所以，我想我明白你想要什么：
- 每月月底接受治疗的患者人数
- 每月开始治疗的患者人数
- 每月月初接受治疗的患者人数*
*这是否包括在当月第一天开始治疗的患者（例如您的样本数据中的每个人）？ - 我假设在这个例子中是这样的。
因此，请加载您的示例数据并确保日期采用正确的date 格式
df <- data.frame(patient_ID= c("AA", "BB", "CC", "DD", "EE", "FF"),
treatment_start_date = as.Date(c("2004-01-01", "2007-01-01", "2012-04-01", "2014-04-01",
"2019-04-01", "2020-04-01")),
treatment_end_date = as.Date(c("2014-12-31", "2017-03-31", "2018-03-31", "2019-03-31",
"2020-03-31", "2021-04-30")))
# make sure the dates are date format
df %>%
as_tibble %>%
mutate(across(treatment_start_date:treatment_end_date, ~ymd(.))) %>%
{. ->> df_1}
df_1
# # A tibble: 6 x 3
# patient_ID treatment_start_date treatment_end_date
# <chr> <date> <date>
# AA 2004-01-01 2014-12-31
# BB 2007-01-01 2017-03-31
# CC 2012-04-01 2018-03-31
# DD 2014-04-01 2019-03-31
# EE 2019-04-01 2020-03-31
# FF 2020-04-01 2021-04-30
然后，我们对每位患者接受治疗的每个日期（包括开始和结束日期）进行排序。
# make a sequence of every date a patient was in the treatment
df_1 %>%
rowwise %>%
mutate(
treatment_days = list(seq(treatment_start_date, treatment_end_date, by = 'day'))
) %>%
select(patient_ID, treatment_days) %>%
unnest(cols = c('treatment_days')) %>%
{. ->> df_2}
df_2
# # A tibble: 12,539 x 2
# patient_ID treatment_days
# <chr> <date>
# AA 2004-01-01
# AA 2004-01-02
# AA 2004-01-03
# AA 2004-01-04
# AA 2004-01-05
# AA 2004-01-06
# AA 2004-01-07
# AA 2004-01-08
# AA 2004-01-09
# AA 2004-01-10
# # ... with 12,529 more rows
然后，我们计算出每天有多少患者在接受治疗，并且只保留每个月的第一天和最后一天。
df_2 %>%
# work out how many patients were in treatment for each day
group_by(treatment_days) %>%
summarise(
n_patients = n_distinct(patient_ID)
) %>%
# make month column
mutate(
month = format(treatment_days, format = '%Y-%m')
) %>%
# keep only the first and last days of each month
group_by(month) %>%
filter(
day(treatment_days) == 1 | day(treatment_days) == max(day(treatment_days))
) %>%
# determine number of patients at the start and end of each month
# ensure the dates are in order
arrange(month, treatment_days) %>%
group_by(month) %>%
summarise(
n_patient_start = nth(n_patients, 1),
n_patient_end = nth(n_patients, 2),
) %>%
{. ->> df_3}
df_3
# # A tibble: 208 x 3
# month n_patient_start n_patient_end
# <chr> <int> <int>
# 2004-01 1 1
# 2004-02 1 1
# 2004-03 1 1
# 2004-04 1 1
# 2004-05 1 1
# 2004-06 1 1
# 2004-07 1 1
# 2004-08 1 1
# 2004-09 1 1
# 2004-10 1 1
# # ... with 198 more rows
所以，现在我们有了每个月初和月底接受治疗的患者总数。
在计算留存率之前，我们需要知道每个月有多少患者开始接受治疗，因此可以将其用于计算留存率。
# how many patients started each month?
df_1 %>%
select(patient_ID, treatment_start_date) %>%
mutate(
month = format(treatment_start_date, format = '%Y-%m')
) %>%
group_by(month) %>%
summarise(
n_starting_patients = n_distinct(patient_ID)
) %>%
{. ->> n_new_per_month}
n_new_per_month
# # A tibble: 6 x 2
# month n_starting_patients
# <chr> <int>
# 2004-01 1
# 2007-01 1
# 2012-04 1
# 2014-04 1
# 2019-04 1
# 2020-04 1
我们将每月开始和月底的开始患者人数与活跃患者人数相结合。然后，我们可以根据您问题中的公式计算留存率。
# now, we join in new patients per month
df_3 %>%
left_join(n_new_per_month) %>%
mutate(
n_starting_patients = ifelse(is.na(n_starting_patients), 0, n_starting_patients)
) %>%
# calculate retention rate
mutate(
ret_rate = (n_patient_end - n_starting_patients) / n_patient_start
)
# # A tibble: 208 x 5
# month n_patient_start n_patient_end n_starting_patients ret_rate
# <chr> <int> <int> <dbl> <dbl>
# 2004-01 1 1 1 0
# 2004-02 1 1 0 1
# 2004-03 1 1 0 1
# 2004-04 1 1 0 1
# 2004-05 1 1 0 1
# 2004-06 1 1 0 1
# 2004-07 1 1 0 1
# 2004-08 1 1 0 1
# 2004-09 1 1 0 1
# 2004-10 1 1 0 1
# # ... with 198 more rows
现在我不太确定这是否正确，因为例如在上面的预览中 - 我们在 2004 年 1 月的保留率是 0，尽管这个月没有患者丢失（实际上我们有一开始治疗）。这是因为患者 AA 于 1 月 1 日开始，因此保留率计算为(number of patients at the end of the month - number of patients that started in that month) / number of patients at the start of the month，或(1 - 1) / 1 = 0 / 1 = 0。
使用当前公式会影响留存率的因素：
- 开始和结束日期是否包含在患者接受治疗的日期中？
- 如果患者在当月的第一天开始，这是否意味着他们被包括或从“患者在月初删除”？如果您想删除在月中开始的患者数量，我可以理解，但对于当前的公式，这对我来说不太有意义。