Reporting and Handling Missing Values in Clinical StudiesReporting and Handling Missing Values in Clinical Studies. ... Complete-case analysis ... In the Conflicus study, ...10.1007/s00134-013-2949... ·

Reporting and Handling Missing Values in Clinical Studies

Electronic material

Aurélien VESIN1,2, Elie AZOULAY3, Stéphane RUCKLY1,2, Lucile VIGNOUD1, Kateřina

RUSINOVÀ4 , Dominique BENOIT5, Marcio SOARES6, Paulo AZEIVEDO-MAIA7, Fekri

ABROUG8, Judith BENBENISHTY9, Jean Francois TIMSIT1,2,10

(1) University Grenoble 1, Albert Bonniot Institute, U823, Grenoble, France

(2) Biostatistical department, Outcomerea organization, Paris, France

(3) Medical ICU, St Louis University Hospital, Paris, France

(4) Medical ICU, Prague University Hospital, Prague, Czech Republic

(5) Department of Intensive Care Medicine, Ghent University Hospital, Ghent, Belgium

(6) Instituto Nacional de Câncer, Rio De Janeiro, Brazil

(7) Department of Anesthesia and Intensive Care, Hospital de S.João, Porto, Portugal

(8) Intensive Care Unit, CHU Fatouma Bourguiba, Monastir, Tunisia

(9) Hadassah Medical Centre, Jerusalem, Israel

(10) University Grenoble 1, Medical ICU, University Hospital Albert Michallon, Grenoble,

France

Electronic supplement 1 : Introduction to different missing data handling methods

Complete-case analysis (or listwise deletion)

This is the most widely used method and consists in deleting observations that have

missing values. Complete-case analysis is the default setting of standard statistical software.

It produces unbiased estimates only with MCAR data, as the analysed subpopulation remains

representative in this situation. Nevertheless, even with MCAR data, the loss of power

induced by the deletion of observations may be problematic if the original dataset is not

large enough.

Mean/median imputation

This method is not recommended when the missing data do not occur at random. In the

Conflicus study, for instance, failure to reply to the item on age was more common among

the oldest healthcare workers and, consequently, replacing these missing data by the mean

age of the sample would introduce bias. Furthermore, the reliability of mean/median

imputation decreases as the proportion of missing data increases; for instance, when half the

values are missing, the same value is assigned to half the observations, leading to loss of

variability, which biases the parameter estimates, masks correlations with other co-variates,

and artificially increases the confidence in the estimates.

Dummy variable adjustment method

It consists in two steps. First, a value is assigned to the missing variable (mean,

median and other methods). Second, a dummy variable is created that is equal to 1 if the first

co-variate is missing, and to 0 otherwise. Both variables are entered simultaneously into the

models so that the dummy variable serves to adjust the completed co-variates. However, this

method is comparable to complete-case analysis as the increase in statistical power is

artefactual[1, 2].

Hot-deck imputation method

In this method, missing values are replaced by existing values from another, similar

observation. Thus, this method involves matched missing value imputation. As an example,

to substitute the number of children reported by a 30-year-old female nurse, we would

choose the value reported by another female nurse of the same age [3].

Multiple Imputation (MI)

MI is certainly the most popular, because it provides a good compromise between

accuracy and understanding. Multiple imputation creates several copies of the original

dataset, in which missing values are imputed by values that differ slightly across the copies.

This approach reflects the uncertainty regarding the imputed value. The greater this

uncertainty, the greater the difference in imputed values across datasets. Then, the statistical

analysis is performed on each dataset and the results are pooled, taking into account both

intra-imputation and inter-imputation variabilities. Imputation techniques deserve special

discussion. Joint modelling or sequential regression multiple imputation (SRMI) can be

used. Joint modelling is supported by mathematical considerations but is not sufficiently

flexible for handling datasets with multiple types of variables, and is restrictive regarding the

pattern of missingness. As an example, the Conflicus multivariate analysis included 13

variables that were 3 different types: continuous (e.g. age), binary (e.g. gender), discrete (e.g.

number of children) or categorical (e.g. position in the ICU). Although incomplete variables

were more often observed in specific set of respondents, there was no clear structure in the

pattern of missingness of the data (and this is probably the case for most of the clinical

studies). SRMI, also known as Multiple Imputation using Chained Equations (MICE), has

not been proved mathematically, but has already shown good efficiency with high flexibility.

