Supplementary Appendix 2: Treatment
and assessment of missing data
Contents
Statistical methods and notes....................................................................................................................... 2
Two types of incomplete data .................................................................................................................. 2
Correction for selection bias of longitudinal cohort ................................................................................. 2
Correction for bias due to loss to follow-up among longitudinal cohort ................................................. 3
Sensitivity analysis .................................................................................................................................... 4
Impact of missing data on logistic regression models .............................................................................. 4
Results ........................................................................................................................................................... 5
Patient flow ............................................................................................................................................... 5
Inverse probability weighting so longitudinal cohort reflects unselected hospital cohort ...................... 5
Multiple Imputation .................................................................................................................................. 6
Sensitivity analysis of primary outcomes .................................................................................................. 7
Conclusion ..................................................................................................................................................... 8
Figures ........................................................................................................................................................... 9
Figure 1a—Patient Flow Diagram (Chart abstraction and patient recruitment) ................................ 10
Figure 1b—Patient Flow Diagram (Patient follow up) ........................................................................ 11
Figure 2: Non-linear but monotonic association between days in hospital and probably of being in
longitudinal cohort (knots placed at 2, 7 and 14 days)....................................................................... 12
Figure 3: Calibration plot of model used to calculate inverse probability weights ............................ 13
Figure 4: Kaplan-Meier curves with and without inverse probability weighting ............................... 14
Fgiure 5: Sensitivity anlaysis of physical recovery .............................................................................. 15
Tables .......................................................................................................................................................... 16
Table 1: Baseline Characteristics of Study Patients (Completers vs. LTFU) ........................................ 17
Table 2: Clinical outcomes (Completers vs. LTFU) .............................................................................. 19
Table 3: Logistic model used to derive probability of patients being in longitudinal cohort. ............ 20
Table 4: Logistic regression models predicting 12-month Physical Recovery after applying inverse
probability weighting .......................................................................................................................... 21
Table 5: Logistic regression models predicting 12-month survival after applying inverse probability
weighting ............................................................................................................................................ 22
Table 6: Linear regression models predicting 12-month SF-36 physical function scores among
survivors after applying inverse probability weighting....................................................................... 23
Table 7: Pearson correlation matrix: .................................................................................................. 24
Table 8: Estimates of 12 month PF recovery rate with 95% confidence intervals. ............................ 24
References .................................................................................................................................................. 25
1
Statistical methods and notes
Two types of incomplete data
There are two sources of incomplete data in this study that could potentially bias estimates of the 12month mortality and physical functioning (PF) recovery rates. Firstly, the longitudinal cohort required
consent and active participation of the family members and was thus a selected group and potentially
not representative of the target population of all patients at least 80 years old admitted to an ICU for at
least 24 hours. For example, patients actively dying, patients in the ICU for a short period, and patients
who did not have caregivers present early in their stay may have been less likely to be enrolled in the
longitudinal cohort. Secondly, 17% of patients in the longitudinal cohort were lost to follow-up before
the primary 12-month assessment. The survival status and PF recovery status are unknown in these
patients and it is conceivable that these data are not missing at random (NMAR). We had a few
mechanisms to determine mortality and once a patient was known to have died their 12-month
mortality and PF recovery status were known for all future time points. For this reason, one might argue
that the survival rate and PF recovery rate may be higher in the patients with missing outcome. On the
other hand, among patients discharged alive from the hospital, follow-up required us to contact the
patient or caregiver and it is conceivable that it was more difficult to make contact with a caregiver
when the patient had died. As a result, it is uncertain as to which direction any bias, if present, is most
likely to take.
The dataset is virtually complete (<0.5% missing) for baseline and hospital data on all patients in the
longitudinal cohort. We have baseline and hospital information (but not follow-up outcomes) on a
hospital cohort which is an unselected representative sample of our target population at the 22
participating ICUs. The hospital cohort data were collected by chart review for all consecutive patients
over 80 admitted to the participating centres until enrolment was stopped at individual centres due to
budgetary constraints. Enrolment in the hospital cohort was unrelated to any patient or hospital
characteristics other than admission date. Therefore, we believe that the hospital cohort is a random
sample of the target population of patients at least 80 years old and in the ICU for > 24 hours.
Correction for selection bias of longitudinal cohort
We employed inverse probability weighting (IPW) so we could use the selected longitudinal cohort
sample to obtain population estimates for the unselected hospital cohort. We applied this method to all
of our 12-month outcomes including all of the regression modelling. With this method we perform the
usual analyses while weighting the observations inversely to the estimated probability of being in the
longitudinal cohort compared to the hospital cohort. The estimation of these weights is based on
logistic regression where the outcome variable is an indicator of the patient belonging to the
longitudinal or hospital cohort and the predictors are carefully selected baseline or hospital outcome
variables available in both cohorts that appear to most strongly predict enrolment in the longitudinal
cohort. Study centre-level characteristics were not included in estimating weights as these were
predictive of differences in enrolment between centres, but not of patients within a given centre. The
probability of a patient belonging to the longitudinal cohort compared to the hospital cohort estimates
2
the proportion of patients with similar characteristics who were enrolled in the longitudinal cohort. So
for example, if patient A in the longitudinal cohort had half the probability of being selected as patient B,
then patients with characteristics similar to patient A are underrepresented in the longitudinal cohort
compared to patients with characteristics similar to patient B by a factor of ½. By weighting the analysis
inversely to this proportion, we can use the longitudinal cohort to estimate population parameters from
the unselected hospital cohort. This IPW approach is frequently used for dealing with missing data or
non-representative samples surveys1.
