SEARCH

SEARCH BY CITATION

Keywords:

  • causal inference;
  • diabetic retinopathy;
  • risk factors;
  • screening interval;
  • time-dependent confounding

Abstract.

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Introduction:  Screening programmes for diabetic retinopathy follow guidelines that ensure that vision-threatening complications are detected even when the disease progression is fast. This implies that patients with slow disease progression will be recommended examinations more often than needed.

Method:  On the basis of previously defined individual risk factors, multiple logistic regression was used to develop a model for individualized determination of the screening interval in diabetic retinopathy, while adjusting for the fact that in the data set used to construct the model, the screening interval acted as a time-dependent confounder. The model was tested on 1372 patients screened during year 2000.

Results:  It was possible to construct a model for calculating the optimal screening interval in low-risk patients in whom the recommended screening interval was longer than 12 months. When the probability of reaching a treatment requiring event was set to 0.5%, none of the patients reached a treatment end-point in a validation of the model, and the screening interval was prolonged on average 2.9 times in patients with type 1 diabetes and 1.2 times in those with type 2 diabetes. The predictive strength of the model depended on the number of variables included.

Conclusions:  It is possible to construct a model for optimizing the examination interval during screening for diabetic retinopathy in low-risk patients. The model can potentially be improved by identifying unknown or unmeasured confounders and by including knowledge of risk factors before and after the examination on the basis of which the prediction is made.


Introduction

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

The implementation of effective screening programmes can eradicate diabetic retinopathy as a frequent cause of visual loss in the Western World (Rohan et al. 1989; Bachmann & Nelson 1998; Stefansson et al. 2000; Jeppesen & Bek 2004; Olafsdottir & Stefansson 2007; WHO 2008). The screening examination consists of an examination of the ocular fundus by ophthalmoscopy or fundus photography, and in many screening settings, also a measurement of the visual acuity. These procedures can be performed by nurse photographers or technicians, but in most settings, ophthalmologists are needed to interpret the clinical data and determine the interval to the next examination. This determination of the screening interval is carried out on the basis of general rules defined to ensure that vision-threatening changes are detected even in patients with fast disease progression (Singer et al. 1992). However, this implies that a number of examinations are performed that do not have any consequences for patients with stable retinopathy. These superfluous examinations could be avoided if the screening interval in each case could be adjusted to the patient’s individual risk profile.

This study describes a model for individualizing the interval between examinations in a screening programme for diabetic retinopathy. The model is based on the results of a previous study that defined individual risk factors for progression of diabetic retinopathy to a vision-threatening stage (Mehlsen et al. 2009). Logistic regression was used to define a model that is suitable for optimizing the examination interval during screening for diabetic retinopathy, and the model was validated on the prospectively collected data from the database of diabetic retinopathy at Aarhus University Hospital.

Materials and Methods

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Clinical data

The clinical data are described in detail in (Mehlsen et al. 2009). In short, the database for diabetic retinopathy at the Department of Ophthalmology, Aarhus University Hospital, was used to define individual risk factors for progression of diabetic retinopathy to a vision-threatening stage. Clinical data from 11 970 patients examined before 31 December 2007 representing 39 559 screening examinations and 263 710 HbA1c measurements obtained after 1 January 1994, and 23 548 standardized blood pressure measurements obtained after 1 January 1999 were cleansed to exclude patients in whom relevant parts of the disease history were unknown because of migration and patients who had not had more than one examination before treatment. This resulted in 5311 patients representing 22 674 screening examinations, 20 983 HbA1c values and 13 508 blood pressure measurements. These data were subjected to multiple logistic regression to identify the association between selected risk factors from the database and treatment events for diabetic retinopathy (Mehlsen et al. 2009). The treatment events were defined as the first treatment given, irrespective of whether the diagnosis was clinically significant macular oedema requiring macular treatment or proliferative diabetic retinopathy requiring pan-retinal photocoagulation, because the number of end-points was insufficient to build a prediction model that discriminated between the two types of end-points.

