Statistic result for Wrist Data
After exploring the data, we found that the main concern of missingness is about “fxtosurgwk” and outcome “chronicpain”.
Part 1: Missing patterns
We divide the data into two groups according to the missingness of outcome “chronic_pain” . Then we compare two groups in term of all other variables.
For continuous variables, we use two sample paired t-test, and for categorical variables, we use pearson chi square test. The following are the p-values of all other variables, under the null hypothesis that for every single variable, two groups have the same distribution.
Table 1
| with missing outcome | with observed outcome | p.value | |
|---|---|---|---|
| astreat exfix | 13 (33.3%) | 47 (32.4%) | 0.789 |
| astreat pinning | 12 (30.8%) | 38 (26.2%) | . |
| astreat VLPS | 14 (35.9%) | 60 (41.4%) | . |
| gender male | 4 (10.3%) | 18 (12.4%) | 0.928 |
| gender female | 35 (89.7%) | 127 (87.6%) | . |
| rapa active | 13 (33.3%) | 69 (47.9%) | 0.26 |
| rapa underactive | 21 (53.8%) | 62 (43.1%) | . |
| rapa sedentary | 5 (12.8%) | 13 (9%) | . |
| osteoatrts_yes no | 26 (68.4%) | 92 (63.4%) | 0.704 |
| osteoatrts_yes yes | 12 (31.6%) | 53 (36.6%) | . |
smoke simple Yes |
23 (60.5%) | 64 (44.1%) | 0.106 |
smoke simple No |
15 (39.5%) | 81 (55.9%) | . |
education simple < high school |
6 (16.2%) | 13 (9.2%) | 0.354 |
education simple high |
31 (83.8%) | 128 (90.8%) | . |
| income 10-30K | 14 (41.2%) | 31 (25.4%) | 0.114 |
| income >60K | 11 (32.4%) | 46 (37.7%) | . |
| income 30-60K | 9 (26.5%) | 45 (36.9%) | . |
| employ retired | 18 (54.5%) | 103 (71%) | 0.104 |
| employ fulltime | 15 (45.5%) | 42 (29%) | . |
| inj_dom No | 24 (70.6%) | 78 (54.2%) | 0.122 |
| inj_dom Yes | 10 (29.4%) | 66 (45.8%) | . |
| usfx Yes | 10 (27.8%) | 65 (46.8%) | 0.063 |
| usfx No | 26 (72.2%) | 74 (53.2%) | . |
ao simple A |
20 (55.6%) | 87 (63%) | 0.529 |
ao simple C |
16 (44.4%) | 51 (37%) | . |
| fxtosurgwk | 1.3 (0.74) | 1.2 (0.68) | 0.402 |
| age | 66.7 (6.88) | 68.9 (7.18) | 0.08 |
| nocomorb | 3.7 (2.68) | 3.3 (2.18) | 0.391 |
| b_radhi | 7.9 (4.26) | 8.4 (3.36) | 0.527 |
| b_radinc | 15.8 (7.62) | 16.1 (5.34) | 0.812 |
| b_vdtilt | -13.1 (15.13) | -14.5 (13.59) | 0.609 |
| b_ulnavar | 1.5 (2.57) | 2.6 (2.98) | 0.035 |
| b_PCS | 33.2 (9.76) | 34.3 (10.38) | 0.535 |
| b_MCS | 47.6 (13.43) | 50.2 (13.88) | 0.297 |
| b_painnorm | 6.8 (15.91) | 3.2 (10.94) | 0.194 |
| b_paindiff | 63.2 (27.78) | 60.8 (27.65) | 0.628 |
Part 2: Covariates adjusted for missing probability — propensity score
Table 2: propensity score model
