Rearrange proportions pages, phase 2

R/ci_for_2indep_prop.qmd

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+---
+title: "Confidence Intervals for Independent Proportions in R"
+---
+
+## Introduction
+
+\[See separate page for general introductory information on confidence intervals for proportions.\]
+
+\[Note: information about cicalc package will be added to this page soon.\]
+
+## Data used
+
+The adcibc data stored [here](../data/adcibc.csv) was used in this example, creating a binary treatment variable `trt` taking the values of `ACT` or `PBO` and a binary response variable `resp` taking the values of `Yes` or `No`. For this example, a response is defined as a score greater than 4.
+
+```{r}
+#| echo: false
+#| include: false
+library(tidyverse)
+library(cardx)
+library(DescTools)
+adcibc2 <- read_csv("../data/adcibc.csv")
+
+adcibc <- adcibc2 |>
+  select(AVAL, TRTP) |>
+  mutate(
+    resp = if_else(AVAL > 4, "Yes", "No"),
+    respn = if_else(AVAL > 4, 1, 0),
+    trt = if_else(TRTP == "Placebo", "PBO", "ACT"),
+    trtn = if_else(TRTP == "Placebo", 0, 1)
+  ) |>
+  select(trt, trtn, resp, respn)
+
+# cardx package required a vector with 0 and 1s for a single proportion CI
+act <- filter(adcibc, trt == "ACT") |>
+  select(respn)
+act2 <- act$respn
+```
+
+The below shows that for the Actual Treatment, there are 36 responders out of 154 subjects = 0.234 (23.4% responders).
+
+```{r}
+#| echo: false
+adcibc |>
+  group_by(trt, resp) |>
+  tally()
+```
+
+## Packages
+
+**The {cardx} package** is an extension of the {cards} package, providing additional functions to create Analysis Results Data Objects (ARDs)^1^. It was developed as part of {NEST} and pharmaverse. This package requires the binary endpoint to be a logical (TRUE/FALSE) vector or a numeric/integer coded as (0, 1) with 1 (TRUE) being the success you want to calculate the confidence interval for.
+
+See [here](R:%20Functions%20for%20Calculating%20Proportion%20Confidence%20Intervals) for full description of the {cardx} proportions equations.
+
+If calculating the CI for a difference in proportions, the package requires both the response and the treatment variable to be numeric/integer coded as (0, 1) (or logical vector).
+
+Instead of the code presented below, you can use `ard_categorical_ci(data, variables=resp, method ='wilson')` for example. This invokes the code below but returns an analysis results dataset (ARD) format as the output.
+
+Methods included are \[TBC\] methods for 2 independent samples.
+
+**The {ratesci} package** is ... \[TBC\]
+
+**The {DescTools} package** has a function BinomDiffCI which produces CIs for two independent proportions (unmatched pairs) including methods for Agresti/Caffo, Wald, Wald with Continuity correction, Newcombe Score, Newcombe score with continuity correction, and more computationally intensive methods such as Miettinen and Nurminen, Mee, Brown Li's Jeffreys, Hauck-Anderson and Haldane. See [here](https://search.r-project.org/CRAN/refmans/DescTools/html/BinomDiffCI.html) for more detail.
+
+**The {presize} package** has a function prec_prop() which also calculates CIs for 2 independent samples using the Wilson, Agresti-Coull, Exact or Wald approaches. The package is not described in further detail here since in most cases **{DescTools}** will be able to compute what is needed. However, it's mentioned due to other functionality it has available such as sample size and precision calculations for AUC, correlations, cronbach's alpha, intraclass correlation, Cohen's kappa, likelihood ratios, means, mean differences, odds ratios, rates, rate ratios, risk differences and risk ratios.
+
+## Methods for Calculating Confidence Intervals for Proportion Difference from 2 independent samples
+
+This [paper](https://www.lexjansen.com/wuss/2016/127_Final_Paper_PDF.pdf)^4^ describes many methods for the calculation of confidence intervals for 2 independent proportions.
+
+### Normal Approximation Method (Also known as the Wald or asymptotic CI Method) using {cardx}
+
+For more technical information regarding the Wald method see the corresponding [SAS page](https://psiaims.github.io/CAMIS/SAS/ci_for_prop.html).
+
+#### Example code
+
+`cardx::ard_stats_prop_test function` uses `stats::prop.test` which also allows a continuity correction to be applied.
+
+Although this website [here](https://rdrr.io/r/stats/prop.test.html) and this one [here](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/prop.test) both reference Newcombe for the CI that this function uses, replication of the results by hand and compared to SAS show that the results below match the Normal Approximation (Wald method).
+
+Both the Treatment variable (ACT,PBO) and the Response variable (Yes,No) have to be numeric (0,1) or Logit (TRUE,FALSE) variables.
+
+The prop.test default with 2 groups, is the null hypothesis that the proportions in each group are the same and a 2-sided CI.