Model building

Time-dependent confounding

The statistical analysis of data collected in screening programmes with individualized screening intervals can be difficult, because standard regression methods can produce biased estimates of the importance of both the allocated screening intervals and the observed risk factors. As an example, patients allocated to 3-month screening intervals experience more events than patients allocated to longer intervals. But, clearly, this observation does not imply that patients should be allocated to longer intervals to reduce their risk of event. In other words, the naive estimate of the importance of the length of the screening interval is biased. This bias is because of the fact that at each examination, the next screening interval is determined on the basis of the observed risk factors at the current examination (and may be also past values).

Thus, the allocated screening intervals are in the causal pathway between the risk factors (the causes) and the event. This implies that standard statistical methods to control for confounders will lead to biased estimates of the influence of the risk factors. An overview of the statistical concepts and techniques to handle these problems can be found in (Robins et al. 2000). We have used the approach to reweight observations, such that the allocated screening intervals appear to be randomly allocated independent of the risk factors. For each patient, the weights are calculated at each examination, and we have used so-called stabilized weights to avoid highly ‘influential’ observations caused by extreme weights occurring for rare combinations of observed risk factors and allocated screening interval (Diggle et al. 2002). If there were no unmeasured confounders, this weighting approach would lead to unbiased estimates.

The prediction model was developed as a multiple logistic regression to calculate the probability of reaching a treatment event in the interval between two screening examinations and with each patient considered as a cluster to take into account the repeated nature of the data (for details, see Appendix S1). A model was built for each of the two diabetes types 1 and 2, because the routine screening intervals had been set differently in these two patient groups (Mehlsen et al. 2009). The following parameters previously shown to be risk factors for the development of diabetic retinopathy (Klein et al. 1988; DCCT 1995; Kohner et al. 1999; Stratton et al. 2001; Younis et al. 2003a; Younis et al. 2003b; Knudsen et al. 2009; Mehlsen et al. 2009) were included in the model: diabetes duration, gender, age at diagnosis of diabetes, haemoglobin A1c, the number of retinal haemorrhages and hard exudates counted in a macula-centred 60 degrees fundus photograph.

The stabilized weights were obtained from a multinomial logistic regression with five outcome categories corresponding to the recommended screening intervals (3, 6, 12, 24 or +36 months) and the risk factors used by the grader to establish the length of the next screening interval: Diabetes type and duration, the number of hard exudates and haemorrhages, and the presence or not of preproliferative changes (intra-retinal microvascular abnormalities or venous beading). The weights were calculated as the inverse of the probability of choosing the recommended interval.

Adjustment of the model

If there were no unmeasured confounders, the use of stabilized weights should lead to unbiased estimates of the risk associated with each screening interval adjusted for the influence of the observed risk factors and vice versa. Thus, unbiased estimates of the risk of reaching an event during the next screening interval should increase with the length of the interval. In that case, the logistic regression model could be replaced with a simpler model, where the risk of reaching an event would increase linearly with the length of the screening interval (Appendix S1). Such a model could be used to calculate an optimal screening interval that ensured that the expected risk of event in the interval was below a predefined risk (decision model). However, the estimated risk profile for the five intervals showed a U-shape for both diabetes types (Fig. 1). The descending leg of the U implies that the model assigned a higher risk for reaching a treatment end-point in the shortest screening intervals (high-risk patients). Therefore, the above-mentioned decision model was only applied to preselected high-risk patients in whom the recommended screening interval was 12 months or longer in T1D and 24 months or longer in T2D (low-risk patients = ascending leg of the U-shape). However, the estimates associated with the risk factors were obtained on all available data, because substantial number of the treatment end-points was in the high-risk group.

image

Figure 1.  The weighted and unweighted regression coefficients for each screening interval for the two diabetes types.

