Predictors of Physical Activity Levels in Children and Adolescents With Cerebral Palsy - a Clinical Cohort Study
Conditions: Cerebral Palsy
Sponsor: University of Southern Denmark

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Statistical Analysis Plan (SAP) for  
“Predictors of physical activity levels in children and adolescents with  
cerebral palsy: clinical cohort study protocol” 
 
1. Administrative information 
Title 
SAP - Predictors of physical activity levels in children and adolescents with 
cerebral palsy: clinical cohort study protocol 
Protocol article 
doi: 10.1136/bmjopen-2020-047522 
Trial registration number 
ClinicalTrials.gov number NCT04614207 
SAP authors 
 
Christina Esmann Fonvig12, Jens Troelsen3, Sören Möller2, Anders Holsgaard 
Larsen12 
 
1Department of Orthopaedics and Traumatology, Odense University 
Hospital, Odense, Denmark 
2Department of Clinical Research, University of Southern Denmark, Odense, 
Denmark 
3Department of Sports Science and Clinical Biomechanics, University of 
Southern Denmark, Odense, Denmark 
 
SAP version 
002 
Date of SAP version 
2022-06-02 
Date of approval 
2022-06-02 
 
Alterations to the SAP 
See ‘Protocol Deviations’ on page 5. 
 
 
 
 
 
 
 
 
 
 

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Table of contents 
1. ADMINISTRATIVE INFORMATION 
1 
ALTERATIONS TO THE SAP 
1 
2. INTRODUCTION 
3 
BACKGROUND AND RATIONAL 
3 
OBJECTIVES/HYPOTHESIS 
3 
3. METHODS 
4 
STUDY DESIGN 
4 
STUDY SIZE 
4 
TIMELINE FOR THE ANALYSIS 
4 
4. STATISTICAL PRINCIPALS 
5 
CONFIDENCE INTERVALS AND P-VALUES 
5 
PROTOCOL DEVIATIONS 
5 
DEFINITION OF THE STUDY POPULATION TO BE ANALYZED 
5 
5. STUDY POPULATION 
6 
SCREENING DATA 
6 
INCLUSION CRITERIA 
6 
RECRUITMENT 
6 
WITHDRAWAL/EXCLUSION 
6 
PARTICIPANT CHARACTERISTICS 
6 
6. VARIABLE DESCRIPTION 
7 
OUTCOME 
7 
EXPOSURE AND ADJUSTMENT VARIABLES 
7 
7. ANALYSIS 
8 
METHOD OF ANALYSIS 
8 
MISSING DATA 
8 
ADVERSE EVENTS 
9 
STATISTICAL SOFTWARE 
9 
8. SUPPLEMENTARY INFORMATION 
9 
SAP TABLES AND FIGURES 
9 
FIGURE 1. FLOWCHART OF PARTICIPANTS 
9 
TABLE 1. PARTICIPANT CHARACTERISTICS 
10 
TABLE 2. PREDICTION OF PHYSICAL ACTIVITY USING CPUP DATA PREDICTIVE VARIABLES (MODEL 1A) 
11 
TABLE 3. PREDICTION OF PHYSICAL ACTIVITY USING QUESTIONNAIRES AS PREDICTIVE VARIABLES (MODEL 1B) 
12 
TABLE 4. PREDICTION MODEL USING “THE BEST” CPUP VARIABLES (PENALIZED REGRESSION, LASSO) (MODEL 2A) 
12 
TABLE 5. PREDICTION MODEL USING “THE BEST” QUESTIONNAIRE VARIABLES (PENALIZED REGRESSION, LASSO) (MODEL 2B) 12 
REFERENCES 
12 
 

