我有重复的测量数据，outcome包括在 149 名患者中进行的总共 310 次测量（每位患者的测量量范围为 1-6 次）。对于所有患者，临床危险因素在基线时测量一次。对于我的分析，我使用以年龄为时间变量的线性混合模型，对所有风险因素与结果变化的关联进行了建模。此外，混合模型包括每个患者的随机截距和残差的连续一阶自回归相关结构，以及结果的自然对数变换（因为这是严重右偏的）。
我的数据如下所示：
# Load packages
library(tidyverse)
library(magrittr)
library(nlme)
library(broom.mixed)
library(GLMMadaptive)
# Get data.
mydata <- structure(list(pat_id = c(2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4,
4, 7, 7, 8, 8, 13, 13, 13, 13, 14, 14, 14, 14, 16, 19, 19, 22,
22, 24, 24, 25, 25, 27, 27, 28, 29, 29, 29, 29, 30, 30, 31, 31,
34, 34, 34, 34, 36, 36, 37, 38, 38, 39, 39, 40, 40, 40, 40, 46,
48, 48, 49, 49, 49, 49, 50, 50, 51, 51, 51, 52, 52, 54, 54, 56,
57, 58, 58, 60, 60, 61, 61, 61, 61, 64, 65, 65, 67, 74, 74, 74,
74, 75, 76, 76, 76, 76, 77, 77, 77, 80, 80, 81, 81, 83, 83, 84,
84, 87, 87, 88, 88, 88, 90, 92, 92, 94, 94, 95, 95, 95, 95, 96,
96, 96, 96, 97, 97, 98, 99, 102, 103, 103, 104, 104, 105, 105,
105, 105, 108, 108, 114, 114, 115, 115, 115, 116, 116, 117, 117,
119, 119, 120, 125, 125, 125, 125, 126, 126, 127, 127, 132, 132,
132, 132, 134, 134, 135, 135, 135, 135, 137, 137, 138, 138, 142,
142, 148, 151, 152, 152, 152, 153, 153, 153, 153, 154, 154, 154,
154, 158, 158, 159, 161, 162, 162, 162, 162, 164, 164, 164, 164,
165, 165, 165, 165, 169, 171, 171, 171, 171, 172, 172, 174, 179,
179, 179, 179, 185, 185, 189, 189, 189, 191, 195, 195, 195, 195,
198, 198, 198, 198, 202, 202, 202, 202, 203, 203, 203, 205, 205,
205, 205, 206, 206, 209, 209, 213, 213, 218, 221, 221, 223, 225,
226, 226, 230, 231, 250, 252, 253, 253, 255, 255, 257, 258, 258,
262, 262, 269, 271, 271, 273, 273, 275, 277, 277, 279, 279, 281,
282, 283, 285, 288, 293, 306, 308, 310, 310, 313, 315, 315, 320,
320, 332, 333, 335, 351, 355, 358, 360, 368, 371, 379, 385, 388,
399, 400), age = c(56.5941136208077, 57.138945927447, 58.7624914442163,
59.27446954141, 59.7782340862423, 62.2888432580424, 43.2169746748802,
45.1088295687885, 51.958932238193, 52.8980150581793, 53.409993155373,
53.9137577002053, 56.3121149897331, 58.507871321013, 62.9568788501027,
57.3990417522245, 61.4045174537988, 57.8015058179329, 58.6584531143053,
59.1622176591376, 61.5605749486653, 52.3613963039014, 53.3141683778234,
53.8179329226557, 56.3915126625599, 62.0342231348392, 54.1875427789185,
60.870636550308, 59.2470910335387, 59.8028747433265, 61.5003422313484,
63.1622176591376, 48.9199178644764, 54.4777549623546, 54.2067077344285,
55.4140999315537, 60.3750855578371, 50.0561259411362, 51.3949349760438,
52.3915126625599, 54.2505133470226, 55.3757700205339, 56.1095140314853,
48.5941136208077, 50.8637919233402, 64.1889117043121, 64.8021902806297,
65.8370978781656, 68.3860369609856, 68.2847364818617, 68.8405201916496,
66.6721423682409, 60.5147159479808, 64.8350444900753, 56.5119780971937,
60.8870636550308, 62.7049965776865, 63.27446954141, 63.7782340862423,
66.3819301848049, 43.8357289527721, 49.0403832991102, 49.8398357289528,
60.9582477754962, 61.8206707734428, 62.8172484599589, 65.2867898699521,
