Table 3.

Causal inference using the doubly robust estimating approach to correct for bias due to baseline differences in WOMAC scores between laser and traditional moxibustion treatments

WOMAC index (percentage of change from baseline, %)*	Time point	Laser moxibustion (n = 84) (%)	Traditional moxibustion (n = 55) (%)	Naïve estimate of treatment effect† (%)	Doubly robust causal treatment effect‡ (%)	P value§
Pain	Mid-term	− 32.62 ± 41.15	− 24.65 ± 43.42	− 8.0	− 7.5	0.222
	End of treatment	− 47.66 ± 46.37	− 52.87 ± 31.57	5.2	2.9	0.383
	Follow-up	− 57.57 ± 46.59	− 57.90 ± 31.77	0.3	10.1	0.298
Stiffness	Mid-term	− 28.55 ± 49.32	− 13.32 ± 69.19	− 15.2	− 15.2	0.087
	End of treatment	− 42.28 ± 56.45	− 38.28 ± 52.71	− 4.0	− 3.1	0.396
	Follow-up	− 53.99 ± 45.17	− 45.44 ± 46.92	− 8.6	− 8.0	0.217
Function	Mid-term	− 28.88 ± 47.46	− 21.71 ± 79.25	− 7.2	− 7.1	0.279
	End of treatment	− 41.43 ± 49.30	−39.03 ± 71.26	− 2.4	− 2.9	0.403
	Follow-up	− 55.95 ± 37.91	− 50.84 ± 43.67	− 5.1	− 23.1	0.006

^*Percentage of change of WOMAC index (%, the lower the better) = (post-treatment − baseline)/baseline × 100%

^†Naïve estimate of treatment effect: unadjusted estimate of treatment effect using original data, i.e., the difference of the percentage of change from baseline between the two groups (change % _{laser moxibustion} − change % _{traditional moxibustion})

^‡Doubly robust causal treatment effect: adjusted estimate of the treatment effect using double robust causal estimation

^§P values for comparing the two groups using doubly robust causal inference approach