Briefly, it specifies an imputation model for each incomplete variable, using other variables

as predictors. The imputed variables are used in subsequent imputation models, and the

process is repeated until convergence occurs. For example, continuous variables may be

imputed by linear regression and dichotomous variables by logistic regression. SRMI is

available in several statistical software packages including IVEware for SAS (free of charge

download at http://www.isr.umich.edu/src/smp/ive/), MICE for Splus, R, or ICE in Stata.

We used the IVEware program to perform imputation on the Conflicus study data[1, 4, 5].

Electronic supplement 2: SAS Code for multiple imputation using IVEware and imputation

parameterisation

a) SAS code example:

%IMPUTE ( NAME=SETUP, /* Name of the MI Setup file*/

DIR=C:/…/, /* Directory of the setup file */

SETUP=NEW /* Here we create a new setup file */

);

DATAIN CONF.RESP_IVEWARE; /* Input Dataset */

DATAOUT CONF.IMPUT_IVEWARE ALL; /* Output Dataset */

DEFAULT DROP; /* variables not cited in the file will be dropped from the

output dataset */

CONTINUOUS HOSP_BEDS_C DIRECT_C ICU_MORT_C AGE

H_TRAVAIL H_SEMAINE JOBSTRAIN;

/* Continuous variables to use for imputation and to be imputed */

CATEGORICAL Australia Austria Belgium Brazil Canada Mediterranean_islands

Czech_Republic Finland France Germany Hong_Kong Hungary Israel

Italy New_Zealand Portugal Slovenia Spain Sweden Switzerland Tunisia UK USA …

/* Categorical variables to use for imputation and to be imputed*/

MIXED AS_C /* Count variables to use for imputation and to be imputed

(Zero-Inflated models are used) */

COUNT FDV_CARE_J7 ICU_BED_C PAT_YEAR_C NURS_C REA_C

VISIT_C

AN_REA SEM_LAST_VACANCES ENFANTS

/* Count variables to use for imputation and to be imputed (Poisson regression is used) */

TRANSFER OBS PAYS CENTRE HOSP_BEDS_C_CLASS

ICU_BED_C_CLASS PAT_YEAR_C_CLASS

ICU_MORT_C_CLASS NURSES_C_CLASS AS_C_CLASS REA_C_CLASS

VISIT_C_CLASS

INTERNET_SUP340 CONFLIT;

/* Variables that are kept in the output dataset without being used in the imputation process

*/

BOUNDS AGE (>=18,<=75) H_TRAVAIL (>=1,<=24) H_SEMAINE (>=1,<=100)

JOBSTRAIN (>=-3,<=9)

AN_REA (>=0,<=AGE-18) SEM_LAST_VACANCES (>=0,<=90)

FDV_CARE_J7 (>=0,<=20) ENFANTS (>=0,<=10);

/* Declare the lower and upper limit values for imputation */

MAXPRED 200; /* Maximum number of predictors to be used for imputation */

ITERATIONS 5; /* Number of cycles the imputation program will carry out */

MULTIPLES 20; /* Number of imputations to be performed */

PRINT DETAILS COEF; /* Results Printout desired */

RUN;

There are many other parameters that can be used. A reader-friendly guide is available at the

following address:

ftp://monitoringthefuture.org/pub/src/smp/ive/ive_user.pdf

b) Imputation parameterisation

Statistical software used SAS 9.3 (Cary, NC)

MIXED procedure (for multivariate model fitting)

MIANALYZE Procedure (for combining results of imputed

datasets)

IVEWARE V0.1 for SAS (Survey Research Center, Institute

for Social Research, University of Michigan available at

http://www.isr.umich.edu/src/smp/ive/)

Explanatory variables

proposed for imputation

(but need preliminary

imputation)

