Are U-shaped relationships between risk factors and outcomes artifactual?

1 INTRODUCTION

Many epidemiologic studies have reported a U- or J-shaped relationship between a variety of risk factors and future serious health outcomes, in which both high and low levels of the risk factor are more strongly related to the outcome than intermediate levels of the risk factor.^{1, 2} Examples of such relationships include the link between systolic blood pressure (BP), diastolic BP,^3-6 fasting blood glucose,⁷ glycosylated hemoglobin (HbA1c),⁸ body mass index,^{9, 10} sodium intake,¹¹ alcohol intake,¹² and 25-OH vitamin D¹³ with mortality; low-density lipoprotein cholesterol levels,¹⁴ BP,⁵ and sodium intake¹⁵ with cardiovascular events; and birthweight with stillbirth.¹⁶

These epidemiologic observations have been used to justify the conclusion that levels of a certain risk factor that are below or above a specific nadir are unsafe, and if that risk factor is modifiable, those lower or higher levels should be avoided. However, different nadirs for the relationship between a specific risk factor and an outcome have been reported in different studies. Thus, for BP, the nadir has ranged from 110 to 169 mm Hg and from 55 to 94 mm Hg for systolic and diastolic BP, respectively.² These differences may be due to biases such as reverse causation, confounding by other residual risk factors such as critical illness or selection bias, and low numbers of individuals with either low or high levels of the risk factor.^{2, 17-19} An additional, novel explanation for these relationships is the possibility that the observed nadir for the relationship between a particular risk factor and future health outcome is related to the distribution of the risk factor within the population sample being analyzed.

The ORIGIN trial^20-22 recruited and followed 12 537 participants with dysglycemia and other cardiovascular risk factors for a median of 6.2 years during which the effect of insulin glargine and/or omega 3 fatty acids on cardiovascular and other outcomes was assessed. ORIGIN trial data were used to identify the levels of three common cardiovascular risk factors (weight, systolic BP, and plasma insulin) at baseline that predicted the lowest incidence of the composite cardiovascular outcome (i.e., the nadir value) and to test the hypothesis that these nadirs emerge as a consequence of the baseline distribution of the risk factor within the population.

2 METHODS

3 RESULTS

As noted in Table 1, 12 527 participants were included in the weight analyses, 12 525 in the systolic BP analyses, and 8401 participants for whom insulin levels were available were included in the insulin analyses. Participants for all three analyses had a mean age of 64 years, 59% had a prior cardiovascular event, and 12% had prediabetes. Their mean weight varied between 83 and 84 kg, mean systolic BP was 146 mm Hg, and mean serum insulin level was 2.0 IU/L.

As expected, participants included in the high risk factor level subgroup had higher mean levels of the risk than those in the low risk factor level subgroup factor, whereas the mean level of both subgroups combined fell between the two subgroups. For example, the mean (SD) weights of 6312 and 6217 participants in the high- and low-level groups were 91.1 kg (15.8) and 75.3 kg (14.4), respectively, whereas the mean weight of all 12 527 participants was 83.2 kg (17.0) (Table 2). Similar patterns were noted for systolic BP (Table 3) and serum insulin concentrations (Table 4). Mean levels or proportions of other variables in participants assigned to the two subgroups for each of the three risk factors are noted in Tables 2–4.

Spline curves for the relationship between each of the three risk factors (weight, systolic BP, and serum insulin) and MACE that were based on all available data (i.e., combined subgroups) were all consistent with a U- or J-shaped relationship (Figure 1A,D,G). Notably, for each of the three risk factors, the relationship between the risk factor and MACE in the high-level subgroup was distributed around a higher nadir level of the risk factor than in the low-level subgroup, whereas the nadir of the of the combined subgroups fell between the two (Figure 1B,C,E,F,H,I). Thus, the nadirs for the high-weight, low-weight, and combined subgroups were 97.7, 89.9, and 93.3 kg, respectively; for systolic BP, 139.9, 129.5, and 134.8 mm Hg, respectively; and for serum insulin concentrations, 5.12, 0.9, and 1.47 IU/L, respectively.

4 DISCUSSION

This epidemiologic analysis of more than 12 000 people with a baseline weight and BP and more than 8000 people with a baseline insulin level demonstrated a U- or J-shaped relationship between each of these measurements and incident cardiovascular events occurring during a median follow-up period of 6.2 years. Our study adds to the existing body of literature that has shown a U-shaped relationship between BP,^{3, 5, 6} weight,²⁷ and insulin^28-30 and cardiovascular events. It also demonstrates that the nadir value for each of these risk factors was determined by the mean value of the risk factor in the sample. Samples with a higher mean level had a higher nadir, and samples with a lower mean had a lower nadir. Thus, at least for these three risk factors, the distribution of the risk factor within the sample analyzed is an important determinant of the nadir of the relationship.

These findings have a variety of implications. First, when a U- or J-shaped relationship is reported, investigators should also report the distribution of that risk factor within the population. Second, it also demonstrates that the nadir value of the U for each of these risk factors is affected by the distribution of the risk factor in the population such that populations with a higher mean or median value had a higher nadir and populations with a lower mean or median value had a lower nadir. Third, identification of a nadir for a modifiable risk factor (e.g., BP) from epidemiologic relationships should be construed as hypothesis generating with respect to therapeutic targets, and the therapeutic implications of targeting a particular value need to be explored in randomized controlled trials. For example, BP researchers have clearly shown that therapies that drive the systolic BP below the epidemiologic nadir clearly reduce outcomes.³¹

The sample size, number of outcomes, and qualitative consistency of findings for three different risk factors are clear strengths of these analyses. The fact that the distributions of the three risk factors were all drawn from the same population limits generalizability while increasing confidence that the findings are not due to unmeasured determinants of the distribution. Although these analyses do not imply that when there is a U- or J-shaped relationship between risk factors and outcomes, the nadir is always related to its distribution within the population, they illustrate that this possibility must be considered before ascribing biologic or therapeutic significance to the distribution. Simulation studies would be required to determine whether this phenomenon holds true for all U-shaped relationships between risk factors and health outcomes.

In conclusion, the distribution of a risk factor in the population is an important determinant of its nadir value, and populations with high or low values may have high and low nadirs, respectively. The possibility of a distribution bias should therefore always be considered when confronted with a U- or J-shaped relationship between a risk factor and an outcome.

AUTHOR CONTRIBUTIONS

Reema Shah: Study design; statistical analysis; interpretation of results; drafting the manuscript; guarantor. Lehana Thabane: Study concept and design; critical revision of the manuscript. Hertzel C. Gerstein: Study concept and design; interpretation of results; drafting and critical revision of the manuscript.

FUNDING INFORMATION

The ORIGIN trial was funded by Sanofi.

DISCLOSURE STATEMENT

Reema Shah and Lehana Thabane have no conflicts of interest to disclose. Hertzel C. Gerstein has received research grant support from Sanofi, Lilly, AstraZeneca, and Merck and honoraria for speaking or consulting from Sanofi, Novo Nordisk, Lilly, Boehringer Ingelheim, AstraZeneca, Merck, and Abbot.