非线性混合效应模型基于异速生长方程拟合上下法实验数据确定儿童右美托咪定半数有效量

doi:10.3969/j.issn.1674-8115.2021.10.007

摘要/Abstract

摘要：

目的·探索采用非线性混合效应模型基于异速生长方程拟合上下法临床实验数据，以确定儿童半数有效量（median effective dose，ED₅₀）的可行性。方法·对22例2~12岁阻塞型睡眠呼吸暂停（obstructive sleep apnea，OSA）患儿采用右美托咪定复合艾司氯胺酮诱导睡眠并实施气道镜检查（drug-induced sleep endoscopy，DISE）。患儿静注艾司氯胺酮0.5 mg/kg，同时开始静脉输注预设剂量右美托咪定10 min，如置入内镜时无体动和/或呛咳并完成DISE检查视为镇静成功，反之为镇静失败。根据上下法确定右美托咪定剂量，初始剂量1.0 μg/kg（剂量间隔1.2倍）。10 min后开始DISE检查。Dixon-Massey公式和非线性混合效应模型拟合用于计算ED₅₀。结果·9例OSA患儿镇静成功，13例患儿失败。Dixon-Massey公式计算的右美托咪定ED₅₀值1.9 μg/kg与非线性混合效应模型拟合值2.0 μg/kg相似。引入异速生长方程模型拟合效果显著改善（P<0.05），将成人体质量标准化为70 kg后，儿童ED₅₀和ED₉₅值分别为5.76×（体质量/70） μg/kg和11.5×（体质量/70） μg/kg，量效关系的斜率为4.25。结论·上下法实验数据可采用非线性混合效应模型基于异速生长方程拟合。相比Dixon-Massey公式的优点是可同时确定药物ED₅₀、ED₉₅以及量效关系的斜率，且这种方法有助于确定协变量的影响。

关键词: 儿童, 右美托咪定, 非线性混合效应, 异速生长, 上下法

Abstract:

Objective·To explore the application of nonlinear mixed effects model based on the allometric equation on up-and-down data to determine the half effective dose (ED₅₀) in pediatric patients.

Methods·Twenty-two pediatric patients aged 2 to 12 years with obstructive sleep apnea (OSA) who were undergoing drug-induced sleep endoscopy (DISE) were enrolled. All patients received intravenous bolus S⁺-ketamine 0.5 mg/kg. At the same time, a predetermined bolus dose of dexmedetomidine was infused continuously over 10 min for anesthesia induction. The bolus dose of dexmedetomidine was calculated according to the Dixon up-and-down method with initial dose 1.0 μg/kg and step size 1.2 times. DISE was conducted 10 min after dexmedetomidine infusion, and the response of the patients to the procedure was recorded. Dixon-Massey formula and nonlinear mixed effects model fitting are used to calculate ED₅₀.

Results·There were 9 and 13 children with successful and failed sedation. The value of dexmedetomidine ED₅₀, 1.9 μg/kg, calculated by Dixon-Massey formula was similar to the fitting value, 2.0 μg/kg, of nonlinear mixed effects model. The introduction of allometric equation significantly improved the model (P<0.05). After normalizing adults' body weight to 70 kg, the ED₅₀and ED₉₅were 5.76×(body weight/70) μg/kg and 11.5×(body weight/70) μg/kg, and the slope (γ) of the dose-response relationship of dexmedetomidine is 4.25.

Conclusion·The experimental data from the up-and-down method can be fitted with a nonlinear mixed effects model based on the allometric equation. Compared with the Massey formula, the advantage is that the ED₅₀, ED₉₅ and γ can be determined at the same time, and this method helps to determine the possible effect of covariates.

Key words: children, dexmedetomidine, nonlinear mixed effects, allometric, up-and-down method

中图分类号:

R969

许文音, 黄贞玲, 黄咏磊, 张瑞冬, 王璐, 张莺, 白洁, 郑吉建. 非线性混合效应模型基于异速生长方程拟合上下法实验数据确定儿童右美托咪定半数有效量[J]. 上海交通大学学报(医学版), 2021, 41(10): 1313-1317.

