Risk prediction in carotid stenosis with time dependency of high-impact variables and multiple endpoint analysis

doi:10.21203/rs.3.rs-2581564/v1

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Risk prediction in carotid stenosis with time dependency of high-impact variables and multiple endpoint analysis

https://doi.org/10.21203/rs.3.rs-2581564/v1

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Electronic patient records represent a potential data source for the future, as digital free text extraction by artificial intelligence is coming closer to safe options for handling of confidential information. Big data from patient records could in turn be applied to improve risk prediction for several disease groups. In this project, a pilot dataset based on information from patient journals was collected to explore the suitability of free text information in risk prediction for patients with carotid stenosis. 863 patients with the ICD-10 diagnosis carotid stenosis were included, and the risk of stroke was analysed in relation to treatment and variables previously shown to impact disease progression or stroke risk. Variables previously shown to have a strong impact on this risk were included with time dependency, to allow analysis of trends in risk in relation to changes in risk profile over time. Multiple endpoint analysis was performed to explore the excess risk in patients who suffered more than one event. Results from the suggested model were compared to results from traditional cox regression, and concordance analysis was performed to compare these two models. In analysis of the pilot dataset, the expanded model with time dependency and multiple endpoint analysis appears to provide a better model fit then a traditional cox regression analysis performed on the same dataset.

carotid stenosis

stroke

carotid endarterectomy

real world data

time dependent variables

multiple endpoint analysis

Over the past two decades, risk prediction tools have received growing interest. To develop a risk prediction model, survival analysis is commonly applied, analysing the time to a given condition of interest in relation to a selection of predefined patient properties and/or treatments. These variables are usually registered at the start of follow up, and survival time is defined as the time to the first event, or else right censoring at the end of follow-up. For carotid stenosis, this event is an ipsilateral ischemic stroke in most studies. Some studies select a combined endpoint, such as ipsilateral stroke or death, or a combined cardiovascular event by myocardial infarction or stroke. Strokes are usually defined as ischemic, but the cause of ischemia is not always specified.

Numerous studies have been performed to predict stroke risk in carotid stenosis patients, in order to estimate who benefits the most from treatment (1–3). This still appears to have a sparse impact on decision making(4).

Our hypothesis is that improvement of risk prediction for carotid stenosis patients is possible, and that an extended survival analysis could be a better fit when a long observation time is desired. Our suggested model is designed for analysis of patient record data. The model accounts for the occurrence of more than one endpoint, and important clinical events which happens during the time of follow-up. This has not previously been combined in the same model for this patient group.

The pilot data material is based on “all comer” analysis from a single centre electronic patient record system, and is of moderate size. Thus, the intention of the analysis is to explore the model potential. Expansion of power is considered the next step, for a robust and clinically applicable risk estimator.

The background for our patient record data approach and model design has been separately described. In this article we present the resulting risk estimate and evaluate the model potential.

The method for patient inclusion and data collection has been separately described. Statistical analysis is performed using SAS software 9.4, SAS Institute Inc., Cary, NC, USA for the extended model and for testing of model fitness. Manual data preparation for time dependent variables and the multiple event analysis matrix was performed in SPSS. Some simple analyses and graphics are also performed in SPSS.

The matrix

The extended prediction model includes repeat event analysis and time dependent variables. This is analysed by the use of a matrix set-up, with intervals defining the time to occurrence of a variable change or new event. Stratification by endpoint is performed for each time interval. The stratification interval number rises in the time interval after an event, but not for time intervals ending due to a change in time dependent variables. Different stratification intervals are made in relation to the different endpoint definitions for each of the analyses, i.e. for the endpoint “any left sided stroke”, the interval number only increases after a left sided ischemic stroke without a specified cause. It is seen as essential that each time interval depends on the previous one for the same patient, as one event is known to increase the risk of a new event, as proposed by Prentice, Williams and Peterson(5). The sandwich estimator is chosen, to adjust for the allowance of repeated events for each individual, with each patient recognised by a unique Id number.