In an unadjusted analysis, we compared all common baseline characteristics and hospital outcomes
between the hospital and longitudinal cohort (table 1 and 2 main manuscript). Variables different
between the cohorts at p<0.25 were treated as candidate variable in a backward stepwise logistic
regression with entry and exit criteria of 0.15. Variables that were redundant (for example hospital
mortality was considered instead of ICU mortality) or which reflected data collection artefacts rather
than patient characteristics were not considered in the model. For example, centre was a strong
predictor of being in the longitudinal cohort but we did not include this in our model because centre
reflects differences in study management between centres rather than differences in the characteristics
of patients in the longitudinal and hospital cohorts. Strong interactions were considered and the
linearity of continuous variables was assessed. When necessary, continuous variables were represented
by a restricted cubic spline with knots selected based on prior understanding of the data2.
Odds ratios of the final selected model are presented. The model’s goodness of fit (calibration) is
depicted by a calibration plot and tested by the Hosmer-Lemeshow goodness of fit test. The ability to
discriminate between the two cohorts is summarized by the c-statistic (i.e. area under the receiver
operating curve, a.k.a. the concordance index). The more the patient characteristics differ between the
two cohorts, the higher the c-statistics will be and the stronger the effect of the IPW will be. On the
other hand, if the model does not discriminate at all (c-statistic = 0.5) then this implies the two cohorts
are similar on the observed patient characteristics and IPW is unnecessary and will not alter the results.
Correction for bias due to loss to follow-up among longitudinal cohort
Of the 610 patients participating in the longitudinal cohort 17% have unknown 12 month mortality or
return to baseline PF status. We have the primary outcome collected at baseline, 3, 6 and 9 months.
Some baseline characteristics, and especially the earlier measures of outcome, were strongly correlated
with the final 12 month primary outcome making this dataset a good candidate for multiple imputation
(MI)3.
We used fully conditional multiple imputation with a logistic model to multiply impute the primary
outcome of 12-month PF recovery while allowing for arbitrary missing pattern among the other
variables4. In addition to PF recovery, the imputation model included: age, APACHE 2, primary admission
diagnosis, Charlson comorbidity index, IQ code, and the SF-36 PF domain at months 3, 6, 9 and 12. The
model was implemented by the FCS statement of PROC MI in SAS Version 9.45. One hundred randomly
imputed datasets were created and analyzed and results were combined according to the method of
Rubin6.
3
By assuming that the multivariate correlation structure of the missing data is similar to that among the
observed data, MI randomly imputes values of the missing data from their expected distribution
conditional on the observed data. Thus MI assumes that the outcome is missing at random after
conditioning on all observed data. This assumption, known as missing at random (MAR), is weaker and
much more realistic than the missing completely at random assumption (MCAR) required by complete
case analysis. For example, if patients with higher PF recovery rates were more likely to be lost to
follow-up then the data would not be MCAR, but would be MAR if those same patients had observed
information that was predictive of their unobserved PF recovery rate.
Sensitivity analysis
The IPW and MI methods should reduce bias, and could entirely eliminate bias if the IPW weighting
model and the MI model are correct. Both methods make the MAR assumption. Unfortunately, there is
no way to test the MAR assumption and biases could remain if the data is not missing at random
(NMAR). Therefore, we have used a pattern mixture approach to perform a sensitivity analysis to assess
the possible range of 12 month survival and PF recovery given the amount of missing data7. The pattern
mixture approach is simple, intuitive, transparent and allows us to model the outcome over the entire
possible range of missing data assumptions.
With the pattern mixture approach, we model the unknown true sample value as a weighed mixture of
the observed and missing data. For example, in the simple case of a binary proportion, the true sample
proportion Ptrue=m*Pmiss+(1-m)*Pobs where m is the proportion of missing data, Pobs is the proportion
among observed data and Pmiss is the unobserved proportion among the missing data. By plotting Ptrue (yaxis) versus the possible range of Pmiss (x-axis), we can see what the true value would be under the entire
range of possible missing values, and we can assess we how much Pmiss would have to differ from Pobs to
induce meaningful changes in Ptrue.
Since our primary outcome is a composite of survival and PF recovery among survivors, we have created
a contour plot which shows the true PF recovery rate across the possible range of survival and PF
recovery among survivors. In this contour plot, the x-axis and y-axis represent the survival rate and the
PF recovery rate of survivors respectively among the patients lost to follow-up. Contours on the plot
depict the resulting overall true PF recovery rate.
Impact of missing data on logistic regression models
We used inverse weighting in our logistic regression models so that our longitudinal cohort could be
used to make inference to the unselected hospital cohort. This was necessary because when both
predictors and outcomes are missing, as is the case when an entire patient is not represented in the
sample, then logistic regression can provide biased estimates.
However, with logistic regression we do not need to worry about bias due loss to follow-up among the
longitudinal cohort. This is because if no predictors are missing, as is essentially our case, the odds ratio
estimates from logistic regression remain unbiased even when the outcome is NMAR. 8 For this reason,
we did not perform multiple imputation or sensitivity analysis on the logistic regression models. The
4
estimates of odds and risks derived from the logistic regression would be biased if the outcome was
NMAR, but we only report odds ratios which remain unbiased.
