threshold value for
## statistical significance is 0.196 (alpha = 0.05). To reach that
## threshold, 98.47% of the (0.003) estimate would have to be due to
## bias. This implies that to sustain an inference one would expect to
## have to replace 4923 (98.47%) observations with effect of 0 with
## cases with effect of 0.196 (RIR = 4923).
## 
## See Frank et al. (2013) for a description of the method.
## 
## Citation: Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. (2013).
## What would it take to change an inference?
## Using Rubin's causal model to interpret the robustness of causal inferences.
## Education, Evaluation and Policy Analysis, 35 437-460.

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

1.4) Sustain, `eff_thr != NA` (user-entered threshold)

## eff_thr != NA (user entered)
pkonfound(est_eff = 0.09, std_err = 0.1, n_obs = 5000, n_covariates = 10, alpha = .05, tails = 2, index = "RIR", nu = 0, model_type = "ols", eff_thr = 0.2, to_return = "print")

## Robustness of Inference to Replacement (RIR):
## TO SUSTAIN:
## 
## RIR = 2705
## 
## You entered an effect size of 0.09, and specified a threshold
## for inference of 0.2. To reach that threshold, 54.092% of the
## (0.09) estimate would have to be due to bias. This implies
## that to sustain an inference one would expect to have to replace 
## 2705 (54.092%) observations with effect of 0 with cases
## with effect of 0.196 (RIR = 2705).
## 
## See Frank et al. (2013) for a description of the method.
## 
## Citation: Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. (2013).
## What would it take to change an inference?
## Using Rubin's causal model to interpret the robustness of causal inferences.
## Education, Evaluation and Policy Analysis, 35 437-460.

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

2) Output Language for RIR in Non-linear Model

2.1) Invalidate, `changeSE = TRUE`

In this example, added p-values are <0.000 and 0.051 and RIR_perc is 16.37%

# Case 2: Non-linear
## Case 2-1: changeSE = TRUE, Invalidate
pkonfound(-0.3, 0.01, 5000, n_covariates = 0, alpha = .05, tails = 2, nu = 0, n_treat = 2500, switch_trm = TRUE, model_type = "logistic", to_return = "print")

## RIR = 220
## 
## The table implied by the parameter estimates and sample sizes you entered:
## 
##           Fail Success
## Control   1157    1343
## Treatment 1344    1156
## 
## The reported effect size = -0.300, SE = 0.010, p-value = 0.000. 
## The SE has been adjusted to 0.057 to generate a real number in the 
## implied table. Numbers in the table cells have been rounded 
## to integers, which may slightly alter the estimated effect from 
## the value originally entered.
## 
## To invalidate the inference that the effect is different from 0 
## (alpha = 0.050) one would need to replace 220 (16.37%) treatment failure 
## cases with cases for which the probability of failure in the control 
## group (46.28%) applies (RIR = 220). This is equivalent to transferring 
## 118 cases from treatment failure to treatment success (Fragility = 118).
## 
## Note that RIR = Fragility/[1-P(failure in the treatment group)]
## 
## The transfer of 118 cases yields the following table:
## 
##           Fail Success
## Control   1157    1343
## Treatment 1226    1274
## Effect size = -0.111, SE = 0.057, p-value = 0.051. 
## Indicate that this is based on t = estimated effect/standard error

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

2.2) Invalidate, `changeSE = FALSE`

## Case 2-2: changeSE = FALSE, Invalidate
pkonfound(-0.3, 0.1, 5000, n_covariates = 10, alpha = .05, tails = 2, n_treat = 2500, switch_trm = TRUE, model_type = "logistic", to_return = "print")