The included variables were selected based on results from previous studies (1, 6–12). We then chose the variables to be analysed with time dependency based on the evidence of these having a strong impact on risk. The assumption is that the individual risk could be altered if these variables change during the observation time, such as the registration of an increased degree of stenosis after a certain period of time. In our pilot analysis, the time dependent variables are carotid stenosis and TIAs. CEA/CAS is registered with time dependency, but to avoid confounding, this is included in the pilot model by changing the time dependent carotid stenosis variable to 0 on the treated side in the time intervals following the procedure, if not registered otherwise. In addition to the time dependent variables, a selection of time independent variables (such as gender and diabetes mellitus), are included in the analysis. In the pilot analysis we only include traditional cardiovascular risk factors. Some variables which can change during follow up, such as blood pressure and smoking, are included as time independent. These variables are seen as weak predictors of stroke, and time dependency is assumed to have little impact on the risk estimation.

A regular phreg procedure in SAS is used. The procedure includes both time dependent and time independent variables, identifies each individual by their unique id number, and stratifies time intervals to an event by interval numbers.

Sidedness

A carotid stenosis associated stroke can occur by direct embolization by thrombosis or plaque rupture, or from hypoperfusion due to reduced flow through a severely stenotic or occluded carotid artery. For embolic episodes, only strokes on the same side as the stenosis can occur. For hypoperfusion strokes, precerebral multivessel disease may render the patient at increased risk in both hemispheres. This is assumed to be the case in bilateral high degree carotid stenosis or occlusion. Each cerebral hemisphere is therefore considered to carry a separate risk, depending on all precerebral arteries and the circle of Willis. Analyses for both strokes affecting each separate hemisphere and strokes in any hemisphere has been performed in our study, and the degree of stenosis of both carotid arteries are included in all of the analyses with time dependency.

Figure 1 shows the assumed changes in risk for a fictive patient, in association to changes that might occur in the time dependent variables.

Tables 1 and 2 show the results for asymptomatic and symptomatic patients, when traditional risk factors are included as variables. Other variables registered in the dataset are explored, but found of low additional value in the risk prediction model.

Table 1 The table shows the results of a cox regression analysis of the asymptomatic patients, included after an incidental diagnosis of carotid stenosis. A traditional cox regression is performed by analysing time from diagnosis to the first stroke or censoring at the end of follow up. In the extended analysis, time runs until the end of follow up for all participants, and accounts for the occurrence of more than one stroke in some patients. The time to left and right sided strokes are analysed separately

Asymptomatic at diagnosis	Traditional Cox, time to first event		Extended Cox model, right sided events		Extended Cox model, left sided events
Variable	HR (95% CI)	p	HR (95% CI)	p	HR ( 95% CI)	p
Age, years (at time of diagnosis)	1.02 (0.98, 1.06)	0.35	1.02 (0.97, 1.07)	0.36	1.01 (0.95, 1.07)	0.71
Sex (f)	0.82 (0.46, 0.48)	0.51	0.79 (0.35, 1.77)	0.56	2.16 (1.05, 4.48)	0.04
Systolic blood pressure(at time of diagnosis), 10mmHg	1.10 (0.99, 1.02)	0.34	1.00 (0.98, 1.01)	0.87	1.10 (0.99, 1.03)	0.32
Diabetes mellitus	0.67 (0.32, 1.39)	0.28	0.72 (0.23, 2.24)	0.57	2.80 (1.26, 6.25)	0.01
Current smoker	0.82 (0.46, 1.45)	0.49	1.31 (0.65, 2.65)	0.45	1.67 (0.79, 3.64)	0.18
No statin therapy after diagnosis	1.27 (0.64, 2.50)	0.50	0.60 (0.23, 1.51)	0.27	0.81 (0.35, 1.86)	0.62
No anticoagulation after diagnosis	2.26(0.85, 6.06)	0.10	0.63 (0.21, 1.87)	0.40	0.23 (0.03, 1.81)	0.16
No antihypertensive treatment	0.52 (0.28, 0.98)	0.05	2.10 (0.80, 5.47)	0.13	1.06 (0.44, 2.55)	0.89
Carotid stenosis, right side* 0			ref		ref
< 50%	ref	0.06	1.95(0.57, 6.75)	0.29	1.02 (0.28, 3.65)	0.98
50–69%	1.24 (0.60, 2.55)	0.57	1.02 (0.26, 3.97)	0.03	1.27 (0.40, 4.04)	0.69
70–99%	2.40 (1.18, 4.89)	0.16	4.01 (1.14, 14.07)	0.03	1.97 (0.58 ,6.67)	0.28
100%	2.4 (0.96, 5.88)	0.62	4.98 (1.39, 17.80)	0.01	0.35 (0.05, 2.27)	0.27
Carotid stenosis, left side 0			ref		ref
< 50%	ref	0.16	0.72 (0.22, 2.36)	0.59	3.60 (1.29, 10.08)	0.04
50–69%	2.00 (0.97, 4.12)	0.06	1.15 (0.41, 3.24)	0.79	4.18 (1.40, 12.48)	0.01
70–99%	2.08 (1.01, 4.28)	0.46	1.18 (0.38, 3.64)	0.77	5.23 (2.04, 13.38)	0.00
100%	1.89 (0.67, 5.34)	0.23	3.07 (0.86, 10.94)	0.08	1.96 (0.58, 6.68)	0.28
Right sided TIA			1.89 (0.50 ,7.19)	0.35	1.25 (0.25, 6.25)	0.78
Left sided TIA			0.90 (0.28, 2.93)	0.86	2.02 (1.08, 3.78)	0.03
TIA, unknown side			1.03 (0.24, 4.42)	0.96	Err (few events)	err
CEA asymptomatic	2.04 (0.75, 5.55)	0.16

