Merge pull request #369 from yannickvandendijck/tobit-regression

Tobit regression - added R-SAS Comparison

Comp/r-sas_tobit.qmd

@@ -0,0 +1,47 @@
+---
+title: "R vs SAS Tobit Regression"
+---
+
+```{r setup, include=FALSE}
+knitr::opts_chunk$set(echo = TRUE)
+```
+
+# Tobit Regression Comparison
+
+The following table shows the types of Two Sample t-test analysis, the capabilities of each language, and whether or not the results from each language match.
+
+| Analysis | Supported in R | Supported in SAS | Results Match | Notes |
+|----------|----------------|------------------|---------------|-------|
+| Tobit Regression (normal distributed data assumption) | [Yes](../R/tobit%20regression.html) | [Yes](../SAS/tobit%20regression%20SAS.html) | Yes | The results from `censReg::censReg` and `survival::survreg` match the SAS `PROC LIFEREG` results
+                                        |
+
+## Comparison Results
+
+### Normally distributed data assumption
+
+Here is a table of comparison values between the R functions `censReg::censReg`, `survival::survreg`, `VGAM::vglm`, and SAS `PROC LIFEREG` for the dataset used.
+The statistics around the treatment effect (difference between group A and B, B-A) are provided. Further we also present the estimate of $\sigma$. All numbers are rounded to 4 digits
+
+| Statistic          | censReg()  | survreg() | vglm() | LIFEREG | Match | Notes |
+|--------------------|------------|-----------|--------|---------|-------|-------|
+| Treatment effect   | 1.8225          | 1.8225          | 1.8226          | 1.8225          | Yes | see below
+| Standard error     | 0.8061          | 0.8061          | 0.7942          | 0.8061          | Yes | see below
+| p-value            | 0.0238          | 0.0238          | 0.0217          | 0.0238          | Yes | see below
+| 95% CI (Wald based)| 0.2427 ; 3.4024 | 0.2427 ; 3.4024 | 0.2661 ; 3.3791 | 0.2427 ; 3.4024 | Yes | see below
+| $\sigma$           | 1.7316          | 1.7316          | 1.7317          | 1.7316          | Yes | see below
+
+
+Note: The results of `VGAM::vglm()` are slightly different since an iteratively reweighted least squares (IRLS) algorithm is used for estimation.
+
+
+# Summary and Recommendation
+
+Comparison between SAS `PROC LIFEREG` and R functions `censReg::censReg` and `survival::survreg` show identical results for the dataset tried. 
+
+Historically and typically the Tobit model is based on the assumption of normal distributed data. Within SAS `PROC LIFEREG` and R `survival::survreg` multiple other different distributional assumption are possible. These include *weibull*, *exponential*, *gaussian*, *logistic*, *lognormal* and *loglogistic* for `survival::survreg`. These include *EXPONENTIAL*, *GAMMA*, *LLOGISTIC*, *LOGISTIC*, *LOGNORMAL*, *NORMAL*, *WEIBULL* for `PROC LIFEREG`.
+
+# References
+
+Breen, R. (1996). Regression models. SAGE Publications, Inc., https://doi.org/10.4135/9781412985611
+
+Tobin, James (1958). "Estimation of Relationships for Limited Dependent Variables". Econometrica. 26 (1): 24-36. doi:10.2307/1907382

R/tobit regression.qmd

@@ -115,13 +115,16 @@ summary(res_survreg)
 lsm = emmeans(res_survreg, specs = trt.vs.ctrl ~ ARM)
 lsm$emmeans
 
-# Difference between groups (Wald CIs)
+# Difference between groups
 lsm_contrast = broom::tidy(lsm$contrasts, conf.int=TRUE, conf.level=0.95)
 gt(lsm_contrast) %>%
   fmt_number(decimals = 3)
+
+# Wald-based CIs
+round(stats::confint(res_survreg, level = 0.95)[2,], 3)
 ```
 
-The output provides an estimate of difference between groups A and B (B-A), namely 1.823 (se=0.806). The presented p-value is a two-sided p-value based on the Z-test. The output also provides an estimate for $log(\sigma) = 0.549$. Using the `emmeans` package/function least square means and contrast can be easily obtained. The confidence intervals and p-value is based on the t-test. 
+The output provides an estimate of difference between groups A and B (B-A), namely 1.823 (se=0.806). The presented p-value is a two-sided p-value based on the Z-test. The output also provides an estimate for $log(\sigma) = 0.549$. Using the `emmeans` package/function least square means and contrast can be easily obtained. The confidence intervals and p-value is based on the t-test using `emmeans`. Wald based confidence intervals can be obtained by the `stats::confint` function.
 
 
 ### vglm