Download figure to PowerPoint

Basically, the logistic regression had the following form (Equation 1):

  • image(1)

where p denotes the probability of reaching a treatment event within the following screening interval with the length T (months), x denotes the set of observed risk factors at the current examination, and β represents the regression coefficients obtained by the logistic regression (Table 1). This equation can be used to calculate a screening interval T within which the risk of reaching a treatment event is at most a predetermined risk value p assuming that the patient belongs to the low-risk group. For some patients, the calculated risk was above the predetermined risk even with a screening interval of 0 months, i.e. the model could not predict a positive interval (‘treat the patient immediately’).

Table 1.   The regression data used for the model building. The regression coefficients constitute the constants β in eqn 1.
Risk factorRegression coefficient (β)95% confidence intervalp
T1D 5795 examinations, 1275 patients, 171 events
 Gender
  Men0.417−0.428;1.2620.33
  women0.000 –
 Age at diagnosis (yrs)0.031−0.021;0.0840.24
 Diabetes duration (yrs)0.017−0.017;0.0500.33
 Retinal haemorrhages (no.)1.0160.672;1.361<0.001
 Hard exudates (no.)−0.009−0.019;0.0020.10
 Time to next screening (12 months+)0.0340.007;0.0610.01
 Haemoglobin A1c (%), mean0.3800.110;0.6500.01
 Intercept (ß0)−11.630−15.175;−8.095
T2D 8987 examinations, 3572 patients, 388 events
 Gender
  Men−0.064−0.467;0.3390.76
  Women0.000 –
 Age at diagnosis (yrs)0.016−0.002;0.0340.08
 Diabetes duration (yrs)0.010−0.018;0.0380.48
 Retinal haemorrhages (no.)0.8490.601;1.096<0.001
 Hard exudates (no.)0.002−0.006;0.0090.64
 Time to next screening (24 months+)0.0300.002;0.0580.04
 Haemoglobin A1c (%), mean0.2060.118;0.294<0.001
 Intercept (ß0)−8.152−9.466;6.838

Performance of the model

The first screening examination performed during year 2000 on all the patients screened this year (872 examinations on patients with T2D and 500 examinations on those with T1D) was selected to study the performance of the decision model. Among these, 208 (15.2%, 98 T1D/110 T2D) had reached a treatment end-point by 31 December 2007. For each of these examinations, the screening interval corresponding to a given value of p was calculated from eqn 1. All predictions of the screening interval were compared with: the screening interval recommended after the clinical examination and the time elapsed until treatment in those who had been treated. The calculations were performed including all variables, while p (see eqn 1) was set to each of the following values: 0.1%, 0.5%, 1%, 5% and 10%. Furthermore, the calculations were repeated with p set to 0.5% and after removing each of the following variables separately: HbA1c, number of hard exudates and retinal haemorrhages and diabetes duration.

Results

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Table 1 shows the regression coefficients included in the model for, respectively, T1D and T2D. It appears that in both diabetes types, the number of retinal haemorrhages, haemoglobin A1c and the recommended screening interval was statistically significant predictors for reaching a treatment end-point (p < 0.05). In the unadjusted model, also diabetes duration and the age of diagnosis of T2D were significant (not shown).

Table 2 shows the number of patients screened during year 2000 who would have reached an end-point within the screening interval predicted by the model as a function of the risk p of reaching a treatment end-point. It appears that for both diabetes types, no patients had a treatment event during the predicted screening interval, if the risk of reaching a treatment end-point of 0.5% or less was allowed.

Table 2.   The number of patients screened during year 2000, who would have reached an end-point within the screening interval (first column), after the screening interval (second column) and the percentage of the patients who were lost (reached a treatment end-point during the predicted screening interval) as a function of the risk p (in percentage) for reaching a treatment end-point.
Risk (%)Events before next screeningEvents after next screening(%) Lost patients
T1D
  0.10350
  0.50350
  1.03328.6
  5.0161945.7
 10.026974.3
T2D
  0.10210
  0.50210
  1.051623.8
  5.014766.7
 10.018385.7

Table 3 shows the number of patients with a prolongation of <1, and more than one, two and three times the screening interval, as a function of the risk of reaching a treatment end-point. The prolongation was calculated as the ratio between the recommended screening interval and the interval predicted by the model, except for those in whom the screening interval could not be predicted.

