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Table 1 Univariable meta-regression analyses

From: Placebo response in pharmacological and dietary supplement trials of autism spectrum disorder (ASD): systematic review and meta-regression analysis

Covariate

Social-communication difficulties

Repetitive behaviors and restricted interests

Overall core symptoms

k, n

β [95% CI]

p

R2 (%)

k, n

β [95% CI]

p

R2 (%)

k, n

β [95% CI]

p

R2 (%)

Intervention

Route (ref. not oral)

52, 1497

0 [− 0.205, 0.206]

0.998

0

52, 1492

− 0.166 [− 0.391, 0.059]

0.148

8.13

45, 1063

− 0.042 [− 0.301, 0.217]

0.749

0

Experimental intervention (ref. dietary supplement)

52, 1497

− 0.082 [− 0.229, 0.064]

0.268

2.61

52, 1492

− 0.081 − 0.262, 0.1]

0.382

0

45, 1063

− 0.023 [− 0.228, 0.181]

0.822

0

Dose schedule (ref. fixed)**

51, 1491

− 0.095 [− 0.229, 0.038]

0.163

2.57

51, 1486

− 0.195 [− 0.351, − 0.038]

0.015

27.03

44, 1057

− 0.044 [− 0.276, 0.189]

0.713

0

Study design

Publication year

52, 1497

0.016 [0.003, 0.03]

0.017

31.53

52, 1492

− 0.006 [− 0.022, 0.009]

0.416

0

45, 1063

− 0.004 [− 0.021, 0.013]

0.607

0

Country (ref. outside US/mixed)

52, 1497

− 0.002 [− 0.139, 0.135]

0.973

0

52, 1492

− 0.024 [− 0.194, 0.145]

0.778

0

45, 1063

− 0.054 [− 0.257, 0.148]

0.598

0.03

Sponsorship (ref. no)

50, 1469

0.078 [− 0.054, 0.21]

0.246

2.89

51, 1470

0.002 [− 0.172, 0.175]

0.984

0

43, 996

0.057 [− 0.152, 0.266]

0.590

0

No. sites*

48, 1395

− 0.003 [− 0.008, 0.003]

0.295

0

48, 1427

− 0.004 [− 0.011, 0.003]

0.287

0

41, 957

− 0.025 [− 0.045, − 0.005]

0.015

31.62

% academic sites

46, 1340

− 0.196 [− 0.435, 0.044]

0.11

10.66

47, 1383

− 0.08 [− 0.397, 0.236]

0.619

0

41, 957

− 0.117 [− 0.461, 0.227]

0.505

0

No. arms

52, 1497

− − 0.036 [− 0.208, 0.136]

0.684

0

52, 1492

0.035 [− 0.182, 0.252]

0.753

0

Insufficient data

Duration (weeks)

52, 1497

0.002 [− 0.007, 0.012]

0.669

0

52, 1492

− 0.009 [− 0.021, 0.003]

0.124

5.63

45, 1063

0.00 3[− 0.009, 0.015]

0.677

0

Washout (ref. no)

46, 1404

− 0.064 [− 0.204, 0.076]

0.369

0

47, 1339

− 0.006 [− 0.165, 0.153]

0.943

0

39, 995

− 0.021 [− 0.248, 0.205]

0.855

0

Sample size**

52, 1497

0 [− 0.001, 0.001]

0.967

0

52, 1492

− 0.002 [− 0.003, − 0.001]

0.004

29.38

45, 1063

− 0.001 [− 0.004, 0.001]

0.213

9.89

% participants on placebo

52, 1497

0.172 [− 0.625, 0.968]

0.673

0

52, 1492

− 0.333 [− 1.31, 0.643]

0.503

0

45, 1063

0.401 [− 0.981, 1.783]

0.569

0

Rater (ref. clinician)***

51, 1491

− 0.164 [− 0.315, − 0.012]

0.034

21.48

51, 1483

0.131 [− 0.033, 0.294]

0.117

12.20

43, 1009

− 0.148 [− 0.361, 0.065]

0.174

0

Sequence generation (ref. unclear)

52, 1497

0.147 [− 0.047, 0.34]

0.138

6.46

52, 1492

− 0.043 [− 0.302, 0.216]

0.743

0

45, 1063

0.243[− 0.048, 0.533]

0.102

1.70

Allocation concealment (ref. unclear)

52, 1497

− 0.045 [− 0.228, 0.138]

0.631

0

52, 1492

− 0.012 [− 0.233, 0.208]

0.912

0

45, 1063

− 0.252 [− 0.485, − 0.019]

0.034

17.23

Blinding (ref. unclear/high)

52, 1497

0.083 [− 0.068, 0.235]

0.28

0

52, 1492

0.006 [− 0.191, 0.202]

0.953

0

45, 1063

− 0.019 [− 0.269, 0.231]

0.881

0

Missing outcome (ref. unclear/high)

52, 1497

− 0.141 [− 0.293, 0.01]

