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A4 Primary Results

ATRI Biostatistics

Source: vignettes/A4-Primary-Results.Rmd
A4-Primary-Results.Rmd

The Anti-Amyloid Treatment in Asymptomatic Alzheimer’s Disease (A4) study was a Phase 3, double-blind, placebo-controlled study of solanezumab in subjects with preclinical Alzheimer’s Disease (Sperling et al. 2023). The code below demonstrates how to reproduce some primary findings of the A4 trial (Sperling et al. 2023) using R Core Team (2024). Data were downloaded from https://www.a4studydata.org/ on 2025-08-08.

Load required R packages 

library(tidyverse)
library(arsenal)
library(kableExtra)
library(nlme)
library(emmeans)
library(splines)
library(clubSandwich)
library(A4LEARN)

formatp <- function(x) case_when(
  x < 0.001 ~ "p<0.001",
  x > 0.01 ~ Hmisc::format.pval(x, digits=2, eps=0.01, nsmall=2),
  TRUE ~ Hmisc::format.pval(x, digits=3, eps=0.001, nsmall=3))

Organize data 

# Outcomes collected at Visit 1
V1OUTCOME <- A4LEARN::ADQS %>%
  dplyr::filter(VISITCD == "001") %>%
  select(BID, QSTESTCD, QSSTRESN) %>%
  pivot_wider(values_from = QSSTRESN, names_from = QSTESTCD)

# Outcomes collected at Visit 6
V6OUTCOME <- A4LEARN::ADQS %>%
  dplyr::filter(VISITCD == "006") %>%
  select(BID, QSTESTCD, QSSTRESN) %>%
  pivot_wider(values_from = QSSTRESN, names_from = QSTESTCD)

SUBJINFO <- A4LEARN::SUBJINFO %>%
  left_join(V6OUTCOME, by = "BID") %>%
  left_join(V1OUTCOME %>%
      select(BID, CDRSB, CFITOTAL, CFISP, CFIPT, ADLPQPT, ADLPQSP), 
    by = "BID")

# Filter A4LEARN::ADQS for PACC collected in the blinded phases among mITT population
ADQS_PACC <- A4LEARN::ADQS %>%
  dplyr::filter(MITTFL== 1) %>%
  dplyr::filter(EPOCH == "BLINDED TREATMENT" | AVISIT == "006") %>%
  dplyr::filter(QSTESTCD == "PACC") %>%
  rename(PACC = QSSTRESN) %>%
  select(BID, ASEQNCS, TX, ADURW, TX, AGEYR, 
    AAPOEGNPRSNFLG, EDCCNTU, SUVRCER, QSVERSION, PACC) %>%
  mutate(TX = factor(TX, levels = c("Placebo", "Solanezumab"))) %>%
  arrange(BID, ADURW) %>%
  na.omit()

Baseline characteristics of the A4 trial 

A4labels <- list(TX = "Treatment group", AGEYR = "Age (y)", 
  EDCCNTU = "Education (y)", SUVRCER = "FBP SUVr", AMYLCENT = "FBP Centiloid", 
  LMIIa = "LM Delayed Recall",  MMSE = "MMSE", 
  CFITOTAL = "CFI Combined", ADLPQSP = "ADL Partner", CDRSB = "CDR-SB",
  SEX = "Sex", RACE = "Racial categories", ETHNIC = "Ethnicity", 
  MARITAL = "Marital Status",  WRKRET = "Retirement Status", 
  APOEGNPRSNFLG = "APOE e4", APOEGN = "APOE Genotype")

table1 <- tableby(TX ~ AGEYR + EDCCNTU + SEX + RACE + ETHNIC + MARITAL + WRKRET + 
    SUVRCER + AMYLCENT + chisq(APOEGN) + chisq(APOEGNPRSNFLG) + 
    PACC + LMIIa + MMSE + CFITOTAL + ADLPQSP + CDRSB, 
  data = SUBJINFO %>% dplyr::filter(MITTFL== 1), 
  control = tableby.control(test=TRUE,
    stats.labels = list(Nmiss = "Missing")))