## RIR = 207
## 
## The table implied by the parameter estimates and sample sizes you entered:
## 
##           Fail Success
## Control   2246     254
## Treatment 2307     193
## 
## The reported effect size = -0.300, and SE = 0.100, p-value = 0.003. 
## Values have been rounded to the nearest integer. This may cause 
## a little change to the estimated effect for the table.
## 
## To invalidate the inference that the effect is different from 0 
## (alpha = 0.050) one would need to replace 207 (8.97%) treatment failure 
## cases with cases for which the probability of failure in the control 
## group (89.84%) applies (RIR = 207). This is equivalent to transferring 
## 21 cases from treatment failure to treatment success (Fragility = 21).
## 
## Note that RIR = Fragility/[1-P(failure in the treatment group)]
## 
## The transfer of 21 cases yields the following table:
## 
##           Fail Success
## Control   2246     254
## Treatment 2286     214
## Effect size = -0.189, SE = 0.097, p-value = 0.052. 
## Indicate that this is based on t = estimated effect/standard error

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

2.3) Sustain, `changeSE = TRUE` (where RIR_perc exceeds 100%)

## Case 2-3: changeSE = TRUE, Sustain
pkonfound(-0.03, 0.2, 50, n_covariates = 5, alpha = .005, tails = 2, nu = 0, n_treat = 25, switch_trm = TRUE, model_type = "logistic", to_return = "print")

## RIR = 21
## 
## The table implied by the parameter estimates and sample sizes you entered:
## 
##           Fail Success
## Control     12      13
## Treatment   13      12
## 
## The reported effect size = -0.030, SE = 0.200, p-value = 0.779. 
## The SE has been adjusted to 0.566 to generate a real number in the 
## implied table. Numbers in the table cells have been rounded 
## to integers, which may slightly alter the estimated effect from 
## the value originally entered.
## 
## To reach the threshold that would sustain an inference that the 
## effect is different from 0 (alpha = 0.005) one would need to replace 21 
## (175.00%) treatment success cases with cases for which the probability of 
## failure in the control group (48.00%) applies (RIR = 21). This is equivalent 
## to transferring 10 cases from treatment success to treatment failure
## (Fragility = 10).
## 
## Note that RIR = Fragility/[1-P(success in the treatment group)]
## 
## Note the RIR exceeds 100%. Generating the transfer of 10 cases would
## require replacing more cases that are in the treatment success condition.
## 
## The transfer of 10 cases yields the following table:
## 
##           Fail Success
## Control     12      13
## Treatment   23       2
## Effect size = -2.522, SE = 0.839, p-value = 0.004. 
## Indicate that this is based on t = estimated effect/standard error

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

2.4) Sustain, `changeSE = FALSE`

## Case 2-4: changeSE = FALSE, Sustain
pkonfound(-0.03, 0.2, 500, n_covariates = 10, alpha = .05, tails = 2, nu = 0, n_treat = 250, switch_trm = TRUE, model_type = "logistic", to_return = "print")

## RIR = 24
## 
## The table implied by the parameter estimates and sample sizes you entered:
## 
##           Fail Success
## Control    180      70
## Treatment  182      68
## 
## The reported effect size = -0.030, and SE = 0.200, p-value = 0.841. 
## Values have been rounded to the nearest integer. This may cause 
## a little change to the estimated effect for the table.
## 
## To reach the threshold that would sustain an inference that the 
## effect is different from 0 (alpha = 0.050) one would need to replace 24 
## (35.29%) treatment success cases with cases for which the probability of 
## failure in the control group (72.00%) applies (RIR = 24). This is equivalent 
## to transferring 17 cases from treatment success to treatment failure
## (Fragility = 17).
## 
## Note that RIR = Fragility/[1-P(success in the treatment group)]
## 
## The transfer of 17 cases yields the following table:
## 
##           Fail Success
## Control    180      70
## Treatment  199      51
## Effect size = -0.417, SE = 0.211, p-value = 0.049. 
## Indicate that this is based on t = estimated effect/standard error

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

3) Output Language for RIR in Non-linear Model (`needtworows = T`)

Examining code line by line, needtworows = TRUE is a relatively rare case. Additionally, there are constraints that prevent invalidate_ob = TRUE when needtworows = TRUE.
For instance, an extremely small alpha value (e.g., 0.0001) combined with a small number of observations (n_obs, e.g., fewer than 50) is a major factor leading to needtworows = TRUE.
However, this scenario also results in a larger thr_t, which tends to make invalidate_ob = TRUE in almost all cases.
Therefore, even though language outputs are made for the all possible needtworows = TRUE scenario, finding a real case that satisfies this condition might be challenging.
Similarly, a small n_obs is closely associated with minse being greater than user_std_err. Consequently, it is also difficult to find a real case where changeSE = FALSE under the needtworows = TRUE condition.