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2. Introduction 
Background and rational 
Children and adolescents with cerebral palsy may be trapped in a vicious circle of low physical fitness, 
resulting in deconditioning that causes a further decrease in physical activity (PA), a lower quality of life and 
an increased risk of developing non-communicable diseases. Therefore, establishing a healthy and active 
lifestyle during childhood is even more important for individuals with a disability. However, the factors that 
influence habitual PA in children and adolescents with cerebral palsy remain unknown. 
In Scandinavia, healthcare professionals offer standardized clinical examinations throughout childhood 
using the Cerebral Palsy Follow-Up Program (CPUP). Identifying objective predictors of PA from this 
national clinical quality database, as well as from proxy-reported questionnaires concerning quality of life, 
functional status, and personal factors by means of a conceptual statistical framework (e.g.  the 
International Classification of Functioning, Disability and Health (ICF)) may be used for an elaborated 
knowledge on habitual PA in children with CP. Specifically, the results will allow for early detection and 
potential improved interventions.  
Objectives/hypothesis 
The objective of this study is to identify and investigate potential predictors of habitual physical activity in 
children and adolescents with cerebral palsy. We hypothesize that potential predictors of habitual physical 
activity can be identified through the CPUP Program database, as well as in proxy-reported questionnaires, 
using the ICF as a conceptual statistical framework. 
 
 

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3. Methods 
A protocol article for the study has been published (1). 
Study design 
The present study is a prospective clinical cohort study. Variables from historical registry data (from the 
Cerebral Palsy Follow-Up Program (CPUP)), along with proxy-reported questionnaires, will be used as 
predictive variables. Accelerometry data on physical activity will be used as outcome. For more details on 
the included variables, see the study protocol article (1). 
Study size 
The expected study size of 300-400 children, as mentioned in the protocol article, was obtained for consent 
given to participate. However, due to the COVID-19 pandemic, and consequences thereof, accelerometer 
data was only obtained for 123 children. Furthermore, due to the incompleteness of registered children in 
the CPUP database, only 78 of these children are eligible for analysis with CPUP data.  
Timeline for the analysis 
All analyses are to be performed after the SAP has been published on ClinicalTrials.gov (NCT04614207). 
 
 

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4. Statistical principals 
Confidence intervals and p-values 
The significance level for statistically significant differences will be set at an α = 0.05 level (two-tailed 
testing) and will be presented as means and 95% confidence interval unless stated otherwise. 
Protocol deviations 
Due to the COVID-19 pandemic and related shutdown of schools and after school activities, data collection 
was hindered and thus resulted in a reduced number of expected participants. Thus, deviations to protocol 
(as published (1), and initially registered at ClinicalTrials.gov November 3, 2020) are as follows: 
- 
Data collection ended  January 31st 2022 
- 
It is not a requirement for the children to be registered in the CPUP  
- 
Primary analysis: Due to a relatively large amount of included children not being registered in the 
CPUP, additional analyses will be performed on all children with accelerometry data (Model 1b): 
o Model 1 
a) Multiple linear regression analysis between accelerometer counts (response 
variable) and all CPUP variables within each ICF component (predictive variables), 
using the latest CPUP registration prior to accelerometer data collection. 
b) Multiple linear regression analysis between accelerometer counts (response 
variable) and all questionnaire variables within each ICF component (predictive 
variables), using the questionnaire data. 
- 
Secondary analysis. Due to the limited amount of children and adolescents included in the study, 
the protocol’s model 2a (backward stepwise regression with accelerometer counts as the response 
variable and all included CPUP variables as predictive variables) will be performed for both model 
1a and 1b using penalized regression. Furthermore, the initial model 2b (Multiple linear regression 
analysis between accelerometer counts (response variable) and all included variables as predictive 
variables) will be eliminated: 
o Model 2 
a) Penalized regression (lasso) with accelerometer counts as the response variable 
and covariates as chosen by lasso to obtain an optimal fit from model 1a as 
predictive variables to determine which variables to retain in the model.  
b) Penalized regression (lasso) with accelerometer counts as the response variable 
and covariates as chosen by lasso to obtain an optimal fit from model 1b as 
predictive variables to determine which variables to retain in the model.  
- 
The expected study size of 300-400 children was obtained for consent given to participate. 
However, due to the COVID-19 pandemic, and consequences thereof, accelerometry data was only 
obtained for 123 children. Furthermore, due to the incompleteness of registered children in the 
CPUP database, only 78 of these children are eligible for analysis with CPUP data.  
- 
Due to the reduced number of expected participants, the model will not be testing the significance 
of CPUP data collection periods relative to the time in months from the measure of PA, for 
differences in prediction analyses between the following time periods: 0≤12 months, 13≤24 months 
and 25+ months 
Definition of the study population to be analyzed 
Analysis will be performed on children and adolescents that have all completed the a-priori defined 
minimum number of valid wear days of the accelerometer (four, including one weekend day) (1). 