59.9780971937029, 60.8405201916496, 61.9575633127995, 62.8774811772758,
63.8740588637919, 52.9774127310062, 53.8973305954825, 52.0383299110199,
57.0431211498973, 71.151266255989, 64.1314168377823, 68.1889117043121,
68.974674880219, 45.2457221081451, 46.031485284052, 54.9541409993155,
56.1478439425051, 57.1444216290212, 59.4661190965092, 72.684462696783,
56.2847364818617, 57.3963039014374, 24.4380561259411, 54.6283367556468,
55.4277891854894, 55.9315537303217, 58.2696783025325, 60.8788501026694,
57.5523613963039, 58.4093086926762, 58.9130732375086, 61.4045174537988,
60.7063655030801, 61.5687885010267, 64.4052019164956, 40.6817248459959,
44.8350444900753, 64.7583846680356, 68.8350444900753, 36.2847364818617,
40.8350444900753, 66.5133470225873, 70.4010951403149, 56.9199178644764,
58.031485284052, 57.3771389459274, 58.3737166324435, 60.517453798768,
50.9568788501027, 54.9596167008898, 60.8980150581793, 56.9555099247091,
58.299794661191, 56.0492813141684, 57.3004791238877, 58.2970568104038,
60.5037645448323, 51.0499657768652, 52.0383299110199, 53.0102669404517,
55.460643394935, 71.0554414784394, 75.8357289527721, 69.0513347022587,
27.0554414784394, 64.0903490759754, 52.0876112251882, 53.3004791238877,
67.0691307323751, 72.0191649555099, 60.0739219712526, 61.2621492128679,
62.258726899384, 64.2929500342231, 68.1259411362081, 74.8583162217659,
66.1492128678987, 67.3757700205339, 45.264887063655, 48.8487337440109,
51.9917864476386, 60.1697467488022, 61.2621492128679, 75.170431211499,
79.3347022587269, 58.2039698836413, 59.2607802874743, 49.201916495551,
67.2498288843258, 68.0520191649555, 69.0485968514716, 71.4004106776181,
35.2443531827515, 36.435318275154, 65.2484599589322, 66.0506502395619,
46.3189596167009, 46.9349760438056, 47.9315537303217, 50.3490759753593,
67.2991101984942, 68.186173853525, 50.3025325119781, 50.8199863107461,
51.8165639972622, 54.2696783025325, 65.3032169746749, 65.8781656399726,
48.3039014373717, 53.0184804928131, 47.4962354551677, 48.1478439425051,
53.6262833675565, 48.662559890486, 61.6618754277892, 62.5681040383299,
65.4264202600958, 64.684462696783, 65.429158110883, 65.9712525667351,
68.35318275154, 55.6632443531828, 56.5256673511294, 57.0294318959617,
59.8877481177276, 51.7070499657769, 57.8015058179329, 73.7056810403833,
63.7262149212868, 47.7262149212868, 48.7173169062286, 49.3552361396304,
51.3867214236824, 53.5715263518138, 54.5051334702259, 55.0088980150582,
57.2292950034223, 74.7433264887064, 75.6577686516085, 76.1615331964408,
78.7843942505133, 82.7816563997262, 55.8220396988364, 56.6023271731691,
57.1060917180014, 59.6139630390144, 62.8199863107461, 66.8336755646817,
59.9014373716632, 60.9171800136893, 61.6399726214921, 62.1437371663244,
64.517453798768, 63.9315537303217, 67.8357289527721, 69.0650239561944,
69.8945927446954, 73.0184804928131, 42.2039698836413, 61.2566735112936,
61.927446954141, 62.4312114989733, 65.056810403833, 55.2553045859001,
55.8685831622177, 56.37234770705, 58.403832991102, 63.2936344969199,
63.9069130732375, 64.4106776180698, 66.3271731690623, 46.2943189596167,
