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Dynamic Prediction of Transition to Psychosis Using Joint Modelling
1,2H. P. Yuen, MSc*3,4A. Mackinnon, PhD1,2J. Hartmann, PhD1,2G. P. Amminger, MD, PhD (Habil)1,2C. Markulev, M Psych Clin1,2S. Lavoie, PhD1M. R. Schäfer, MD1,2,5A. Polari, MD, FRANZCP6N. Mossaheb, MD7M. Schlögelhofer, MA8S. Smesny, MD, PhD9I. B. Hickie MD10G. Berger, MD11E. Y. H. Chen, MD12L. de Haan, MD, PhD12D. H. Nieman, PhD13M. Nordentoft, MD, PhD14A. Riecher-Rössler, MD, PhD15S. Verma, MD1,16A. Thompson, MD, MBBS1,17A. R. Yung, MD, FRANZCP1,2P.D. McGorry, MD, PhD1,2B. Nelson, PhD1Orygen, The National Centre of Excellence in Youth Mental Health, Melbourne, Australia2Centre for Youth Mental Health, The University of Melbourne, Australia3Centre for Mental Health, Melbourne School of Population and Global Health, The University of Melbourne, Australia.4Black Dog Institute and University of New South Wales, New South Wales, Australia.5Orygen Youth Health, Melbourne, Australia.6Department of Psychiatry and Psychotherapy, Clinical Division of Social Psychiatry, Medical University of Vienna, Austria7Department of Child and Adolescent Psychiatry, Medical University of Vienna, Austria8University Hospital Jena, Germany9Brain and Mind Research Institute, University of Sydney, Australia10Child and Adolescent Psychiatric Service of the Canton of Zurich, Zurich, Switzerland11Department of Psychiatry, University of Hong Kong, Hong Kong12Academic Medical Center, Amsterdam, the Netherlands13Mental Health Centre Copenhagen, Mental Health Services in the Capital Region, Copenhagen University Hospital, Denmark14Psychiatric University Clinics Basel, Basel, Switzerland15Department of Psychosis, Institute of Mental Health, Singapore, Singapore16Division of Mental Health and Wellbeing, Warwick Medical School, University of Warwick, Coventry, England, and North Warwickshire Early Intervention in Psychosis Service, Coventry and Warwickshire NHS Partnership Trust, England17Institute of Brain, Behaviour and Mental Health, University of Manchester, Manchester, UK, and Greater Manchester West NHS Mental Health Foundation Trust, Manchester, England
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*Corresponding author:Hok Pan YuenOrygen, The National Centre of Excellence in Youth Mental Health,Locked Bag 10, ParkvilleVictoria 3052Australia+61 3 9342 2975Email address: [email protected]
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Abstract
Considerable research has been conducted seeking risk factors and constructing prediction
models for transition to psychosis in individuals at ultra-high risk (UHR). Nearly all such
research has only employed baseline predictors, i.e. data collected at the baseline time point,
even though longitudinal data on relevant measures such as psychopathology have often been
collected at various time points. Dynamic prediction, which is the updating of prediction at a
post-baseline assessment using baseline and longitudinal data accumulated up to that
assessment, has not been utilized in the UHR context. This study explored the use of dynamic
prediction and determined if it could enhance the prediction of frank psychosis onset in UHR
individuals. An emerging statistical methodology called joint modelling was used to
implement the dynamic prediction. Data from the NEURAPRO study (n=304 UHR
individuals), an intervention study with transition to psychosis study as the primary outcome,
were used to investigate dynamic predictors. Compared with the conventional approach of
using only baseline predictors, dynamic prediction using joint modelling showed significantly
better sensitivity, specificity and likelihood ratios. As dynamic prediction can provide an up-
to-date prediction for each individual at each new assessment post entry, it can be a useful
tool to help clinicians adjust their prognostic judgements based on the unfolding clinical
symptomatology of the patients. This study has shown that a dynamic approach to psychosis
prediction using joint modelling has the potential to aid clinicians in making decisions about
the provision of timely and personalized treatment to patients concerned.
Keywords: UHR, Transition to psychosis, Dynamic prediction, Joint modelling
Abstract word count: 247
Text body count: 4046
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HPY received support through an Australian Government Research Training Program
Scholarship. JH was supported by a University of Melbourne McKenzie Fellowship. BN was
supported by an NHMRC Senior Research Fellowship.