3.1) `needtworows = T`, `sustain`, `changeSE = TRUE`

## Case 3: needtworows = T, Sustain, changeSE = T, 
pkonfound(0.25, 0.5, 70, n_covariates = 20, alpha = .001, tails = 2, nu = 0, n_treat = 20, switch_trm = TRUE, model_type = "logistic", to_return = "print")

## RIR = 37
## 
## The table implied by the parameter estimates and sample sizes you entered:
## 
##           Fail Success
## Control     27      23
## Treatment   10      10
## 
## The reported effect size = 0.250, SE = 0.500, p-value = 0.763. 
## The SE has been adjusted to 0.530 to generate a real number in the 
## implied table. Numbers in the table cells have been rounded 
## to integers, which may slightly alter the estimated effect from 
## the value originally entered.
## 
## The inference cannot be sustained merely by switching cases in
## only one treatment condition. Therefore, cases have been switched from
## treatment failure to treatment success and from control success to control failure.
## The final Fragility(= 17) and RIR(= 37) reflect both sets of changes. 
## Please compare the after transfer table with the implied table.
## 
##           Fail Success
## Control     35      15
## Treatment    1      19
## Effect size = 3.792, SE = 1.071, p-value = 0.001. 
## Indicate that this is based on t = estimated effect/standard error

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

3.2) Another case for `needtworows = T`, `sustain`, `changeSE = TRUE`

## Case 3: needtworows = T, Sustain, changeSE = T, 
pkonfound(0.8, 0.2, 50, n_covariates = 20, alpha = .001, tails = 2, nu = 0, n_treat = 20, switch_trm = FALSE, model_type = "logistic", to_return = "print")

## RIR = 19
## 
## The table implied by the parameter estimates and sample sizes you entered:
## 
##           Fail Success
## Control     19      11
## Treatment    8      12
## 
## The reported effect size = 0.800, SE = 0.200, p-value = 0.120. 
## The SE has been adjusted to 0.593 to generate a real number in the 
## implied table. Numbers in the table cells have been rounded 
## to integers, which may slightly alter the estimated effect from 
## the value originally entered.
## 
## The inference cannot be sustained merely by switching cases in
## only one treatment condition. Therefore, cases have been switched from
## control success to control failure and from treatment failure to treatment success.
## The final Fragility(= 12) and RIR(= 19) reflect both sets of changes. 
## Please compare the after transfer table with the implied table.
## 
##           Fail Success
## Control     29       1
## Treatment    6      14
## Effect size = 4.215, SE = 1.128, p-value = 0.001. 
## Indicate that this is based on t = estimated effect/standard error

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

3.3) Part of code of language output for possible case, `needtworows = T` & `invalidate` & `changeSE = TRUE`

       else {

          ### when needtworows = T
          ### changeSE = T
            cat(paste0(
            sprintf("The inference cannot be invalidated merely by switching cases in"),
            sprintf("\nonly one treatment condition. Therefore, cases have been switched from"),
            c("\n"), transferway, c(" and from "),
            transferway_extra, c("."), c("\n"),
            sprintf("The final Fragility(= %d) and RIR(= %d)", final_solution$final_switch, RIR),
            c(" reflect both sets of changes. \nPlease compare the after transfer table with the implied table.")
            )
              )
        }

4) Output Language for RIR with 2by2 table

4.1) 2by2 table with `print` option (`test="fisher"`)

# 2 by 2 table: printed output
pkonfound(a = 35, b = 17, c = 17, d = 38, alpha = 0.05, switch_trm = T, test = "fisher", replace = "control", "to_return" = "print")