46.9267624914442, 47.4305270362765, 53.3524982888433, 53.927446954141,
54.4312114989733, 56.3860369609856, 50.3764544832307, 55.5318275154004,
39.4332648870637, 42.8336755646817, 55.5099247091034, 59.0417522245038,
58.9568788501027, 57.741273100616, 60.8350444900753, 48.933607118412,
65.9520876112252, 56.952772073922, 61.8398357289528, 46.0123203285421,
58.2012320328542, 38.8911704312115, 23.9288158795346, 59.9288158795346,
61.8343600273785, 57.9301848049281, 59.8357289527721, 53.0239561943874,
64.1013004791239, 65.8343600273785, 52.2546201232033, 53.8343600273785,
44.4325804243669, 40.4079397672827, 41.8343600273785, 57.5195071868583,
59.0417522245038, 34.5106091718001, 53.5605749486653, 54.8336755646817,
51.6769336071184, 53.4784394250513, 48.0547570157426, 49.7905544147844,
20.7912388774812, 19.8302532511978, 59.9096509240246, 50.9075975359343,
65.9630390143737, 42.1738535249829, 61.1882272416153, 62.694045174538,
58.2121834360027, 58.0616016427105, 59.4004106776181, 54.0588637919233,
54.8336755646817, 29.5195071868583, 56.5338809034908, 48.6351813826146,
56.0958247775496, 59.4004106776181, 56.5366187542779, 49.5359342915811,
40.6707734428474, 70.7460643394935, 53.0732375085558, 44.1478439425051,
49.264887063655, 32.7611225188227, 57.8015058179329), sex = structure(c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L,
2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L,
2L, 2L, 2L, 2L, 1L), .Label = c("Female", "Male"), class = "factor"),
smoking = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L,
1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L,
2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L,
2L), .Label = c("Ever smoker", "Never smoker"), class = "factor"),
obesity = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
2L), .Label = c("No", "Yes"), class = "factor"), diab = structure(c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("No", "Yes"
), class = "factor"), hypt = structure(c(1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L,
2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L,
2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L,
1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L,
2L, 1L, 2L, 1L, 1L, 2L), .Label = c("No", "Yes"), class = "factor"),
hyperchol = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
2L), .Label = c("No", "Yes"), class = "factor"), ckd = structure(c(2L,
2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L,
1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L,
2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L,
2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L), .Label = c("Above 90",
"Below 90"), class = "factor"), outcome = c(99.18212890625,
510.1, 176.8329668964, 122.0704375001, 254.490352094, 629.4,
0, 42.205078125, 0, 0, 0, 0, 0, 0, 732.421875, 0, 10.4, 0,
0, 0, 282.28759765625, 0, 26.7029082031, 0, 568.4, 2002.71606445312,
0, 6.71267700195312, 549.31640625, 623.43045915852, 95.4,
111.97342532814, 0, 0, 0, 19.0041765469, 0, 0, 0, 0, 0, 376.366821289062,