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1. Introduction
1.1 Background
Strategies for identifying people at ultra-high risk (UHR) of developing psychosis
(Klosterkötter, 2001; Schultze-Lutter et al., 2007; Schultze Lutter, 2009; Yung et al., 2004;
Yung, 1998; Yung et al., 1996) (otherwise termed ‘clinical high risk’) established over the
past twenty years have been an important step in providing early intervention to prevent or
mitigate the devastating effects of psychotic disorders. Upon receiving treatment, some of
these individuals will nevertheless progress to a psychotic disorder. Therefore much research
has focussed on identifying risk factors for transition to psychosis in UHR individuals.
Recent developments towards this goal include the use of machine learning (Koutsouleris et
al., 2015; Mechelli et al., 2016), Bayesian probabilistic models (Clark et al., 2016) and the
construction of risk calculators (Cannon et al., 2016; Fusar-Poli et al., 2017). These
developments, like nearly all past UHR research in the context of seeking risk factors for
transition, make use of baseline predictor variables, typically variables assessed at service
entry (Cannon et al., 2008; Nelson et al., 2013; Nieman et al., 2014; Ruhrmann et al., 2010;
Yung et al., 2004). Baseline predictor variables include fixed predictors whose values are
constant (such as gender) and the baseline values of measures (whose values can change over
time). However, the increasingly recognised changeable nature of psychopathology (Nelson
et al., 2017c; van Os, 2013) suggests that using only baseline information may be under-
utilizing the available information and limiting predictive ability. Hence interest has emerged
to investigate whether the changeable nature of psychopathology can be used to improve
prediction of the onset of psychosis (Nelson et al., 2017c; Yuen and Mackinnon, 2016; Yuen
et al., 2018). This is the idea behind dynamic prediction, which is to update prediction
continuously over time as more and more information about changes in patients’ conditions is
obtained. The aim of this paper is to apply dynamic prediction to a dataset on UHR
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individuals and to determine its potential usefulness over prediction based on baseline
predictors only.
1.2 Dynamic Prediction
Studies of psychosis prediction usually require follow-up of participants over time in order
to ascertain which individuals transition to psychosis and when they do so. The longitudinal
nature of these studies provides the opportunity to capture the changing characteristics of
psychopathology by conducting multiple assessments on various symptom measures over the
study period. Measures assessed repeatedly over time can be used to provide dynamic
prediction of the onset of psychosis and are called time-dependent predictors (TDPs) (or
covariates in some contexts). Specifically, dynamic prediction would be applied as follows.
Based on an existing dataset, appropriate fixed predictors and TDPs are used to construct a
dynamic prediction model. For a new patient, after the baseline assessments have been
completed, the patient’s data on the relevant fixed predictors and TDPs are input into the
dynamic prediction model to provide a risk estimate for the patient. At this point, only
baseline data is available and so only baseline data is used to estimate the risk. Based on the
risk estimate and any other relevant information, clinicians can make a decision about
indicated treatments. Assuming that the patient has not transitioned and is reassessed on a
subsequent occasion, say one month later, the patients’ data on the relevant fixed predictors
and TDPs are entered into the prediction model again to generate an updated risk estimate.
For this second round, the data of the TDPs used come from both the baseline and second
assessments. The updated risk estimate gives an indication of the current risk and how much
improvement or deterioration has occurred. The risk estimate can continue to be updated with
more longitudinal data of the TDPs obtained from further subsequent assessments until the
patient is discharged or transition occurs. Updated risk estimates can be used to make
decisions regarding modifying treatment type or intensity.
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In the past, a lack of suitable statistical methodology and software has impeded the use of
TDPs. Over the past two decades, statistical methodology that can combine the time-to-
transition aspect and the longitudinal aspect of TDPs in one model has emerged. The
methodology is called joint modelling (Chi and Ibrahim, 2006; Rizopoulos, 2012; Tang and
Tang, 2015; Tang et al., 2014). Corresponding software for implementing joint modelling has
also become available in mainstream statistical software packages (Gould et al., 2015; Yuen
and Mackinnon, 2016). With the advent of joint modelling and the corresponding software,
dynamic prediction has been examined in various areas of medicine (Ediebah et al., 2015;
Gueorguieva et al., 2012; Guler et al., 2014; Levine et al., 2015; Li et al., 2017; Mauguen et
al., 2015; Njagi et al., 2013; Pilla Reddy et al., 2012; Sweeting, 2017) but not in psychosis
prediction in UHR research. Our previous work has described the joint modelling
methodology and its use in the context of transition to psychosis (Yuen et al., 2018). In this
paper, we sought to determine whether dynamic prediction through joint modelling could
enhance the prediction of transition to psychosis among UHR individuals.