+
+```{r}
+indat1 <- adcibc2 |>
+  select(AVAL, TRTP) |>
+  mutate(
+    resp = if_else(AVAL > 4, "Yes", "No"),
+    respn = if_else(AVAL > 4, 1, 0),
+    trt = if_else(TRTP == "Placebo", "PBO", "ACT"),
+    trtn = if_else(TRTP == "Placebo", 1, 0)
+  ) |>
+  select(trt, trtn, resp, respn)
+
+# cardx package required a vector with 0 and 1s for a single proportion CI
+# To get the comparison the correct way around Placebo must be 1, and Active 0
+
+indat <- select(indat1, trtn, respn)
+
+cardx::ard_stats_prop_test(
+  data = indat,
+  by = trtn,
+  variables = respn,
+  conf.level = 0.95,
+  correct = FALSE
+)
+cardx::ard_stats_prop_test(
+  data = indat,
+  by = trtn,
+  variables = respn,
+  conf.level = 0.95,
+  correct = TRUE
+)
+```
+
+### Normal Approximation (Wald) and Other Methods for 2 independent samples using {DescTools}
+
+For more technical information regarding the derivations of these methods see the corresponding [SAS page](https://psiaims.github.io/CAMIS/SAS/ci_for_prop.html) or {DescTools} package documentation [here](https://search.r-project.org/CRAN/refmans/DescTools/html/BinomDiffCI.html). **The {DescTools} package** has a function BinomDiffCI which produces CIs for two independent proportions (unmatched pairs) including methods for Agresti/Caffo, Wald, Wald with Continuity correction, Newcombe Score, Newcombe score with continuity correction, and more computationally intensive (less commonly used) methods such as Miettinen and Nurminen, Mee, Brown Li's Jeffreys, Hauck-Anderson, Haldane and Jeffreys-Perks.
+
+#### Example code
+
+With 2 groups, the null hypothesis that the proportions in each group are the same and a 2-sided CI.
+
+```{r}
+count_dat <- indat |>
+  count(trtn, respn)
+count_dat
+
+# BinomDiffCI requires
+# x1 = successes in active,  n1 = total subjects in active,
+# x2 = successes in placebo, n2 = total subjects in placebo
+
+DescTools::BinomDiffCI(
+  x1 = 36,
+  n1 = 154,
+  x2 = 12,
+  n2 = 77,
+  conf.level = 0.95,
+  sides = c("two.sided"),
+  method = c(
+    "wald",
+    "waldcc",
+    "score",
+    "scorecc",
+    "ac",
+    "mn",
+    "mee",
+    "blj",
+    "ha",
+    "hal",
+    "jp"
+  )
+)
+```
+
+## Methods for Calculating Confidence Intervals for Relative Risk from 2 independent samples
+
+\[TBC\]
+
+### 
+
+## Methods for Calculating Confidence Intervals for Odds Ratio from 2 independent samples
+
+\[TBC\]
+
+## Continuity Adjusted Methods
+
+\[TBC\]
+
+## Consistency with hypothesis tests
+
+\[TBC\] - cf. chi-squared tests
+
+## References
+
+1.  [pharmaverse cardx package](https://insightsengineering.github.io/cardx/main/#:~:text=The%20%7Bcardx%7D%20package%20is%20an%20extension%20of%20the,Data%20Objects%20%28ARDs%29%20using%20the%20R%20programming%20language.)
+2.  [PropCIs package](https://cran.r-project.org/web//packages/PropCIs/PropCIs.pdf)
+3.  D. Altman, D. Machin, T. Bryant, M. Gardner (eds). Statistics with Confidence: Confidence Intervals and Statistical Guidelines, 2nd edition. John Wiley and Sons 2000.
+4.  <https://www.lexjansen.com/wuss/2016/127_Final_Paper_PDF.pdf>

R/ci_for_paired_prop.qmd

@@ -0,0 +1,134 @@
+---
+title: "Confidence Intervals for Paired Proportions in R"
+---
+
+## Introduction
+
+\[See separate page for general introductory information on confidence intervals for proportions.\]
+
+\[Note: information about cicalc package will be added to this page soon.\]
+
+## Data used
+
+The adcibc data stored [here](../data/adcibc.csv) was used in this example, creating a binary treatment variable `trt` taking the values of `ACT` or `PBO` and a binary response variable `resp` taking the values of `Yes` or `No`. For this example, a response is defined as a score greater than 4.
+
+```{r}
+#| echo: false
+#| include: false
+library(tidyverse)
+library(cardx)
+library(DescTools)
+adcibc2 <- read_csv("../data/adcibc.csv")
+
+adcibc <- adcibc2 |>
+  select(AVAL, TRTP) |>
+  mutate(
+    resp = if_else(AVAL > 4, "Yes", "No"),
+    respn = if_else(AVAL > 4, 1, 0),
+    trt = if_else(TRTP == "Placebo", "PBO", "ACT"),
+    trtn = if_else(TRTP == "Placebo", 0, 1)
+  ) |>
+  select(trt, trtn, resp, respn)
+
+# cardx package required a vector with 0 and 1s for a single proportion CI
+act <- filter(adcibc, trt == "ACT") |>
+  select(respn)
+act2 <- act$respn
+```
+
+The below shows that for the Actual Treatment, there are 36 responders out of 154 subjects = 0.234 (23.4% responders).
