基于时间变量固定连续增加的数据点线性插值函数
Function for linear interpolation of data points based on a fixed continuous increase in the time-variable
我的数据 res 中的 CIF 中存储了三个治疗组。基于可重现的例子：
> table(res$CIF)
Control SSA SSTR
35 25 5
对于每个 res$CIF，在时间 res$time 有一个结果的估计概率 res$P。概率为 95%-CI，如 res$lower 和 res$upper。
因此
> head(res,10)
CIF P time lower upper
1: SSTR 0.12500000 1.00 0.032811154 0.4140186
2: SSTR 0.31250000 2.00 0.143720822 0.5953967
3: SSTR 0.62500000 3.00 0.402281539 0.8457738
4: SSTR 0.81250000 4.00 0.597544067 0.9539839
5: SSTR 0.87500000 5.00 0.672015645 0.9793250
6: SSA 0.02777778 0.72 0.003960129 0.1812693
7: SSA 0.08333333 1.00 0.027663184 0.2365298
8: SSA 0.11111111 1.02 0.043219272 0.2694809
9: SSA 0.13888889 1.08 0.060294215 0.3020083
10: SSA 0.16666667 1.48 0.078561410 0.3338737
我需要在 res$time 当前未给出的时间点线性插值 res$P 和相应的 res$lower + res$upper。
我正在寻找一个函数（或类似的解决方案 - 也许是 dplyr 中的解决方案？）扩展 res 以便 res$time 的范围从 0 到每个 res$CIF 最多 res$time。 res$time 应连续增加 .01。
即，从0到105.16、30.85和5.00分别由.01：
> tapply(res$time,res$CIF,max)
Control SSA SSTR
105.16 30.85 5.00
预期输出示例
# Before interpolation
> head(res[res$CIF=="SSA"],5)
CIF P time lower upper
1: SSA 0.02777778 0.72 0.003960129 0.1812693
2: SSA 0.08333333 1.00 0.027663184 0.2365298
3: SSA 0.11111111 1.02 0.043219272 0.2694809
4: SSA 0.13888889 1.08 0.060294215 0.3020083
5: SSA 0.16666667 1.48 0.078561410 0.3338737
应该给
CIF P time lower upper
SSA 0 0.00 0 0
SSA interpolate 0.01 interpolate interpolate
(....)
SSA 0.02777778 0.72 0.003960129 0.1812693
(....)
SSA 0.08333333 1.00 0.027663184 0.2365298
SSA interpolate 1.01 interpolate interpolate
SSA 0.11111111 1.02 0.043219272 0.2694809
SSA interpolate 1.03 interpolate interpolate
SSA interpolate 1.04 interpolate interpolate
SSA interpolate 1.05 interpolate interpolate
SSA interpolate 1.06 interpolate interpolate
SSA interpolate 1.07 interpolate interpolate
SSA 0.13888889 1.08 0.060294215 0.3020083
我的数据res
res <- structure(list(CIF = c("SSTR", "SSTR", "SSTR", "SSTR", "SSTR",
"SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA",
"SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA",
"SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "Control", "Control",
"Control", "Control", "Control", "Control", "Control", "Control",
"Control", "Control", "Control", "Control", "Control", "Control",
"Control", "Control", "Control", "Control", "Control", "Control",
"Control", "Control", "Control", "Control", "Control", "Control",
"Control", "Control", "Control", "Control", "Control", "Control",
"Control", "Control", "Control"), P = c(0.125, 0.3125, 0.625,
0.8125, 0.875, 0.0277777777777778, 0.0833333333333333, 0.111111111111111,
0.138888888888889, 0.166666666666667, 0.305555555555556, 0.361111111111111,
0.388888888888889, 0.416666666666667, 0.444444444444445, 0.472222222222222,
0.527777777777778, 0.555555555555556, 0.583333333333333, 0.613095238095238,
0.642857142857143, 0.672619047619048, 0.672619047619048, 0.732142857142857,
0.761904761904762, 0.791666666666667, 0.821428571428572, 0.858630952380953,
0.895833333333333, 0.970238095238095, 0.025, 0.025, 0.025, 0.025,
0.025, 0.05, 0.075, 0.1, 0.125, 0.15, 0.15, 0.175, 0.2, 0.225,
0.25, 0.275, 0.3, 0.325, 0.35, 0.375, 0.4, 0.425, 0.45, 0.478333333333333,
0.506666666666667, 0.535, 0.565909090909091, 0.596818181818182,
0.631590909090909, 0.666363636363636, 0.701136363636364, 0.735909090909091,