2. Methods
2.1 The Data
The data came from the NEURAPRO Study, which was a multi-centre placebo-controlled
randomized trial of the effect of omega-3 polyunsaturated fatty acids on transition rate and
other outcomes of UHR individuals. The intervention period was for 6 months. The sample
size was 304. There were in total 40 known transitions (see Supplement Section 1 for
definition of transition), 30 of which occurred within one year from baseline. No significant
difference was found between the two trial treatments in terms of transition rate and
symptomatic and functional outcomes. Details about the methodology of the study are
provided in Markulev et al (Markulev et al., 2017) and the results of the trial are reported in
McGorry et al (McGorry et al., 2017).
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Study assessments were conducted monthly during the first 6 months and then at months 9
and 12. In particular, these repeated assessments involved the following psychopathology
measures: Brief Psychiatric Rating Scale (BPRS) (McGorry et al., 1988), Montgomery
Asberg Depression Rating Scale (MADRS) (Montgomery and Asberg, 1979), Young Mania
Rating Scale (YMRS) (Young et al., 1978) and Scale for the Assessment of Negative
Symptoms (SANS) (Andreasen, 1982). These measurements were used as TDPs in
developing the dynamic prediction model.
In addition to TDPs, fixed predictors were also considered. They included: gender, age at
entry, duration between symptom onset and treatment/acceptance at UHR service, years of
education, ethnicity (Caucasian vs. non-Caucasian), migrant status (Yes=participant
immigrant or both parents immigrants and No=otherwise), recruiting site (Melbourne, Vienna
and other sites (Sydney, Basel, Zurich, Jena, Copenhagen, Hong Kong, Singapore and
Amsterdam)), functioning (Social and Occupational Functioning Assessment Scale (Goldman
et al., 1992) and Global Functioning: Social and Role Scales (Auther et al., 2006; Niendam et
al., 2006)) and Comprehensive Assessment of the At-Risk Mental State (Yung et al., 2005)
positive symptoms. The summary statistics of these variables and the baseline values of the
TDPs are presented in Table 1.
2.2 Joint Modelling
In joint modelling, the trajectories of the TDPs over time are estimated using linear mixed-
effects modelling (Fitzmaurice et al., 2011). The estimated trajectories are then incorporated
into the Cox regression framework (Lee and Wang, 2013) to enable the estimation of the
effects of TDPs on the risk of the event outcome (Rizopoulos, 2012), which is transition in
our context. The usual assumption underlying joint modelling is that the risk of transition
depends on the current values of the TDPs at any given time point. This is called the basic
joint model (Rizopoulos, 2012), which was used in this paper. Further information about joint
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modelling can be obtained from Rizopoulos (Rizopoulos, 2012) and Yuen et al (Yuen and
Mackinnon, 2016; Yuen et al., 2018).
The JM R package Version 1.4-0 (Rizopoulos, 2010; Rizopoulos, 2012) was used to
implement joint modelling. This package allows various specifications for the baseline hazard
of the Cox regression aspect. For the purpose of this paper, the baseline hazard was specified
as a piecewise-constant function, i.e. it was assumed to have different constant values at
different intervals over the timeframe concerned. Such a specification allows some degree of
flexibility because the baseline hazard is not assumed to be associated with any specific
probability distribution. The JM package also provides estimates for the survival probability,
which, in the present context, is the probability of remaining non-psychotic. The survival
probability can be estimated from a given joint model at a specified time for a particular
individual with particular values for the predictors concerned up to that point.
2.3 Analysis
The steps that were used in developing a dynamic prediction model of transition using
joint modelling were as follows. The level of significance used was 0.05.
1. An appropriate variable selection method was firstly used to determine which baseline
variables were significant predictors of transition. As different variable selection methods
could produce different results, both stepwise regression and least absolute shrinkage and
selection operator (LASSO) were used to provide a consistency check. Baseline variables
in this step included the fixed predictors mentioned above and baseline values of the
TDPs. Longitudinal information from the TDPs was not used in this step.