summary(table1, labelTranslations = A4labels, digits = 1,
  title = "Characteristics of the A4 participants by randomized treatment group (Modified Intention-to-Treat Population of those who received at least one dose of solanezumab or placebo and underwent assessment for the primary end point).")
Characteristics of the A4 participants by randomized treatment group (Modified Intention-to-Treat Population of those who received at least one dose of solanezumab or placebo and underwent assessment for the primary end point).
Placebo (N=583) Solanezumab (N=564) Total (N=1147) p value
Age (y) 0.923
   Mean (SD) 71.9 (5.0) 72.0 (4.7) 72.0 (4.8)
   Range 65.0 - 85.7 65.0 - 85.5 65.0 - 85.7
Education (y) 0.785
   Mean (SD) 16.6 (2.9) 16.6 (2.7) 16.6 (2.8)
   Range 8.0 - 30.0 7.0 - 30.0 7.0 - 30.0
Sex 0.481
   Male 231 (39.6%) 235 (41.7%) 466 (40.6%)
   Female 352 (60.4%) 329 (58.3%) 681 (59.4%)
Racial categories 0.831
   American Indian or Alaskan Native 0 (0.0%) 1 (0.2%) 1 (0.1%)
   Asian 13 (2.2%) 11 (2.0%) 24 (2.1%)
   Black or African American 15 (2.6%) 12 (2.1%) 27 (2.4%)
   More than one race 3 (0.5%) 5 (0.9%) 8 (0.7%)
   Unknown or Not Reported 3 (0.5%) 4 (0.7%) 7 (0.6%)
   White 549 (94.2%) 531 (94.1%) 1080 (94.2%)
Ethnicity 0.910
   Hispanic or Latino 18 (3.1%) 16 (2.8%) 34 (3.0%)
   Not Hispanic or Latino 560 (96.1%) 542 (96.1%) 1102 (96.1%)
   Unknown or Not reported 5 (0.9%) 6 (1.1%) 11 (1.0%)
Marital Status 0.208
   Divorced 80 (13.7%) 89 (15.8%) 169 (14.7%)
   Married 415 (71.2%) 405 (71.8%) 820 (71.5%)
   Never married 26 (4.5%) 14 (2.5%) 40 (3.5%)
   Unknown or Not Reported 12 (2.1%) 6 (1.1%) 18 (1.6%)
   Widowed 50 (8.6%) 50 (8.9%) 100 (8.7%)
Retirement Status 0.722
   No 142 (24.4%) 126 (22.3%) 268 (23.4%)
   Not Applicable 9 (1.5%) 9 (1.6%) 18 (1.6%)
   Yes 432 (74.1%) 429 (76.1%) 861 (75.1%)
FBP SUVr 0.903
   Mean (SD) 1.3 (0.2) 1.3 (0.2) 1.3 (0.2)
   Range 1.0 - 2.1 1.0 - 2.1 1.0 - 2.1
FBP Centiloid 0.903
   Mean (SD) 65.9 (32.1) 66.2 (33.5) 66.0 (32.8)
   Range 0.3 - 205.4 0.3 - 201.7 0.3 - 205.4
APOE Genotype 0.624
   E2/E2 0 (0.0%) 1 (0.2%) 1 (0.1%)
   E2/E3 33 (5.7%) 28 (5.0%) 61 (5.3%)
   E2/E4 22 (3.8%) 13 (2.3%) 35 (3.1%)
   E3/E3 208 (35.7%) 202 (35.8%) 410 (35.7%)
   E3/E4 273 (46.8%) 273 (48.4%) 546 (47.6%)
   E4/E4 47 (8.1%) 47 (8.3%) 94 (8.2%)
APOE e4 0.896
   No 241 (41.3%) 231 (41.0%) 472 (41.2%)
   Yes 342 (58.7%) 333 (59.0%) 675 (58.8%)
PACC 0.831
   Mean (SD) -0.0 (2.6) 0.0 (2.7) 0.0 (2.7)
   Range -12.5 - 7.8 -10.3 - 6.4 -12.5 - 7.8
LM Delayed Recall 0.757
   Missing 1 0 1
   Mean (SD) 12.7 (3.5) 12.6 (3.8) 12.6 (3.7)
   Range 2.0 - 22.0 0.0 - 23.0 0.0 - 23.0
MMSE 0.763
   Mean (SD) 28.8 (1.2) 28.8 (1.3) 28.8 (1.3)
   Range 24.0 - 30.0 22.0 - 30.0 22.0 - 30.0
CFI Combined 0.045
   Missing 2 0 2
   Mean (SD) 3.6 (3.3) 4.0 (3.6) 3.8 (3.5)
   Range 0.0 - 20.0 0.0 - 22.0 0.0 - 22.0
ADL Partner 0.266
   Mean (SD) 43.5 (2.6) 43.4 (2.7) 43.4 (2.6)
   Range 26.8 - 45.0 25.0 - 45.0 25.0 - 45.0
CDR-SB 0.154
   Mean (SD) 0.0 (0.2) 0.1 (0.2) 0.1 (0.2)
   Range 0.0 - 2.0 0.0 - 1.0 0.0 - 2.0