Table 3.   The number of patients with a prolongation of <1, and more than one, two and three times the screening interval, as a function of the risk p of reaching a treatment end-point. Numbers in parentheses indicate the number of patients having reached a treatment end-point within the predicted screening interval.
Prolongation Risk (%)No prediction0 – 0.991–1.992–2.993+Median
T1D
  0.12617750 41231.38
  0.51095364 611642.88
  1.060 32 (1)47 64 (1)248 (1)3.74
  5.081 15 (1) 34 (1)393 (14)6.62
 10.003  6 (1) 12 (1)430 (24)8.27
T2D
  0.1631180  000.15
  0.5102215284 4801.24
  1.04983190 (3)282 (2)452.12
  5.0113 42 (1)109 (3)484 (10)4.31
 10.01118 87 (4)542 (14)5.36

Table 4 shows the number of patients with a prolongation of <1, and more than one, two and three times the screening interval, when each of the risk factors had been excluded separately. It appears that exclusion of individual variables, especially the values of haemoglobin A1c and the number of haemorrhages from the model, shortens the recommended screening interval.

Table 4.   The number of patients with a prolongation of <1, and more than one, two and three times the screening interval, after exclusion of each of the risk factors separately and the risk of reaching an end-point set to 0.5%. Numbers in parentheses indicate the number of patients having reached a treatment end-point within the predicted screening interval.
Prolongation Excluded(Predicted screening interval)/(given screening interval)Median
No prediction0 – 0.991–1.992–2.993+
T1D
 None1095364611642.88
 Duration1134574601592.76
 Hard exudates1075566611622.81
 HbA1c11547 (1)7981 (1)129 (2)2.64
 Haemorrhages28452422746 (1)1.72
 All36652276 (1)00.67
T2D
 None1022152844801.24
 Hard Exudates1022102875001.25
 Duration1092122923601.21
 HbA1c85190374001.22
 Haemorrhages51412213000.35
 All6490000

Table 5 shows characteristics of the patients in which the model could make no prediction of the screening interval and the patients in whom this interval could be predicted. It appears that higher HbA1c, number of retinal haemorrhages and exudates, longer diabetes duration and blood pressure are associated with a ‘no prediction’. These patients always had hard exudates or a haemoglobin A1c value higher than 10.6%, complying with the fact that these patients belonged to a high-risk group that would be recommended a short screening interval per se.

Table 5.   Characteristics of the patients in whom the model could predict a screening interval and those in whom no prediction could be made with a 0.5% risk of reaching a treatment end-point.
VariableT1DT2D
No Prediction MeanPositive predictionpdiffNo prediction MeanPositive predictionpdiff
Hard Exudates2.30.50.020.40.00.0002
Haemorrhages35.33.6<0.00118.10.4<0.001
Duration25.118.6<0.00113.76.4<0.001
Age at diagnosis19.116.60.0252.849.50.04
HbA1c9.28.4<0.0019.38.50.0022
Mean blood pressure102.798.10.01107.1106.10.65

Discussion

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

This is the first study to present an evidence-based model for individualized determination of the interval to the following examinations in a screening programme for diabetic retinopathy. Several methods could have been used for building such a model. A prediction model based on the Bayesian networks method would have taken into account the fact that the included variables were not independent and would not have been sensitive to a lack of one or more variables during decision making for the individual patient (Jensen 1996). A prediction model could also have been built as a parametric statistical model with one of the parameters as a regression coefficient for the length of the screening interval. However, because approximately 75% of the patients had not reached a treatment end-point (Mehlsen et al. 2009), standard parametric survival analysis models could not have been used. Instead, we used logistic regression to estimate the probability of reaching an event within a given time interval that was included as a variable.