Results
Patient flow
Figure 1a depicts the patient selection to the longitudinal and hospital cohorts. Figure1b shows the
follow-up among the longitudinal cohort. 610 patients were enrolled into the longitudinal cohort. 103
patients were lost to follow-up by one year and 2 patients missed their assessment of baseline physical
functioning leaving 505 of 610 (83%) patients evaluable for the primary outcome of recovery to baseline
physical functioning. Most of the baseline characteristics of the 505 patients with known primary
outcome were similar to the 105 with unknown primary outcome, except patients missing their primary
outcome were on average 1 year younger and had a SOFA score one point lower. Although a similar
proportion of patients missing their primary outcome lived at home before hospital admission, they
were more likely to have lived with a family member then alone compared to patients with known 12month PPS change. Table 2 shows that some hospital outcomes differed between patients with known
and unknown primary outcome. This is expected since the primary outcome is known for any patient
who died in the hospital. Thus the ICU and hospital mortality rate is zero among patient lost to followup, because they survived at least till hospital discharge, compared to 17% and 31% among completers.
Inverse probability weighting so longitudinal cohort reflects unselected
hospital cohort
Table 3 provides the model selected to estimate the probability of belonging to the longitudinal cohort
compared to the unselected hospital cohort. In particular, higher APACHE II and increased mortality
were independently associated with a lower chance of being enrolled in the longitudinal cohort, but use
of vasoactive drugs, longer hospital stay and live discharge from the hospital were associated with a
greater chance of being enrolled in the longitudinal cohort.
Site was a strong predictor of enrolment, but we decided to leave it out of the model because it
reflected differences in study management between sites rather than differences in the characteristics
of patients in the two cohorts. Furthermore, since centre enrolment rates varied from 72% to 0%,
including centre in the model resulted in some patients being weighted over a hundred times more than
others. Finally, we noted that when centre was included in the prediction model, the corresponding
weighting scheme resulted in estimates of 12 month mortality and PF recovery that were essentially
unchanged from the unweighted estimates confirming our concern that the prediction model including
centre was representing something other than differences between the patient populations of the
hospital and longitudinal cohorts.
Figure 2 shows the non-linear association between hospital length of stay and probability of being
enrolled in the longitudinal cohort. The knots were selected a-priori at 2, 7 and 14 days; there was a
known threshold at 7 days because the recruitment focused on patients in the ICU for less than 7 days.
5
Figure 3 shows the calibration plot of the actual cohort membership (y-axis) versus the predicted
membership (x-axis). The 610 points near the top of the figure represent patients in the longitudinal
cohort, while the 894 points near the bottom of the figure represent the patients in the hospital cohort.
The points have been randomly jittered slightly so that they are easier to distinguish. The nonparametric LOESS smoother shows the local proportion of actual membership in the longitudinal cohort
against the model prediction. The dotted 45 degree line represents perfect calibration. It may be seen
that the calibration of this model in this sample is excellent. Also it may be noted that the cohorts
overlap slightly over the entire range of predicted probabilities which is required for the longitudinal
cohort to be able to estimate the hospital cohort. The points in the top left of the figure represent the
relatively few subjects in the longitudinal cohort with low probability of enrolment. These patients will
be weighted more heavily than the relatively over-represented patients depicted at the top right of the
figure. For example, a patient with an estimated probability of 0.1 will be weighted 8 times higher than a
patient with a probability of 0.8. The inverse probability weights ranged from 1.3 to 11.2.
Figure 4 shows the Kaplan-Meier estimates of 12-month survival using the original unweighted data and
inverse probability weighting. As expected the survival is slightly lower in the weighed estimate
reflecting the lower survival in the hospital cohort compared to the observed longitudinal cohort. In
particular, the unweighted and weighed 12-month survival estimates were 56% and 50% respectively.
Both the weighted and unweighted Kaplan-Meier estimates still assume that censoring is uninformative;
that is that censoring time is unrelated to the mortality time. This assumption is addressed in the
sensitivity analysis.
Return to baseline physical functioning at 12 months (the primary outcome of this study) is defined as
alive with a SF-26 physical functioning (PF) domain least 10 points and not 10 points or more below
baseline. 103 of the 610 patients in the longitudinal cohort were lost to follow-up by 12 months and
two additional patient missed their baseline physical functioning assessment leaving a total of 505/610
(83%) of patients evaluable for this outcome. The unweighted and weighed estimates of this outcome
were 24% (95% CI, 18% to 30%) and 22% (95% CI, 15% to 29%) reflecting the longitudinal and overall
hospital cohorts respectively. Similar to the Kaplan-Meier survival estimates, the estimates of PF
recovery assume that the probability of being missing is unrelated to the rate of PF recovery. This may
or may not be true and leads us to our next section which may reduce potential bias by assuming only
that data is missing at random after controlling for other observed data (MAR) rather than missing
completely at random (MCAR). Our final section will then perform a sensitivity allowing for the data to
be not missing at random even after controlling for all observed data (NMAR).
Tables 4, 5 and 6 report the regression models after applying inverse probability weighting. In all cases,
the estimates remain similar and conclusions are unchanged from unweighted regression models
provided in the main manuscript.