Primary analyis of the PACC

Preclinical Alzheimer Cognitive Composite (PACC, Donohue et al. (2014)) data was modeled using natural cubic splines as described in Donohue et al. (2023). The fixed effects included the following terms: (i) spline basis expansion terms (two terms), (ii) spline basis expansion terms-by-treatment interaction (two terms), (iii) PACC test version administered, (iv) baseline age, (v) education, (vi) APOE4 Carrier Status (yes/no), and (vii) baseline florbetapir cortical SUVr. The model is constrained to not allow a difference between treatment group means at baseline. The following variance-covariance structures were assumed in sequence until a model converged: (i) heterogeneous unstructured, (ii) heterogeneous Toeplitz, (iii) heterogeneous autoregressive order 1, (iv) heterogeneous compound symmetry, and (v) compound symmetry. The first structure, heterogeneous unstructured, did not converge. Here we fit the second, heterogeneous Toeplitz, which did converge.

ggplot(ADQS_PACC, aes(x=ADURW, y=PACC, color=TX)) +
  geom_line(aes(group = BID), alpha=0.2) +
  theme(legend.position = "inside", legend.position.inside = c(0.2, 0.2)) +
  xlab("Weeks since Randomization") +
  scale_x_continuous(breaks = seq(0, max(ADQS_PACC$ADURW), by = 24))
Spaghetti plot of PACC data over time by treatment group.

Spaghetti plot of PACC data over time by treatment group. 

# Spline basis expansion functions
# CAUTION: these function depend on the ADQS_PACC data frame object in the 
# global environment. If ADQS_PACC changes, so do these funtions
ns21 <- function(t){
  as.numeric(predict(splines::ns(ADQS_PACC$ADURW, df=2,
    Boundary.knots = c(0, max(ADQS_PACC$ADURW))), t)[,1])
}
ns22 <- function(t){
  as.numeric(predict(splines::ns(ADQS_PACC$ADURW, df=2,
    Boundary.knots = c(0, max(ADQS_PACC$ADURW))), t)[,2])
}

assign("ns21", ns21, envir = .GlobalEnv)
assign("ns22", ns22, envir = .GlobalEnv)

# GLS model fit:
pacc_fit <- gls(PACC ~ 
    I(ns21(ADURW)) + I(ns22(ADURW)) +
    (I(ns21(ADURW)) + I(ns22(ADURW))):TX + 
    AGEYR + AAPOEGNPRSNFLG + EDCCNTU + SUVRCER + QSVERSION,
  data = ADQS_PACC,
  weights = varIdent(form = ~ 1 | ASEQNCS),
  correlation = corARMA(form = ~ ASEQNCS | BID, p = 10))
ref_grid(pacc_fit,
  at = list(ADURW = c(0,240), TX = levels(ADQS_PACC$TX)),
  vcov. = clubSandwich::vcovCR(pacc_fit, type = "CR2") %>% as.matrix(), 
  data = ADQS_PACC, 
  mode = "satterthwaite") %>%
  emmeans(~ ADURW | TX) %>%
  pairs(reverse = TRUE) %>%
  as_tibble() %>%
  mutate(p.value = formatp(p.value)) %>%
  kable(caption = "Mean PACC change from baseline at week 240 by treatment 
    group estimated from spline model.", digits = 2, booktabs = TRUE) %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Mean PACC change from baseline at week 240 by treatment group estimated from spline model.
contrast TX estimate SE df t.ratio p.value
ADURW240 - ADURW0 Placebo -1.13 0.16 10791 -6.88 p<0.001
ADURW240 - ADURW0 Solanezumab -1.43 0.21 10791 -6.95 p<0.001 
contrast240 <- ref_grid(pacc_fit, 
  at = list(ADURW = 240, TX = levels(ADQS_PACC$TX)),
  vcov. = clubSandwich::vcovCR(pacc_fit, type = "CR2") %>% as.matrix(), 
  data = ADQS_PACC, 
  mode = "satterthwaite") %>%
  emmeans(specs = "TX", by = "ADURW") %>%
  pairs(reverse = TRUE, adjust = "none")