## Background Information:
## This function calculates the number of cases that would have to be replaced
## with zero effect cases (RIR) to invalidate an inference made about the association
## between the rows and columns in a 2x2 table.
## One can also interpret this as switches from one cell to another, such as from
## the treatment success cell to the treatment failure cell.
## 
## Conclusion:
## To invalidate the inference, one would need to replace 14 treatment success
## cases for which the probability of failure in the control group applies (RIR = 14). 
## This is equivalent to transferring 9 cases from treatment success to treatment failure.
## For the User-entered Table, the estimated odds ratio is 4.530, with p-value of 0.000:
## 
## User-entered Table:
##           Fail Success
## Control     35      17
## Treatment   17      38
## 
## 
## For the Transfer Table, the estimated odds ratio is 2.278, with p-value of 0.051:
## Transfer Table:
##           Fail Success
## Control     35      17
## Treatment   26      29
## 
## RIR:
## RIR = 14

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

4.2) 2by2 table with `raw_output` option (`test="fisher"`)

# 2 by 2 table: raw output
pkonfound(a = 35, b = 17, c = 17, d = 38, alpha = 0.05, switch_trm = T, test = "fisher", replace = "control", "to_return" = "raw_output")

## For interpretation, check out to_return = 'print'.

## $RIR_primary
## [1] 14
## 
## $RIR_supplemental
## [1] 0
## 
## $RIR_perc
## [1] 36.84211
## 
## $fragility_primary
## [1] 9
## 
## $starting_table
##           Fail Success
## Control     35      17
## Treatment   17      38
## 
## $final_table
##           Fail Success
## Control     35      17
## Treatment   26      29

4.3) 2by2 table with `print` option (`test="chisq"`)

# 2 by 2 table: printed output
pkonfound(a = 35, b = 17, c = 17, d = 38, alpha = 0.05, switch_trm = T, test = "chisq", replace = "control", "to_return" = "print")

## Background Information:
## This function calculates the number of cases that would have to be replaced
## with zero effect cases (RIR) to invalidate an inference made about the association
## between the rows and columns in a 2x2 table.
## One can also interpret this as switches from one cell to another, such as from
## the treatment success cell to the treatment failure cell.
## 
## Conclusion:
## To invalidate the inference, one would need to replace 15 treatment success
## cases for which the probability of failure in the control group applies (RIR = 15). 
## This is equivalent to transferring 10 cases from treatment success to treatment failure.
## For the User-entered Table, the Pearson's chi square is 14.176, with p-value of 0.000:
## 
## User-entered Table:
##           Fail Success
## Control     35      17
## Treatment   17      38
## 
## 
## For the Transfer Table, the Pearson's chi square is 3.640, with p-value of 0.056:
## Transfer Table:
##           Fail Success
## Control     35      17
## Treatment   27      28
## 
## RIR:
## RIR = 15

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

4.4) 2by2 table with `raw_output` option (`test="chisq"`)

# 2 by 2 table: raw output
pkonfound(a = 35, b = 17, c = 17, d = 38, alpha = 0.05, switch_trm = T, test = "chisq", replace = "control", "to_return" = "raw_output")

## For interpretation, check out to_return = 'print'.

## $RIR_primary
## [1] 15
## 
## $RIR_supplemental
## [1] 0
## 
## $RIR_perc
## [1] 39.47368
## 
## $fragility_primary
## [1] 10
## 
## $starting_table
##           Fail Success
## Control     35      17
## Treatment   17      38
## 
## $final_table
##           Fail Success
## Control     35      17
## Treatment   27      28

5) Newly Added Functions that need review

5.1) calculation of p-value in Implied/Transferred Table

The calculation of p-values in pkonfound should ideally depend on the research context.
Absent specific context, the sign of t_obs might be used to choose between upper or lower p-value tests.
However, this approach is not ideal and warrants additional insights for more accurate statistical analysis.