Multiple Imputation
There was virtually no missing data at baseline (actually from 3 patients: 1 missing APACHE II, 2
unknown prior living arrangements, 1 missing IQcode and 2 missed baseline SF-36 PF. Five patients had
6
missing ethnicity, but ethnicity was not considered in any models). However, there was considerable
missing follow-up data. We observed that 58% of patients with an unknown 12-month PF recovery
status have at least one post baseline SF-36 PF score. Table 7 provides the rank-based Spearman
correlation among variables. In this table, patients who died were assigned a negative SF-36 PF score. It
may be seen that 12-month PF recovery and 12-month mortality are strongly correlated with the post
baseline PF scores. These correlations were exploited to perform multiple imputation and re-estimate
the primary outcome of 12-month PF recovery. By using multiple imputation our estimated 12 month
PF recovery rate increased by 2% for both the un-weighted and inverse probability weighted estimates.
This result is consistent with patients lost to follow-up having a slightly higher PF recovery rate which
could be in part due to these patients having a higher survival rate.
Sensitivity analysis of primary outcomes
Our primary estimate of 12-month mortality was 44% based on the Kaplan-Meier estimate. This
estimate censored the 103 patients with unknown 12-month mortality status at last follow-up. All
patients were followed at least until hospital discharge, and the average follow-up duration among the
103 patients with unknown survival status was 129 days. If no patients died after censoring then the
mortality rate would decrease only to 41%. On the other hand if the hazard rate doubled after a patient
was censored then the overall mortality rate would increase to 47%.
The contours in figure 5 depict the PF recovery across the entire possible range of missing survival and
recovery among survivors. The raw recovery rate among the observed values was 24%. The possible
range of PF recovery rates is from 20% to 37%, but such extremes are highly unlikely. If missing cases
had half the PF recovery rate as non-missing cases the then true overall recovery rate would reduce to
22%. Conversely if the recovery rate was twice as high among the patients with unknown recovery
status then the true recovery rate would be 29%. Our primary analysis used multiple imputation which
estimated a PF recovery rate of 26% before inverse probability weighting and 24% after weighting. In all
scenarios, it seems highly likely that the true PF recovery rate is between 22% and 29%.
Table 8 provides estimates of our primary outcome, PF recovery by 12 months, using: 1) various
methods to account for potential clustering by site, 2) with and without multiple imputation and 3) with
and without inverse probability weighting so the longitudinal cohort would reflect the unselected
hospital cohort. The method used to account for centre had no impact on the rate estimate and only a
slight impact on the width of the confidence intervals. Using multiple imputation consistently increased
the recovery rate by 2% while inverse probability weighting consistently decreased the recovery rate by
2%. These changes are consistent with our belief that the survival rate and by extension PF recovery
rate may be slightly higher among patients lost to follow-up but slightly lower in the unselected hospital
cohort than our more selected longitudinal cohort. Nevertheless, these differences are not clinically
important.
7
Conclusion
The estimates of 12-month mortality and PF recovery appeared to remain fairly insensitive to selection
bias, loss to follow-up bias and the statistical method used to account for between centre clustering. In
all scenarios, we found that patients over 80 years old and in the ICU for 24 hours had about a 1 in 2
chance of surviving one year after admission and about a 1 in 4 chance of surviving with the SF-36
physical functioning domain of at least 10 points and no more than 10 points below baseline.
The estimates in the logistic regression models remained similar after applying inverse probability
weighting, and are robust to loss to follow-up. In particular, the significant independent predictors of
higher 12-month PF recovery remained as: younger age, lower APACHE II score, primary ICU admission
for CABG or valve replacement, lower baseline PF score, lower Charlson co-morbidity index, and lower
frailty index; while patients with an admission diagnosis of stroke were much less likely to achieve a 12month PF recovery.
8
Figures
9
Figure 1a—Patient Flow Diagram (Chart abstraction and patient recruitment)
All consecutive patients > 80 years old were assessed for eligibility (n = 3064)
Patient already in longitudinal
cohort (n=610)
Site already met chart
abstraction quota (n=1393)
Not eligible for follow-up (n=1405)
614 ICU stay< 24 hours
420 Family caregiver did not visit the patient within
96 hours of ICU admission
258 Patient acutely dying
86 Family caregiver does not speak English or French
17 Family caregiver is paid to provide care
8 Patient is not a resident of Canada
2 Family caregiver < 18 yrs old
Eligible for follow-up (n=1659)
Consecutive hospital chart abstractions
(n=1061)
Eligible but excluded from follow-up
(n=1049)
Patient in ICU<24 hours
(n=167)
Hospital only cohort (n=894)
474 Missed the caregiver
464 Caregiver refused consent
44 Family dynamics precluded consent
67 Other
Longitudinal cohort (n =610)
10
Figure 1b—Patient Flow Diagram (Patient follow up)
Longitudinal cohort
(n =610)
Death or drop out in hospital (n=164)
85 died in ICU
73 died in hospital after ICU discharge
6 withdrew consent
Any quarterly follow-up data (n =446)
7 Refused
45 Lost
14 Missed
40 Died
18 Withdrew
9 Refused
55 Lost
8 Missed
70 Died
23 Withdrew
13 Refused
64 Lost
16 Missed
85 Died
27 Withdrew
5 Refused
57 Lost
6 Missed
95 Died
29 Withdrew
3-month follow-up
322-Completed follow-up
198-Died
90-Missing
6-month follow-up
281-Completed follow-up
228-Died
101-Missing
9-month follow-up
241-Completed follow-up
243-Died
126-Missing
12-month follow up
254-Completed follow-up
253-Died
103-Missing
505 patients evaluable for
physical recovery at one year
11
Figure 2: Non-linear but monotonic association between days in hospital and probably of
being in longitudinal cohort (knots placed at 2, 7 and 14 days)
Shaded area is 95% confidence interval. Circles represent actual days in hospital of patients in the
hospital cohort (y=0) and longitudinal cohort (y=1). The restricted cubic spline with 3 knots used 2
degrees of freedom. The adequacy of fit was confirmed by a non-parametric loess smooth (not shown).