0.770681818181818, 0.805454545454545, 0.840227272727273), time = c(1,
2, 3, 4, 5, 0.72, 1, 1.02, 1.08, 1.48, 2, 2.76, 2.82, 2.83, 3,
3.08, 3.57, 5.07, 5.49, 8.03, 9, 9.2, 9.25, 10.8, 11, 11.04,
14.2, 15.05, 21.42, 30.85, 0.23, 0.26, 0.49, 0.53, 0.69, 3.15,
3.25, 4.5, 5.12, 5.78, 6.67, 7.65, 7.79, 7.85, 9, 9.99, 11.37,
12.68, 13.11, 15.05, 15.83, 16.89, 18.17, 22.7, 23.59, 29.6,
32.65, 35.81, 43, 43.79, 45.37, 46.45, 46.65, 69.02, 105.16),
lower = c(0.0328111539708764, 0.143720822077878, 0.402281538850257,
0.597544067030214, 0.672015645447537, 0.00396012891352548,
0.0276631838805069, 0.0432192720492351, 0.0602942151317983,
0.0785614100173507, 0.18231512406141, 0.228150254051563,
0.251830579852024, 0.275990636539769, 0.300615683301302,
0.32569554091635, 0.377199241260733, 0.403622389357051, 0.430498943169836,
0.45921123839169, 0.48851369241709, 0.518429809974778, 0.518429809974778,
0.580243253031609, 0.612241368451204, 0.645062949439568,
0.678811652981003, 0.718192077960655, 0.761035083198697,
0.86875565093952, 0.00355981698627006, 0.00355981698627006,
0.00355981698627006, 0.00355981698627006, 0.00355981698627006,
0.0127444761396915, 0.0248237564000704, 0.0387548083597935,
0.0540289278928447, 0.0703518337133965, 0.0703518337133965,
0.0875349177801499, 0.105448804967606, 0.124000413393049,
0.143120415258911, 0.162755851975246, 0.182865529959695,
0.20341701986178, 0.22438463188234, 0.245748013164318, 0.267491158005832,
0.289601702577961, 0.312070423267255, 0.337084153386502,
0.362632734261147, 0.388713550110491, 0.417009262625303,
0.446060748331539, 0.478344299849033, 0.511927776545623,
0.546903575783177, 0.583428286459313, 0.621755981338108,
0.662308487815083, 0.705837515898454), upper = c(0.414018563190984,
0.595396721303893, 0.845773808747176, 0.953983876394769,
0.979324974514942, 0.181269269945454, 0.236529759895451,
0.269480930499581, 0.302008337476789, 0.333873667543882,
0.483459160112475, 0.539346001089099, 0.566541091565836,
0.593255777919075, 0.619498863619302, 0.645275418976181,
0.695431242848002, 0.719802607844794, 0.743691288858428,
0.769343219994671, 0.794279647503738, 0.818479990760844,
0.818479990760844, 0.864527983506889, 0.886263823263894,
0.907030011614637, 0.926703065538918, 0.951295364401731,
0.971948922997515, 0.997717755344036, 0.164514540888494,
0.164514540888494, 0.164514540888494, 0.164514540888494,
0.164514540888494, 0.185453879855473, 0.214782436042548,
0.244858945502003, 0.274592902916402, 0.303763783420835,
0.303763783420835, 0.332343773644891, 0.360355238540763,
0.387832132523894, 0.414808316400823, 0.441314057995926,
0.467375240079267, 0.493013472868414, 0.518246474164134,
0.543088485840094, 0.56755064509021, 0.591641285440807, 0.615366163389952,
0.642996938577391, 0.669919078034907, 0.696160621236471,
0.724897048548371, 0.752630120302531, 0.78395657751485, 0.813600779732339,
0.841596636148257, 0.867931528334935, 0.892542509012415,
0.91530398695896, 0.935999137248638)), row.names = c(NA,
-65L), class = c("data.table", "data.frame"))
这是 tidyr 的 complete 和 zoo 的 na.approx 的方法：
library(dplyr)
library(tidyr)
library(zoo)
res %>%
group_by(CIF) %>%
complete(time = seq(0, max(time), by = 0.01)) %>%
mutate_at(vars(P,lower,upper),
.funs = list(~ifelse(time == 0 & is.na(.), 0, .))) %>%
mutate_at(vars(P,lower,upper),
.funs = list(~ zoo::na.approx(.)))
