Bayesian cost-effectiveness analysis for censored data: an application to antiplatelet therapy

Figures & data

Table 1.  Baseline characteristics, medical history, and drug therapy during the follow-up.

	Total sample (n = 14,627)	Aspirin (n = 11,463)	Aspirin + PPI (n = 538)	Clopidogrel (n = 2036)	Clopidogrel + PPI (n = 590)
Cost (unit:NTD; mean ± SD)	2623 ± 8148	412 ± 593	575 ± 752	12,662 ± 15,606	12,807 ± 15,769
Time to GI hospitalization (unit: days; mean ± SD)	1601 ± 8*	1596 ± 10*	1636 ± 39*	1577 ± 21*	1468 ± 40*
Age	71.09 ± 11.31	70.98 ± 11.45	70.79 ± 11.20	71.50 ± 10.63	72.17 ± 11.00
Gender
Female, n (%)	5849 (40)	4562 (40)	227 (42)	809 (40)	251 (43)
Male, n (%)	8778 (60)	6901 (60)	311 (58)	1227 (60)	339 (57)
GI history
Outpatient visits (1 year prior study entry)	4.37 ± 6.33	4.22 ± 6.32	4.84 ± 6.34	5.16 ± 6.59	4.17 ± 5.33
Hospitalization (1 year prior study entry)	0.53 ± 0.63	0.49 ± 0.61	0.87 ± 0.68	0.56 ± 0.63	0.91 ± 0.57
Medication use during the follow-up
Clopidogrel per day (unit:DDD; mean ± SD)	0.11 ± 0.39	–	–	0.60 ± 0.73	0.61 ± 0.80
Aspirin per day (unit:DDD; mean ± SD)	0.41 ± 0.73	0.51 ± 0.77	0.50 ± 0.79	–	–
PPIs per day (unit:DDD; mean ± SD)	0.03 ± 0.31	–	0.22 ± 0.87	–	0.45 ± 1.18

*The mean survival time and its standard error are estimated by the Kaplan-Meier method.

Table 2.  Bayesian estimates and the corresponding 95% confident intervals for the parameters of the bivariate regression models under censored and non-censored assumptions.