12
Figure 3: Calibration plot of model used to calculate inverse probability weights
13
Figure 4: Kaplan-Meier curves with and without inverse probability weighting
14
0.8
0.
33
0.6
0.2
Observed
X recovery
rate
0.3
1
0.2
8
9
7
0.2
0.4
0.
34
0.
32
0.
3
0.2
0.
35
6
0.2
0.24
0.25
0.23
0.22
0.21
0.0
Assumed PF recovery rate among survivors with uknown status
1.0
Fgiure 5: Sensitivity anlaysis of physical recovery
0.0
0.2
0.4
0.6
0.8
1.0
Assumed survival rate among 103 patients with unknown survival status
15
Tables
16
Table 1: Baseline Characteristics of Study Patients (Completers vs. LTFU)
Age
Sex
Male
Female
Admission APACHE II Score
Baseline SOFA
Charlson Co-morbidity Index
Co-morbidity of Cancer
Co-morbidity of Dementia
Frailty Index
Fit: <0.2
Mild: 0.2 to 0.4
Moderate/Severe: >0.4
Baseline PF score
Admission type
Medical
Surgical elective
Surgical emergency
Primary ICU admitting diagnosis
Cardiovascular/vascular
Respiratory
Sepsis
Gastrointestinal
Stroke
Neurologic
Trauma
Metabolic
Hematologic
CABG/valve replacement
Renal
Gynecologic
Orthopedic
Patient’s residential living status before this
hospital admission
Lives alone at home
Lives with family member at home
Lives with someone else
Lives in a supervised residence setting
Lives in a nursing home
Missing
Ethnicity
Asian/Pacific Islander
African/Black North American
Caucasian
East Indian
Native Canadian
Other (specify)
Missing
Completers
(n=505)
85±3 (80-99)
LTFU
(n=105)
84±3 (80-94)
285 (56.4%)
220 (43.6%)
22±7 (7-49)
6±3 (0-15)
2±2 (0-11)
113 (22%)
31 (6%)
0.3±0.1 (0.0-0.6)
202 (40.0%)
208 (41.2%)
95 (18.8%)
40± 30 (0-100)
53 (50.5%)
52 (49.5%)
21±6 (9-36)
5±3 (0-11)
2±2 (0- 8)
19 (18%)
8 (8%)
0.3±0.1 (0.0-0.7)
48 (45.7%)
39 (37.1%)
18 (17.1%)
44± 30 (0-100)
317 (62.8%)
69 (13.7%)
119 (23.6%)
60 (57.1%)
14 (13.3%)
31 (29.5%)
72 (14.3%)
84 (16.6%)
113 (22.4%)
95 (18.8%)
21 (4.2%)
16 (3.2%)
36 (7.1%)
7 (1.4%)
14 (2.8%)
39 (7.7%)
1 (0.2%)
1 (0.2%)
6 (1.2%)
22 (21.0%)
10 (9.5%)
22 (21.0%)
15 (14.3%)
6 (5.7%)
4 (3.8%)
10 (9.5%)
1 (1.0%)
4 (3.8%)
10 (9.5%)
1 (1.0%)
0 (0.0%)
0 (0.0%)
p
values
0.06
0.26
0.15
0.04
0.40
0.33
0.57
0.49
0.56
0.18
0.43
0.49
0.01
147 (29.1%)
186 (36.8%)
99 (19.6%)
53 (10.5%)
19 (3.8%)
1 (0.2%)
18 (17.1%)
54 (51.4%)
22 (21.0%)
5 (4.8%)
5 (4.8%)
1 (1.0%)
21 (4.2%)
7 (1.4%)
455 (90.1%)
8 (1.6%)
7 (1.4%)
4 (0.8%)
3 (0.6%)
5 (4.8%)
0 (0.0%)
92 (87.6%)
3 (2.9%)
1 (1.0%)
2 (1.9%)
2 (1.9%)
0.61
17
Legend: This table compares completers (patients with known 12-month primary outcome) to patients
LTFU (patients with unknown 12-month primary outcome). Statistics are mean ± standard deviation
(min-max) or count (%). P-values are from the Wilcoxon-Mann-Whitney test for continuous variables
and the Chi-Squared test for categorical variables. LTFU: lost to follow-up; APACHE II: Acute Physiology
and Chronic Health Evaluation score; PF: physical function; SOFA: Sequential Organ Failure Assessment
scores. N/A: Not assessed in the Hospital cohort.