如果您想使用非线性方法，您可以尝试 spline:
res %>%
group_by(CIF) %>%
complete(time = seq(0, max(time), by = 0.01)) %>%
mutate_at(vars(P,lower,upper),
.funs = list(~ifelse(time == 0 & is.na(.), 0, .))) %>%
mutate_at(vars(P,lower,upper),
.funs = list(~ spline(time, . ,n=n())$y))
这不会替换 NA，而是用内插值替换 所有 值。
我的数据 res 中的 CIF 中存储了三个治疗组。基于可重现的例子：
> table(res$CIF)
Control SSA SSTR
35 25 5
对于每个 res$CIF，在时间 res$time 有一个结果的估计概率 res$P。概率为 95%-CI，如 res$lower 和 res$upper。
因此
> head(res,10)
CIF P time lower upper
1: SSTR 0.12500000 1.00 0.032811154 0.4140186
2: SSTR 0.31250000 2.00 0.143720822 0.5953967
3: SSTR 0.62500000 3.00 0.402281539 0.8457738
4: SSTR 0.81250000 4.00 0.597544067 0.9539839
5: SSTR 0.87500000 5.00 0.672015645 0.9793250
6: SSA 0.02777778 0.72 0.003960129 0.1812693
7: SSA 0.08333333 1.00 0.027663184 0.2365298
8: SSA 0.11111111 1.02 0.043219272 0.2694809
9: SSA 0.13888889 1.08 0.060294215 0.3020083
10: SSA 0.16666667 1.48 0.078561410 0.3338737
我需要在 res$time 当前未给出的时间点线性插值 res$P 和相应的 res$lower + res$upper。
我正在寻找一个函数（或类似的解决方案 - 也许是 dplyr 中的解决方案？）扩展 res 以便 res$time 的范围从 0 到每个 res$CIF 最多 res$time。 res$time 应连续增加 .01。
即，从0到105.16、30.85和5.00分别由.01：
> tapply(res$time,res$CIF,max)
Control SSA SSTR
105.16 30.85 5.00
预期输出示例
# Before interpolation
> head(res[res$CIF=="SSA"],5)
CIF P time lower upper
1: SSA 0.02777778 0.72 0.003960129 0.1812693
2: SSA 0.08333333 1.00 0.027663184 0.2365298
3: SSA 0.11111111 1.02 0.043219272 0.2694809
4: SSA 0.13888889 1.08 0.060294215 0.3020083
5: SSA 0.16666667 1.48 0.078561410 0.3338737
应该给
CIF P time lower upper
SSA 0 0.00 0 0
SSA interpolate 0.01 interpolate interpolate
(....)
SSA 0.02777778 0.72 0.003960129 0.1812693
(....)
SSA 0.08333333 1.00 0.027663184 0.2365298
SSA interpolate 1.01 interpolate interpolate
SSA 0.11111111 1.02 0.043219272 0.2694809
SSA interpolate 1.03 interpolate interpolate
SSA interpolate 1.04 interpolate interpolate
SSA interpolate 1.05 interpolate interpolate
SSA interpolate 1.06 interpolate interpolate
SSA interpolate 1.07 interpolate interpolate
SSA 0.13888889 1.08 0.060294215 0.3020083
我的数据res
res <- structure(list(CIF = c("SSTR", "SSTR", "SSTR", "SSTR", "SSTR",
"SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA",
"SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA",
"SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "SSA", "Control", "Control",
"Control", "Control", "Control", "Control", "Control", "Control",
"Control", "Control", "Control", "Control", "Control", "Control",
"Control", "Control", "Control", "Control", "Control", "Control",
"Control", "Control", "Control", "Control", "Control", "Control",
"Control", "Control", "Control", "Control", "Control", "Control",
"Control", "Control", "Control"), P = c(0.125, 0.3125, 0.625,
0.8125, 0.875, 0.0277777777777778, 0.0833333333333333, 0.111111111111111,
0.138888888888889, 0.166666666666667, 0.305555555555556, 0.361111111111111,
0.388888888888889, 0.416666666666667, 0.444444444444445, 0.472222222222222,
0.527777777777778, 0.555555555555556, 0.583333333333333, 0.613095238095238,
0.642857142857143, 0.672619047619048, 0.672619047619048, 0.732142857142857,
0.761904761904762, 0.791666666666667, 0.821428571428572, 0.858630952380953,
0.895833333333333, 0.970238095238095, 0.025, 0.025, 0.025, 0.025,
0.025, 0.05, 0.075, 0.1, 0.125, 0.15, 0.15, 0.175, 0.2, 0.225,
0.25, 0.275, 0.3, 0.325, 0.35, 0.375, 0.4, 0.425, 0.45, 0.478333333333333,
0.506666666666667, 0.535, 0.565909090909091, 0.596818181818182,
0.631590909090909, 0.666363636363636, 0.701136363636364, 0.735909090909091,
0.770681818181818, 0.805454545454545, 0.840227272727273), time = c(1,
