Supporting information
1 Patient selection criteria
Inclusion criteria:
 adult patients (minimum age 16 years)
 demonstration of irreversible pulpitis by complaint of spontaneous, thermal, and
percussion test pain (Tronstad, 2008)
 pulpitis caused by caries (primary or repeated)
 indication for permanent endodontic treatment
 acceptable periodontal health in the affected quadrant
 absence of alveolysis or periapical radiolucency concerning the affected tooth and its
neighbors
 available for and willing to undergo endodontic treatment at D7 and a follow-up visit
at 6 months.
Exclusion criteria:
 children under 16
 all other causes of pulpitis (including endo-periodontal lesions)
 fractured or cracked teeth
 immature teeth
 any tooth for which the possibility of periodontal disease could not be
excluded internal or external resorptions
 any patient presenting
◦ local or regional (ENT sphere) infectious foci
◦ any contraindication for endodontic treatment
◦ known allergy or intolerance to corticosteroids, ibuprofen, codeine, tramadol, or
acetaminophen
◦ any contraindication for glucocorticoid intake (including insulin-dependent
diabetes, current infectious disease, recent immunization, psychosis)
◦ pregnancy or breastfeeding
◦ inability to understand the trial protocol (which was described in a written note
and explained orally)
◦ unwillingness to sign the informed consent form
2 Data collection
Dentist-observed data were collected on a multicopy Case Rport Form allowing data
monitoring according to Good Clinical Practice (“Bonnes Pratiques Cliniques”). The patients
recorded their daily spontaneous and percussion pain on a small booklet later joined to the Case
Report Form as “Original Data”.
3 Statistical analysis methods
Since a few data were missing (see the Results section), it was necessary to assess their
impact (imprecision, possible bias) on the statistical analysis (1). An attempt at multiple imputations
by chained equations (2) leads to dubious results; therefore we decided to construct a Bayesian
network modeling the joint distribution of our data and to carry out Bayesian analysis of our results.
This model allowed for a “natural” missing data imputation, using the same model for imputation
and analysis under a “Missing At Random” (MAR) assumption. The model, which is described in
the online Appendix, aims to assess the joint probability distribution of the most important prerandomization variables and the post-randomization results. It is implemented as a multilevel
mixed-model regression in the JAGS dialect (3) of the Bugs Bayesian modeling language (4),
piloted from the R statistical language (5) using Spiegelhalter et al (6) and Gelman and Hill (7) as
guidelines.
We assessed the influence of one variable on another by a posteriori distribution of the
relevant regression coefficient(s) and its (their) position in relation to 0, as summarized by its (their)
median(s), 50% and 95% Highest Posterior Density credible sets (CrI95), and probability of a value
of a sign opposed to that of the median (“pseudo p” in the tables). It should be noted that the
numerical values of the regression coefficient for polychoric ordered regression have no intrinsic
interpretation when the same scale is used for more than one measurement (e.g. pain scale); they
should be interpreted in terms of positions relative to zero.
4 The Bayesian model
The model aims to assess the joint probability distribution of the most important prerandomization variables and the post-randomization results. These data are modeled as a multilevel
regression:
Group
Variables
Predictors
A
Group (treatment), dental center
Unmodeled
B
Demographics: sex, age, education level
A
C
General dental health: missing teeth, date of last dental A+B
visit
D
Causal lesion: arch, group, etiology
E
Symptomatology: duration of pain,
(spontaneous and percussion) pain
F
Immediate results: treatment duration, postoperative pain A+B+C+D+E
G
Waiting period pain (recorded by the patient)
A+B+C+D+E+intraligamental
anesthesia
H
D7 pain
A+B+C+D+E + intraligamental
anesthesia
I
Other D7 results: clinical examination, intercurrent “minimal” set : Group, centre if
events
possible.
J
6 month pain level
K
6 months results: clinical examination, intercurrent “minimal” set : Group, centre if
events, current state of the treated tooth
possible.
A+B+C
intensity
of A+B+C+D
A+B+C+D+E + intraligamental
anesthesia
Group
Other
Variables
See text
Predictors
“minimal” set : Group, center if
possible.
All data were modeled at a minimum on group (treatment allocation) and treatment center
wherever possible1, thus allowing for intergroup balance checking; constant and “almost constant”
data (e.g. boolean variables occurring once or twice in the dataset) were excluded from further
modeling to avoid separation effects; all other pre-randomization variables, as well as intraligamental infiltration were used to model main post-randomization variables. The elementary
models were linear regression for the numeric variables, logistic regression for the boolean
variables, and polychoric ordered logistic regression for the ordinal variables, an exception being
the number of missing teeth, modeled as a zero-inflated Poisson variable.
We modeled pain measurements by modeling a pain scale specific to each patient and
common to all his/her pain measurements; this allows for intrapatient correlations (mixed-effects
model).
We used vague proper priors2, improper “flat” priors being incompatible with JAGS
algorithms. The variability of the SPI and SPID indices was assessed by simulation at each iteration
of new values of the pain measurements for the same patients, using the current regression
coefficients (i.e., a hypothetical repetition of the trial conditional to the current value of the
parameters) and computation of the resulting indices.
The model's convergence was assessed by monitoring the autocorrelations (especially the
Gelman and Rubin PSRF index) and by visual assessment of the traces.
Posterior distributions are tabulated by their medians, their 95% Credible Interval (Highest
Posterior Density set, here always an open interval), and the probability of a value of a sign opposed
to the sign of the median (“pseudo p”).
1
One cannot model a boolean variable occurring only once on two predictors simultaneously
(aliasing)...
2
The prior of a regression coefficient expected to be a few units from 0 was a normal of mean
0 and variance 104.
