tlf-04-efficacy.RmdFollowing the ICH E3 guidance, we need to summarize primary and secondary efficacy endpoints, in Section 11.4, Efficacy Results and Tabulations of Individual Patient.
library(esubdemo)## Warning in eval(ei, envir): The current R version is not the same with the
## current project in 4.1.0
library(haven) # Read SAS data
library(dplyr) # Manipulate data
library(tidyr) # Manipulate data
library(r2rtf) # Reporting in RTF format
library(emmeans) # LS means estimation
library(stringr) # String manipulationFor efficacy analysis, we only analyze change from baseline glucose data at Week 24.
To prepare analysis dataset, we need both adsl and adlbc datasets for this analysis.
We first define the analysis dataset using efficacy population flag EFFFL and all records post baseline (AVISITN > 1) and on or before Week 24 (AVISITN <= 24). Here the variable AVISITN is the numerical analysis visit. For example, if the analysis visit is recorded as “Baseline”, i.e., AVISIT = Baseline, then AVISITN = 0; if the analysis visit is recorded as “Week 24”, i.e., AVISIT = Week 24, then AVISITN = 24; if the analysis visit is blank, then AVISITN is also blank. We will discuss these missing values in Section 6.4.
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)))
ana <- gluc %>%
filter(AVISITN > 0 & AVISITN <= 24) %>%
arrange(AVISITN) %>%
mutate(AVISIT = factor(AVISIT, levels = unique(AVISIT)))Below is the first few records of the analysis dataset.
## # A tibble: 4 × 6
## USUBJID TRTPN AVISIT AVAL BASE CHG
## <chr> <dbl> <fct> <dbl> <dbl> <dbl>
## 1 01-701-1015 0 " Week 2" 4.66 4.72 -0.0555
## 2 01-701-1023 0 " Week 2" 5.77 5.33 0.444
## 3 01-701-1047 0 " Week 2" 5.55 5.55 0
## 4 01-701-1118 0 " Week 2" 4.88 4.05 0.833We first summarize observed data at Baseline and Week 24
t11 <- gluc %>%
filter(AVISITN %in% c(0, 24)) %>%
group_by(TRTPN, TRTP, AVISITN) %>%
summarise(
n = n(),
mean_sd = fmt_est(mean(AVAL), sd(AVAL))
) %>%
pivot_wider(
id_cols = c(TRTP, TRTPN),
names_from = AVISITN,
values_from = c(n, mean_sd)
)## `summarise()` has grouped output by 'TRTPN', 'TRTP'. You can override using the
## `.groups` argument.
t11## # A tibble: 3 × 6
## # Groups: TRTPN, TRTP [3]
## TRTP TRTPN n_0 n_24 mean_sd_0 mean_sd_24
## <fct> <dbl> <int> <int> <chr> <chr>
## 1 Placebo 0 79 57 " 5.7 ( 2.23)" " 5.7 ( 1.83)"
## 2 Xanomeline Low Dose 54 79 26 " 5.4 ( 0.95)" " 5.7 ( 1.26)"
## 3 Xanomeline High Dose 81 74 30 " 5.4 ( 1.37)" " 6.0 ( 1.92)"We also summarize observed change from baseline glucose at Week 24.
t12 <- gluc %>%
filter(AVISITN %in% 24) %>%
group_by(TRTPN, AVISITN) %>%
summarise(
n_chg = n(),
mean_chg = fmt_est(
mean(CHG, na.rm = TRUE),
sd(CHG, na.rm = TRUE)
)
)## `summarise()` has grouped output by 'TRTPN'. You can override using the
## `.groups` argument.
t12## # A tibble: 3 × 4
## # Groups: TRTPN [3]
## TRTPN AVISITN n_chg mean_chg
## <dbl> <dbl> <int> <chr>
## 1 0 24 57 " -0.1 ( 2.68)"
## 2 54 24 26 " 0.2 ( 0.82)"
## 3 81 24 30 " 0.5 ( 1.94)"In clinical trials, missing data is inevitable. In this study, there are also missing values in glucose data.
count(ana, AVISIT)## # A tibble: 8 × 2
## AVISIT n
## <fct> <int>
## 1 " Week 2" 229
## 2 " Week 4" 211
## 3 " Week 6" 197
## 4 " Week 8" 187
## 5 " Week 12" 167
## 6 " Week 16" 147
## 7 " Week 20" 126
## 8 " Week 24" 113For simplicity and illustration purpose, we use the last observation carried forward (LOCF) approach to handle missing data. LOCF approach is a single imputation approach that is not recommended in real studies. Interested readers can find more discussion on missing data approaches in the book: The Prevention and Treatment of Missing Data in Clinical Trials.
We start to analyze the imputed data using ANCOVA model with treatment and baseline glucose as covariates.