Linear regression : Age, average hours of work/day, average

hours of work/week

Logistic or generalized logistic model : Sex, formal training

in ethics or communication, born in the country of current

employment, Single, Job title, At least one treatment-

limitation decision shared during the last week, Graduated in

the country of current employment, At least one death over the

last week, Receiving antidepressant therapy

Poisson regression : Number of end-of-life patients cared for

during the last week, Years of experience in the ICU, Number

of weeks since last vacation, Number of children

Explanatory variables

proposed for imputation

(that are already

complete)

Country dummy variables : Australia, Austria, Belgium,

Brazil, Canada, Mediterranean islands, Czech Republic,

Finland, France, Germany, Hong Kong, Hungary, Israel, Italy,

New Zealand, Portugal, Slovenia, Spain, Sweden, Switzerland,

Tunisia, United Kingdom, USA

306 ICU dummy variables (one for each ICU)

Centre-related characteristics: Type of hospital, number of

hospital beds, type of ICU, percentage of direct admissions,

number of ICU beds, number of admissions per year, senior

physician on-site 24 h a day, junior physician on-site 24 h a

day, open ICU, ICU mortality, number of nurses, number of

nursing assistants, number of intensivists, availability of

psychologist, regular unit-level meeting, involvement of

nurses in research, presence of nurses during physician rounds,

participation of staff in working groups, number of visiting

hours per week, relatives able to sleep in the ICU, ICU worker

in charge of informing the relatives, availability of a written

procedure for family information, information leaflet routinely

given to relatives, relatives sharing patient decisions, relatives

given the option of participating in patient care, availability of

a room for family interactions, recent change in the number of

visiting hours, meetings of nurses and physicians for each

treatment-limitation decision, ICU worker in charge of

symptom control during end-of-life care, involvement of

nurses in treatment-limitation decisions, information of family

about treatment-limitation decisions, presence of nurses during

information of family about treatment-limitation decisions,

ICU worker in charge of implementing treatment-limitation

decisions, use of terminal extubation, discharge of dying

patients to wards.

Bounds forced for

imputed values

18 ≤ Age ≤ 75 ; 1 ≤ Average hours of work/day ≤ 24 ; 1 ≤

Average hours of work/week ≤ 100 ; 0 ≤ Years of experience

in the ICU ≤ (Age-18) ; 0 ≤ Number of weeks since last

vacation ≤ 90 ; 0 ≤ Number of end-of life patients cared for

during the last week ≤ 20 ; 0 ≤ Number of children ≤ 10

Maximum number of

explanatory variables to

be included in a

imputation model

200

Number of different

imputed datasets

20

Explanation : For example, the missing 'age' values will be imputed using linear regression

including all other variables as predictors, then the completed age variable is used as a

predictor in imputation models for others variables. Then the process repeats itself until it

converges.

Electronic supplement 3: Density plots of variables included in the multivariate model, comparison of observed (solid line) and imputed values (dotted line)

Visual inspection of density plots did not show marked differences between the observed and the imputed distribution. We did not unmask abusive influence of observed outliers in imputed values. The parameterization of bounds for imputed values prevents the occurrence of this problem.

10 20 30 40 50 60 70 80

Age

Den

sity

0 2 4 6 8

Nb of children

0 10 20 30 40

Years of experience in the ICU

0 10 20 30 40 50 60

Weeks since last vacations

4 6 8 10 12 14 16

Hour of work per day

0 2 4 6 8 10

Nb of EOL patients cared for

Electronic supplement 4: Bivariate scatter plots and boxplot of Job strain to explore the consistency of observed (white boxes or thin black dots) and imputed (red box or red bold squares) values for different multivariate model variables*

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

2030

4050

6070

JobStrain

Age

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

02

46

8

JobStrain

Nb

of c

hild

ren

Imputed Born foreign

Observed Born foreign

Imputed Born in job country

Observed Born in job country

-20

24

68

JobS

train

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

010

2030

40

JobStrain

Yea

rs o

f exp

erie

nce

in th

e IC

U

Imputed Doctors

Observed Doctors

Imputed Nurses

Observed Nurses

Imputed Others

Observed Others

Imputed Physioth.