  if (tails == 2) {
    p_start <- (2 * (1 - pt(abs(final_solution$t_start), n_obs - n_covariates - 2)))
    p_final <- (2 * (1 - pt(abs(final_solution$t_final), n_obs - n_covariates - 2)))
  } 
  # For a one-tailed test (assuming upper tail)
  else if (tails == 1 & t_obs > 0) {
    p_start <- (1 - pt(final_solution$t_start, n_obs - n_covariates - 2))
    p_final <- (1 - pt(final_solution$t_final, n_obs - n_covariates - 2))
  } 
  # For a one-tailed test (assuming lower tail)
  else if (tails == 1 & t_obs < 0) {
    p_start <- (pt(final_solution$t_start, n_obs - n_covariates - 2))
    p_final <- (pt(final_solution$t_final, n_obs - n_covariates - 2))
  }

## 1-tail, lower tail
pkonfound(-0.03, 0.2, 50, n_covariates = 5, alpha = .005, tails = 1, nu = 0, n_treat = 25, switch_trm = TRUE, model_type = "logistic", to_return = "print")

## RIR = 19
## 
## The table implied by the parameter estimates and sample sizes you entered:
## 
##           Fail Success
## Control     12      13
## Treatment   13      12
## 
## The reported effect size = -0.030, SE = 0.200, p-value = 0.389. 
## The SE has been adjusted to 0.566 to generate a real number in the 
## implied table. Numbers in the table cells have been rounded 
## to integers, which may slightly alter the estimated effect from 
## the value originally entered.
## 
## To reach the threshold that would sustain an inference that the 
## effect is different from 0 (alpha = 0.005) one would need to replace 19 
## (158.33%) treatment success cases with cases for which the probability of 
## failure in the control group (48.00%) applies (RIR = 19). This is equivalent 
## to transferring 9 cases from treatment success to treatment failure
## (Fragility = 9).
## 
## Note that RIR = Fragility/[1-P(success in the treatment group)]
## 
## Note the RIR exceeds 100%. Generating the transfer of 9 cases would
## require replacing more cases that are in the treatment success condition.
## 
## The transfer of 9 cases yields the following table:
## 
##           Fail Success
## Control     12      13
## Treatment   22       3
## Effect size = -2.072, SE = 0.734, p-value = 0.004. 
## Indicate that this is based on t = estimated effect/standard error

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

## 1-tail, upper tail
pkonfound(0.8, 0.25, 5000, n_covariates = 50, alpha = .05, tails = 1, nu = 0, n_treat = 2500, switch_trm = TRUE, model_type = "logistic", to_return = "print")

## RIR = 625
## 
## The table implied by the parameter estimates and sample sizes you entered:
## 
##           Fail Success
## Control     52    2448
## Treatment   24    2476
## 
## The reported effect size = 0.800, and SE = 0.250, p-value = 0.001. 
## Values have been rounded to the nearest integer. This may cause 
## a little change to the estimated effect for the table.
## 
## To invalidate the inference that the effect is different from 0 
## (alpha = 0.050) one would need to replace 625 (25.24%) treatment success 
## cases with cases for which the probability of failure in the control 
## group (2.08%) applies (RIR = 625). This is equivalent to transferring 
## 13 cases from treatment success to treatment failure (Fragility = 13).
## 
## Note that RIR = Fragility/[1-P(success in the treatment group)]
## 
## The transfer of 13 cases yields the following table:
## 
##           Fail Success
## Control     52    2448
## Treatment   37    2463
## Effect size = 0.346, SE = 0.217, p-value = 0.055. 
## Indicate that this is based on t = estimated effect/standard error

## For other forms of output, run ?pkonfound and inspect the to_return argument

## For models fit in R, consider use of konfound().

Output Language Revision Trial_v2

Jihoon Choi

2023-12-22

Summary

1. Output Language Update

2. Several Notes with Examples

* Citation link has been added in the “Viewer” Pane See here

* Handling of Rare Cases:

* Updates on RIR percentage and p-value

* Example using tkonfound (2by2 table) See here

* Newly Added Functions that need review See here

* Quick Question

0) install `konfound` from github repository

1) Output Language for RIR in Linear Model

1.1) Invalidate, `eff_thr = NA`

* Example image of citation hyperlink (automatically poped-up in viewer pane)

1.2) Invalidate, `eff_thr != NA` (user-entered threshold)