18
Table 2: Clinical outcomes (Completers vs. LTFU)
Patients undergoing non-invasive
mechanical ventilation
Average duration of non-invasive
mechanical ventilation
Patients undergoing invasive
mechanical ventilation
Average days of invasive mechanical
ventilation
Patients receiving vasoactive drugs in
ICU
Average days of vasoactive drugs
Initial ICU LOS (days)
Total ICU LOS (days)
Patients who had at least one ICU
readmission
Patients discharged from ICU to
intermediate care unit
Number of intermediate care unit
admissions after index ICU admission
Average days of each intermediate
care unit stay
Total Hospital LOS (days)
ICU mortality
Hospital mortality
Discharged from hospital among survivors:
Ward in another hospital
ICU in another hospital
Long term care facility
Home
Rehab
Palliative Care
Other
Discharged home among patients living at
home before hospitalization:
Fit: <0.2
Mild: 0.2 to 0.4
Moderate/Severe: >0.4
Completers
(n=505)
LTFU
(n=105)
p values
98 (19.4%)
11 (10.5%)
0.03
2 [1 to 4] (1-39)
2 [1 to 4] (1-5)
0.36
362 (71.7%)
77 (73.3%)
0.73
5 [2 to 10] (1- 116)
3 [2 to 9] (1-44)
0.03
312 (61.8%)
60 (57.1%)
0.38
3 [2 to 5] (1-28)
6 [3 to 10] (1-95)
6 [3 to 11] (1-95)
2 [1 to 4] (1-18)
5 [3 to 7] (1-40)
5 [3 to 8] (1-40)
0.007
0.10
0.09
39 (7.7%)
6 (5.7%)
0.47
88 (17.4%)
25 (23.8%)
0.13
1.2±0.6 (1-4)
1.2±0.5 (1-3)
0.64
6 [3 to 8] (1-52)
5 [3 to 10] (2-87)
0.85
21[11 to 39] (1-185)
85 (16.8%)
158 (31.3%)
n=347
104 (30.0%)
8 (2.3%)
60 (17.3%)
147 (42.4%)
22 (6.3%)
1 (0.3%)
5 (1.4%)
22[12 to 49] (3-202)
0 (0.0%)
0 (0.0%)
n=105
28 (26.7%)
3 (2.9%)
21 (20.0%)
50 (47.6%)
3 (2.9%)
0 (0.0%)
0 (0.0%)
0.21
<0.001
<0.001
0.57
135/432 (31.1%)
44/94 (46.8%)
0.004
68/189 (50%)
49/180 (36%)
18/63 (13%)
24/47 (55%)
18/34(41%)
2/13 (5%)
P=0.12*(completers)
P=0.08* (LTFU)
Legend: This table compares completers (patients with known 12-month primary outcome) to patients
LTFU (patients with unknown 12-month primary outcome). Statistics are median [Q1-Q3] (min-max),
mean±standard deviation (min-max) or count (%). Except where noted, p-values are from the WilcoxonMann-Whitney test for continuous variables and the Chi-Squared test for categorical variables.
LTFU: lost to follow-up; SOFA –Sequential Organ Failure Assessment; LOS-Length of stay; ICU-Intensive
Care Unit;
*P value represents a test of significance across the three frailty groups by the Cochran-Armitage Trend
Test.
19
Table 3: Logistic model used to derive probability of patients being in longitudinal cohort.
Selected Predictor
OR (95% CI)
APACHE II score (per 10 points)
0.86 (0.73-1.02)
Received vasoactive drugs in ICU
1.56 (1.23-1.98)
Days in hospital (non-linear)
See figure 2
Hospital discharge disposition
Death
Referent
Home
1.41 (1.06-1.87)
Other hospital
1.82 (1.33-2.49)
Long term care facility
1.14 (0.79-1.63)
Rehab
4.76 (2.15-10.57)
Palliative care or other
1.54 (0.50-4.74)
Total model degrees of freedom/events =9/610
c-statistic = 0.64
Hosmer-Lemeshow goodness of fit test p=0.80
p-value
0.074
<0.001
<0.001
<0.001
Odds ratio >1 indicates that the characteristic is associated with an
increased rate of enrolment in the longitudinal cohort.
20
Table 4: Logistic regression models predicting 12-month Physical Recovery after applying inverse probability weighting
Single Predictor
OR (95% CI)
c*
0.85 (0.70, 1.02)
0.53
0.75 (0.52, 1.09)
0.53
0.48 (0.32, 0.72)
0.62
0.87 (0.61, 1.25)
0.52
0.69 (0.48, 0.97)
0.54
0.64
4.71 (2.94, 7.54)
1.94 (1.05, 3.58)
0.63
5.23 (2.93, 9.36)
0.97 (0.39, 2.43)
1.69 (0.61, 4.64)
0.48 (0.17, 1.32)
0.73 (0.35, 1.55)
0.65 (0.25, 1.68)
0.18 (0.02, 1.61)
0.63 (0.22, 1.81)
1.16 (0.88, 1.53)
0.51
0.60 (0.48, 0.74)
0.60
0.73 (0.54, 0.99)
0.59
0.44 (0.33, 0.58)
0.63
Multivariable Predictor
Model
OR (95% CI)
P-value
0.79 (0.61, 1.02)
0.07
0.82 (0.54, 1.25)
0.36
0.48 (0.26, 0.89)
0.02
1.05 (0.69, 1.61)
0.81
0.72 (0.45, 1.14)
0.16
0.43
1.65 (0.75, 3.62)
1.67 (0.67, 4.17)
<0.0001
4.46 (2.14, 9.29)
0.98 (0.42, 2.30)
0.98 (0.33, 2.92)
0.63 (0.23, 1.71)
1.00 (0.33, 3.00)
1.13 (0.36, 3.48)
0.09 (0.01, 0.81)
0.46 (0.13, 1.64)
0.35 (0.24, 0.50)
<0.0001
0.74 (0.58, 0.95)
0.02
0.95 (0.71, 1.28)
0.75
0.31 (0.18, 0.51)
<0.0001
Variables
P-value
Age (per 5 years)
0.08
Sex (Male vs. Female)
0.14
APACHE II score (per 10 points)
0.0003
Marital status (Married or living as married vs. Other)
0.46
Baseline SOFA score (per 5 points)
0.03
Admission type (Medical vs. Surgical)
<0.0001
Surgical elective vs. Medical
Surgical emergency vs. Medical
Primary ICU diagnosis
<0.0001
CABG/Valve vs. Cardiovascular/vascular
Gastrointestinal vs. Cardiovascular/vascular
Neurologic vs. Cardiovascular/vascular
Other vs. Cardiovascular/vascular
Respiratory vs. Cardiovascular/vascular
Sepsis vs. Cardiovascular/vascular
Stroke vs. Cardiovascular/vascular
Trauma vs. Cardiovascular/vascular
Baseline PF score (per 50 points)
0.30
Charlson Comorbidity Index (per 2 units)
<0.0001
IQCODE at baseline (per 0.5 point)
0.04
Frailty Index (per 0.2 point)
<0.0001
Family preferences for life sustaining treatment
0.72 (0.27, 1.95)
Comforts measures vs. other
0.71 (0.27, 1.86)
0.53
0.49
0.52
**Total model degrees of freedom/events
1 to 8/123
20/123
*c-statistic
0.51 to 0.64
0.78
Legend: The outcome of this model alive and with Physical Function (PF) no lower than 10 points below baseline. OR>1 indicate favorable
association. Higher score for all scales means a worse outcome with the exception of PF where a higher score is a better outcome.