*The reference category for the simple Cox regression is set to <50% (including 0) to mimic other traditional analyses. This is a very common categorization, as small plaques are considered of no hemodynamic significance. Still, a plaque of any size is considered to have the potential to progress over time, and no stenosis (0) is used as the reference category in the time dependent analysis, with plaque <50% as a separate category.

Table 2

The table shows the results of a cox regression analysis of the patient group presenting with an ischemic event at the time of inclusion. A traditional cox regression is performed by analysing time to the first ipsilateral stroke or censoring at the end of follow up. In the extended analysis, in the same way as for the asymptomatic patients, time runs until the end of follow up for all participants, and accounts for more than one stroke occurring in some patients. The time to ipsilateral and contralateral strokes is analysed separately.
Included after symptoms of a cerebral ischemic event	Traditional cox, time to first ipsilateral event		Extended cox model, time to ipsilateral events		Extended cox model, time to contralateral events
Variable	HR (95% CI)	p	HR (95% CI)	p	HR (95% CI)	p
Age, years (at index event)	1.01 (0.98, 1.04)	0.64	1.01 (0.99, 1.03)	0.41	1.01 (0.95, 1.07)	0.82
Sex (f)	0.96 (0.51 ,1.82)	0.91	0.83 (0.47, 1.45)	0.50	0.48 (0.16, 1.46)	0.20
Systolic blood pressure (at time of diagnosis), 10 mmHg	1.10 (1.00, 1.02)	0.15	1.00 (0.99, 1.01)	0.70	1.22 (1.00, 1.04)	0.06
Diabetes mellitus	0.86 (0.42, 1.77)	0.68	0.97 (0.51, 1.82)	0.92	0.46 (0.08, 2.60)	0.38
Current smoker	1.34 (0.63, 2.85)	0.44	0.85 (0.50, 1.47)	0.57	0.99 (0.31, 3.17)	0.98
No statin therapy after diagnosis	1.02 (0.45, 2.32)	0.97	0.80 (0.35, 1.81)	0.59	0.41 (0.04, 3.97)	0.44
No anticoagulation after diagnosis	4.43 (1.04, 18.54)	0.04	3.95 (1.03 ,15.19)	0.05	-	-
No antihypertensive treatment	0.96 (0.47, 1.97)	0.92	0.99 (0.53, 1.84)	0.98	1.03 (0.32, 3.32)	0.96
Carotid stenosis. ipsilateral to index side 0			ref		ref
< 50%	ref		1.23 (0.46, 3.31)	0.68	0.73 (0.06, 8.51)	0.80
50–69%	0.80 (0.31, 2.10)	0.65	1.61 (0.70, 3.71)	0.27	1.29 (0.21, 7.96)	0.78
70–99%	1.85 (0.78, 4.37)	0.16	2.25 (1.03, 4.94)	0.04	0.52 (0.04, 7.16)	0.62
100%	1.59 (0.61, 4.15)	0.34	2.93 (1.45, 3.07)	0.00	3.67 (0.90, 14.90)	0.07
Carotid stenosis. contralateral to index side 0			ref		ref
< 50%	ref		1.48 (0.81, 2.73)	0.20	6.30 (0.74, 53.78)	0.09
50–69%	0.55 (0.21, 1.43)	0.22	0.66 (0.30, 1.46)	0.31	15.43 (2.22, 107.23)	0.01
70–99%	0.58 ( 0.22, 1.51)	0.26	0.55 (0.21, 1.43)	0.22	12.08 (1.30, 112.26)	0.03
100%	0.41 (0.06, 3.22)	0.41	0.49 (0.09, 2.68)	0.49	-	-
New ipsilateral TIA			1.13 (0.41, 3.07)	0.82	0.46 (0.17, 1.24)	0.12
New contralateral TIA			1.75 (0.62, 4.95)	0.29	4.05 (1.18, 13.88)	0.03
New TIA. unknown side			1.54 (0.57, 4.13)	0.40	20.86 (3.20, 136.19)	0.00
CEA after index	0.32 (0.14, 0.71)	0.01

