倾向性评分与疾病风险评分匹配对已测量混杂因素的控制效果评价

卢珍珍; 赵恩慧; 黄丽红

doi:10.16462/j.cnki.zhjbkz.2024.02.018

倾向性评分与疾病风险评分匹配对已测量混杂因素的控制效果评价

doi: 10.16462/j.cnki.zhjbkz.2024.02.018

卢珍珍^{1, 2},
赵恩慧³,
黄丽红^{1, 2, ,}

1.
复旦大学附属中山医院生物统计室，上海 200032
2.
复旦大学附属中山医院临床医学研究院临床研究中心，上海 200032
3.
复旦大学公共卫生学院流行病与卫生统计学系，上海 200032

卢珍珍和赵恩慧为共同第一作者

基金项目:

国家自然科学基金 82273733

详细信息

通讯作者:
黄丽红，E-mail: huang.lihong@zs-hospital.sh.cn

中图分类号: R181.3
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- 被引次数: 0
出版历程
- 收稿日期: 2023-03-22
- 修回日期: 2023-07-04
- 网络出版日期: 2024-03-30
- 刊出日期: 2024-02-10

Evaluation of the control effect for measured confounders between propensity score matching and disease risk score matching

LU Zhenzhen^{1, 2},
ZHAO Enhui³,
HUANG Lihong^{1, 2
, ,}

1.
Department of Biostatistics, Zhongshan Hospital, Fudan University, Shanghai 200032, China
2.
School of Public Health, Fudan University, Shanghai 200032, China
3.
Department of Epidemiology and Health Statistics, Clinical Research Unit, Institute of Clinical Science, Zhongshan Hospital of Fudan University, Shanghai 200032, China

LU Zhenzhen and ZHAO Enhui contributed equally to this article

Funds:

National Natural Science Foundation of China 82273733

More Information

Corresponding author: HUANG Lihong, E-mail: huang.lihong@zs-hospital.sh.cn

摘要

摘要: 目的比较在组间倾向性评分(propensity score, PS)重叠较好和较差的场景下应用PS和疾病风险评分(disease risk score, DRS)进行1∶1匹配的效果，同时探索DRS匹配的最优卡钳值。方法设置不同的试验组样本量占比、结局事件发生率和PS重叠情况，模拟6种场景比较PS和DRS匹配前后的协变量均衡性和处理效应估计偏差，并进行实例分析。结果 PS重叠较好的场景下，DRS重叠也较好，PS匹配优于DRS，PS匹配最优卡钳值为标准差的10%~20%，DRS匹配相对最优卡钳值为标准差的0.5%。在PS重叠较差的场景中，DRS重叠也变差，但DRS匹配优于PS，DRS匹配最优卡钳值为标准差的15%~20%。此外，PS和DRS匹配对协变量均衡性的改善效果与处理效应估计偏差相一致。结论当PS重叠较好时，优选PS匹配；当PS重叠较差时，可选DRS，其最优卡钳值为标准差的15%~20%。在实际应用中，可根据匹配前后组间协变量均衡性指标的改善情况评价匹配效果。
- 倾向性评分 /
- 疾病风险评分 /
- 匹配 /
- 混杂偏倚
Abstract: Objective To compare propensity score (PS) matching and disease risk score (DRS) matching in the scenarios of good PS overlap and poor PS overlap, and to investigate the optimal caliper width for DRS matching. Methods According to the different proportions of the test group and events as well as the different PS overlap situations, 6 scenarios were simulated to compare the balance of covariables and the bias before and after PS matching or DRS matching, followed by analysis of an actual case. Results In the scenarios with good PS overlap, the DRS overlap was also good, and PS matching was more accurate than DRS matching. The optimal caliper width was found to be 10%-20% of the PS standard deviation (SD) for PS matching, and the relative optimal caliper width was 0.5% of the DRS SD for DRS matching. In the scenarios with poor PS overlap, the DRS overlap was also poor, but the DRS matching was more accurate than PS matching. The optimal caliper width was found to be 15%-20% of the DRS SD. In addition, the improvement on the balance of covariates was consistent with the estimation bias of treatment effect. Conclusions When the overlap of PS is good, PS matching is preferred; when the overlap of PS is poor, DRS matching can be selected, and the optimal caliper width is 15%-20% of the DRS SD. In practical application, the control effect for measured a confounder can be evaluated according to the improvement on the covariable balance between groups.
- Propensity score /
- Disease risk score /
- Matching /
- Confounding bias

