“Progression” of a risk factor on cardiovascular outcome: A valuable point, a questionable interpretation

Cardiovascular disease (CVD) risk factors (RFs), such as systolic blood pressure and serum lipids, play pivotal roles in clinical practice and research. Since RFs causally influence the natural course of CVDs, they have been the targets of clinical treatment via lifestyle modification and/or pharmacological agent(s). Since RFs have been shown to predict future risk of CVDs, they have been incorporated in risk prediction models such as the SCORE1 and the Framingham CVD score,2 and the use of such prediction models is recommended by the major clinical guidelines.1,2 The predicting property of some RFs, however, seem to be lessened in recent years.3 In line with this contemporary concern, a group of researchers from the PROG-IMT consortium4 has tested an interesting hypothesis: average measurements of risk factors assessed at a separate time point ((RF1+RF2)/2), but not “progression” between the measures (defined as the difference (RF2–RF1)), predicts future CVD risk.5 The authors selected four RF measures to examine the hypothesis: systolic blood pressure, concentrations of total cholesterol, low-density lipoprotein cholesterol, and high-density lipoprotein cholesterol.5 By inserting the average and the difference of a RF in one model, the authors showed that the former had a positive and expected association with CVD risk whereas the latter had a null to minimum association. The consortium used a large-sized sample (n = 34,072), pooling data from multiple cohort studies with the average time between the two RF measurements ranging from 2.2–6.6 years, and the durations of follow-up after the second RF assessment varying from 3.9–14.2 years. The authors concluded that the results “suggest that measuring risk factor progression based on two measurements only a few years apart has a very low signal to noise ratio which does not allow for appropriate individual risk prediction.” The authors raised a valuable and relevant point for the prediction of CVD risk in modern era. Clearly, the results should not be interpreted as evidence of lack of causal effect of those RFs on CVDs. Rather, one should seek potential reasons why the “progression” did not predict a risk in recent years. First, as indicated by the authors and others,3 recent treatment for a risk factor such as statin has become so potent and widespread in many populations that measured RF tends to reflect more “treated” values, which is likely to weaken its predictive property as compared with “non-treated” values in the past. Secondly, the second measurement (RF2) may not be so different from the first measurement (RF1) owing to a relatively stable lifestyle and/or biological condition over the two time-points. This would make the regression to the mean phenomena come into play for the difference (RF2–RF1), leading to a low signal-to-noise ratio. In that case, it is no surprise that the average ((RF1+RF2)/2) value has a stronger relation with risk than the “progression” (RF2–RF1) because the latter has little information beyond RF1 (i.e. RF2 takes a similar value to RF1). For effective risk prediction, therefore, “measurements taken over a longer time span … may be necessary” per the authors which I totally agree with. From the methodological viewpoint, the authors additionally argued that in assessing the association of “progression” with disease risk, one must adjust for the average but not for baseline value alone (i.e. RF1) because, per the authors, the latter adjustment model leads to a biased estimate, thus, to be avoided. I do not entirely agree with this argument because, in my opinion, both models can be misleading for the reasons I detail below. Note that E(Y) stands for a disease risk, and b1, b2 are regression coefficients for RF1, RF2, respectively (no assumption is made regarding equality of b1 and b2, contrasting to the authors' explanation in their appendix). An intercept, the rest of the adjusting covariates, and residual errors were omitted for simplicity. Equation (2) indicates that the coefficient of “progression”, which seems to represent the effect of RF progression, is in fact the strength of association (b2) of RF2 when adjusting for RF1 in the model. This makes sense intuitively because adjusting for a covariate in a regression model means to keep that covariate constant. When RF1 is kept constant in the model, the source of variation of “progression (RF2–RF1)” is only from RF2. Therefore, I disagree with the following authors statement: “the adjustment for the baseline value of a risk factor instead of risk factor average induces a bias in assessing the true associations between the progression of conventional risk factors and CVD risk.” It is not wrong to conduct the model mathematically, and the model (2) by itself does not necessarily induce a bias. It is the interpretation of the coefficient from the model that confuses people. Therefore, I do not recommend this model. I would rather recommend the model that corresponds to Equation (1) for simplicity and ease of interpretation. A similar opinion to mine along with useful discussion using real example of mathematically analogous to our problem, but not the same clinical setting, has been reported elsewhere.6 Similarly, from Equation (3) we learn that, in this model, the regression coefficient for the average of RF1 and RF2 is always larger in the absolute sense than that of “progression” as long as b1 and b2 are in a same direction (i.e. both take either positive or negative values). To put this in other words, in the model including both average and “progression,” a near-zero coefficient of “progression” does not mean a near-zero effect of “progression.” Rather, it means that the strength of association of RF2 is nearly equal to that of RF1 with an outcome. This was likely the case for systolic blood pressure shown in the PROG-IMT article, which showed a near-zero coefficient of “progression” using the model corresponding to Equation (3), but a significantly positive coefficient in the model corresponding to Equation (2). Again, it is a valid model mathematically but the correct interpretation of the model is not straightforward and, thus, I am not keen on this model (Equation (3)) either. Note that whether or not use of the model adjusting for “b1*RF1+b2*RF2” is appropriate from the viewpoints of causal chain and/or “independent assumption” between the two variables (RF1, RF2) is beyond the scope of this editorial. Such viewpoints should be considered separately in a given specific setting. Nevertheless, considering a simple causal diagram (directed acyclic graph),7 the model adjusting for RF1 is indeed appropriate in assessing the effect of RF2 on CVD (Figure 1). From the practical point, this model is easier and more straightforward in interpreting the coefficients compared with either of the ”progression” models, although all of the three models are mathematically equivalent. A directed acyclic graph depicting the relationship between a risk factor measured at baseline (RF1), at follow-up (RF2), and the outcome of cardiovascular disease (CVD). When assessing the effect of RF2 on CVD risk (an arrow from RF2 to CVD), the graph indicates “confounding” by RF1 because of the arrows from RF1 pointing to both RF2 and CVD, which supports the appropriateness of the adjustment for RF1 in a regression model. A directed acyclic graph depicting the relationship between a risk factor measured at baseline (RF1), at follow-up (RF2), and the outcome of cardiovascular disease (CVD). When assessing the effect of RF2 on CVD risk (an arrow from RF2 to CVD), the graph indicates “confounding” by RF1 because of the arrows from RF1 pointing to both RF2 and CVD, which supports the appropriateness of the adjustment for RF1 in a regression model. Lastly, I do agree with the authors' point that the heterogenous findings among similar studies are likely to be due to differences in the statistical model, at least in part. In assessing the effect of “progression” on CVD outcomes, we need to pay very careful attention to the model(s) used for each study, and to draw the appropriate interpretation(s). In summary, Bahls et al. from the PROG-IMT consortium have raised a very noteworthy and valuable point in modern CVD epidemiology and clinical prevention: that the predicting property of some RFs seem to have lessened in recent years. The rising phenomenon challenges our traditional practice of risk prediction, and the reasons for it are likely multifactorial. For understanding the phenomenon, we need to pay careful attention to the statistical method used in the assessment of change in RF over time, and need to interpret the results appropriately according to the method. The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. The author(s) received no financial support for the research, authorship, and/or publication of this article.