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5. Study population 
Screening data 
Screening data to describe representativeness of the study population will be presented (age, gender, 
region of residence, CP type and subtype, GMFCS level) for children and adolescents participating in the 
study as well as for all additional children and adolescents registered in the CPUP database.  
Inclusion criteria 
- 
Children and adolescents diagnosed with cerebral palsy, 
- 
at a Gross Motor Function Classification System level I-III (independent gait function with or 
without assistive devices), 
- 
born in the period 2003-2013, 
- 
alive and living in Denmark. 
Recruitment 
Social security number (CPR-number) and names of parents of a child diagnosed with cerebral palsy, 
retrieved from the Danish National Patient Register, was used to invite potential families to participate via 
secure digital mail (e-Boks) on November 3, 2020.  
Information on recruitment will be included in the flow diagram (Figure 1). 
Withdrawal/exclusion 
Potential participants (parents) received an invitation to participate via secure electronic mail (e-Boks). For 
those who did not respond to the invitation, a reminder to accept/decline consent to participate in the 
study was sent an additional two times. Participants who had given consent to participate, but had not 
stated an address to which the accelerometer could be sent, received a mail stating the importance of this 
information and requesting the address be stated. Families who returned an accelerometer and stated that 
they did not use it, were contacted via mail to ask whether they could be interested in receiving a new 
accelerometer.  
Reasons for exclusion will be presented in the manuscript as well as Figure 1. 
Participant characteristics 
Characteristics of participants will be outlined in Table 1.  
 
 

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6. Variable description 
Outcome  
Daily average accelerometer counts will be used as outcome variable. The child/adolescent is encouraged 
to wear the belt with the Axivity AX3 accelerometer for seven consecutive days, but must have worn the 
accelerometer for a minimum of four days, including one weekend day, to be included in this study. The 
variable, daily average accelerometer counts, is weighted 5/7 and 2/7 for weekdays and weekend days, 
respectively.  
Accelerometry data is collected 6-15 months post index date (see study diagram below).  
 
 
Exposure and adjustment variables 
Questionnaire variables and CPUP variables within each ICF component will be used as predictors for 
predicting the outcome. See the protocol article for a list of included predictors (1). 
Gender, region of residence, GMFCS level, and cerebral palsy subtype will be used as covariates and will be 
extracted from the CPUP database. Age will be calculated as age in years at index date.  For non-
participants, index date will be set at November 3, 2020. 
For children and adolescents without CPUP data, gender, region of residence and GMFCS level will be 
extracted from parent-reported questionnaires. Age will be calculated as age in years at index date. 
 
 

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7. Analysis 
Method of analysis 
Descriptive statistics – participant characteristics 
Gaussian distribution of numerical variables will be inspected by normal quantile plots (qq-plots). If 
variables are normally distributed, these will be presented as means with standard deviations (SD) and 
compared by two-sample t-tests. If variables are not normally distributed, they will be presented as 
medians and quartiles and compared by non-parametric equality-of-medians test. 
Categorical variables will be presented as counts and proportions and compared with chi-squared test (or 
Fisher’s exact test in case of counts below 5). 
We will perform two descriptive comparisons: Participants with CPUP data versus participants without 
CPUP data, as well as, participants with CPUP data versus non-participants included in CPUP. 
Regression models 
Models will be checked using graphic inspection of diagnostic plots. Splines will be used to account for non-
linear effects, and interactions will be included in the model based on relevant subject-matter knowledge. 
The coefficient of determination, adjusted R-squared, will illustrate the percentage of variance in PA that is 
explained by the predictive variables. The higher the coefficient, the stronger the relationship. The root 
mean squared error of the estimate will indicate the accuracy of the predictions.  
The following models will be applied: 
o Model 1 
a) Multiple linear regression analysis between accelerometer counts (response variable) and all 
CPUP variables within each ICF component (predictive variables), using the latest CPUP 
registration prior to accelerometer data collection. 
b) Multiple linear regression analysis between accelerometer counts (response variable) and all 
questionnaire variables within each ICF component (predictive variables), using the 
questionnaire data. 
o Model 2 
a) Penalized regression (lasso) with accelerometer counts as the response variable and covariates 
as chosen by lasso to obtain an optimal fit from model 1a as predictive variables to determine 
which variables to retain in the model.  
b) Penalized regression (lasso) with accelerometer counts as the response variable and covariates 
as chosen by lasso to obtain an optimal fit from model 1b as predictive variables to determine 
which variables to retain in the model.  
Missing data 
Missing outcome data (accelerometer data) will exclude the child from the study population. Missing data 
on predictors (CPUP and questionnaire data, including personal factors) will be handled by multiple 
imputation by multivariate imputation using chained equation (MICE) including all predictors and 100 
imputation samples.  
In model 2a and 2b the imputation will be performed before applying the lasso, and afterwards the 
predictors will be ordered by proportion of imputation sets in which they are included. From this prioritized 
list, we will construct a final prediction model including all predictors included in at least 50% of the 