## glm(formula = miss_y ~ ., family = binomial(link = "logit"),
## data = D)## Estimate Std. Error p.value significance
## (Intercept) -10.78 1466.08 0.994
## as.factor.dat.astreat.pinning -0.49 0.89 0.583
## as.factor.dat.astreat.VLPS -1.30 1.02 0.201
## as.factor.dat.gender.male 0.23 1.19 0.849
## as.factor.dat.rapa.sedentary 1.40 1.60 0.381
## as.factor.dat.rapa.underactive 0.87 0.79 0.275
## as.factor.dat.osteoatrts_yes.yes -1.34 1.12 0.233
## as.factor.dat..smoke.simple..Yes 0.71 0.83 0.395
## as.factor.dat..education.simple..high -4.86 1.81 0.007 **
## as.factor.dat.income.>60K 22.46 1466.07 0.988
## as.factor.dat.income.10-30K 23.11 1466.07 0.987
## as.factor.dat.income.30-60K 21.91 1466.07 0.988
## as.factor.dat.employ.retired -2.01 1.07 0.060 .
## as.factor.dat.inj_dom.Yes -0.89 0.78 0.252
## as.factor.dat.usfx.Yes -1.98 0.95 0.037 *
## as.factor.dat..ao.simple..C 1.45 0.81 0.073 .
## dat.fxtosurgwk 0.83 0.56 0.140
## dat.age -0.13 0.10 0.185
## dat.nocomorb 0.01 0.18 0.972
## dat.b_radhi 0.05 0.17 0.776
## dat.b_radinc -0.11 0.11 0.339
## dat.b_vdtilt -0.03 0.03 0.317
## dat.b_ulnavar -0.55 0.25 0.030 *
## dat.b_PCS 0.00 0.04 0.945
## dat.b_MCS 0.00 0.03 0.885
## dat.b_painnorm 0.01 0.03 0.818
## dat.b_paindiff 0.02 0.02 0.340
Part 3: inverse probability weighted (IPW) logistic regression
We use inverse-propensity as every sample’s weight to fit a logistic regression.
Table 3: IPW Full model
## glm(formula = y0 ~ ., family = binomial(link = "logit"), data = D,
## weights = w)## Estimate Std. Error p.value significance
## (Intercept) -1.47 3.59 0.683
## as.factor.dat.astreat.pinning 0.06 0.69 0.926
## as.factor.dat.astreat.VLPS -1.58 0.65 0.014 *
## as.factor.dat.gender.male 1.36 0.88 0.123
## as.factor.dat.rapa.sedentary -1.27 0.95 0.182
## as.factor.dat.rapa.underactive 0.12 0.50 0.817
## as.factor.dat.osteoatrts_yes.yes 0.57 0.59 0.331
## as.factor.dat..smoke.simple..Yes 0.69 0.50 0.167
## as.factor.dat..education.simple..high -0.80 1.05 0.445
## as.factor.dat.income.>60K 1.23 1.13 0.274
## as.factor.dat.income.10-30K 0.79 1.10 0.474
## as.factor.dat.income.30-60K -0.12 1.04 0.910
## as.factor.dat.employ.retired 0.46 0.56 0.415
## as.factor.dat.inj_dom.Yes -0.49 0.47 0.297
## as.factor.dat.usfx.Yes -0.07 0.46 0.886
## as.factor.dat..ao.simple..C 0.20 0.51 0.700
## dat.fxtosurgwk 1.28 0.39 0.001 **
## dat.age 0.01 0.04 0.751
## dat.nocomorb -0.07 0.14 0.621
## dat.b_radhi -0.04 0.12 0.720
## dat.b_radinc 0.06 0.07 0.427
## dat.b_vdtilt -0.02 0.02 0.216
## dat.b_ulnavar 0.07 0.09 0.392
## dat.b_PCS -0.01 0.03 0.800
## dat.b_MCS -0.03 0.02 0.068 .
## dat.b_painnorm -0.01 0.02 0.765
## dat.b_paindiff 0.01 0.01 0.277Table 4: IPW Model after feature selecting
## glm(formula = y0 ~ as.factor.dat.astreat. + as.factor.dat.gender. +
## as.factor.dat..smoke.simple.. + dat.fxtosurgwk + dat.b_vdtilt +
## dat.b_MCS + dat.b_paindiff, family = binomial(link = "logit"),
## data = D, weights = w)## Estimate Std. Error p.value significance
## (Intercept) -0.95 1.13 0.400
## as.factor.dat.astreat.pinning 0.37 0.55 0.499
## as.factor.dat.astreat.VLPS -1.37 0.52 0.009 **
## as.factor.dat.gender.male 1.11 0.65 0.089 .
## as.factor.dat..smoke.simple..Yes 0.69 0.43 0.108
## dat.fxtosurgwk 1.02 0.33 0.002 **
## dat.b_vdtilt -0.02 0.02 0.137
## dat.b_MCS -0.02 0.02 0.099 .
## dat.b_paindiff 0.02 0.01 0.021 *