contrast240 %>% 
  as_tibble() %>%
  left_join(contrast240 %>% 
      confint() %>%
      as_tibble() %>%
      select(contrast, lower.CL, upper.CL), by="contrast") %>%
  relocate(p.value, .after = last_col()) %>%
  mutate(p.value = formatp(p.value)) %>%
  kable(caption = "Mean PACC group change from baseline at week 240 by treatment 
    group estimated from spline model.", digits = 2, booktabs = TRUE) %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Mean PACC group change from baseline at week 240 by treatment group estimated from spline model.
contrast ADURW estimate SE df t.ratio lower.CL upper.CL p.value
Solanezumab - Placebo 240 -0.3 0.26 10791 -1.13 -0.82 0.22 0.26 
ref_grid(pacc_fit, 
  at = list(ADURW = seq(0, 312, by=12), TX = levels(ADQS_PACC$TX)),
  vcov. = clubSandwich::vcovCR(pacc_fit, type = "CR2") %>% as.matrix(), 
  data = ADQS_PACC, 
  mode = "satterthwaite") %>%
  emmeans(specs = "TX", by = "ADURW") %>%
  as_tibble() %>%
  ggplot(aes(x=ADURW, y=emmean)) +
  geom_line(aes(color=TX)) +
  geom_ribbon(aes(ymin = lower.CL, ymax = upper.CL, fill = TX), alpha = 0.2) +
  scale_x_continuous(breaks = seq(0, 312, by=24)) +
  ylab("Mean PACC with 95% confidence intervals") +
  xlab("Weeks since Randomization") +
  theme(legend.position = 'inside', legend.position.inside = c(0.2, 0.2))
Mean PACC per treatment group over time as estimated by spline model. Shaded region depicts 95% confidence intervals.

Mean PACC per treatment group over time as estimated by spline model. Shaded region depicts 95% confidence intervals.

Primary analyis of the CFI 

# Filter A4LEARN::ADQS for CFITOTAL collected in the blinded phases among mITT population
ADQS_CFI <- A4LEARN::ADQS %>%
  dplyr::filter(MITTFL== 1) %>%
  dplyr::filter(EPOCH == "BLINDED TREATMENT" | AVISIT == "001") %>%
  dplyr::filter(QSTESTCD == "CFITOTAL") %>%
  select(BID, ASEQNCS, TX, ADURW, TX, AGEYR, 
    AAPOEGNPRSNFLG, EDCCNTU, SUVRCER, QSSTRESN) %>%
  mutate(TX = factor(TX, levels = c("Placebo", "Solanezumab"))) %>%
  arrange(BID, ADURW) %>%
  na.omit()
ggplot(ADQS_CFI, aes(x=ADURW, y=QSSTRESN, color=TX)) +
  geom_line(aes(group = BID), alpha=0.2) +
  theme(legend.position = "inside", legend.position.inside = c(0.2, 0.9)) +
  xlab("Weeks since Randomization") +
  ylab("CFI Participant and Partner")
Spaghetti plot of CFI data over time by treatment group.

Spaghetti plot of CFI data over time by treatment group. 

  scale_x_continuous(breaks = seq(0, max(ADQS_CFI$ADURW), by = 24))
<ScaleContinuousPosition>
 Range:  
 Limits:    0 --    1
# Spline basis expansion functions
# CAUTION: these function depend on the ADQS_CFI data frame object in the 
# global environment. If ADQS_CFI changes, so do these funtions
ns21 <- function(t){
  as.numeric(predict(splines::ns(ADQS_CFI$ADURW, df=2,
    Boundary.knots = c(0, max(ADQS_CFI$ADURW))), t)[,1])
}
ns22 <- function(t){
  as.numeric(predict(splines::ns(ADQS_CFI$ADURW, df=2,
    Boundary.knots = c(0, max(ADQS_CFI$ADURW))), t)[,2])
}

assign("ns21", ns21, envir = .GlobalEnv)
assign("ns22", ns22, envir = .GlobalEnv)