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imputation sets, but other cutoffs than 50% will be evaluated by an elbow plot, and if a different cutoff 
appears convincing from the plot, this cutoff will be applied. 
Adverse events 
Measuring habitual PA by accelerometry is a non-invasive method commonly used in research and has no 
known risks or side effects. However, should there be any reports of adverse events then these will be 
reported.  
Statistical software  
All statistical analyses will be performed using Stata/IC 17 or later for Windows (Stata-Corp LLC, College 
Station, TX, USA). Random seeds will be specified for imputation.  
8. Supplementary information 
SAP tables and figures 
 Figure 1. Flowchart of participants 
 
 

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Table 1. Participant characteristics 
 
Participants with 
CPUP data (n=  ) 
 
Participants 
without CPUP 
data (n=  ) 
 
Non-participants 
from CPUP (n=  ) 
Age in years (mean (SD)) 
 
 
 
 
At index date  
xx (xx) 
xx (xx) 
xx (xx)* 
Time in months from index date (mean (SD))  
 
 
 
To collection of questionnaire data 
xx (xx) 
xx (xx) 
- 
 
To collection of accelerometer data 
xx (xx) 
xx (xx) 
- 
 
To collection of CPUP data 
xx (xx) 
- 
xx (xx) 
Gender (n (%)) 
 
 
 
Boy 
xx (%) 
xx (%) 
xx (%) 
 
Girl 
xx (%) 
xx (%) 
xx (%) 
Region of residence (n (%)) 
 
 
 
Capital Region of Denmark 
xx (%) 
xx (%) 
xx (%) 
 
Central Denmark Region 
xx (%) 
xx (%) 
xx (%) 
 
Region of Northern Denmark 
xx (%) 
xx (%) 
xx (%) 
 
Region Zealand 
xx (%) 
xx (%) 
xx (%) 
 
Region of Southern Denmark 
xx (%) 
xx (%) 
xx (%) 
Cerebral palsy subtype (n (%)) 
 
 
 
Spastic 
 
xx (%) 
- 
xx (%) 
 
Ataxic 
 
xx (%) 
- 
xx (%) 
 
Dyskinesia 
 
xx (%) 
- 
xx (%) 
 
Mixed/not classified 
 
xx (%) 
- 
xx (%) 
 
Missing data 
 
xx (%)  
- 
xx (%)  
GMFCS level (n (%)) 
 
 
 
I  
xx (%) 
xx (%)** 
xx (%) 
 
II 
 xx (%) 
xx (%)** 
xx (%) 
 
III 
xx (%) 
xx (%)** 
xx (%) 
Accelerometer count (mean (SD)) 
 
 
 
 
xx (xx) 
xx (xx) 
- 
 
 
 
 
 
Abbreviations: GMFCS: Gross Motor Function Classification System, CPUP: Cerebral Palsy Follow-Up Program 
Index date= date on which consent was given for participation, *= the time of mass release of invitation to the study (November 3, 2020), **=as 
reported by parents 
 
 
 
 