Observed Physioth.

-20

24

68

JobS

train

(*) There were no missing values for "Formal training in ethics or communication" and "conflict in the ICU"

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

010

2030

4050

60

JobStrain

Wee

ks s

ince

last

vac

atio

ns

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

05

1015

20

JobStrain

Hou

r of w

ork

per d

ay

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

05

1015

2025

JobStrain

Nb

of E

OL

patie

nts

care

d fo

r

Imputed No TL decision

Observed No TL decision

Imputed TL decision

Observed TL decision

-20

24

68

JobS

train

Imputed No AD therapy

Observed No AD therapy

Imputed AD therapy

Observed AD therapy

-20

24

68

JobS

train

Electronic supplement 5:

Variation of estimates and standard error for both imputation techniques as compared to complete case analysis

VariableComplete-case

analysis

Median/Most frequent modality

imputation

Multiple imputation

n= 5504 (76,3%) n=7209 (100%) n=7209 (100%)

Beta SE

Beta variatio

n %

SE variation

%

Beta variation

%

SE variation

%Age in years< 28 0 (-)28 - 34 -0,349 0,095 29,8% 12,6% 38,1% 10,5%34 – 42 -0,195 0,113 7,7% 14,2% 55,9% 10,6%≥ 42 -0,2 0,132 38,5% 15,2% 60,0% 11,4%Female -0,13 0,072 20,0% 11,1% 23,1% 9,7%Number of childrenNo children 0 (-)1 Child -0,05 0,088 52,0% 18,2% 30,0% 11,4%≥ 2 Children 0,212 0,084 24,1% 10,7% 44,8% 9,5%Born in the country of current employment -0,495 0,103 28,9% 13,6% 24,6% 13,6%Years of experience in the ICU< 2 years 0 (-)2 – 5 years -0,531 0,09 7,3% 11,1% 5,6% 11,1%6 – 11 years -0,471 0,106 12,5% 15,1% 16,8% 12,3%≥ 12 years -0,464 0,118 0,4% 13,6% 3,4% 11,9%Job titlePhysician 0 (-)Nurse -1,041 0,088 0,2% 10,2% 0,5% 10,2%Physiotherapist -0,099 0,151 7,1% 9,3% 23,2% 9,3%Other -0,541 0,144 26,2% 13,2% 29,6% 12,5%>4 months since last vacations 0,247 0,071 10,1% 9,9% 10,1% 9,9%Average hours of work >8/day 0,285 0,071 4,6% 11,3% 1,1% 9,9%Formal training in ethics or communication -0,359 0,062 2,5% 11,3% 1,1% 11,3%End-of-life patients cared for within the last weekNone 0 (-)One patient -0,27 0,085 15,6% 15,3% 3,3% 7,1%More than one patient -0,574 0,081 9,2% 9,9% 4,0% 8,6%At least one treatment-limitation decision shared within the last week -0,357 0,074 1,1% 9,5% 6,4% 9,5%

Receiving antidepressant therapy 0,76 0,109 7,6% 10,1% 7,2% 10,1%At least one conflict in the ICU -0,504 0,072 7,3% 12,5% 6,5% 13,9%

Electronic supplement 6: Analysis of the management of missing data in 44 articles from intensive care journal issues published in October

2010

N° PMID Journal Type of study n 1/ Did the dataset

have missing

values?

2/ Are the missing values

mentioned in the text

(methods or results

section)?

3/ Was a specific

technique used to handle

missing data? If so,

which one?