682.831509766, 0, 0, 278.472900390625, 397.6406882053, 162.5097656245,
205.99365234375, NA, NA, 64.849853515625, 39.2521362304688,
0, 83.9, 1453.3, 3128, 1947.9, 4489.9032793011, 4489.89868164062,
0, 339.508056640625, 319.923370711, 41.961669921875, 33.78520275005,
10.72340001563, 217.437744140625, 240.325927734375, 277.595608875,
148.8, 39.4191863525, 98.8, 1069.62071228027, 1293.183697266,
0, 0, 438.690185546875, 0, 1296.9970703125, 2474.450875227,
0, 0, 0, 28.595733375, 30.517609375, 34.332275390625, NA,
0, 0, 0, 164.031982421875, 30.517609375, 184.759523508, 34.332275390625,
153.73388671875, 183.10546875, 232.5625000005, 186.9203574223,
190.73486328125, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240.3, 450.1,
1190.2, 1193.9776708285, 400.543623047, 398.8, 386, 133.514404296875,
0, 0, 0, 0, 1762.4, 2373.146013416, 1959.685165932, 2483.4,
0, 0, 0, 0, 3198.6, 1598.35815429688, 30.517578125, 0, 209.808349609375,
1499.2, 1670.839113281, 41.961669921875, 38.1, 106.5, 311.9,
299.2, 273.1, 591.2, 1049.04174804688, 26.702880859375, 102.99693164068,
38.1, 57.8, 80.108642578125, 0, 0, 3604.9, 5512.3, 125.885009765625,
68.6646210938, 0, 289.9169921875, 339.4183043813, 495.9111523433,
381.4697265625, 0, 0, 7.62939453125, 52.7892921094, 259.3994140625,
345.7630540544, 129.6998398438, 343.32275390625, 0, 0, 0,
5.20535762305, 55.8731089424, 26.7, 0, 0, 18.8704833984375,
38.14697265625, 255.6, 597.5471151571, 0, 15.2587890625,
NA, NA, NA, 359.098083496094, 135.888671875, 261.1158471676,
446.3, 244.140625, 507.35525586, 485.9332674133, 1789.09301757812,
396.8, 1056.67114257812, 87.738037109375, 217.437744140625,
152.6, 45.7764140625, 76.3800358535, 22.88818359375, 0, 53.4,
14, 53.40576171875, 22.88818359375, 99.1822304688, 186.625251914,
640.918884277344, 57.220458984375, 304.204055786133, 442.96875,
451.0797414142, 877.38037109375, 1384.27734375, 3284.4, 3147.12524414062,
30.517578125, 91.552828125, 142.344612272, 34.332275390625,
21.3, 34.332275390625, 515, 194.549759766, 251.8, 0, 99.18212890625,
49.5911152344, 60.0625, 41.961669921875, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 186.9, 83.9234257813, 68.6646210938, 125.885009765625,
0, 0, 0, 0, 308.990478515625, 793.6, 427.24609375, 26.702880859375,
0, 0, 2273.5595703125, 0, 122.0703125, 0, 80.108642578125,
0, 0, 20.4, 15.2587890625, 0, 0, 0, 118.255615234375, 64.849853515625,
3.5, 0, 0, 0, 0, 454, 438.690185546875, 0, 22.88818359375,
45.7763671875, 961.3, 1201.6, 0, 0, 0, 0, 164.031982421875,
39.9904327392578, 0, 0, 495.8, 728.607177734375, 61.03515625,
87.738037109375, 153, 282.28759765625, 232.696533203125,
0, 274.658203125, 0, 5.80126953125, 4821.77734375, 354.766845703125,
34.332275390625, 0, 3292.08374023438, 686.6455078125, 0,
0, 0, 7.62939453125), outcome_log = c(4.60698981851472, 6.23656526577423,
5.18084472150775, 4.8127568540662, 5.54318464804626, 6.44635453854367,
0, 3.76595803753151, 0, 0, 0, 0, 0, 0, 6.59772108202634,
0, 2.43361335540045, 0, 0, 0, 5.64646262774987, 0, 3.32153739696389,