Tables for Supporting Information
Variable
Randomization to
Prednisolone
Pulpotomy
Group
95% Credible
effect
interval
pseudo p
Female sex
24 (51%)
32 (68%)
-0.743
(-1.664, 0.107 )
0.045
Age
28.23±8.94
29.02±8.40
-0.848
(-4.401, 2.698 )
0.315
Primary
10 (21%)
12 (26%)
Junior high
school
13 (27%)
9 (19%)
High school
14 (30%)
18 (38%)
College
6 (13%)
5 (11%)
MS, MA
4 (9%)
2 (4%)
PhD
0 (0%)
1 (2%)
0.049
(-0.790, 0.891 )
0.457
0.052
(-0.790, 0.839 )
0.451
Education
General pathology
Last dental visit
Missing teeth
1 (2%) (sickle-cell 0 (0%) (1 NA)
anemia)
1 week
2 (4%)
3 6%)
2 weeks
1 (4%)
0 (0%)
1 months 3 (6%)
2 (4%)
2 months 2 (4%)
2 (4%)
3 months 1 (2%)
2 (4%)
4 months 0 (0%)
3 (6%)
5 months 2 (4%)
3 (6%)
6 months 20 (43%)
14 (30%)
never
15 (32%)
18 (38%)
NA
1 (2%)
0 (0%)
-0.095
(-0.969, 0.732 )
0.412
0
24 (51%)
28 (60%)
-0.563
(-1.630, 0.378 )
0.136
1
3 (6%)
5 (11%)
2
3 (6%)
7 (15%)
3
1 (2%)
1 (2%)
4
13 (28%)
5 (11%)
5
1 (2%)
0 (0%)
6
2 (4%)
0 (0%)
7
0(0%)
1 (2%)
0.800
(-0.029, 2.037 )
0.026
Table S1: Patient characteristics : raw data and statistical analysis results of the intergroup
differences at baseline. Group effect = median of the posterior distribution of the “Treatment”
regression parameter, CrI95 = Highest Posterior Density set (here always an interval) of this
coefficient; pseudo p = posterior probability of this coefficient being opposite to the sign of the
median.
Regression coefficient
Daily average of spontaneous pain
Daily difference between groups for spontaneous pain
Daily average of percussion pain
Daily difference between groups for percussion pain
Day Med
95% Credible
Interval
pseudo.p
1
3.108 (2.412 , 3.841 )
<1.43.10-4
2
1.723 (1.078 , 2.378 )
<1.43.10-4
3
1.561 (0.932 , 2.231 )
<1.43.10-4
4
-1.543 (-2.449, -0.702)
<1.43.10-4
5
-0.784 (-1.509, -0.060)
0.015
6
-1.775 (-2.605, -0.997)
<1.43.10-4
7
-2.269 (-3.212, -1.437)
<1.43.10-4
1
-1.439 (-3.783, 0.853 )
0.106
2
-1.746 (-3.939, 0.614 )
0.064
3
-1.238 (-3.544, 1.003 )
0.153
4
-3.741 (-6.614, -0.861)
0.003
5
-1.120 (-3.707, 1.165 )
0.180
6
-1.874 (-4.285, 0.586 )
0.065
7
-2.493 (-5.143, 0.010 )
0.023
1
2.540 (1.891 , 3.185 )
<1.43.10-4
2
1.394 (0.790 , 2.033 )
<1.43.10-4
3
0.015 (-0.613, 0.642 )
0.478
4
-1.015 (-1.706, -0.336)
0.001
5
-0.909 (-1.586, -0.259)
0.004
6
-0.992 (-1.655, -0.308)
0.002
7
-1.032 (-1.768, -0.389)
0.001
1
-6.102 (-8.375, -4.087)
<1.43.10-4
2
-6.346 (-8.554, -4.195)
<1.43.10-4
3
-6.152 (-8.325, -4.005)
<1.43.10-4
4
-6.346 (-8.569, -4.145)
<1.43.10-4
5
-6.194 (-8.478, -4.029)
<1.43.10-4
6
-6.000 (-8.285, -3.862)
<1.43.10-4
7
-5.995 (-8.270, -3.823)
<1.43.10-4
Table S2: Modelization of the evolution of spontaneous and percussion pain during the 7-days
waiting period. The pain intensities are analyzed as a polychoric ordered regression, whose
(latent) intensity is modeled by time and between-group difference ; the table reports the median,
95 % credible interval and pseudo-p of the regression coefficient.
References for the supporting information
1 Little Roderick JA, Rubin Donald B. Statistical analysis with missing data. Wiley; 2002.
2 van Buuren Stef, Groothuis-Oudshoorn Karin. mice: Multivariate Imputation by Chained
Equations in R. J Stat Softw 2011;45(3):1–67.
3 Plummer Martyn. JAGS: A program for analysis of Bayesian graphical models using Gibbs
sampling 2003.
4 Lunn David, Spiegelhalter David, Thomas Andrew, Best Nicky. The BUGS project: Evolution,
critique and future directions. Stat Med 2009;28(25):3049–67. Doi: 10.1002/sim.3680.
5 R Core Team. R: A Language and Environment for Statistical Computing. Vienna, Austria: R
Foundation for Statistical Computing; 2012.
6 Spiegelhalter David J, Abrams Keith R, Myles Jonathan P. Bayesian approaches to clinical trials
and health-care evaluation. John Wiley and Sons; 2004.
7 Gelman Andrew, Hill Jennifer. Data Analysis Using Regression and Multilevel/Hierarchical
Models. 1st ed. Cambridge University Press; 2006.. 1st ed. Cambridge University Press; 2006.