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图 1 不同场景设置下组间PS和DRS分布情况

PS：倾向性评分；DRS：疾病风险评分；A: 场景A1组间PS分布；B: 场景A1组间DRS分布；C: 场景A2组间PS分布；D: 场景A2组间DRS分布；E: 场景A3组间PS分布；F: 场景B3组间DRS分布；G: 场景B1组间PS分布；H: 场景B1组间DRS分布；I: 场景B2组间PS分布；J: 场景B2组间DRS分布；K: 场景B3组间PS分布；L: 场景B3组间DRS分布。

Figure 1. Distribution of PS and DRS between groups under different scenarios

PS: propensity score; DRS: disease risk score; A: PS distribution between groups in scenario A1; B: DRS distribution between groups in scenario A1; C: PS distribution between groups in scenario A2; D: DRS distribution between groups in scenario A2; E: PS distribution in scenario A3; F: DRS distribution between groups in scenario B3; G: PS distribution between groups in scenario B1; H: DRS distribution between groups in scenario B1; I: PS distribution between groups in scenario B2; J: DRS distribution between groups in scene B2; K: PS distribution in scenario B3; L: DRS distribution between groups in scenario B3.

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图 2 不同场景匹配前后组间各协变量标准化差异绝对值

PS：倾向性评分，DRS：疾病风险评分，SD：标准化差异；场景A1~A3中PS卡钳值设置为标准差的20%，DRS卡钳值设置为标准差的0.05%；场景B1~B3中PS和DRS卡钳值均设置为标准差的20%。

Figure 2. Absolute value of standardized difference of covariables between two groups before and after matching under different scenarios

PS: propensity score, DRS: disease risk score, SD: standardized difference; In the scenario A1-A3, the caliper width of PS matching is set to 20% of the standard deviation, and the caliper width of DRS is set to 0.05% of the standard deviation; both the caliper widths of PS matching and DRS matching in the scene B1-B3 are set to 20% of the standard deviation.

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图 3 PS与DRS分布及匹配效果

PS：倾向性评分；DRS：疾病风险评分；APACHE Ⅲ: 急性生理与慢性健康Ⅲ评分；A: 匹配前组间DRS分布；B: 匹配前组间DRS分布；C: 匹配前后组间各协变量标准化差异绝对值。

Figure 3. Distribution and matching effect of PS and DRS

PS: propensity score, DRS: disease risk score; A: distribution of PS between group; APACHE Ⅲ: acute physiology and chronic health evaluation Ⅲ; B: distribution of DRS between group; C: absolute value of standardized difference of covariables between two groups before and after matching.

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表 1 协变量与分组因素和结局的关联

Table 1. The correlation with smoking and outcome

与吸烟关联 Association with smoking	与某疾病关联 Association with a certain disease
与吸烟关联 Association with smoking	有关 Associate	无关 Not associate
有关 Associate	x₁, x₂, x₃, b₁, b₂, b₃, b₄, b₅	x₅, b₆, b₇
无关 Not associate	x₄, b₈, b₉	x₆, b₁₀