# GLS model fit:
cfi_fit <- gls(QSSTRESN ~ 
    I(ns21(ADURW)) + I(ns22(ADURW)) +
    (I(ns21(ADURW)) + I(ns22(ADURW))):TX + 
    AGEYR + AAPOEGNPRSNFLG + EDCCNTU + SUVRCER,
  data = ADQS_CFI,
  weights = varIdent(form = ~ 1 | ASEQNCS),
  correlation = corARMA(form = ~ ASEQNCS | BID, p = 5))
ref_grid(cfi_fit,
  at = list(ADURW = c(0,240), TX = levels(ADQS_CFI$TX)),
  vcov. = clubSandwich::vcovCR(cfi_fit, type = "CR2") %>% as.matrix(), 
  data = ADQS_CFI, 
  mode = "satterthwaite") %>%
  emmeans(~ ADURW | TX) %>%
  pairs(reverse = TRUE) %>%
  as_tibble() %>%
  mutate(p.value = formatp(p.value)) %>%
  kable(caption = "Mean CFI change from baseline at week 240 by treatment 
    group estimated from spline model.", digits = 2, booktabs = TRUE) %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Mean CFI change from baseline at week 240 by treatment group estimated from spline model.
contrast TX estimate SE df t.ratio p.value
ADURW240 - ADURW0 Placebo 1.51 0.19 1437.56 7.96 p<0.001
ADURW240 - ADURW0 Solanezumab 2.09 0.21 1768.38 9.77 p<0.001 
contrast240 <- ref_grid(cfi_fit, 
  at = list(ADURW = 240, TX = levels(ADQS_CFI$TX)),
  vcov. = clubSandwich::vcovCR(cfi_fit, type = "CR2") %>% as.matrix(), 
  data = ADQS_CFI, 
  mode = "satterthwaite") %>%
  emmeans(specs = "TX", by = "ADURW") %>%
  pairs(reverse = TRUE, adjust = "none")

contrast240 %>% 
  as_tibble() %>%
  left_join(contrast240 %>% 
      confint() %>%
      as_tibble() %>%
      select(contrast, lower.CL, upper.CL), by="contrast") %>%
  relocate(p.value, .after = last_col()) %>%
  mutate(p.value = formatp(p.value)) %>%
  kable(caption = "Mean CFI group change from baseline at week 240 by treatment 
    group estimated from spline model.", digits = 2, booktabs = TRUE) %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Mean CFI group change from baseline at week 240 by treatment group estimated from spline model.
contrast ADURW estimate SE df t.ratio lower.CL upper.CL p.value
Solanezumab - Placebo 240 0.58 0.29 1769.54 2.04 0.02 1.14 0.04 
ref_grid(cfi_fit, 
  at = list(ADURW = seq(0, 312, by=12), TX = levels(ADQS_CFI$TX)),
  vcov. = clubSandwich::vcovCR(cfi_fit, type = "CR2") %>% as.matrix(), 
  data = ADQS_CFI, 
  mode = "satterthwaite") %>%
  emmeans(specs = "TX", by = "ADURW") %>%
  as_tibble() %>%
  ggplot(aes(x=ADURW, y=emmean)) +
  geom_line(aes(color=TX)) +
  geom_ribbon(aes(ymin = lower.CL, ymax = upper.CL, fill = TX), alpha = 0.2) +
  scale_x_continuous(breaks = seq(0, 312, by=24)) +
  ylab("Mean CFI with 95% confidence intervals") +
  xlab("Weeks since Randomization") +
  theme(legend.position = 'inside', legend.position.inside = c(0.2, 0.9))
Mean CFI per treatment group over time as estimated by spline model. Shaded region depicts 95% confidence intervals.

Mean CFI per treatment group over time as estimated by spline model. Shaded region depicts 95% confidence intervals.

References

Donohue, Michael C, Oliver Langford, Philip S Insel, Christopher H van Dyck, Ronald C Petersen, Suzanne Craft, Gopalan Sethuraman, Rema Raman, Paul S Aisen, and Alzheimer’s Disease Neuroimaging Initiative. 2023. “Natural Cubic Splines for the Analysis of Alzheimer’s Clinical Trials.” Pharmaceutical Statistics. https://doi.org/10.1002/pst.2285.
Donohue, Michael C, Reisa A Sperling, David P Salmon, Dorene M Rentz, Rema Raman, Ronald G Thomas, Michael Weiner, Paul S Aisen, et al. 2014. “The Preclinical Alzheimer Cognitive Composite: Measuring Amyloid-Related Decline.” JAMA Neurology 71 (8): 961–70. https://doi.org/10.1001/jamaneurol.2014.803.
R Core Team. 2024. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
Sperling, Reisa A, Michael C Donohue, Rema Raman, Michael S Rafii, Keith Johnson, Colin L Masters, Christopher H van Dyck, et al. 2023. “Trial of Solanezumab in Preclinical Alzheimer’s Disease.” New England Journal of Medicine 389 (12): 1096–1107. https://doi.org/10.1056/NEJMoa2305032.