Aims and objectives
This chapter describes the development and internal validation of a model framework that predicts key CVD and nonvascular events among individuals without and with previous CVD using the IPD from 16 randomised statin versus control trials in the CTTC database.
Risk equations were developed for four vascular events, myocardial infarction (MI), stroke, coronary revascularisation (CRV) and vascular death (VD), and two nonvascular events, incident cancer and nonvascular death (NVD). These equations were developed separately for participants with and participants without previous CVD.
The risk equations formed the basis of a CVD microsimulation model to predict the risk of each of these events for each individual over time. Calibration plots were used to assess model performance in categories of individuals.
Methods
Data
There were 22 statin versus control trials in the CTTC that recruited over the years 1988–2000, with a median follow-up of 4.8 years.6 Trials that recruited exclusively patients with CKD or chronic heart failure (4D, AURORA, CORONA and GISSI-HF) were excluded from the analysis.6,29 Furthermore, two further trials, LIPS and PostCABG, were excluded because they did not record non-fatal stroke events. Following these exclusions, 68,018 participants without previous CVD at entry from 11 trials and 49,878 participants with previous CVD at entry from 16 trials contributed to the estimation of the risks of first post-randomisation occurrences of the aforementioned six disease events. Ten of the trials included both participants with and participants without previous CVD. Collectively, the trials recruited across Europe, North and South America, Australia, Israel, New Zealand and South Africa. Further details of the individual trials can be found elsewhere.29
Handling of missing data
No ethnicity data were available for participants in the LIPID trial, and all 9014 participants were classified as ethnicity ‘not recorded’ and included in an ‘other’ category in analysis. Missing data for disease history at baseline, including treated hypertension, were assumed to indicate no such history. For 292 of participants with missing LDL-C levels, total cholesterol, high-density lipoprotein cholesterol (HDL-C) and triglycerides were available and used to estimate their LDL-C level using the Friedewald formula.34 The extent of further missing data was as follows: age (49 participants), smoking status (101 participants), body mass index (BMI) (530 participants), LDL-C (1551 participants), HDL-C (394 participants), creatinine (1331 participants), systolic blood pressure (BP) (364 participants) and diastolic BP (373 participants). All missing values for BMI were replaced with mean BMI values in categories by study, sex, age group and prior diabetes. All other missing values were replaced by respective mean values in categories by study, treatment allocation, sex, age group and treated hypertension.
Risk equations
Cox proportional hazard (PH) regression models were used to fit the hazard equations for each event. Trials were assumed to each have their own hazard but with the assumption of proportionality between trials over time, and trial indicators were included as binary covariates in the models to account for differences in hazards between trials. Time was measured in years from randomisation into the trial. Allocation to treatment was also included in risk equations (except the incident cancer and NVD equations) to account for effect of study treatments. Participants’ age and sex were retained in all risk equations.
Participant characteristics and interactions indicated in previous studies to be associated with disease risks of interest were considered in developing the modelling. The following baseline covariates were considered for inclusion in all risk equations: ethnicity, smoking status, BMI, LDL-C, HDL-C, creatinine, systolic BP, diastolic BP, treated hypertension and history of diabetes, cancer and CVD. Participant age was fitted as a time-varying covariate. Histories of previous non-fatal events during study follow-up (other than the event subject to modelling) were included as time-varying covariates when modelling each event of interest. In view of the large data set and to ensure robust risk models, variables were selected for inclusion at the 1% significance level using backward variable selection and checked for stability using forward selection with backward steps.35 Forward variable selection with backward steps at the 1% significance level was then used to select the following six interactions for inclusion: sex and diabetes, age and LDL-C, age and BP, age and smoker, age and diabetes, and age and sex. These interactions were considered for inclusion in all models except those for CRV.
The PH assumption was checked prior to modelling using log–log plots and cumulative hazard plots and post modelling using PH assumption tests and plots of the scaled Schoenfeld residuals.
Microsimulation model
The risk equations were then used in a microsimulation model to predict the annual incidence (risk) of each event for each participant. The model was run 300 times for each participant over 5 years. For each participant, for each year in the model, the point estimate of the annual incidence of each event was the average number of occurrences across the 300 simulations. The cumulative sum of these incidences was then calculated to obtain the predicted cumulative incidence over time.
Internal model validation
The performance of the predictions from the microsimulation model was checked using calibration plots of observed versus predicted cumulative incidence for each event.