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Table 2. Prediction of physical activity using CPUP data predictive variables (Model 1a) 
ICF constructs 
Variables 
Coef. [95% CI] 
p-value 
Adj.R2 
Body Function & Structure 
 
 
 
xx 
 
ROM 
xx [xx,xx] 
xx 
 
 
Pain 
xx [xx,xx] 
xx 
 
 
Muscle tone (modified Ashworth Scale) 
xx [xx,xx] 
xx 
 
 
GMFCS level 
xx [xx,xx] 
xx 
 
Activities 
 
 
 
xx 
 
FMS  
xx [xx,xx] 
xx 
 
 
GMFM-66 score 
xx [xx,xx] 
xx 
 
 
Ability to climb stairs 
xx [xx,xx] 
xx 
 
 
Bikes 
xx [xx,xx] 
xx 
 
Participation 
 
 
 
xx 
 
Participation in PT at school 
xx [xx,xx] 
xx 
 
 
Participation in recreational activities 
xx [xx,xx] 
xx 
 
Personal Factors 
 
 
 
xx 
 
Age 
xx [xx,xx] 
xx 
 
 
Gender 
xx [xx,xx] 
xx 
 
 
CP classification  
xx [xx,xx] 
xx 
 
Environmental Factors 
 
 
 
xx 
 
Residence region 
xx [xx,xx] 
xx 
 
 
Use of orthosis 
xx [xx,xx] 
xx 
 
 
Use of wheelchair 
xx [xx,xx] 
xx 
 
Abbreviations: ROM: Range of motion; FMS: Functional Mobility Scale, PODCI: Pediatric Outcomes Data Collection Instrument; PT: physical training;  
 
 

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Table 3. Prediction of physical activity using questionnaires as predictive variables (Model 1b) 
ICF constructs 
Variables 
Coef. [95% CI] 
p-value 
Adj.R2 
Body Function & Structure 
 
 
 
xx 
 
ROM 
xx [xx,xx] 
xx 
 
 
Number of hours of sleep per night 
xx [xx,xx] 
xx 
 
 
GMFCS level 
xx [xx,xx] 
xx 
 
 
PODCI – pain/comfort scale 
xx [xx,xx] 
xx 
 
Activities 
 
 
 
xx 
 
FMS (5m, 50m 500m) 
xx [xx,xx] 
xx 
 
 
Means of transport to school 
xx [xx,xx] 
xx 
 
 
Hours of screen time per day 
xx [xx,xx] 
xx 
 
Participation 
 
 
 
xx 
 
Participation in PT at school  
xx [xx,xx] 
xx 
 
 
Participation in recreational activities 
xx [xx,xx] 
xx 
 
 
PODCI - Global Function score 
xx [xx,xx] 
xx 
 
 
PODCI - Sports and Physical Functioning score 
 
 
 
Personal Factors 
 
 
 
xx 
 
Age 
xx [xx,xx] 
xx 
 
 
Gender 
xx [xx,xx] 
xx 
 
 
Parent’s educational level 
xx [xx,xx] 
xx 
 
Environmental Factors 
 
 
 
xx 
 
Residence region 
xx [xx,xx] 
xx 
 
Quality of Life 
 
 
 
xx 
 
PedsQL 
xx [xx,xx] 
xx 
 
Abbreviations: ROM: Range of motion; FMS: Functional Mobility Scale, PODCI: Pediatric Outcomes Data Collection Instrument; PT: physical training; 
PedsQL: Pediatric Quality of Life Inventory, CP Module 
 
Table 4. Prediction model using “the best” CPUP variables (penalized regression, lasso) (model 2a) 
(Like table 2, only including the variables that the lasso regression has selected) 
 
Table 5. Prediction model using “the best” questionnaire variables (penalized regression, lasso) 
(model 2b) 
(Like table 3, only including the variables that the lasso regression has selected) 
  
 
References 
1. 
Fonvig CE, Troelsen J, Dunkhase-Heinl U, Lauritsen JM, Holsgaard-Larsen A. Predictors of 
physical activity levels in children and adolescents with cerebral palsy: clinical cohort study protocol. BMJ 
Open. 2021;11(9):e047522.