0.067

12.03

52, 1492

− 0.052 [− 0.247, 0.143]

0.6

0

45, 1063

− 0.162 [− 0.362, 0.038]

0.111

12.72

Selective reporting (ref. unclear/high)

52, 1497

− 0.014 [− 0.254, 0.227]

0.912

0

52, 1492

− 0.156 [− 0.471, 0.160]

0.333

0.33

Insufficient data

Other bias (ref. unclear/high)

52, 1497

− 0.160 [− 0.299, − 0.021]

0.024

27.38

52, 1492

− 0.091 [− 0.303, 0.120]

0.398

0

45, 1063

− 0.033 [− 0.254, 0.188]

0.768

0

Participant

Age group (ref. adults/mixed)

52, 1497

− 0.057 [− 0.27, 0.155]

0.597

0

52, 1492

− 0.107 [− 0.323, 0.109]

0.33

1.55

45, 1063

0.148 [− 0.124, 0.42]

0.287

9.35

Mean age

51, 1478

0.002 [− 0.011, 0.014]

0.809

0

51, 1486

0.003 [− 0.008, 0.014]

0.547

0

45, 1063

− 0.007 [− 0.021, 0.007]

0.297

7.37

% female

50, 1453

0.131 [− 0.65, 0.911]

0.743

0

50, 1482

− 0.282 − 1.114, 0.55]

0.507

0

45, 1063

0.277 [− 0.650, 1.203]

0.559

0

% intellectual disability

17, 620

− 0.328 [− 0.672, 0.017]

0.063

42.21

21, 672

0.128 [− 0.335, 0.59]

0.588

0

14, 316

0.382 [− 0.105, 0.869]

0.124

20.87

% Caucasian or Hispanic

29, 963

0.036 [− 0.351, 0.423]

0.855

0

29, 971

− 0.157 [− 0.715, 0.402]

0.583

0

21, 545

− 0.42 [− 1.204, 0.364]

0.294

0

Associated conditions at baseline (ref. no)

52, 1497

− 0.068 [− 0.212, 0.075]

0.351

3.45

52, 1492

0.111 [− 0.065, 0.287]

0.216

5.83

45, 1063

− 0.012 [− 0.242, 0.218]

0.919

0

Baseline mean BMI

12, 445

− 0.063 [− 0.156, 0.029]

0.179

19.01

12, 461

− 0.02 [− 0.132, 0.091]

0.720

0

8, 254

− 0.033 [− 0.122, 0.057]

0.476

0

Baseline mean CGI− S

26, 917

− 0.042 [− 0.25, 0.167]

0.694

0

26, 925

0.033 [− 0.227, 0.292]

0.805

0

17, 513

− 0.077 [− 0.442, 0.288]

0.678

0

Baseline mean ABC− Irritability

31, 917

− 0.017 [-0.028, − 0.006]

0.002

100

30, 884

− 0.005 [− 0.022, 0.013]

0.608

0

17, 340

− 0.006 [− 0.035, 0.023]

0.68

0

Minimum threshold of core symptoms for inclusion (ref. no)**

52, 1497

0.085 [− 0.094, 0.264]

0.358

0.88

52, 1492

− 0.346 [− 0.516, − 0.175]

< 0.001

53.85

Insufficient data

  1. A negative coefficient represent an increase of placebo response. For dichotomous covariates, the reference level is mentioned. Meta-regression with dichotomous covariates were not performed when there were less than five data points for a level of the covariate (e.g., placebo lead-in or number of medications). For continuous covariates, the covariate refer to a change of 1 point of the variable, e.g., per year for publication year: decrease of placebo response in social-communication difficulties by 0.016 per year, % percentage of intellectual disability: increase of placebo response in social-communication difficulties by − 0.328 from 0 to 1 (100%) of the participants had intellectual disability. *The effect of number of sites on placebo response in overall core symptoms was not significant (k = 40, coefficient 0.0182 [− 0.268, 0.0631], p = 0.4287), when one outlier study with 26 sites was excluded (Bolognani 2019). **Placebo response in repetitive behaviors was not found to be predicted by sample size (k = 49, coefficient − 0.001 [− 0.002, 0.000], p = 0.052), flexible-dosing (k = 48, coefficient − 0.073 [− 0.189, 0.043], p = 0.218) and using a minimum threshold of core symptoms (k = 49, coefficient − 0.083 [− 0.24, 0.073], p = 0.2950), when three antidepressant trials (Herscu 2019, King 2009, and Reddihough 2019) were excluded. ***In the meta-regression of type of rater, Niederhofer 2003 was not included in social-communication difficulties (aggregated caregiver/teacher rating of ABC-L/SW), Saad 2015 was not included in overall core symptoms (it was not clear if CARS was rated only by parents or also filled by clinicians), and Anagnostou_2012 was not included in overall core symptoms and repetitive behaviors (SRS and RBS-R might have been rated as self-reports)