When compared to the traditional Cox model, the extended model shows a clear and consistent risk association in relation to the degree of stenosis to events on the same side. In the analysis of the asymptomatic patients, the wide confidence interval for carotid stenosis is interpreted as model instability due to insufficient power (table 1). For the patients presenting with symptoms and the endpoint “ipsilateral stroke” the model stability seems better (Table 2).

In the traditional Cox analysis CEA is included as a variable, and no clear benefit is seen in the asymptomatic patients, whereas the risk is significantly reduced for the symptomatic patients after treatment. This is consistent with results from previous studies.

Model testing

The model shows a strong association between the degree of stenosis and the risk of stroke, which is less apparent in a traditional Cox analysis of the same historical data. This suggests that the model could provide improved prediction based on the selected variables, and thereby a possible way of applying regular patient record data in risk prediction. We would like to explore this further by model testing.

To evaluate the predictive value of the extended model in comparison to a traditional Cox regression concordance analysis is applied (13). The SAS concordance statistics function currently does not perform analyses with time intervals and stratification. In order to perform the analysis, we therefore simplify the extended model. Rather than expressing observation time in intervals as start time and stop time, we calculated a single observation time as the difference between the start and stop time. This means that each time difference will be interpreted as a separate survival time with variable values as for this given time interval, with the possibility of several survival times for each patient. If no events occur and the time dependent variables remain unchanged, the patient has one survival time and a single row in the matrix setup, with censoring at the end of follow up. The time dependent variables can leave each individual at a different risk for each survival time. Patients who experience an event will be under risk again in the following time interval with or without a change in time dependent variable. Unfortunately, no stratification can be performed in SAS’ concordance analysis which means that the time intervals cannot be expressed as dependent on previous intervals within the same patient. We are not familiar with other software providing this function. This is a drawback in the model test, as identification of each time interval belonging to the same patient, and allowing these to depend on each other, is considered a key feature of the model. Still, stratification is considered very likely to improve the model fit compared to an unstratified model, which makes is likely that the performed model test provides a “worst case” concordance estimate. If this is true, the full model will represent a better fit than the one simplified in order to perform the concordance analysis.

Concordance analysis will evaluate predictive performance as a value C. If C = 0.5 the model has no informative predictive value, whereas C = 1 equals a perfect association. Uno`s C using SAS is considered to be the best method(14), as Harrell’s C (15) will provide a shortcoming when there is a large variation in time to censoring, which is the case in our data material. Concordance analysis is first applied on a traditional Cox model of the symptomatic dataset (Fig. 1). The endpoint is here defined as a stroke caused by the carotid stenosis, ipsilateral to the index event. Carotid surgery after the index event is included as an independent variable.

As seen in Fig. 2, it seems like the early predictive value is fair, but after the first 1–2 years the predictive value is around 0.65, which is low. The Area Under the Curve (AUC) is initially high, which suggests good prediction for the first month, but falls after a year and stays low for the following years. This is well illustrated by Receiver Operating Characteristic (ROC) curves after 30 days, one year, two years, and up to five years, as illustrated in Fig. 3. These curves are plots of sensitivity against one minus specificity for the given time points. The higher the curve rises above the 45-degree line, the better the model.