##
## Call:
## lm(formula = CHG ~ BASE + TRTP, data = ana_locf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9907 -0.7195 -0.2367 0.2422 7.0754
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.00836 0.39392 7.637 6.23e-13 ***
## BASE -0.53483 0.06267 -8.535 2.06e-15 ***
## TRTPXanomeline Low Dose -0.17367 0.24421 -0.711 0.478
## TRTPXanomeline High Dose 0.32983 0.24846 1.327 0.186
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.527 on 226 degrees of freedom
## (2 observations deleted due to missingness)
## Multiple R-squared: 0.2567, Adjusted R-squared: 0.2468
## F-statistic: 26.01 on 3 and 226 DF, p-value: 1.714e-14Then we use the emmeans R package to obtain within and between group least square mean (LS mean)
fit_within <- emmeans(fit, "TRTP")
fit_within## TRTP emmean SE df lower.CL upper.CL
## Placebo 0.0676 0.172 226 -0.272 0.407
## Xanomeline Low Dose -0.1060 0.173 226 -0.447 0.235
## Xanomeline High Dose 0.3975 0.179 226 0.045 0.750
##
## Confidence level used: 0.95
t13 <- fit_within %>%
as_tibble() %>%
mutate(ls = fmt_ci(emmean, lower.CL, upper.CL)) %>%
select(TRTP, ls)
t13## # A tibble: 3 × 2
## TRTP ls
## <fct> <chr>
## 1 Placebo " 0.07 (-0.27, 0.41)"
## 2 Xanomeline Low Dose "-0.11 (-0.45, 0.23)"
## 3 Xanomeline High Dose " 0.40 ( 0.05, 0.75)"
fit_between <- pairs(fit_within, reverse = TRUE)
fit_between## contrast estimate SE df t.ratio p.value
## Xanomeline Low Dose - Placebo -0.174 0.244 226 -0.711 0.7571
## Xanomeline High Dose - Placebo 0.330 0.248 226 1.327 0.3814
## Xanomeline High Dose - Xanomeline Low Dose 0.504 0.249 226 2.024 0.1087
##
## P value adjustment: tukey method for comparing a family of 3 estimates
t2 <- fit_between %>%
as_tibble() %>%
mutate(
ls = fmt_ci(
estimate,
estimate - 1.96 * SE,
estimate + 1.96 * SE
),
p = fmt_pval(p.value)
) %>%
filter(str_detect(contrast, "- Placebo")) %>%
select(contrast, ls, p)
t2## # A tibble: 2 × 3
## contrast ls p
## <chr> <chr> <chr>
## 1 Xanomeline Low Dose - Placebo "-0.17 (-0.65, 0.30)" " 0.757"
## 2 Xanomeline High Dose - Placebo " 0.33 (-0.16, 0.82)" " 0.381"We combine t11, t12 and t13 to get the first part of the report data
t1 <- cbind(
t11 %>% ungroup() %>% select(TRTP, ends_with("0"), ends_with("24")),
t12 %>% ungroup() %>% select(ends_with("chg")),
t13 %>% ungroup() %>% select(ls)
)
t1## TRTP n_0 mean_sd_0 n_24 mean_sd_24 n_chg mean_chg
## 1 Placebo 79 5.7 ( 2.23) 57 5.7 ( 1.83) 57 -0.1 ( 2.68)
## 2 Xanomeline Low Dose 79 5.4 ( 0.95) 26 5.7 ( 1.26) 26 0.2 ( 0.82)
## 3 Xanomeline High Dose 74 5.4 ( 1.37) 30 6.0 ( 1.92) 30 0.5 ( 1.94)
## ls
## 1 0.07 (-0.27, 0.41)
## 2 -0.11 (-0.45, 0.23)
## 3 0.40 ( 0.05, 0.75)Then we use r2rtf to prepare the table format for t1. We also highlight how to handle special character in this example.
Special characters ^ and _ are used to define superscript and subscript of text. And {} is to define the part that will be impacted. For example, {^a} provide a superscript a for footnote notation. r2rtf also support most LaTeX characters. Examples can be found in r2rtf Get Started Page. The text_convert argument in r2rtf_xxx functions control whether convert special characters.
t1_rtf <- t1 %>%
data.frame() %>%
rtf_title(c(
"ANCOVA of Change from Baseline Glucose (mmol/L) at Week 24",
"LOCF",
"Efficacy Analysis Population"
)) %>%
rtf_colheader("| Baseline | Week 24 | Change from Baseline",
col_rel_width = c(2.5, 2, 2, 4)
) %>%
rtf_colheader(paste(
"Treatment |",
paste0(rep("N | Mean (SD) | ", 3), collapse = ""),
"LS Mean (95% CI){^a}"
),
col_rel_width = c(2.5, rep(c(0.5, 1.5), 3), 2)
) %>%
rtf_body(
text_justification = c("l", rep("c", 7)),
col_rel_width = c(2.5, rep(c(0.5, 1.5), 3), 2)
) %>%
rtf_footnote(c(
"{^a}Based on an ANCOVA model after adjusting baseline value. LOCF approach is used to impute missing values.",
"ANCOVA = Analysis of Covariance, LOCF = Last Observation Carried Forward",
"CI = Confidence Interval, LS = Least Squares, SD = Standard Deviation"
))
t1_rtf %>%
rtf_encode() %>%
write_rtf("tlf/tlf_eff1.rtf")we also use r2rtf to prepare the table format for t2
t2_rtf <- t2 %>%
data.frame() %>%
rtf_colheader("Pairwise Comparison | Difference in LS Mean (95% CI){^a} | p-Value",
col_rel_width = c(4.5, 4, 2)
) %>%
rtf_body(
text_justification = c("l", "c", "c"),
col_rel_width = c(4.5, 4, 2)
)
t2_rtf %>%
rtf_encode() %>%
write_rtf("tlf/tlf_eff2.rtf")Finally we combine the two parts to get the final table using r2rtf. This is achieved by providing a list of t1_rtf and t2_rtf as input for rtf_encode.
list(t1_rtf, t2_rtf) %>%
rtf_encode() %>%
write_rtf("tlf/tlf_eff.rtf")In conclusion, the procedure to generate the above efficacy results table is summarized as follows.
adsl and adlb.gluc). The second dataset is the collection of all records post baseline and on or before week 24 (ana).ana dataset after imputation as ana_locf.gluc, i.e., calculate the mean and standard derivation, and then format it into a rtf table.ana_locf, i.e., calculate the pairwise comparison by ANCOVA model, and then format it into a rtf table.