2. Joint modelling was then applied to determine the significance of each TDP individually
adjusting for the significant baseline predictors found in Step 1. The rationale underlying
this approach is that, since a prediction model based on only baseline data is simpler than
one based on longitudinal data, the latter would only be used if it could be shown that the
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longitudinal data enhances prediction significantly after adjusting for the contribution of
the significant baseline predictors.
3. Established joint modelling software accommodates only a single TDP. Accordingly, the
most significant TDP together with the significant baseline predictors found in step 1
were used to produce a prediction model using joint modelling. We refer to this as
JM_model.
In order to provide a benchmark for the joint model, a Cox regression prediction model using
only the significant baseline predictors found in step 1 was also included. We refer to this as
BL_model. The performance of the prediction models was then evaluated using the
procedure outlined below.
Prediction of transition within one year after entry was carried out using each of the
above two models. The timeframe of one year was used because the data only allowed the
estimation of the trajectories of the TDPs within this period. Prediction was carried out as
follows. For BL_model, the one-year survival probability for each individual was estimated
from the model. If the estimated survival probability was less than a specified cut-off value,
then the predicted one-year transition status was ‘yes’; otherwise it was ‘no’. The possible
cut-off values for the survival probability considered were 0, 0.01, 0.02, …, 1, i.e. the entire
probability range with increments of 0.01. For each cut-off probability, the predicted and
observed transition status for each individual were used to compute sensitivity and specificity
values.
For the joint model, the prediction of transition for each individual was determined by
estimating the one-year survival probability from the model incrementally. Specifically, for
each individual, a first estimation of the survival probability was made using the baseline
score of the TDP. If the estimated probability was less than a specified cut-off value, the
individual’s predicted one-year transition status was set as ‘yes’ and estimation stopped.
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Otherwise, a second estimation of the survival probability was made using the next available
follow-up score of the TDP together with its baseline score. Two conditions were considered
at this step. The first condition was whether the estimated survival probability fell below a
specified cut-off value. The second condition was whether the change in the estimated
survival probability compared with the estimated baseline survival probability was less than a
specified cut-off value. This second condition could indicate that insufficient improvement or
even deterioration had occurred in the patient’s condition. If either of these conditions were
satisfied, then the predicted one-year transition status was set as ‘yes’ and the estimation
stopped. Otherwise, the next follow-up score of the TDP together with all previous scores
were used in the next step to perform the prediction. This process continued until the
predicted transition status was set as ‘yes’ or until the scores were exhausted. Each of the two
conditions above had separate cut-off values. The entire probability range of 0 to 1 with
increments of 0.01 were used as possible cut-off values for the first condition. The second
condition pertained to change in probability and visual inspection of the estimated survival
probability values indicated that a reasonable range for the possible cut-offs was 0.1 to 0.1
with increments of 0.01. Sensitivity and specificity were computed for each combination of
the two sets of cut-off values.
The performance of the prediction models was compared using receiver operating
characteristic (ROC) curves. The area under the ROC curve (AUC) for each model was
computed using the trapezoidal rule. The significance of the difference between AUCs was
evaluated by estimating the standard deviation of the difference between the two AUCs using
500 bootstrap draws. The AUC difference divided by the standard deviation was then
compared to the normal distribution to provide a statistical test (Efron and Tibshirani, 1993).
Positive and negative likelihood ratios (Guyatt et al., 2015) were also used to compare the
prediction models.
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3. Results
The significant baseline predictors identified using stepwise Cox regression (step 1 above)
were baseline BPRS total (p=2×10-7), ethnicity (p=0.002) and migrant status (p=0.033). The
same variables were chosen using LASSO. Accordingly, BL_model was a Cox regression
prediction model consisting of these three variables. See supplement 2 for the significance of
the other baseline predictors after adjusting for these three chosen variables.
With the exception of BPRS total, the significance of each TDP was evaluated using joint
modelling after adjusting for baseline BPRS total, ethnicity and migrant status (step 2 above).