The same analysis is performed on the multiple event and time dependent variable set-up for the symptomatic dataset, with the same endpoint definition (Fig. 4). The AUC curve in Fig. 4 suggests a better long-term predictive value, but the confidence interval is still large, which indicates a high degree of uncertainty. This is assumed possible to improve by an increased power.

This can similarly be illustrated by the ROC curves (Fig. 5), which show an opposite trend compared with the traditional Cox model. The initial time interval of 30 days seems better predicted by a traditional Cox, as can be expected, as time dependent variable changes and multiple endpoint analysis is unlikely to affect prediction short term. The lack of stratification in the concordance analysis could also contribute to the weak early predictive value. This will impact the predictive properties of the model if the start risk in each stratum is different, which is assumed to be the case in this patient group. In the simplified expanded model, each individual with more than one event will have the same baseline risk at the start of each stratum, as the risk associated with the previous event will not be carried on to the next time interval as is expressed in the model by stratification. The area over the 45-degree line increases after the first 30-day period for the extended model, and decreases for the traditional cox.

As described, SAS does not have a function for concordance analysis for time intervals and stratification, and we needed to simplify the model for this is analysis. When we compare the HRs in the simplified analysis with the original analysis, the estimates are only slightly different. The similar results are interpreted as an indication of a reliable concordance analysis in the simplified model. Results from the simplified model compared to the original extended model for symptomatic patients are shown in Table 3.

Table 3

To prepare the results from the extended cox regression model for concordance analysis, simplification is necessary. This is performed by calculation of time differences (number of days) rather than time intervals, and by elimination of the stratification function. The table shows that the results from the simplified model are only slightly different from those of the original extended model. The simplification is therefore considered acceptable for this analysis.
	Simplified model for concordance analysis		Original extended model
Variable	HR (CI)	p	HR (CI)	p
Age, years (at index event)	1.01 (0.98, 1.04)	0.54	1.01 (0.99, 1.03)	0.50
Sex (f)	0.81 (0.47, 1.39)	0.45	0.83 (0.47, 1.45)	0.50
Systolic blood pressure (at time of diagnosis), 10 mmHg	1.00 (0.99, 1.01)	0.91	1.00 (0.99, 1.01)	0.70
Diabetes mellitus	0.99 (0.54, 1.80)	0.96	0.96 (0.51, 1.82)	0.92
Current smoker	0.89 (0.52, 1.52)	0.66	0.85 (0.50, 1.47)	0.57
No statin therapy after diagnosis	0.84 (0.39, 1.79)	0.64	0.80 (0.35, 1.81)	0.59
No anticoagulation after diagnosis	3.87 (0.96, 15.6)	0.057	3.95 (1.03, 15.2)	0.046
No antihypertensive treatment	0.95 (0.51, 1.77)	0.88	0.99 (0.53, 1.85)	0.98
Carotid stenosis, ipsilateral to index side 0	ref		ref
< 50%	1.45 (0.55, 3.85)	0.45	1.23 (0.46, 3.31)	0.68
50–69%	1.75 (0.78, 3.94)	0.18	1.61 (0.70, 3.71)	0.27
70–99%	2.39 (1.11, 5.15)	0.03	2.25 (1.03, 4.95)	0.04
100%	3.49 (1.72, 7.08)	0.00	2.92 (1.45, 5.89)	0.00
Carotid stenosis, contralateral to index side 0	ref		ref
< 50%	1.53 (0.84, 2.77)	0.16	1.48 (0.81, 2.73)	0.20
50–69%	0.72 (0.32, 1.60)	0.42	0.65 (0.30, 1.46)	0.31
70–99%	0.56 (0.21, 1.47)	0.24	0.55 (0.21, 1.43)	0.22
100%	0.56 (0.07, 4.19)	0.57	0.49 (0.09, 2.68)	0.41
New ipsilateral TIA	0.56 (0.21, 1.44)	0.23	1.13 (0.41, 3.07)	0.82
New contralateral TIA	0.96 (0.26, 3.56)	0.96	1.75 (0.62, 4.95)	0.29
New TIA. unknown side	0.63 (0.07, 5.42)	0.68	1.54 (0.57, 4.13)	0.40

Accepting these results, we perform the concordance analysis in the same way for the asymptomatic dataset.