1.3) Sustain, `eff_thr = NA`

1.4) Sustain, `eff_thr != NA` (user-entered threshold)

2) Output Language for RIR in Non-linear Model

2.1) Invalidate, `changeSE = TRUE`

2.2) Invalidate, `changeSE = FALSE`

2.3) Sustain, `changeSE = TRUE` (where RIR_perc exceeds 100%)

2.4) Sustain, `changeSE = FALSE`

3) Output Language for RIR in Non-linear Model (`needtworows = T`)

3.1) `needtworows = T`, `sustain`, `changeSE = TRUE`

3.2) Another case for `needtworows = T`, `sustain`, `changeSE = TRUE`

3.3) Part of code of language output for possible case, `needtworows = T` & `invalidate` & `changeSE = TRUE`

4) Output Language for RIR with 2by2 table

4.1) 2by2 table with `print` option (`test="fisher"`)

4.2) 2by2 table with `raw_output` option (`test="fisher"`)

4.3) 2by2 table with `print` option (`test="chisq"`)

4.4) 2by2 table with `raw_output` option (`test="chisq"`)

5) Newly Added Functions that need review

5.1) calculation of p-value in Implied/Transferred Table

Output Language Revision Trial_v2

Jihoon Choi

2023-12-22

Summary

1. Output Language Update

2. Several Notes with Examples

* Citation link has been added in the “Viewer” Pane See here

* Handling of Rare Cases:

* Updates on RIR percentage and p-value

* Example using tkonfound (2by2 table) See here

* Newly Added Functions that need review See here

* Quick Question

0) install konfound from github repository

1) Output Language for RIR in Linear Model

1.1) Invalidate, eff_thr = NA

* Example image of citation hyperlink (automatically poped-up in viewer pane)

1.2) Invalidate, eff_thr != NA (user-entered threshold)

1.3) Sustain, eff_thr = NA

1.4) Sustain, eff_thr != NA (user-entered threshold)

2) Output Language for RIR in Non-linear Model

2.1) Invalidate, changeSE = TRUE

2.2) Invalidate, changeSE = FALSE

2.3) Sustain, changeSE = TRUE (where RIR_perc exceeds 100%)

2.4) Sustain, changeSE = FALSE

3) Output Language for RIR in Non-linear Model (needtworows = T)

3.1) needtworows = T, sustain, changeSE = TRUE

3.2) Another case for needtworows = T, sustain, changeSE = TRUE

3.3) Part of code of language output for possible case, needtworows = T & invalidate & changeSE = TRUE

4) Output Language for RIR with 2by2 table

4.1) 2by2 table with print option (test="fisher")

4.2) 2by2 table with raw_output option (test="fisher")

4.3) 2by2 table with print option (test="chisq")

4.4) 2by2 table with raw_output option (test="chisq")

5) Newly Added Functions that need review

5.1) calculation of p-value in Implied/Transferred Table

0) install `konfound` from github repository

1.1) Invalidate, `eff_thr = NA`

1.2) Invalidate, `eff_thr != NA` (user-entered threshold)

1.3) Sustain, `eff_thr = NA`

1.4) Sustain, `eff_thr != NA` (user-entered threshold)

2.1) Invalidate, `changeSE = TRUE`

2.2) Invalidate, `changeSE = FALSE`

2.3) Sustain, `changeSE = TRUE` (where RIR_perc exceeds 100%)

2.4) Sustain, `changeSE = FALSE`

3) Output Language for RIR in Non-linear Model (`needtworows = T`)

3.1) `needtworows = T`, `sustain`, `changeSE = TRUE`

3.2) Another case for `needtworows = T`, `sustain`, `changeSE = TRUE`

3.3) Part of code of language output for possible case, `needtworows = T` & `invalidate` & `changeSE = TRUE`

4.1) 2by2 table with `print` option (`test="fisher"`)

4.2) 2by2 table with `raw_output` option (`test="fisher"`)

4.3) 2by2 table with `print` option (`test="chisq"`)

4.4) 2by2 table with `raw_output` option (`test="chisq"`)