Screening programmes with fixed intervals between examinations are known in many medical specialties, and the statistical analysis of such data can be handled with standard techniques. However, screening programmes in which the time interval to the following examination depends on the severity of the disease are more difficult to analyse, because the time interval is not allocated at random but acts as a time-dependent confounder. This problem has many similarities with so-called dynamic treatment regimes in which treatment may change over time depending on the treatment response (Robins et al. 2000). Several methods have been described in the statistical literature to account for this, such as using propensity scores to stratify patients into groups with similar characteristics or by weighting each observation to remove the effect of the time-dependent confounder. These methods are based on the assumption that all independent variables are included in the model.

In this study, it was not possible to construct a model suitable for predicting the screening interval in patients with a high risk of reaching a treatment event. Thus, to use the model for predicting the screening interval in each individual case, one should formally decide whether the patient would have been given a screening interval of 12 months or longer for T1D or 24 months or longer for T2D, by the standard procedures of the screening programme. The patients in whom the predicted screening interval was shorter all had hard exudates, higher HbA1c and haemorrhage count and longer diabetes duration (Table 5), implying that they belonged to a high-risk group, which is normally not followed in a screening programme but has already been referred for evaluation for treatment. Although the model is thus suitable for implementation in a screening programme in which the challenge is to optimize the screening interval for low-risk patients, it would be desirable if it could be extended to also include patients in whom the primary assessment recommended a short screening interval. The descending part of the U-shape in Fig. 1 may be because of over-treatment of the patients assigned short screening intervals when compared to the patients assigned long screening intervals. Thus, it is possible that patients with exudates and other lesions that implied shorter screening intervals were subjected to a more active treatment strategy than needed. Alternatively, the descending leg may be because of confounding variables unknown to the model. Such confounding variables might have been the location and dynamics of retinopathy lesions, which has previously been found to be independent risk factors for progression of the disease to a treatment-requiring stage (Dobree 1970; Hove et al. 2004, 2006), but also other risk factors such as genetic disposition (Patel et al. 2008) and serum lipids (Chew et al. 1996; Klein et al. 2002) might be considered. It would therefore be a major challenge to investigate the significance of these and other variables to further improve the model. Finally, it would be desirable to be able to discriminate between the risk of reaching clinically significant macular oedema and proliferative diabetic retinopathy, but this discrimination would require a much larger data material, which was not available for the model building.

In screening programmes, each examination should by definition have a sensitivity of 100%, implying that all treatment events are detected before they become treatment requiring. This ideal requirement is challenged in a probabilistic model where the prediction of a screening interval implies a certain risk that patients may develop a treatment-requiring event during this interval. The testing of the model showed that with a probability of reaching a treatment end-point of 0.5% from one screening examination to the next, no treatment-requiring events would have occurred within the screening interval recommended to any of the patients examined during year 2000 in our screening clinic. We therefore propose to use this risk level in clinical practice. This risk level predicted intervals that were both shorter and longer than those of the already used non-individualized decision model, but on average, the screening interval could be prolonged by approximately 2.9 times in T1D and 1.2 times in patients with T2D. Thus, a considerable number of screening examinations could be saved using this model, either reducing costs for the health care system or benefitting other patients with diabetes mellitus who might be offered to enter the screening programme. However, the prediction by the model assumes availability of relevant risk factors at the time of the examination, and it does neither consider historic data of the rate of progression before the examination nor the influence of the possible future development of these risk factors, which might lead to a modification of the screening intervals. Inclusion of these time aspects in the decision model will be the subject for a future study.

In conclusion, we have taken the first steps to develop a model for individualizing the examination intervals in a screening programme for diabetic retinopathy. The model can prolong the screening intervals several times for patients with low risk of disease progression, for which the population screening programmes for diabetic retinopathy are essentially designed. It will be a future challenge to extend the model to include patients with high risk of progression as well as including historic and future information about the development of the disease.

Acknowledgments

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

This study was supported by the VELUX Foundation and the Jochum and Marie Jensen Foundation.

References

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

AppendixS1 The logistic regression model

As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer-reviewed and may be re-organized for online delivery, but are not copy-edited. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.

FilenameFormatSizeDescription
AOS_1882_sm_AppendixS1.doc275KSupporting info item

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.