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Table.3 Summary of the balanced baseline characteristics for the trial population

From: Simple compared to covariate-constrained randomization methods in balancing baseline characteristics: a case study of randomly allocating 72 hemodialysis centers in a cluster trial

Criteria

Constrained randomization method

Unconstrained/simple

Prognostic baseline characteristics

Principal components

11 prognostic characteristics c

Number of constrained baseline characteristics that were balanced in all 1000 (100%) sampled allocations

0 of 11 (0%) a

2 of 11 (18%)

2 of 11 (18%)

Number of constrained baseline characteristics that were balanced in at least 950 (95%) sampled allocations

6 of 11 (55%)

10 of 11 (91%)

7 of 11 (64%)

Number of constrained baseline characteristics that were balanced in at least 900 (90%) sampled allocations

8 of 11 (73%)

10 of 11 (91%)

9 of 11 (82%)

Median (25th and 75th percentile) number of baseline characteristics that were balanced across the 1000 selected randomization schemes

10 (9, 11) b

11 (10, 11)

10 (10, 11)

29 baseline characteristics used in the principal component analysisd

Number of constrained baseline characteristics that were balanced in all 1000 (100%) sampled allocations

8 of 29 (28%)

12 of 29 (41%)

12 of 29 (41%)

Number of constrained baseline characteristics that were balanced in at least 950 (95%) sampled allocations

19 of 29 (66%)

23 of 29 (79%)

25 of 29 (86%)

Number of constrained baseline characteristics that were balanced in at least 900 (90%) sampled allocations

24 of 29 (83%)

25 of 29 (86%)

26 of 29 (90%)

Median (25th and 75th percentile) number of baseline characteristics that were balanced across the 1000 selected randomization schemes

27 (26, 28)

28 (27, 28)

28 (28, 29)

All 156 available baseline characteristics

Number of constrained baseline characteristics that were balanced in all 1000 (100%) sampled allocations

41 of 156 (26%)

46 of 156 (28%)

55 of 156 (35%)

Number of constrained baseline characteristics that were balanced in at least 950 (95%) sampled allocations

104 of 156 (67%)

115 of 156 (74%)

118 of 156 (76%)

Number of constrained baseline characteristics that were balanced in at least 900 (90%) sampled allocations

125 of 156 (80%)

132 of 156 (85%)

134 of 156 (86%)

Median (25th and 75th percentile) number of baseline characteristics that were balanced across the 1000 selected randomization schemes

147 (142, 150)

149 (146, 151)

150 (147, 151)

  1. The trial population included patients on hemodialysis as of April 1, 2014, and new patients who started in-center hemodialysis during the 3-year follow-up. We conducted simple randomization without any restrictions
  2. aFor example, for simple randomization, 2 of the 11 chosen prognostic baseline characteristics were always balanced across 1000 randomly sampled allocation schemes
  3. bFor example, for simple randomization, 500 of 1000 allocation schemes had at least ten balanced baseline characteristics out of the 11 prognostic baseline characteristics. As such, there is a 50% probability that a randomly selected allocation will have at least 10 of the 11 prognostic baseline characteristics balanced and a 75% probability that at least 9 of the 11 prognostic baseline characteristics will be balanced
  4. cPrognostic baseline characteristics: Constraining on a set of baseline characteristics that thought to be important a priori and included the following patient-level information: age at index date, living in a rural area, Black race, Modified Charlson comorbidity index, number of hospital visits in the previous 12 months, number of unique drugs the patient was prescribed in the 6 months before the index date, as well as history in the last 5 years of diagnosis for peripheral vascular disease, congestive heart failure, coronary artery disease, myocardial infarction, and number of nephrology consults in the previous 12 months before the index date
  5. dResults are shown for the 29 baseline characteristics included in the principal component analysis. We did not include any cluster-level baseline characteristics in the constraining process
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Trials

ISSN: 1745-6215