As in the previous concordance analysis, the endpoint “carotid-caused stroke” is chosen. In the first analysis, any side is allowed as endpoint. The AUC plots for the regular Cox model and the extended Cox model are shown in Figs. 6 and 7, respectively. The difference between the two models is small and the confidence interval is wide for the regular model.

We performed the same analysis for the extended Cox model with sides defined. Figures 8 and 9 show the plots for right and left sided strokes, respectively.

Although the AUC strongly diverges for the sides after about 3500 days, the extended model seems to give a good 10-year prediction of risk if sidedness is defined. The overall C is 0.68 for the traditional cox model, 0.81 for the extended model for right sided events and 0.78 for left sided events.

For the asymptomatic patients 183 patients had more than ten years of follow up. Of these, ten events occurred during the follow up time after ten years or more. Four right sided and six left sided. Improved power is thus obviously desirable for a reliable result and clinically applicable prediction tool.

Carotid stenosis is a complicated disease to work with in respect to risk prediction. As a result, the number needed to treat remains high, and the indication for treatment, particularly in asymptomatic patients, remains controversial. The development of a model for risk prediction has been attempted for many years, with limited success. We still consider statistical modelling based on individual patient properties to have potential in future prediction of the course of this disease that we already have vast information about.

The moderate sample size in our analysis leaves some uncertainty about the model strength. which cannot be overcome unless the power is increased. The idea has been to enable prediction based on data extraction from all existing patient records, in order to make a live system which performs automatic correction of the risk estimator in real time. As electronic patient records have become gold standard worldwide, and AI has solutions for extraction of data from free-text, this could be possible in the near future. By applying AI to extract the parameters of interest, a large database of patient record information could potentially be established while maintaining confidentiality.

Several of the included traditional cardiovascular risk factors are considered to be weak stroke predictors, and time dependency is assumed to have little impact on the risk estimation. In an expansion of the sample size, time dependency of these variables can still easily be included if desirable.

There are still unknown factors in our understanding of the development of plaques prone to embolization and progression of stenosis. Improved quality and interpretation of imaging studies is expected to improve plaque risk assessment, and deep learning imaging technology could alter the way we understand carotid disease in the future. This could add information to the long-term evaluation of plaque progression and improve risk prediction.

In our suggested extended model for risk prediction, the use of stratification allows each time interval to carry a new risk on to the next, depending on the previous intervals. When concordance analysis is performed, no stratification of time intervals can be included, as this is not an option in the software. This means that for the patients with several time intervals due to events or changes in the time dependent variables, the observation time will start from zero for each row, as if this was the time of inclusion. This could be the reason for the poor early predictive performance expressed by the area under the curve and ROC plots.

Long term risk prediction in carotid stenosis patients seems to be improved by a model where time dependent variables and multiple event analysis is introduced.

Ethics approval and consent to participate

The main intention with this study has been to explore real life patient records as a data source, and public availability of our data is not provided due to confidentiality. Written informed consent was taken from participants to participate in the study. For deceased individuals with the given diagnosis, waiver for consent to participate was given by the Regional Ethical Committee of North Norway (ref. 2018/161/REK nord). All methods were performed in accordance with the Declaration of Helsinki.

Protocols were approved by the Regional Ethical Committee of North Norway and the Ethics committee of the University Hospital of North Norway

Consent to publish

Availability of data and materials

The dataset analysed during the current study can be available from the corresponding author on reasonable request, after removal of person identifiable data such as date of events, procedures and death for deceased individuals.

Competing interests

The authors have no competing interests to report.

Funding

The project has received funding by Northern Norway Regional Health Authority.

Authors’ contributions

Hervik and Kjørstad wrote the main manuscript text, and Wilsgaard significantly contributed in development of the statistical model and model testing. Myrmel has contributed through valuable advice and guidance throughout the process of the project. All authors have reviewed the manuscript.

Acknowledgements

The statistical model is developed in close cooperation with statisticians at the Department of Clinical Research at The University of North-Norway.

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Risk prediction in carotid stenosis with time dependency of high-impact variables and multiple endpoint analysis

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Abstract

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Introduction

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Discussion

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