[6] 20975552 CCM Retrospective

observational

study

415 impossible to know No

[7] 20975551 CCM Prospective

observational

study


[8] 20975548 CCM Retrospective 778 impossible to know No

multicentre

randomised

controlled trial

[9] 20959789 CCM Prospective,

observational,

registry-based

study

765 Yes Yes Patients with missing

data were excluded

[10

]

20959787 CCM Retrospective case

series review

3213 Yes, for each

variable, up to 11%

Yes and % of missing

values is reported

The cases with missing

data were excluded

[11

]

20959785 CCM Retrospective

analysis

1126 Yes Yes, materials and

methods

Imputation of baseline

characteristics using

Multiple imputation in

SAS (m=5) no details

[12


observational


] study

[13

]

20959555 AJRCCM Clinical trial 75 /

branch

Yes, 21% patients

missing for at least

1 dose

Yes No assumption was done,

simply ignored

[14

]

20935112 AJRCCM Cohort 4636 Yes No Exclude patient with no

valid spirometry

[15

]

20935108 AJRCCM Cohort 190 impossible to know No

[16

]

20935107 AJRCCM Longitudinal

cohort

1006 Yes Yes (results) No information probably

ignored

[17

]

20935105 AJRCCM Case-control 22 cases impossible to know No

[18

]

20889910 AJRCCM Observational

study of risk

factors for asthma

3245 Yes, up to 8% Yes Excluded from analysis,

there is more missing in

one group

[19

]

20889909 AJRCCM Observational

cohort study


[20

]

20889908 AJRCCM Retrospective

analysis of several

cohorts

> 5000 impossible to know No

[21

]

20889905 AJRCCM Cohort: Asthma

and swimming

pool

5700 Yes, large number

of missing values

(up to 45%)

Yes, statistical analysis

section and complete

table of missing data in

the electronic

supplement

They exclude them

[22

20889903 AJRCCM Prospective cohort 6814 Yes Yes They exclude them (46%

of the original cohort)

]

[23

]

20889902 AJRCCM Population-based

cohort: nested

case-control

560 cases Yes (<0.5%) Yes Ignore

[24

]

20889901 AJRCCM Cross-sectional

study

692 Yes In the electronic

supplement

Probably excluded

[25

]

20818232 CCM Prospective

population-based

cohort study

351 Yes, 80 values

missing for one

variable

yes yes, several approaches :

missing indicator

variable adjustment,

median coding,

complete-case analysis

[26

]

20802326 CCM Matched cohort

study, 1:2

31 cases impossible to know no

20802324 CCM Retrospective 138 Yes (11 patients) yes excluded

[27

]

study

[28

]

20802323 CCM Cross-sectional

study

87166 Yes (up to 28%) yes excluded

[29

]


observational

study

171 Yes yes (discussion) excluded

[30

]

20683260 CCM Prospective cohort 749 impossible to know no

[31

]


study

85 impossible to know no

[32


observational


] cohort study

[33

]


observational

cohort study


[34

]

20558625 AJRCCM Prospective cohort 162 impossible to know no

[35

]

20538961 AJRCCM Trial (ITT) 1218 Yes (33 patients) yes excluded

[36

]

20661726 ICM Prospective cohort 72 Yes, 18 yes excluded

[37

]

20533022 ICM Randomised

controlled trial

40 no no

[38

]

20535605 ICM Prospective cohort 10 no no

[39

]

20521025 ICM Prospective cohort 21 no no

[40

]

20532477 ICM Retrospective

cohort

72 16 no excluded

[41

]

20577713 ICM 40 cases/10

controls


[42

]


cohort

250 no no not described even in the

tables

20658124 ICM Retrospective 2699 8 missing sodium no despite 2 pages of

[43

]

cohort values statistics not even a word

on missing data

[44

]

20464542 ICM Prospective cohort 115

ICU/932

patients

27 no not described even in the

tables

[45

]


cohort

70 no no no

[46

]


analysis of a

prospective cohort

344 no no no

[47

]

20502874 ICM Prospective cohort 1113 245 (69 protocol

violations)

described not included

[48

20549184 ICM Prospective cohort 149,894 impossible to know no

]

[49

]

20533023 ICM Prospective cohort 8616 About 5% of

missing values

in the electronic

supplement, but no

further information

not described

ICM, Intensive Care Med; AJRCCM, American Journal of Critical Care and Medicine; CCM, Critical Care Medicine

References:

For Critical Care medicine and AJRCCM journals the e-publication date was

considered whereas journal publication date was considered for Intensive Care Med.

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