This article is to illustate how to conduct an (Analysis of Covariance) ANCOVA model to determine whether or not the change from baseline glucose is affected by treatment significantly. In other words, using ANCOVA to compare the adjusted means of two or more independent groups while acounting for one or more covariates.

As an example dataset, I'll use the `cdiscpilot01`

from CDSIC that contains the AdaM and SDTM datasets for a single study. And then our purpose is to conduct efficacy analysis by ANCOVA with LS mean estimation. Suppose that we want to know whether or not the treatment has an impact on `Glucose`

while accounting for the baseline of glucose. The patients are limited to who reach the visit of `end of treatment`

but have not been discontinued due to AE.

#### Assumptions

ANCOVA makes several assumptions about the input data, such as:

- Linearity between the covariate and the outcome variable
- Homogeneity of regression slopes
- The outcome variable should be approximately normally distributed
- Homoscedasticity
- No significant outliers

Maybe we need to additional article to talk about how to conduct these assumptions, but not in here. So we suppose that all assumptions have been met for the ANCOVA.

#### Data preparation

Install and load the following required packages. And then load `adsl`

and `adlbc`

datasets from `cdiscpilot01`

study, which can be referred to another article: Example of SDTM and ADaM datasets from the CDISC.

```
library(tidyverse)
library(emmeans)
library(gtsummary)
library(multcomp)
adsl <- haven::read_xpt(file = "./phuse-scripts/data/adam/cdiscpilot01/adsl.xpt")
adlb <- haven::read_xpt(file = "./phuse-scripts/data/adam/cdiscpilot01/adlbc.xpt")
```

#### Data manipulation

Per the purpose, we need to filter the efficacy population and focus on `Glucose (mg/dL)`

lab test.

```
gluc <- adlb %>%
left_join(adsl %>% select(USUBJID, EFFFL), by = "USUBJID") %>%
# PARAMCD is parameter code and here we focus on Glucose (mg/dL)
filter(EFFFL == "Y" & PARAMCD == "GLUC") %>%
arrange(TRTPN) %>%
mutate(TRTP = factor(TRTP, levels = unique(TRTP)))
```

And then to produce the analysis datasets by filtering the target patients who have reach out the end of treatment and not been discontinued due to AE.

```
ana_dat <- gluc %>%
filter(AVISIT == "End of Treatment" & DSRAEFL == "Y") %>%
arrange(SUBJID, AVISITN) %>%
mutate(AVISIT = factor(AVISIT, levels = unique(AVISIT)))
```

#### Summary of analysis datsets

Once we have the datasets for analysis, we need to examine the datasets first. I find `tbl_summary`

function in `gtsummary`

package can calculate descriptive statistics and provide a very nice table with clinical style, as shown below:

```
ana_dat %>%
dplyr::select(AGEGR1, SEX, RACE, TRTP, AVAL, BASE, CHG) %>%
tbl_summary(by = TRTP, missing = "no") %>%
add_n() %>%
as_gt() %>%
gt::tab_source_note(gt::md("*This data is from cdiscpilot01 study.*"))
```

Here we can see the descriptive summary for each variables by the treatment group. Certainly we can also do some visualization like boxplot or scatterplot, but not present here.

#### Fit ANCOVA model

We use `lm`

function to fit ANCOVA model with treatment(`TRTP`

) as independent variable, change from baseline(`CHG`

)as response variable, and baseline(`BASE`

) as covariates.

```
fit <- lm(CHG ~ BASE + TRTP, data = ana_dat)
summary(fit)
```

The summary output for regression coefficients as follows. If you would like to obtain anova tables, should use `anova(fit)`

instead of `summary(fit)`

.

```
Call:
lm(formula = CHG ~ BASE + TRTP, data = ana_dat)
Residuals:
Min 1Q Median 3Q Max
-3.1744 -0.7627 -0.0680 0.5633 5.0349
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.5579 0.8809 -0.633 0.528
BASE 0.1111 0.1329 0.837 0.405
TRTPXanomeline Low Dose -0.2192 0.5433 -0.404 0.688
TRTPXanomeline High Dose 0.4447 0.5528 0.804 0.424
Residual standard error: 1.328 on 77 degrees of freedom
(1 observation deleted due to missingness)
Multiple R-squared: 0.06702, Adjusted R-squared: 0.03068
F-statistic: 1.844 on 3 and 77 DF, p-value: 0.1462
```

From above results, we can easily conclude the regression coefficient and model, and the significance comparing to zero. With the coefficient, we can predict the any change based on baseline and treatment.

Besides we can use `contrasts`

function to obtain contrast metrices so that understand the dummy variables for `TRTP`

in the multiple regression model here.

```
> contrasts(ana_dat$TRTP)
Xanomeline Low Dose Xanomeline High Dose
Placebo 0 0
Xanomeline Low Dose 1 0
Xanomeline High Dose 0 1
```

From the anova table as shown below, it can been seen that the treatment have no statistical significance for the change in glucose under the control of the effects of baseline.

```
> anova(fit)
Analysis of Variance Table
Response: CHG
Df Sum Sq Mean Sq F value Pr(>F)
BASE 1 1.699 1.6989 0.9629 0.3295
TRTP 2 8.061 4.0304 2.2844 0.1087
Residuals 77 135.853 1.7643
```

If you would like to make the output more pretty, `tbl_regression(fit)`

can be used as mentioned before.

If we want to obtain the least square(LS) mean between treatment groups, `emmeans`

or `multcomp`

package can provide the same results. In addition the process to calculate the LS mean is also very worth to leaning and understanding.

```
# by multcomp
postHocs <- glht(fit, linfct = mcp(TRTP = "Tukey"))
summary(postHocs)
# by emmeans
fit_within <- emmeans(fit, "TRTP")
pairs(fit_within, reverse = TRUE)
```

The summary output as shown below:

```
> summary(postHocs)
Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: Tukey Contrasts
Fit: lm(formula = CHG ~ BASE + TRTP, data = ana_dat)
Linear Hypotheses:
Estimate Std. Error t value Pr(>|t|)
Xanomeline Low Dose - Placebo == 0 -0.2192 0.5433 -0.404 0.9116
Xanomeline High Dose - Placebo == 0 0.4447 0.5528 0.804 0.6937
Xanomeline High Dose - Xanomeline Low Dose == 0 0.6639 0.3113 2.132 0.0855 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Adjusted p values reported -- single-step method)
```

Now it's clear a significant difference was observed between the pairs `Low Dose vs. Placebo`

, `High Dose vs. Placebo`

, and `High Dose vs. Low Dose`

.

#### Reference

https://r4csr.org/efficacy-table.html#efficacy-table

ANCOVA in R

How to perform ANCOVA in R

An Introduction to ANCOVA (Analysis of Variance)

How to Conduct an ANCOVA in R