Predictors with p≤0.05 are in bold.
The total sample size ranged from 505 in some single predictor models to 502 in the full models due to 3 patients with missing covariates.
OR-Odds ratio; CI-Confidence interval; FI-Frailty Index; APACHE II: Acute Physiology and Chronic Health Evaluation score; SOFA: Sequential
Organ Failure Assessment scores; IQCODE: Informant Questionnaire on Cognitive Decline in the Elderly; ICU: Intensive Care Unit
21
Table 5: Logistic regression models predicting 12-month survival after applying inverse probability weighting
Variables
Age (per 5 years)
Sex (Male vs. Female)
APACHE II score (per 10 points)
Marital status (Married or living as married vs. Other)
Baseline SOFA score (per 5 points)
Admission type (Medical vs. Surgical)
Surgical elective vs. Medical
Surgical emergency vs. Medical
Primary ICU diagnosis
CABG/Valve vs. Cardiovascular/vascular
Gastrointestinal vs. Cardiovascular/vascular
Neurologic vs. Cardiovascular/vascular
Other vs. Cardiovascular/vascular
Respiratory vs. Cardiovascular/vascular
Sepsis vs. Cardiovascular/vascular
Stroke vs. Cardiovascular/vascular
Trauma vs. Cardiovascular/vascular
Baseline PF score (per 50 points)
Charlson Comorbidity Index (per 2 units)
IQCODE at baseline (per 0.5 point)
Frailty Index (per 0.2 point)
Family preferences for life sustaining treatment
Comforts measures vs. other
**Total model degrees of freedom/deaths
*c-statistic
Single Predictor
OR (95% CI)
c*
P-value
0.92 (0.75, 1.14)
0.51
0.46
0.66 (0.49, 0.88)
0.55
0.005
0.45 (0.35, 0.59)
0.63 <0.0001
0.89 (0.71, 1.12)
0.52
0.33
0.54 (0.41, 0.73)
0.59 <0.0001
4.53 (2.34, 8.78)
1.73 (1.12, 2.66)
9.17 (3.35, 25.14)
0.77 (0.40, 1.49)
2.07 (0.77, 5.56)
0.70 (0.27, 1.81)
0.73 (0.37, 1.45)
0.53 (0.28, 0.97)
0.86 (0.50, 1.49)
1.24 (0.55, 2.82)
1.67 (1.28, 2.17)
0.61 (0.49, 0.75)
0.85 (0.71, 1.02)
0.46 (0.39, 0.55)
0.59 (0.34, 1.05)
1 to 8/252
0.51 to 0.65
0.61
<0.0001
0.62
<0.0001
0.58
0.63
0.56
0.65
0.0001
<0.0001
0.08
<0.0001
0.54
0.07
Multivariable Predictor Model
OR (95% CI)
P-value
0.92 (0.71, 1.20)
0.55
0.70 (0.47, 1.04)
0.08
0.54 (0.39, 0.74)
0.0001
1.08 (0.77, 1.52)
0.65
0.65 (0.40, 1.05)
0.08
0.37
1.35 (0.70, 2.63)
1.29 (0.78, 2.13)
<0.0001
8.21 (2.77, 24.35)
0.76 (0.35, 1.66)
1.01 (0.42, 2.41)
1.09 (0.42, 2.84)
0.87 (0.36, 2.09)
0.74 (0.36, 1.51)
0.49 (0.26, 0.95)
0.99 (0.43, 2.29)
0.88 (0.56, 1.39)
0.59
0.74 (0.58, 0.94)
0.02
1.04 (0.85, 1.27)
0.70
0.56 (0.37, 0.85)
0.007
0.53 (0.31, 0.91)
20/252
0.75
0.02
The total sample size ranged from 505 in some single predictor models to 502 in the full models due to 3 patients with some missing
covariates.
OR-Odds ratio; CI-Confidence interval; FI-Frailty Index.
The outcome of this model is survival at 12 months. OR>1 indicate favorable association.
Predictors with p≤0.05 are in bold.