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表 2 模拟试验场景参数设置

Table 2. Parameter setting of simulation scenarios

场景 Scenarios	组间PS分布重叠 PS overlap	发生疾病的比例/% Disease incident /%	分组模型系数设置 Grouping model coefficient setting c(α₀, α₁, α₂, α₃, α₄, α₅, α₆, α₇, α₈, α₉, α₁₀, α₁₁)	结局模型系数设置 Outcome model coefficient setting c(β₀, β₁, β₂, β₃, β₄, β₅, β₆, β₇, β₈, β₉, β₁₀, β₁₁)
A1	较好 Good	30	c(-1.5, -0.6, 0.5, 0.5, -0.3, 0.6, -0.2, 0.2, 0.3, 0.5, -0.5, -0.2)	c(-1.5, 0.5, -0.5, 0.5, -0.2, -0.5, 0.6, 0.5, 0.2, -0.5, 0.5, -0.2)
A2	较好 Good	20	c(-1.5, -0.6, 0.5, 0.5, -0.3, 0.6, -0.2, 0.2, 0.3, 0.5, -0.5, -0.2)	c(-2.1, 0.5, -0.5, 0.5, -0.2, -0.5, 0.6, 0.5, 0.2, -0.5, 0.5, -0.2)
A3	较好 Good	10	c(-1.5, -0.6, 0.5, 0.5, -0.3, 0.6, -0.2, 0.2, 0.3, 0.5, -0.5, -0.2)	c(-3, 0.5, -0.5, 0.5, -0.2, -0.5, 0.6, 0.5, 0.2, -0.5, 0.5, -0.2)
B1	较差 Poor	30	c(-1.5, 1.5, -1.2, 1.5, -1.1, -1.2, 0.5, -1, 1.5, -1.2, 1.6, -1.1)	c(-1.5, 0.5, -0.5, 0.5, -0.2, -0.5, 0.6, 0.5, 0.2, -0.5, 0.5, -0.2)
B2	较差 Poor	20	c(-1.5, 1.5, -1.2, 1.5, -1.1, -1.2, 0.5, -1, 1.5, -1.2, 1.6, -1.1)	c(-2.2, 0.5, -0.5, 0.5, -0.2, -0.5, 0.6, 0.5, 0.2, -0.5, 0.5, -0.2)
B3	较差 Poor	10	c(-1.5, 1.5, -1.2, 1.5, -1.1, -1.2, 0.5, -1, 1.5, -1.2, 1.6, -1.1)	c(-3, 0.5, -0.5, 0.5, -0.2, -0.5, 0.6, 0.5, 0.2, -0.5, 0.5, -0.2)
注：PS，倾向性评分。 Note: PS, propensity score.