		Clopidogrel vs Aspirin						Clopidogrel vs Aspirin plus PPIs						Aspirin plus PPI vs Clopidogrel plus PPI
		Effectiveness			Cost			Effectiveness			Cost			Effectiveness			Cost
		mean	2.5%	97.5%	mean	2.5%	97.5%	mean	2.5%	97.5%	mean	2.5%	97.5%	mean	2.5%	97.5%	mean	2.5%	97.5%
\hskip -15pc Under censored assumption	Intercept	1922.0	1616.0	2189.0	388.8	−1101.0	1,321.0	1843.0	1293.0	2364.0	1454.0	−237.2	3151.0	−68.5	−595.1	472.0	174.4	−1779.0	2105.0
	D1 vs D0	112.8	19.8	209.6	9947.0	9570.0	10,320.0	−66.8	−215.9	76.4	5040.0	3759.0	6322.0	113.8	77.5	155.1	−707.8	−2627.0	1197.0
	Age	0.3	−2.1	2.8	−9.4	−17.2	−2.1	1.5	−3.3	6.6	13.6	−31.6	56.2	24.8	19.4	30.7	1642.0	1348.0	2131.0
	Gender (male vs female)	−58.8	−108.5	−9.8	215.5	9.2	422.1	47.7	−52.0	146.9	913.6	−77.1	1902.0	−9.1	−46.4	29.0	92.0	−1848.0	2045.0
	Clopidogrel (DDDs) per day on average	−429.2	−540.5	−287.4	3630.0	3203.0	4,141.0	−454.2	−524.4	−390.0	4874.0	3816.0	5983.0	−94.6	−134.5	−8.3	545.2	−1410.0	2469.0
	Aspirin (DDDs) per day on average	−332.3	−362.0	−301.7	199.1	−22.8	497.4	−278.6	−488.0	−77.5	−92.9	−1515.0	1333.0	−78.7	−117.5	−43.3	−403.9	−2303.0	1533.0
	PPI (DDDs) per day on average	–	–	–	–	–	–	−41.2	−215.9	135.1	427.7	−944.2	1800.0	47.0	14.5	80.5	−606.9	−2572.0	1286.0
	Outpatient visits (1 year prior study entry)	−10.2	−17.0	−3.8	15.9	−2.2	34.1	−12.3	−21.5	−2.8	116.5	28.9	205.8	−6.3	−29.9	17.6	−483.5	−1882.0	839.8
	Hospitalization (1 year prior study entry)	−152.4	−210.1	−92.3	57.3	−127.5	248.0	−37.8	−285.8	205.5	56.1	−782.0	902.7	−15.3	−80.8	49.3	66.1	−1880.0	2052.0
	Propensity score	344.9	−1650.0	2539.0	−87.4	−1892.0	1,705.0	−520.3	−2295.0	1286.0	198.9	−1783.0	2179.0	400.1	−1302.0	2060.0	61.7	−1782.0	1891.0
	Effectiveness (the time of last observation)	–	–	–	0.2	−0.2	1.1	–	–	–	3.7	1.6	6.0	–	–	–	60.0	50.1	70.6
\hskip -15pc Under non-censored assumption	Intercept	1096.0	927.5	1258.0	1508.0	−287.2	3,148.0	873.9	590.7	1192.0	2641.0	816.4	4439.0	−71.0	−1236.0	1044.0	1145.0	−749.2	3088.0
	D1 vs D0	−65.6	−97.1	−34.2	9897.0	9483.0	10,300.0	−190.0	−246.8	−131.6	4679.0	3106.0	6167.0	291.2	237.2	349.4	70.3	−1758.0	1918.0
	Age	1.7	0.6	2.8	−7.6	−16.5	1.4	0.4	−1.9	2.7	85.6	35.0	142.4	9.4	4.9	14.2	466.3	365.6	570.3
	Gender (male vs female)	−9.8	−27.5	8.0	197.8	−14.3	408.1	0.7	−39.4	40.5	1374.0	420.0	2363.0	28.4	−14.1	71.8	1376.0	−288.1	3034.0
	Clopidogrel (DDDs) per day on average	−267.8	−298.4	−236.9	3241.0	2526.0	3,970.0	−270.1	−298.0	−241.7	3491.0	1909.0	4964.0	−251.7	−304.6	−201.5	504.0	−1383.0	2356.0
	Aspirin (DDDs) per day on average	−212.8	−225.0	−200.6	−105.9	−619.2	435.5	−102.5	−188.4	−15.8	−581.4	−2006.0	829.0	−195.2	−249.6	−145.2	−779.2	−2407.0	858.5
	PPI (DDDs) per day on average	–	–	–	–	–	–	−112.6	−191.8	−34.3	30.2	−1427.0	1454.0	45.3	12.0	79.9	−4104.0	−5409.0	−2795.0
	Outpatient visits (1 year prior study entry)	8.0	3.5	12.4	11.9	−5.8	29.7	−5.8	−10.8	−1.1	87.6	3.2	171.6	1.9	−7.8	11.5	100.8	−163.1	373.5
	Hospitalization (1 year prior study entry)	249.8	215.7	282.9	217.0	−265.3	681.7	238.0	102.7	383.5	−123.1	−1047.0	836.8	34.5	−24.4	94.9	1347.0	−182.0	2878.0
	Propensity score	−3612.0	−5209.0	−1959.0	93.2	−1876.0	2,012.0	−1222.0	−2349.0	−181.6	446.8	−1499.0	2398.0	48.8	−1593.0	1748.0	725.8	−1208.0	2676.0
	Effectiveness (the time of last observation)	–	–	–	–1.0	−3.4	1.4	–	–	–	−0.4	−6.4	5.1	–	–	–	−37.5	−47.0	−28.7

Figure 1.  The comparison of cost-effectiveness between clopidogrel and aspirin. (a) Joint posterior sample of cost and effect differences on the CE plane. (b) Bayesian cost-effectiveness acceptability curve. The horizontal line indicated that posterior probability that INB is greater than zero is 0.5. (c) Bayesian 95% confidence intervals of INB (dashed lines) and the posterior means of INB (dotted lines).

Figure 2.  The comparison of cost-effectiveness between clopidogrel vs aspirin plus PPIs. (a) Joint posterior sample of cost and effect differences on the CE plane. (b) Bayesian cost-effectiveness acceptability curve. (c) Bayesian 95% confidence intervals of INB (dashed lines) and the posterior means of INB (dotted lines).

Figure 3.  The comparison of cost-effectiveness between aspirin plus PPIs vs clopidogrel plus PPIs. (a) Joint posterior sample of cost and effect differences on the CE plane. (b) Bayesian cost-effectiveness acceptability curve. (c) Bayesian 95% confidence intervals of INB (dashed lines) and the posterior means of INB (dotted line).