Results
At baseline, participants without and participants with previous CVD contributing to the risk models’ estimation had a mean age of 62 and 63 years, respectively. Most of them were male (65% and 78%), of white ethnicity (72% and 78%) and non-smokers (80% and 81%), and nearly half of them (42% and 48%) were overweight (BMI of 25–30 kg/m2). Among participants with previous CVD at baseline, 83% had a history of only MI (50%), other coronary heart disease (CHD) (19%), peripheral arterial disease (PAD) (6.4%) or stroke (7.8%), and 17% had a history of two or more of these conditions (Table 2).
| Characteristic | Without previous CVD historya,b | With previous CVDa,b |
|---|---|---|
| Number of participants | 68,018 | 49,878 |
| Age, years | 62.3 (9.2) | 62.7 (9.1) |
| Sex, male (%) | 43,972 (65%) | 39,085 (78%) |
| Ethnicity | ||
| Whiteb | 49,170 (72%) | 38,901 (78%) |
| Black | 6110 (9.0%) | 1226 (2.5%) |
| Otherc | 12,738 (19%) | 9751 (20%) |
| Current smoker | 13,873 (20%) | 9554 (19%) |
| BMI (kg/m2) | ||
| < 18.5 | 670 (0.99%) | 251 (0.50%) |
| 18.5–25 | 19,963 (29%) | 15,023 (30%) |
| 25–30 | 28,598 (42%) | 23,711 (48%) |
| 30–35 | 13,532 (20%) | 8487 (17%) |
| 35–40 | 3708 (5.5%) | 1806 (3.6%) |
| ≥ 40 | 1547 (2.3%) | 600 (1.2%) |
| LDL-C (mmol/l) | 3.5 (0.89) | 3.8 (0.85) |
| HDL-C (mmol/l) | 1.3 (0.38) | 1.1 (0.31) |
| Creatinine (μmol/l) | 91 (24) | 98 (23) |
| Systolic BP (mmHg) | 142 (20) | 139 (22) |
| Diastolic BP (mmHg) | 83 (11) | 81 (11) |
| On hypertension treatment | 35,478 (52%) | 25,472 (51%) |
| Prior diabetes | 15,131 (22%) | 7949 (16%) |
| Prior cancer | 32 (0.05%) | 25 (0.05%) |
| Previous CVD | ||
| MI only | 24,866 (50%) | |
| PAD only | 3186 (6.4%) | |
| Stroke only | 3875 (7.8%) | |
| Other CHD onlyd | 9631 (19%) | |
| Two or more of the above | 8320 (17%) | |
The number of participants experiencing disease end points during follow-up are reported in Table 3.
| Without previous CVD | With previous CVD | |
|---|---|---|
| Number of participants | 68,018 | 49,878 |
| MI | 1758 | 4134 |
| Stroke | 1133 | 2160 |
| CRV | 1424 | 4958 |
| Incident cancer | 3085 | 3450 |
| VD | 1118 | 3751 |
| NVD | 1767 | 2242 |
Log–log plots and cumulative hazard plots created prior to the Cox hazard regression modelling of events did not show any major violations of the PH assumption (not shown). Figure 1a–f shows the Cox hazard risk equations for each of the events in turn. With the exception of incident cancer, separate risk equations were fitted for participants without and participants with previous CVD. Contributions of risk factors to the hazard of incident cancer were similar in participants without and participants with previous CVD, and hence a single risk equation was fitted for all participants regardless of CVD history at baseline (see Figure 1f). The tests and plots of Schoenfeld residuals after fitting each of the Cox hazard regressions did not show any major violations of the PH assumption (not shown).
FIGURE 1 Cox hazard equations estimated using IPD from large randomised controlled trials. (a) MI; (b) stroke; (c) CRV; (d) VD; (e) NVD; and (f) incident cancer. Participants with a history of cancer at baseline were excluded. CI. confidence interval; HR, hazard ratio. (Figure not reproduced here; see the original article.)
Figure 2 shows a schematic of the microsimulation model used to predict the annual incidence (risk) of each event for each participant. The model performed well in internal validation (Figure 3).
FIGURE 2 Cardiovascular disease microsimulation model schematic. (Figure not reproduced here; see the original article.)
FIGURE 3 Internal validation of the CVD model in the CTTC database. (a) Without previous CVD; and (b) with previous CVD. Red denotes observed with 95% confidence interval; black denotes prediction from model. (Figure not reproduced here; see the original article.)
Summary
This chapter presented the development and internal validation of a model framework that predicts risks of key vascular and nonvascular events using the IPD from 16 randomised statin versus control trials in the CTTC. This initial model is further developed in a large contemporary UK cohort, the UKB, in Chapter 3.