+
+```{r}
+#| echo: false
+adcibc |>
+  group_by(trt, resp) |>
+  tally()
+```
+
+## Packages
+
+**The {ratesci} package** is ... \[TBC\]
+
+**The {ExactCIdiff} package** produces exact CIs for two dependent proportions (matched pairs).
+
+## Methods for Calculating Confidence Intervals for Proportion Difference from matched pairs using {ExactCIdiff} and {ratesci}
+
+For more information about the detailed methods for calculating confidence intervals for a matched pair proportion see [here](https://psiaims.github.io/CAMIS/SAS/ci_for_prop.html#methods-for-calculating-confidence-intervals-for-a-matched-pair-proportion). When you have 2 measurements on the same subject, the 2 sets of measures are not independent and you have matched pair of responses.
+
+To date we have not found an R package which calculates a CI for matched pair proportions using the normal approximation or Wilson methods although they can be done by hand using the equations provided on the SAS page link above.
+
+**The {ExactCIdiff} package** produces exact CIs for two dependent proportions (matched pairs), claiming to be the first package in R to do this method. However, it should only be used when the sample size is not too large as it can be computationally intensive.\
+NOTE that the {ExactNumCI} package should not be used for this task. More detail on these two packages can be found [here](RJ-2013-026.pdf).
+
+Using a cross over study as our example, a 2 x 2 table can be formed as follows:
+
++-----------------------+---------------+---------------+---------------+
+|                       | Placebo\      | Placebo\      | Total         |
+|                       | Response= Yes | Response = No |               |
++=======================+===============+===============+===============+
+| Active Response = Yes | r             | s             | r+s           |
++-----------------------+---------------+---------------+---------------+
+| Active Response = No  | t             | u             | t+u           |
++-----------------------+---------------+---------------+---------------+
+| Total                 | r+t           | s+u           | N = r+s+t+u   |
++-----------------------+---------------+---------------+---------------+
+
+: The proportions of subjects responding on each treatment are:
+
+Active: $\hat p_1 = (r+s)/n$ and Placebo: $\hat p_2= (r+t)/n$
+
+Difference between the proportions for each treatment are: $D=p1-p2=(s-t)/n$
+
+Suppose :
+
++-----------------------+---------------+---------------+------------------+
+|                       | Placebo\      | Placebo\      | Total            |
+|                       | Response= Yes | Response = No |                  |
++=======================+===============+===============+==================+
+| Active Response = Yes | r = 20        | s = 15        | r+s = 35         |
++-----------------------+---------------+---------------+------------------+
+| Active Response = No  | t = 6         | u = 5         | t+u = 11         |
++-----------------------+---------------+---------------+------------------+
+| Total                 | r+t = 26      | s+u = 20      | N = r+s+t+u = 46 |
++-----------------------+---------------+---------------+------------------+
+
+Active: $\hat p_1 = (r+s)/n$ =35/46 =0.761 and Placebo: $\hat p_2= (r+t)/n$ = 26/46 =0.565
+
+Difference = 0.761-0.565 = 0.196, then PairedCI() function can provide an exact confidence interval as shown below
+
+-0.00339 to 0.38065
+
+```{r}
+#| eval: false
+# ExactCIdiff::PairedCI(s, r+u, t, conf.level = 0.95)
+
+CI <- ExactCIdiff::PairedCI(15, 25, 6, conf.level = 0.95)$ExactCI
+CI
+```
+
+## Methods for Calculating Confidence Intervals for Relative Risk from matched pairs using {ratesci}
+
+\[TBC\]
+
+## Methods for Calculating Confidence Intervals for Conditional Odds Ratio from matched pairs using {ratesci}
+
+\[TBC\]
+
+## Continuity Adjusted Methods
+
+\[TBC\]
+
+## Consistency with Hypothesis Tests
+
+\[TBC\] - cf. McNemar test
+
+##  
+
+##  
+
+## References
+
+1.  [pharmaverse cardx package](https://insightsengineering.github.io/cardx/main/#:~:text=The%20%7Bcardx%7D%20package%20is%20an%20extension%20of%20the,Data%20Objects%20%28ARDs%29%20using%20the%20R%20programming%20language.)
+2.  [PropCIs package](https://cran.r-project.org/web//packages/PropCIs/PropCIs.pdf)
+3.  D. Altman, D. Machin, T. Bryant, M. Gardner (eds). Statistics with Confidence: Confidence Intervals and Statistical Guidelines, 2nd edition. John Wiley and Sons 2000.
+4.  <https://www.lexjansen.com/wuss/2016/127_Final_Paper_PDF.pdf>