0, 6.34458317484394, 7.60275876776194, 0, 2.04286533897829,
6.31049339690497, 6.43683996893536, 4.5685062016165, 4.72715261696732,
0, 0, 0, 2.9959410790976, 0, 0, 0, 0, 0, 5.93321771515634,
6.52771155652669, 0, 0, 5.63290533043696, 5.98806048035461,
5.09687271714384, 5.33268812778915, NA, NA, 4.18737720367087,
3.69516307650511, 0, 4.4414740933173, 7.28227996418366, 8.04846874366888,
7.57502038982798, 8.40980913629405, 8.40980811252165, 0,
5.83043878651559, 5.77120237410526, 3.76030832099716, 3.54919208802184,
2.46158684579961, 5.3865010500956, 5.48614841706325, 5.62976129982523,
5.00930107108312, 3.69930458194852, 4.60316818331742, 6.97599386419496,
7.16563542577826, 0, 0, 6.08607035514364, 0, 7.16857764018329,
7.81417783022041, 0, 0, 0, 3.38763020820397, 3.45054641741155,
3.56479686322093, NA, 0, 0, 0, 5.10613928797727, 3.45054641741155,
5.22445295285155, 3.56479686322093, 5.04170678154724, 5.21550879312103,
5.45344970724784, 5.23601824234065, 5.25611349726835, 0,
0, 0, 0, 0, 0, 0, 0, 0, 5.48604097263099, 6.11168904441435,
7.0827164813698, 7.08588277869187, 5.99531617766414, 5.9909644220663,
5.95842469302978, 4.90167128845167, 0, 0, 0, 0, 7.47499904265293,
7.77239307850824, 7.58104926559275, 7.81778646068515, 0,
0, 0, 0, 8.07078108097467, 7.3773576741798, 3.45054542590184,
0, 5.35094942503542, 7.31335371153554, 7.42167956490058,
3.76030832099716, 3.66612246699132, 4.67749084756772, 5.74588365067484,
5.70444891919936, 5.61349300330874, 6.38384441566749, 6.9565852024058,
3.32153640992895, 4.64436139525114, 3.66612246699132, 4.07414185490458,
4.39578952237477, 0, 0, 8.19032667182022, 8.61491863394208,
4.84328124138846, 4.24369260057567, 0, 5.67303797626514,
5.83017516840655, 6.20841124219481, 5.94664950389253, 0,
0, 2.1551743440304, 3.98507441593456, 5.56221666018787, 5.84864170536274,
4.87290339525682, 5.84157945560271, 0, 0, 0, 1.82541305165329,
4.04082262735395, 3.32143241319329, 0, 0, 2.98923538432203,
3.66732309265895, 5.54751845218154, 6.39450524396661, 0,
2.7886336279454, NA, NA, NA, 5.88637644849708, 4.91916798142725,
5.5687865707969, 6.1032295104388, 5.50183202547328, 6.23118052572546,
6.18812708579464, 7.4900228626121, 5.98594936641987, 6.96382473477956,
4.48568862613631, 5.3865010500956, 5.03435182071357, 3.84537910286301,
4.3487288126155, 3.17338392637304, 0, 3.9963641538619, 2.70805020110221,
3.99647006220102, 3.17338392637304, 4.60699083229332, 5.23444663259896,
6.46446194722966, 4.06423682190672, 5.72098058826739, 6.09575417707235,
6.11385858333018, 6.77807972430084, 7.23365564676939, 8.0972436891071,
8.05456239405103, 3.45054542590184, 4.52777959635922, 4.96525160719335,
3.56479686322093, 3.10458667846607, 3.56479686322093, 6.24610676548156,
5.27581487269655, 5.5325986622727, 0, 4.60698981851472, 3.92377597262303,
4.111897929803, 3.76030832099716, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 5.23590990641942, 4.44174997729904, 4.24369260057567,
4.84328124138846, 0, 0, 0, 0, 5.73654158254177, 6.6778388433805,
