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use continued/started at this visitSatisfCareSatisfaction with Overall Fibro TreatmentSatisfMedSatisfaction with Prescribed MedicationPHQ8PHQ8 total scoreBPIPainBPI Pain scoreBPIInterfBPI Interference score

      For the REFLECTIONS simulated data set, simulation was performed separately for each treatment cohort. First, the original dataset was transformed from a vertical (one observation per patient per time-point) into a horizontal format (one record per patient). Next, a cohort-specific data set was created by random sampling (with replacement) from each original variable. The size of sample was 240, 140, and 620 for opioid, non-narcotic opioid, and other treatment cohort, respectively. The SAS/IML programming language was used to implement the Iman-Conover method following the code of Wicklin (2013) as shown in Program 3.1 using the sampled data (A) and the desired between variables rank-correlations (C).

      Program 3.1: Iman-Conover Method to Create a Simulated REFLECTIONS Data Set

      /* Use Iman-Conover method to generate MV data with known marginals

      and known rank correlation. */

      start ImanConoverTransform(Y, C);

      X = Y;

      N = nrow(X);

      R = J(N, ncol(X));

      /* compute scores of each column */

      do i = 1 to ncol(X);

      h = quantile(“Normal”, rank(X[,i])/(N+1));

      R[,i] = h;

      end;

      /* these matrices are transposes of those in Iman & Conover */

      Q = root(corr(R));

      P = root(C);

      S = solve(Q,P);

      M = R*S; /* M has rank correlation close to target C */

      /* reorder columns of X to have same ranks as M.

      In Iman-Conover (1982), the matrix is called R_B. */

      do i = 1 to ncol(M);

      rank = rank(M[,i]);

      tmp = X[,i];

      call sort(tmp);

      X[,i] = tmp[rank];

      end;

      return( X );

      finish;

      X = ImanConoverTransform(A, C);

      The three cohort-specific simulated matrices (X) were concatenated and then the dropout and missing data were imposed at random in order to reflect the amount of dropout/missingness observed in the actual REFLECTIONS data. Then the structure of the simulated data was converted from horizontal to back to vertical.

      The distributions of variables were almost identical for real and simulated data as displayed in Tables 3.3 and 3.4. This can be expected because the Iman-Conover algorithm simply rearranges the elements of columns of the data matrix. The descriptive statistics for real and simulated data are presented below.

      Table 3.3: Comparison of Actual and Simulated REFLECTIONS Data for One Observation per Patient Variables

real	type
real	simulated
All	N	1575	1000
Cohort		13.65	14.00
NN opioid	ColPctN
opioid	ColPctN	24.00	24.00
other	ColPctN	62.35	62.00
Gender		94.54	93.20
female	ColPctN
male	ColPctN	5.46	6.80
Race		83.62	82.30
Caucasian	ColPctN
Other	ColPctN	16.38	17.70
Insurance		78.10	75.70
private/combination	ColPctN
public/no insurance	ColPctN	21.90	24.30
Doctor Specialty		17.65	17.60
Other Specialty	ColPctN
Primary Care	ColPctN	15.87	15.70
Rheumatology	ColPctN	66.48	66.70
Exercise		10.03	11.00
No	ColPctN
Yes	ColPctN	89.97	89.00
Inpatient hospitalization in last 12 months		89.84	90.70
No	ColPctN
Yes	ColPctN	10.16	9.30
Other missed paid work to help your care in last 12 months		77.71	79.60
No	ColPctN
Yes	ColPctN	22.29	20.40
Have you used an unpaid caregiver in last 12 months		62.86	60.50
No	ColPctN
Yes	ColPctN	37.14	39.50
Have you hired a caregiver in last 12 months		95.56	95.70
No	ColPctN
Yes	ColPctN	4.44	4.30
Have you received disability income in last 12 months		70.86	72.30
No	ColPctN
Yes	ColPctN	29.14	27.70
Age in years	NMiss	0	0
Mean	50.45	50.12
Std	11.71	11.56
BMI at Baseline	NMiss	0	0
Mean	31.30	31.36
Std	7.34	7.01
Duration (in years) of symptoms	NMiss	216	133
Mean	10.28	10.03
Std	9.26	9.02
Time (in years) since initial Dx	NMiss	216	133
Mean	5.73	5.29
Std	6.27	6.05
Time (in years) since initial Trtmnt	NMiss	216	133
Mean	5.22	5.26
Std	6.02	6.18
PHQ 15 total score at Baseline	NMiss	0	0
Mean	13.81	14.03
Std	4.64	4.79
FIQ Total Score at Baseline	NMiss	0	0
Mean	54.54	54.56
Std	13.43	13.47
GAD7 total score at Baseline	NMiss	0	0
Mean	10.81	10.64
Std	5.77	5.67
MFI Physical Fatigue at Baseline	NMiss	0	0
Mean	13.09	13.00
Std	2.28	2.17
MFI Mental Fatigue at Baseline	NMiss	0	0
Mean	11.51	11.52
Std	2.38	2.49
CPFQ Total Score at Baseline	NMiss	0	0
Mean	26.51	26.62
Std	6.44	6.43
ISIX total score at Baseline	NMiss	0	0
Mean	17.64	17.91
Std	5.97	5.74
SDS total score at Baseline	NMiss	0	0
Mean	18.27	18.28
Std	7.50	7.56

      Table 3.4: Comparison of Actual and Simulated REFLECTIONS Data for Visit-wise Variables

real	type
real	simulated
Visit		1575	1000
1	N
Opioids use		76.00	76.00
No	ColPctN
Yes	ColPctN	24.00	24.00
Satisfaction with Overall Fibro Treatment		5.33	6.10
.	ColPctN
1	ColPctN	12.13	12.10
2	ColPctN	20.95	19.70
3	ColPctN	25.27	24.20
4	ColPctN	22.86	24.30
5	ColPctN	13.46	13.60
Satisfaction with Prescribed Medication		10.03	9.80
.	ColPctN
1	ColPctN	7.43	6.80
2	ColPctN	15.81	15.60
3	ColPctN	31.68	31.90
4	ColPctN	23.75	24.30
5	ColPctN	11.30	11.60
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