2, 3, 4, 5, 0.72, 1, 1.02, 1.08, 1.48, 2, 2.76, 2.82, 2.83, 3,
3.08, 3.57, 5.07, 5.49, 8.03, 9, 9.2, 9.25, 10.8, 11, 11.04,
14.2, 15.05, 21.42, 30.85, 0.23, 0.26, 0.49, 0.53, 0.69, 3.15,
3.25, 4.5, 5.12, 5.78, 6.67, 7.65, 7.79, 7.85, 9, 9.99, 11.37,
12.68, 13.11, 15.05, 15.83, 16.89, 18.17, 22.7, 23.59, 29.6,
32.65, 35.81, 43, 43.79, 45.37, 46.45, 46.65, 69.02, 105.16),
lower = c(0.0328111539708764, 0.143720822077878, 0.402281538850257,
0.597544067030214, 0.672015645447537, 0.00396012891352548,
0.0276631838805069, 0.0432192720492351, 0.0602942151317983,
0.0785614100173507, 0.18231512406141, 0.228150254051563,
0.251830579852024, 0.275990636539769, 0.300615683301302,
0.32569554091635, 0.377199241260733, 0.403622389357051, 0.430498943169836,
0.45921123839169, 0.48851369241709, 0.518429809974778, 0.518429809974778,
0.580243253031609, 0.612241368451204, 0.645062949439568,
0.678811652981003, 0.718192077960655, 0.761035083198697,
0.86875565093952, 0.00355981698627006, 0.00355981698627006,
0.00355981698627006, 0.00355981698627006, 0.00355981698627006,
0.0127444761396915, 0.0248237564000704, 0.0387548083597935,
0.0540289278928447, 0.0703518337133965, 0.0703518337133965,
0.0875349177801499, 0.105448804967606, 0.124000413393049,
0.143120415258911, 0.162755851975246, 0.182865529959695,
0.20341701986178, 0.22438463188234, 0.245748013164318, 0.267491158005832,
0.289601702577961, 0.312070423267255, 0.337084153386502,
0.362632734261147, 0.388713550110491, 0.417009262625303,
0.446060748331539, 0.478344299849033, 0.511927776545623,
0.546903575783177, 0.583428286459313, 0.621755981338108,
0.662308487815083, 0.705837515898454), upper = c(0.414018563190984,
0.595396721303893, 0.845773808747176, 0.953983876394769,
0.979324974514942, 0.181269269945454, 0.236529759895451,
0.269480930499581, 0.302008337476789, 0.333873667543882,
0.483459160112475, 0.539346001089099, 0.566541091565836,
0.593255777919075, 0.619498863619302, 0.645275418976181,
0.695431242848002, 0.719802607844794, 0.743691288858428,
0.769343219994671, 0.794279647503738, 0.818479990760844,
0.818479990760844, 0.864527983506889, 0.886263823263894,
0.907030011614637, 0.926703065538918, 0.951295364401731,
0.971948922997515, 0.997717755344036, 0.164514540888494,
0.164514540888494, 0.164514540888494, 0.164514540888494,
0.164514540888494, 0.185453879855473, 0.214782436042548,
0.244858945502003, 0.274592902916402, 0.303763783420835,
0.303763783420835, 0.332343773644891, 0.360355238540763,
0.387832132523894, 0.414808316400823, 0.441314057995926,
0.467375240079267, 0.493013472868414, 0.518246474164134,
0.543088485840094, 0.56755064509021, 0.591641285440807, 0.615366163389952,
0.642996938577391, 0.669919078034907, 0.696160621236471,
0.724897048548371, 0.752630120302531, 0.78395657751485, 0.813600779732339,
0.841596636148257, 0.867931528334935, 0.892542509012415,
0.91530398695896, 0.935999137248638)), row.names = c(NA,
-65L), class = c("data.table", "data.frame"))
这是 tidyr 的 complete 和 zoo 的 na.approx 的方法：
library(dplyr)
library(tidyr)
library(zoo)
res %>%
group_by(CIF) %>%
complete(time = seq(0, max(time), by = 0.01)) %>%
mutate_at(vars(P,lower,upper),
.funs = list(~ifelse(time == 0 & is.na(.), 0, .))) %>%
mutate_at(vars(P,lower,upper),
.funs = list(~ zoo::na.approx(.)))
如果您想使用非线性方法，您可以尝试 spline:
res %>%
group_by(CIF) %>%
complete(time = seq(0, max(time), by = 0.01)) %>%
mutate_at(vars(P,lower,upper),
.funs = list(~ifelse(time == 0 & is.na(.), 0, .))) %>%
mutate_at(vars(P,lower,upper),
.funs = list(~ spline(time, . ,n=n())$y))
这不会替换 NA，而是用内插值替换 所有 值。