Setting hypotheses in R package SPRT - r

Question

I am new to using the SPRT package in R to perform sequential proprortion ratio testing, and vignettes/tutorials for this package seem to be sparse.
By default the SPRT function can receive cumulative values of n & k (trials and events). I will be using this method on a large studies where trials and events will be tallied daily in a cumulative fashion and I want to check my logic on how I have applied SPRT().
SPRT requires users to set explicit null and alternative hypothesis. I have set these to H_0: treat = control
H_1: treat = control * 1.01
In my for-loop that follows I apply the SPRT() function every day to compute the log likelihood ratio of the cumulative data under each hypothesis, and I really just want to confirm that this is the correct way to analyze the data. Most examples I have seen set h0 and h1 in a more explicit fashion (e.g., h0 = .85 & h1 = .85*1.01), while I have set them to reflect the observed rates for each day in the cumulative data as seems more appropriate in the setting of an experiment (e.g., h0 = df_sprt$control[i]/df_sprt$n[i], h1 = (df_sprt$control[i] * MDE)/df_sprt$n[i]).
library(SPRT)
library(tidyverse)
# simulate cumulative data from an AB Test
set.seed(42)
DAYS <- 14
DAILY_N <- 1e3
BASERATE <- .85
MDE <- 1.02
df_sprt <-
tibble(
day = 1:DAYS,
control = rbinom(n = DAYS, size = DAILY_N, prob = BASERATE),
treat = rbinom(n = DAYS, size = DAILY_N, prob = BASERATE*MDE),
n = DAILY_N
) %>%
mutate(
control = cumsum(control),
treat = cumsum(treat),
n = cumsum(n)
)
# apply SPRT in a for loop
wald_a <- vector('numeric', length = nrow(df_sprt))
wald_b <- vector('numeric', length = nrow(df_sprt))
llr <- vector('numeric', length = nrow(df_sprt))
for (i in 1:nrow(df_sprt)) {
out <- SPRT(
distribution = "bernoulli",
type1 = 0.05, type2 = 0.20,
h0 = df_sprt$control[i]/df_sprt$n[i], h1 = (df_sprt$control[i] * MDE)/df_sprt$n[i],
n = df_sprt$n[i],
k = df_sprt$treat[i]
)
wald_a[i] <- out$wald.A
wald_b[i] <- out$wald.B
llr[i] <- out$llr
}
sprt_out <-
tibble(
llr,
wald_a,
wald_b,
cohort_day = 1:DAYS
)
# Plot the results
sprt_out %>%
ggplot(aes(x = cohort_day, y = llr)) +
geom_hline(
yintercept =
c(max(sprt_out$wald_a), max(sprt_out$wald_b)),
color = c('darkgreen', 'red')
) +
geom_point() +
geom_line() +
annotate(
x=10,y=max(sprt_out$wald_b),
label="Reject Alternative Hy & Retain Null Hy",
vjust=-1, geom="text", color = 'red'
) +
annotate(
x=10,y=max(sprt_out$wald_a),
label="Reject Null Hy & Accept Alternative Hy",
vjust=1.5, geom="text", color = 'darkgreen'
) +
scale_y_continuous(breaks = -10:20) +
scale_x_continuous(breaks = 1:20) +
theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))