For the TDP BPRS total, the adjustment was done using ethnicity and migrant status only as
baseline BPRS total is part of the data of this TDP. The following TDPs were found to be
significant: BPRS total (p=4×10-8) and BPRS Psychotic subscale (p=0.001). See Table 2 for
the significance of the other TDPs. As BPRS total was the most significant TDP, JM_model
consisted of ethnicity, migrant status and BPRS total.
Figure 1 shows the ROC curves for the two models. It can be seen that the curve of
JM_model is completely above that of BL_model, i.e. it exhibits better prediction results. The
AUC of the joint model was significantly greater than that of the baseline model (p-
value=0.019). Figure 2 shows the likelihood ratios of the two models. Larger positive
likelihood ratios (LR+) and smaller negative likelihood ratios (LR–) indicate better
predictions. In the present context, a larger LR+ means a prediction of transition occurs more
frequently in transitioned cases than non-transitioned cases, whereas a smaller LR– means no
prediction of transition occurs less frequently in transitioned cases than non-transitioned
cases. As a general rule, LR+ should be greater than 2 and LR– should be less than 0.5 in
order to be practically useful: this desirable region is shown as the shaded region in Figure 2.
It can be seen that both models have points falling into the desirable region. However, all the
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points of BL_model in this region are surpassed by the points of the joint model in the sense
that the latter have better LR+ and/or LR- values.
To provide further insight into the advantage of joint modelling, the point in the ROC
curve closest to the ideal point (i.e. 100% true positive rate and 0% false positive rate) was
evaluated for JM_model and also for BL_model. For this point, the number of predicted
transitions were 97 and 88 respectively for JM_model and BL_model. The corresponding
sensitivity and specificity values were 82.8% and 72.4% respectively for JM_model and
69.0% and 73.8% respectively for BL_model. In this particular scenario, specificity was
about the same between the two models but JM_model showed a higher sensitivity, implying
that JM_model was able to detect more transitioned cases. Although the additional number of
transitions detected by JM_model in this scenario was 4, which was modest, it corresponded
to a 14 point gain in sensitivity with little loss in specificity. The TDP involved in JM_model
was BPRS total. Figure 3 shows the trajectories of BPRS total for these 4 cases. In this figure,
the highlighted point indicates the assessment point at which JM_model yielded a prediction
that transition would occur within the year. For all these cases, there was an early increase in
BPRS total, i.e. an early deterioration in terms of general psychopathology and transition was
correctly predicted at a post-baseline assessment.
4. Discussion and conclusion
4.1 Discussion
To date, psychosis prediction studies have relied on baseline assessment of relevant
variables. It has been argued that changes in measures over time should be taken into account
in predictive modelling, giving rise to dynamic prediction (Nelson et al., 2017c). Joint
modelling is a statistical tool that can incorporate the dynamic characteristics of
psychopathology into analysis of psychosis transition in the form of TDPs. Our previous
work showed that the effect of a TDP may be underestimated if only its baseline values are
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used (Yuen and Mackinnon, 2016; Yuen et al., 2018). The current paper has further shown
that the dynamic approach of prediction through joint modelling can provide a more powerful
means of prediction than the traditional static approach.
The model BL_model was developed using only baseline data. The model JM_model was
developed using joint modelling and allowed the incorporation of longitudinal data. The
results indicate that the joint model provided better sensitivity, specificity and likelihood
ratios than the baseline model. In the current dataset, those true positives detected by the joint
model at a post-baseline time point were identified quite early (within about two months from
entry). This shows that all the true positives detected by the joint model were identified either
at the baseline assessment or at a post-baseline assessment well before the actual time of
transition. The clinical implication of this result is that dynamic prediction may allow
sufficient time to implement an appropriate and targeted intervention to prevent the
occurrence of transition.