6.05969801573823, 3.32153640992895, 0, 0, 7.729541717176,
0, 4.81275583838635, 0, 4.39578952237477, 0, 0, 3.06339092202781,
2.7886336279454, 0, 0, 0, 4.78126921657914, 4.18737720367087,
1.50407739677627, 0, 0, 0, 0, 6.12029741895095, 6.08607035514364,
0, 3.17338392637304, 3.84537810075491, 6.86932625236236,
7.09224115860547, 0, 0, 0, 0, 5.10613928797727, 3.71333869165149,
0, 0, 6.20818753061927, 6.5925062766152, 4.12770126063108,
4.48568862613631, 5.03695260241363, 5.64646262774987, 5.45402340704507,
0, 5.61916170379841, 0, 1.91710929052863, 8.48110525349429,
5.87427558849292, 3.56479686322093, 0, 8.09957971182357,
6.53327345487378, 0, 0, 0, 2.1551743440304)), row.names = c(NA,
-310L), class = c("tbl_df", "tbl", "data.frame"))
我指定的模型如下：
model <-
lme(data=mydata,
fixed=outcome_log ~ age + sex*age + smoking*age + obesity*age + diab*age + hypt*age + hyperchol*age + ckd*age,
random=~1|pat_id,
na.action="na.omit",
method="REML",
correlation=corCAR1(form=~1 + age|pat_id),
control=lmeControl(opt="optim"))
鉴于这个模型，我认为残差图和 QQ 图看起来不太好。具体来说，对于较小的拟合值，残差似乎较大，并且 QQ 图的尾部偏离正态性。获取图的代码：
# Get residuals and fitted values into 1 tibble.
residuals <-
residuals(model, type="normalized") %>%
tibble(.) %>%
rename("log_residuals"=".") %>%
mutate(log_residuals=as.numeric(log_residuals))
fitted <-
predict(model) %>%
tibble(.) %>%
rename("log_fitted"=".") %>%
mutate(log_fitted=as.numeric(log_fitted))
residuals_and_fitted <-
cbind(residuals, fitted)
rm(residuals, fitted)
# Make a residual plot.
residuals_and_fitted %>%
ggplot(aes(x=log_fitted, y=log_residuals)) + geom_point() + theme_classic() +
geom_smooth(method="loess", formula=y~x, se=FALSE) + xlab("Fitted") +ylab("Normalized residuals") +
labs(title="Residual plot")
# Make a quantile-quantile plot.
residuals_and_fitted %>%
ggplot(aes(sample=log_residuals)) + stat_qq() + theme_classic() + labs(title="QQ plot") +
ylab("Normalized residuals") + xlab("Theoretical")
这给出了以下两个图：
残差图中存在的对角线是观察结果为 0 的患者。因此，我认为通过指定一个障碍模型可能会改善模型拟合，该模型包括使用 GLMMadaptive 对结果是否为零的二分指标进行逻辑回归::混合模型。然而，这个模型不会收敛（而且我对统计数据的理解不够好，无法理解为什么）。我尝试通过删除一些固定和/或随机效应使模型更简单，但它仍然不会收敛：
zi_model <-
mixed_model(data=mydata,
fixed=outcome_log ~ age + sex*age + smoking*age + obesity*age + diab*age + hypt*age + hyperchol*age + ckd*age,
random= ~ 1 + age|pat_id,
family=hurdle.lognormal(),
zi_fixed= ~ sex + smoking + obesity + diab + hypt + hyperchol + ckd,
n_phis=1,
zi_random= ~1|pat_id,
control=list(optimizer="optim"))
Error in mixed_fit(y, X, Z, X_zi, Z_zi, id, offset, offset_zi, family, :
A large coefficient value has been detected during the optimization.
Please re-scale you covariates and/or try setting the control argument
'iter_EM = 0'. Alternatively, this may due to a
divergence of the optimization algorithm, indicating that an overly
complex model is fitted to the data. For example, this could be
caused when including random-effects terms (e.g., in the
zero-inflated part) that you do not need. Otherwise, adjust the
'max_coef_value' control argument.
非常感谢任何关于改善残差正态性和/或如何进一步建模多余零点的想法！