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表 3 不同场景下模拟试验结果

Table 3. Simulation results under different scenarios

场景 Scenario	匹配方法 Matching method	卡钳值/% Caliper width/%	匹配比例/% Matching ratio /%	RB/%	MSE/%	95% CI覆盖率/% 95% CI coverage rate/ %	检验效能/% Power/%
场景A1 Scenario A1	PS法 PS method	30	97.0	10.9	6.1	72.8	99.5
		25	95.2	10.2	5.8	76.2	99.8
		20	93.1	9.4	5.4	79.6	99.9
		15	90.8	8.7	5.1	82.9	99.9
		10	88.5	8.1	4.9	85.5	99.9
		5	86.5	7.6	4.8	87.0	99.9
	DRS法 DRS method	30	100.0	13.6	7.1	58.7	99.7
		25	100.0	13.6	7.1	58.7	99.7
		20	100.0	13.6	7.1	58.7	99.7
		15	100.0	13.6	7.1	58.7	99.7
		10	100.0	13.6	7.1	58.7	99.7
		5	99.9	13.6	7.1	58.7	99.7
		0.5	99.8	13.6	7.1	59.1	99.6
		0.05	93.8	13.1	6.9	66.6	99.4
		0.01	61.7	12.0	8.1	81.0	92.7
场景A2 Scenario A2	PS法 PS method	30	94.3	12.6	7.6	69.6	97.6
		25	91.2	11.3	7.1	76.3	98.2
		20	87.6	9.8	6.5	79.0	98.5
		15	84.0	8.5	6.1	84.1	99.1
		10	80.6	7.3	5.9	87.8	99.1
		5	78.1	6.4	5.8	90.1	99.6
	DRS法 DRS method	30	100.0	13.6	7.1	58.7	99.7
		25	100.0	13.6	7.1	58.7	99.7
		20	100.0	13.6	7.1	58.7	99.7
		15	100.0	13.6	7.1	58.7	99.7
		10	100.0	13.6	7.1	58.7	99.7
		5	99.9	14.0	7.9	61.3	98.4
		0.5	99.7	13.6	6.3	62.1	98.4
		0.05	94.4	13.3	7.8	68.0	97.8
		0.01	68.2	12.3	9.3	81.2	88.5
场景A3 Scenario A3	PS法 PS method	30	94.3	10.3	10.1	84.0	86.2
		25	91.2	9.0	9.8	86.9	87.8
		20	87.6	7.5	9.7	89.7	89.5
		15	84.0	6.0	9.8	92.1	89.9
		10	80.6	4.7	10.0	92.0	90.5
		5	78.1	3.9	10.2	93.2	91.0
	DRS法 DRS method	30	100.0	13.6	7.1	58.7	99.7
		25	100.0	13.6	7.1	58.7	99.7
		20	100.0	13.6	7.1	58.7	99.7
		15	100.0	13.6	7.1	58.7	99.7
场景A3 Scenario A3	DRS法 DRS method	10	100.0	13.6	7.1	58.7	99.7
		5	99.9	12.3	9.7	82.4	85.3
		0.5	99.8	12.1	9.7	82.7	85.8
		0.05	97.0	11.4	10.0	85.1	83.4
		0.01	81.8	10.4	12.5	87.7	72.1
场景B1 Scenario B1	PS法 PS method	30	99.9	54.5	88.8	0.0	100.0
		25	90.1	40.9	52.7	0.9	100.0
		20	76.7	25.7	24.6	25.7	100.0
		15	65.1	13.5	11.3	75.3	100.0
		10	55.6	4.3	6.6	94.2	100.0
		5	48.7	2.5	6.1	94.5	99.1
	DRS法 DRS method	30	92.3	9.4	6.0	81.7	100.0
		25	88.7	3.5	3.6	95.0	100.0
		20	84.8	2.4	3.0	96.6	100.0
		15	80.7	7.7	4.2	84.9	100.0
		10	76.8	12.2	6.5	66.5	99.9
		5	73.8	15.2	8.6	52.7	99.0
		0.5	71.9	16.4	9.7	45.3	97.5
		0.05	63.5	16.3	9.9	51.9	95.3
		0.01	40.0	16.2	11.4	70.9	76.0
场景B2 Scenario B2	PS法 PS method	30	99.9	60.4	109.1	0.0	100.0
		25	90.1	45.7	66.2	1.5	100.0
		20	76.7	29.8	32.6	23.8	100.0
		15	65.1	17.2	16.0	68.9	100.0
		10	55.6	7.2	8.9	92.9	99.8
		5	48.7	0.4	7.7	95.9	98.2
	DRS法 DRS method	30	92.6	13.5	9.4	71.1	100.0
		25	89.4	7.3	5.4	92.4	100.0
		20	85.7	0.8	3.5	97.6	100.0
		15	81.6	5.4	3.8	94.4	100.0
		10	77.5	10.7	5.9	80.6	99.2
		5	74.1	14.3	8.3	65.7	97.1
		0.5	72.0	15.7	9.4	59.9	94.7
		0.05	64.3	15.6	10.0	65.8	88.2
		0.01	44.1	15.2	12.5	75.1	68.0
场景B3 Scenario B3	PS法 PS method	30	99.9	68.9	148.0	0.1	100.0
		25	90.1	52.7	92.7	4.0	100.0
		20	76.7	35.5	49.6	31.5	100.0
		15	65.1	22.0	27.6	70.8	99.9
		10	55.7	11.1	17.2	90.2	98.9
		5	48.7	2.7	14.2	95.4	91.3
	DRS法 DRS method	30	95.7	25.1	26.3	45.4	100.0
		25	93.3	18.7	17.4	68.8	100.0
		20	90.1	11.1	10.1	87.6	100.0
		15	86.0	2.7	6.1	96.5	100.0
		10	81.0	5.3	5.8	95.0	98.5
		5	75.9	11.9	8.3	84.6	89.5
		0.5	72.6	14.5	10.2	76.0	80.9
		0.05	66.8	14.0	10.7	80.6	76.1
		0.01	51.0	13.7	14.6	85.8	55.5
注：PS，倾向性评分；DRS，疾病风险评分；RB，相对偏倚；MSE，均方误差。 Note：PS，propensity score；DRS，disease risk score；RB，relative bias；MSE，mean-square error.

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表 4 不同匹配法的分析结果

Table 4. Analysis results of different matching methods

方法 Methods	匹配比例/% Matching ratio/%	60 d死亡人数(占比/%) Number of deaths within 60 days (proportion/%)		OR值 value (95% CI)	P值 value
方法 Methods	匹配比例/% Matching ratio/%	非血小板减少组 Non-thrombocytopenic group	血小板减少组 Thrombocytopenia group	OR值 value (95% CI)	P值 value
PS匹配 PS matching	82.3	27(30.3)	42(47.2)	2.05(1.12~3.82)	0.022
DRS匹配 DRS matching	92.0	39(37.5)	53(50.9)	1.73(0.99~3.02)	0.051
注：PS，倾向性评分；DRS，疾病风险评分。 Note: PS, propensity score；DRS, disease risk score.

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