Tightrope Walking: Using Predictors of 25 (OH)D Concentration Based on Multivariable Linear Regression to Infer Associations with Health Risks
Ning Ding1,2 ning.ding at canberra.edu.au, Keith Dear3, Shuyu Guo2, Fan Xiang2, Robyn Lucas 2,4
1 Faculty of Health, University of Canberra, Canberra, ACT, 2601, Australia,
2 National Centre for Epidemiology and Population Health, Research School of Population Health, The Australian National University, Canberra, ACT, 2600, Australia,
3 Duke Global Health Institute, Duke Kunshan University, Kunshan, Jiangsu, 215316, China,
4 Telethon Kids Institute, University of Western Australia, Perth, WA, 6009, Australia
The debate on the causal association between vitamin D status, measured as serum concentration of 25-hydroxyvitamin D (25[OH]D), and various health outcomes warrants investigation in large-scale health surveys. Measuring the 25(OH)D concentration for each participant is not always feasible, because of the logistics of blood collection and the costs of vitamin D testing. To address this problem, past research has used predicted 25(OH)D concentration, based on multivariable linear regression, as a proxy for unmeasured vitamin D status. We restate this approach in a mathematical framework, to deduce its possible pitfalls. Monte Carlo simulation and real data from the National Health and Nutrition Examination Survey 2005-06 are used to confirm the deductions. The results indicate that variables that are used in the prediction model (for 25[OH]D concentration) but not in the model for the health outcome (called instrumental variables), play an essential role in the identification of an effect. Such variables should be unrelated to the health outcome other than through vitamin D; otherwise the estimate of interest will be biased. The approach of predicted 25 (OH)D concentration derived from multivariable linear regression may be valid. However, careful verification that the instrumental variables are unrelated to the health
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The results indicate that the prediction of 25(OH)D concentration based on multivariable linear regression may be correct, but care needs to be taken when applying this methodology. Even if only one of the instrumental variables used is invalid, the estimates of the association between 25(OH)D concentration and the health outcome will be unreliable. It should be noted that the second requirement of a valid instrument variable, that it should not be a risk factor for the disease, cannot be test mathematically or statistically and can only be judged according to biological findings from past research. Thus, the reasons for the choice of instrumental variables should be discussed, and the lack of correlation with the health outcome confirmed. Previous studies using this methodology have not provided an adequate consideration of the potential biases that could occur. For example, several papers used variables such as physical activity, BMI, smoking status, alcohol intake and race as instrumental variables, despite substantial evidence these factors are strongly associated with many diseases, including the outcomes of interest [6,15-18]. Vitamin D intake has also been used as an instrumental variable [8,19], but may also be associated with disease risk as a marker of a healthier lifestyle and thus lower disease risk .
In some studies, stratification by a potential confounder, or meta-analysis of findings have been used to indicate a greater likelihood of a “real” finding. However, a stratified analysis cannot demonstrate that the results are “correct” or robust. For example, where BMI is used in the predictive model for 25(OH)D score, then the effect estimate of 25(OH)D score on the health outcome, e.g. digestive cancer, maybe compared across strata of BMI. Higher BMI is a known risk factor for digestive cancer and is therefore an invalid instrumental variable. In this case, if the effect estimates from the two strata are the same or similar, then the conclusion may be that the association between 25(OH)D score and the health outcome is the same for both strata, or, alternatively, that the bias caused by the invalid instrumental variable plus the real association is the same for both strata. But it is not possible to distinguish between these two possible conclusions. Similarly, meta-analysis does not help although it is useful to estimate the summary effects over a number of previous studies particularly when the sample size in any single study is insufficient. If all of the individual studies use invalid instrumental variables, all of the effect estimates are biased, and the weighted average of these biased estimations will be similarly biased.
Most recently, variants of genes that affect 25(OH)D synthesis or substrate availability (e.g. CYP2R1, GC and DHCR7) have been used as instrumental variables either individually or through creation of a genetic score that acts as a proxy for long-term 25(OH)D levels . This method does not predict 25(OH)D levels per se, but may be more disease-relevant than a single 25(OH)D measurement for which intraclass correlation coefficients range from 0.42-0.72 between 2 direct measures taken 2-14 years apart [6,22-24]. The substrate from which vitamin D is synthesised is 7-dehydrocholesterol (7-DHC) located in epidermal cells of the skin. The DHCR7 gene encodes the enzyme 7-DHC reductase and both 7-DHC and 7-DHC reductase are part of the cholesterol biosynthesis pathway. Using a genetic synthesis score, a recent metaanalysis showed a modest association between higher genetically instrumented 25(OH)D concentration and lower systolic blood pressure A valid instrument has an effect on the outcome only through the factor that it is a proxy for, in this case 25(OH)D concentration. In the recent study, the synthesis score was highly correlated with measured 25(OH)D concentration, but also had an overall association with higher serum total cholesterol (p = 0.04), suggesting a possible separate pathway of effect of this genetic score on higher systolic blood pressure. Thus genetic 25(OH)D scores should also be used as instrumental variables with caution, given the pleiotropic effects of some vitamin D pathway genes, e.g. GC and its association with lipid metabolism, inflammation and metabolic feedback loops.
In practice, it is common to generate a dichotomous variable based on the predicted score to categorize participants as suffering from vitamin D deficiency or not, and this further complicates the situation. In this situation, the bias caused by use of an invalid instrumental variable will be further distorted by the distribution of the predicted 25(OH)D score. The direction of the bias cannot be determined theoretically.
The method discussed here is similar to the method of Two-Stage Least Squares (2SLS) which is widely used to estimate causal relationships in economics [25,26]. Differences between the two methods include that 25(OH)D concentration is available in the main data for Stage 1, but not Stage II, while 2SLS usually uses the same dataset in both stages. The 2SLS method aims to solve the bias caused by omitted confounders; an instrumental variable can be used only if it: 1) has a strong association with the variable (exposure) of interest; and 2) is not an independent risk factor for the outcome. These two criteria also apply for the methodology using a predicted 25(OH)D score.
Although applying the predicted 25(OH)D score method to identify the association between 25(OH)D concentration and health outcomes is not straightforward, there are clinical applications for predicted data. Recently there have been large increases in vitamin D testing in several countries due to concern about possible widespread vitamin D deficiency and purported links to a wide range of health risks , with considerable costs to healthcare systems . One solution to reduce unnecessary tests is to predict those who are at high risk of vitamin D deficiency using available data, and test only these people. However, when predicted levels are used in large-scale epidemiological studies seeking to clarify links between vitamin D status and disease risks, there is considerable risk of bias in the estimates of effect arising from incorrect specification of an instrumental variable. This must be fully considered and discussed in studies using this methodology.
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