In order for dynamic prediction to be superior to prediction based on baseline data only,
two conditions need to be satisfied: (1) dynamic prediction must have better predictive ability
than baseline prediction and (2) dynamic prediction needs to identify true positive cases at a
time well before the actual time of transition so as to allow enough time to implement
appropriate interventions. Both conditions were satisfied in the analysis of the NEURAPRO
data. It is interesting to see that the best predictor turned out to be BPRS total, which is a
measure of general psychopathology. This result seems to suggest that an overall
psychopathology score may function as a stronger predictor than variables which are more
disorder-specific such as negative symptoms (SANS). This suggests the importance from a
clinical point of view of paying attention to persistence or increase in general
psychopathology as indicative of potential psychosis risk, and not to confine clinical attention
to symptom domains that are considered to be more central to psychotic disorders such as
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positive and negative psychotic symptoms. However, we note that there is inconsistency with
the findings of one of our previous studies, the Pace400 study (Nelson et al., 2013). In the
Pace400 study, we analysed predictors for transition to psychosis within a sample of about
400 UHR individuals and BPRS total did not appear to be a significant predictor. While it is
true that only fixed predictors were used in the Pace400 analysis and no dynamic prediction
was involved, BPRS total was a significant predictor even in the baseline model of the
current data. This inconsistency speaks to the importance of continuing to search for reliable
and replicable clinical predictors in this population (Nelson et al., 2017b). Another possible
reason for the inconsistency is that there were not enough transitions in the current data to
tease out the effects of a multiplicity of predictors. If there had been more transitions, it is
possible that some of the TDPs may have remained significant after adjusting for the fixed
predictors. Further research assembling large representative UHR samples with longitudinal
data should be a priority in future exploration of dynamic prediction models.
It is possible to construct a risk calculator for transition using joint modelling in a similar
way as others have done using baseline predictors (Cannon et al., 2016; Fusar-Poli et al.,
2017). The difference is that the latter provides a single risk estimate based on baseline
measures whereas a joint model can provide updated estimates at each assessment point. A
joint model could also function as an alert system. An alert can be triggered when the risk
estimate is too high and also when the improvement in the risk estimate over time is too little.
For example, an alert might be triggered if the risk estimate is above 80% and also when the
improvement in risk is less than 2%. In this scenario, if a patient has a risk estimate of 75% at
both baseline and a subsequent assessment, then an alert would be triggered even though the
estimate at both time points are below 80%. The rationale for this is that we would expect
improvement over time in response to treatment. If the patient does not show enough
improvement or even deteriorates (in terms of risk), then it would be clinically useful to
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provide an alert even if the risk remains below the specified risk threshold. This is a
difference between dynamic and static prediction in that the former can aid decisions using
change in risk whereas the latter cannot.
4.2 Limitations
The NEURAPRO study was a randomized trial comparing fish oil with placebo in
transition rate. Since no difference was found between the two treatment groups, they were
ignored in our analysis. However, as placebo is not a normal treatment in practice, its
presence could be regarded as a limitation in the development of prediction models.
Currently, established joint modelling software packages, including the JM package used
in this paper, are restricted in allowing the incorporation of only one TDP in a model.
Multiple TDPs need to be combined into a single predictor in order for the software packages
to be utilized. A pragmatic way to combine TDPs is simply to sum them on each occasion of
measurement either without or with standardization (using corresponding baseline means and
SDs). This has been used in other applications of joint modelling (Battes et al., 2015).
However, this is a crude way of utilizing multiple TDPs and the resulting composite variable
may not always be meaningful. For the current data, the TDPs that were found to be
significant individually were BPRS total and BPRS Psychotic subscale. Since one is the
subscale of the other, it is debatable whether it is meaningful to sum them and we decided to
use only BPRS total (the clearly more powerful one) in the joint model. As joint modelling is
an active research area, the limitation of fitting only one TDP may well be overcome in the
near future. In fact, a package for the R environment called joineRML (Hickey et al., 2018)
was recently released. It is designed to accommodate multiple TDPs in one model. However,
it is a user-developed package which has been released for a short time only. So it is
advisable not to employ it for general use until extended exploration of its performance has
been conducted.
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4.3 Conclusion
In this paper, we have demonstrated the potential usefulness of joint modelling in
psychosis prediction and provided empirical support for the value of dynamic prediction in
psychosis research. Further research such as expanding this approach beyond the basic joint
model and incorporating other potential predictors such as neurocognitive variables and
biomarkers would be worthwhile.{Rizopoulos, 2012 #1573} Clinical decision making and
prognostic judgements are generally ‘adaptive’ in nature, i.e. they react to and are updated
based on the unfolding clinical symptomatology of the patient, rather than relying solely on
the profile of the patient’s first clinical presentation (Nelson et al., 2017a). We have shown
that a dynamic approach to psychosis prediction using joint modelling may provide an
empirically-based and rigorous guide for clinical decision making in regard to modifying
preventive intervention in response to the evolution of the patient’s clinical profile.
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