Wen-yin XU, Zhen-ling HUANG, Yong-lei HUANG, Rui-dong ZHANG, Lu WANG, Ying ZHANG, Jie BAI, Ji-jian ZHENG. Half effective bolus dose of dexmedetomidine of children derived from the up-and-down experimental data based on the analysis of nonlinear mixed effects model with allometric equation[J]. JOURNAL OF SHANGHAI JIAOTONG UNIVERSITY (MEDICAL SCIENCE), 2021, 41(10): 1313-1317.

图/表 7

图1 患儿给药剂量和镇静效果Note：Hollow dots indicate failed sedation and solid dots indicate successful sedation.

Fig 1 Administered dosage and sedative effect on patients

表1 纳入研究患儿的一般情况

Tab 1 General condition of children included in this study

Item	Success （n=9）	Failure （n=13）	Total （n=22）
Age/year	5.0±2.1^①	8.4±2	7.0±2.6
Weight/kg	20.7±7.2^②	32.7±13.3	28±12.5
Height/cm	111.9±16.1^③	136±14.1	126±19.0
Sex （male/female）/n	3/6^④	8/5	11/11
Dose of dexmedetomidine /（μg·kg^-1）	2.1±0.5^⑤	1.6±0.5	2.0±0.5

图2 患儿检查期间血压和心率的变化Note：Hollow dots indicate heart rate and solid dots indicate blood pressure. ①P=0.000, compared with beulavesa.

Fig2 Variation in blood pressure and heart rate during examination

表2 模型拟合过程

Tab 2 Model matching process

Run	Covariate	Obj	Degree of Freedom	Comparison	ΔObj	P value
Run1	N/A	25.144	‒	‒	‒	‒
Run2	Sex	25.127	1	Run1	-0.017	0.896
Run3^①	WT/70	19.344	1	Run1	-5.800	0.016
Run4	（WT/70）^0.75	19.896	1	Run3	-0.448	0.458
Run5	（WT/70）^θ	18.983	2	Run3	-0.361	0.424
Run6	AGE/8	18.908	1	Run1	-6.236	0.013
Run7	HT/130	20.445	1	Run1	-4.689	0.030
Run8	Run3+AGE/8	18.179	1	Run3	-1.165	0.250
				Run6	-0.729	0.393
Run9	Run3+HT/130	18.309	1	Run3	-1.035	0.309
				Run7	-2.136	0.144

表3 药效学模型参数拟合结果

Tab 3 Matching results of pharmacodynamics model parameters

Analysis model	ED₅₀/（μg·kg^-1）	ED₉₅/（μg·kg^-1）	γ
Dixon method	1.9 （1.4‒2.6）	N/A	N/A
$P = D γ / D γ + D 50 γ$
Without a covariate	2.0 （1.46‒2.54）	4.47 （0.65‒8.29）	3.67 （0.22‒7.12）
WT standardized	5.76×（WT/70）	11.5×（WT/70）	4.25 （1.47‒7.03）

表3 药效学模型参数拟合结果

Tab 3 Matching results of pharmacodynamics model parameters

Analysis model	ED₅₀/（μg·kg^-1）	ED₉₅/（μg·kg^-1）	γ
Dixon method	1.9 （1.4‒2.6）	N/A	N/A
$P = D γ / D γ + D 50 γ$
Without a covariate	2.0 （1.46‒2.54）	4.47 （0.65‒8.29）	3.67 （0.22‒7.12）
WT standardized	5.76×（WT/70）	11.5×（WT/70）	4.25 （1.47‒7.03）

图3 患儿个体post hoc右美托咪定ED50估计值与年龄的关系Note：The relationship between half effective dose and age (solid dot ~ subaxis) disappeared after adult weight standardization (hollow dot).

Fig3 Relationship between age and estimated post hoc dexmedetomidine ED50 in individual children

图4 复合艾司氯胺酮0.5 mg/kg时右美托咪定负荷剂量与患儿DISE成功率的量效关系Note：Hollow dots indicate failed sedation and solid dots indicate successful sedation.

Fig4 Dose-effect relationship between dexmedetomidine loading dose and DISE success rate in children combined with esketamine 0.5 mg/kg

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