22
Table 6: Linear regression models predicting 12-month SF-36 physical function scores among survivors after applying inverse
probability weighting
Variables
Age (per 5 years)
Sex (Male vs. Female)
APACHE II score (per 10 points)
Marital status (Married or living as married vs. Other)
Baseline SOFA score (per 5 points)
Admission type (Medical vs. Surgical)
Surgical elective
Surgical emergency
Medical
Primary ICU diagnosis
CABG/Valve
Gastrointestinal
Neurologic
Other
Respiratory
Sepsis
Stroke
Trauma
Cardiovascular/vascular
Baseline PF score (per 50 points)
Charlson Comorbidity Index (per 2 units)
IQCODE at baseline (per 0.5 point)
Frailty Index (per 0.2 point)
Family preferences for comfort measures vs. Other
SE - Standard error.
Predictors with p≤0.05 are in bold
Single Predictor
Estimate (SE)
P-value
-4.2 (1.6)
0.02
-1.9 (2.6)
0.47
-11.2 (2.4)
0.0001
5.9 (3.6)
0.12
-7.4 (3.1)
0.02
0.0002
32.9 (7.3)
9.0 (3.8)
Referent
<0.0001
34.7 (6.2)
-6.2 (7.2)
4.9 (10.8)
-14.8 (7.0)
-9.5 (6.8)
-10.7 (7.5)
-16.1 (6.3)
-2.7 (8.4)
Referent
20.9 (2.7)
<0.0001
-7.2 (0.9)
<0.0001
-6.2 (1.9)
0.004
-18.7 (2.0)
<0.0001
-12.0 (5.1)
0.03
Multivariable
Estimate (SE)
P-value
-1.4 (1.7)
0.43
-5.4 (2.8)
0.07
-7.3 (2.2)
0.004
6.2 (3.0)
0.05
-4.9 (2.8)
0.09
0.40
8.4 (6.3)
-0.5 (4.1)
Referent
0.0003
27.8 (6.1)
-1.8 (5.4)
-5.4 (9.0)
-3.0 (4.9)
-7.4 (6.5)
-2.5 (6.1)
-21.7 (5.5)
-5.2 (7.1)
Referent
12.1 (3.2)
0.001
-2.5 (1.7)
0.15
-1.1 (1.0)
0.26
-5.2 (2.9)
0.09
-7.9 (3.5)
0.04
23
Month 12 montality
Hosital Mortality
PF M0
PF M3
PF M6
PF M9
PF M12
ApacheII
Frailty Index
Charleson Co-Index
Comfort Care
PF Recovery
M12 Mortality
Hosital Mortality
PF M0
PF M3
PF M6
PF M9
PF M12
ApacheII
Frailty Index
Charleson Index
Comfort Care
PF Recovery
Table 7: Pearson correlation matrix:
1.00
-0.57
-0.38
0.02
0.56
0.60
0.62
0.69
-0.18
-0.20
-0.15
-0.06
-0.57
1.00
0.68
-0.14
-0.80
-0.85
-0.87
-0.87
0.23
0.25
0.23
0.10
-0.38
0.68
1.00
-0.05
-0.83
-0.85
-0.88
-0.87
0.23
0.11
0.11
0.11
0.02
-0.14
-0.05
1.00
0.25
0.27
0.32
0.30
-0.11
-0.69
-0.22
-0.14
0.56
-0.80
-0.83
0.25
1.00
0.94
0.95
0.91
-0.30
-0.33
-0.19
-0.15
0.60
-0.85
-0.85
0.27
0.94
1.00
0.98
0.95
-0.28
-0.35
-0.21
-0.14
0.62
-0.87
-0.88
0.32
0.95
0.98
1.00
0.97
-0.28
-0.40
-0.22
-0.15
0.69
-0.87
-0.87
0.30
0.91
0.95
0.97
1.00
-0.27
-0.37
-0.23
-0.16
-0.18
0.23
0.23
-0.11
-0.30
-0.28
-0.28
-0.27
1.00
0.13
0.12
-0.10
-0.20
0.25
0.11
-0.69
-0.33
-0.35
-0.40
-0.37
0.13
1.00
0.40
0.11
-0.15
0.23
0.11
-0.22
-0.19
-0.21
-0.22
-0.23
0.12
0.40
1.00
0.00
-0.06
0.10
0.11
-0.14
-0.15
-0.14
-0.15
-0.16
-0.10
0.11
0.00
1.00
Table 8: Estimates of 12 month PF recovery rate with 95% confidence intervals.
Method used to account for
Treatment of missing
potential clustering by site
responses
Ignore site
Exclude missing cases
Ignore site
Multiple imputation
Treat site as primary sampling unit Exclude missing cases
Treat site as primary sampling unit Multiple imputation
GEE clustered by site (robust SE)
Exclude missing cases
GEE clustered by site (robust SE)
Multiple imputation
Site as random effect (REML)
Exclude missing cases
Site as random effect (REML)
Multiple imputation
In the bold row are the estimates reported in our manuscript.
Unweighted
24% (21%-28%)
26% (22%-30%)
24% (18%-30%)
26% (21%-31%)
24% (19%-30%)
26% (22%-31%)
24% (19%-30%)
26% (21%-31%)
Weighted to
reflect hospital
cohort
22% (18%-25%)
24% (20%-30%)
22% (15%-29%)
24% (18%-30%)
20% (14%-28%)
24% (18%-31%)
Not estimable
Not estimable
24
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