The obesity paradox in survival after cancer diagnosis: tools for evaluation of potential bias

Abstract

The effects of overweight or obesity on survival after cancer diagnosis are difficult to discern based on observational data because these associations reflect the net impact of both causal and spurious phenomena. We describe two sources of bias that might lead to underestimation of the effect of increased body weight on survival after cancer diagnosis: collider stratification bias and heterogeneity of disease bias. Given the mixed evidence on weight status, weight change, and post-diagnosis survival for cancer patients, systematic evaluation of alternative explanations is critical. The plausible magnitudes of these sources of bias can be quantified based on expert knowledge about particular cancer types using simple simulation tools. We illustrate each type of bias, describe the assumptions researchers need make in order to evaluate the plausible magnitude of the bias, and provide a simple example of each bias using the setting of renal cancer. Findings from simple simulations, tailored to specific types of cancer, could help distinguish real from spurious effects of body weight on patient survival. Using these results can improve guidance for patients and providers about the relative importance of weight management after a diagnosis.

Introduction

In this issue of the Journal, three papers present results calling into question current perspectives that cancer patients should strive to maintain a weight consistent with normal Body Mass Index (BMI), i.e., BMI below 25. Implicit in this guideline is that survivors who are overweight or obese should attempt to lose weight. However, Cespedes et al. and Meyerhardt et al. demonstrate that weight loss predicts worse survival in some cases and Greenlee et al. show that across multiple cancer types, moderately elevated BMI does not consistently predict higher mortality.(1–3) These findings are consistent with Kroenke et al.’s recent report that overweight prostate cancer patients have better survival than normal weight prostate cancer patients, but stand in contrast to some prior observational research(4) and some current survivor guidelines.(5)

Better survival among overweight and obese compared with normal weight patients has been called the “obesity paradox.” It presents a troubling challenge to researchers, who must sort through the ambiguous evidence and make recommendations for weight management guidelines for cancer patients. Given the many demands on cancer patients, priority-setting is necessary. If intentional weight loss does not have substantial health benefits or may even harm cancer patients, clinical guidelines advising optimal BMI range below 25 for cancer patients should be revisited.(5) Thus, it is important to understand whether better survival among overweight and obese cancer patients reflects a causal effect on reduced mortality (i.e., overweight and obesity are protective for some cancer patients) or a non-causal association. If the protective associations linking overweight and obesity with lower mortality in cancer patients are a non-causal statistical artifact, then it should not be used as a guide for patient care. Previous work has identified several possible artifactual explanations for the obesity paradox in cancer or other chronic conditions,(6, 7) but Shachar and Williams identify plausible physiologic explanations for how excess adipose tissue might be protective for cancer patients.(8) Numerous threats to causal inference occur in obesity research, including measurement of adiposity and accounting for the effects of undiagnosed disease. In this commentary, we focus on only two possible artifactual explanations for the protective association between higher BMI and survival among cancer patients, which we call collider-stratification bias and heterogeneity in disease bias. We use simulations to illustrate how these sources of bias may induce spurious protective associations of overweight and obesity with mortality among cancer patients. In these simulations we focus on weight status at diagnosis, rather than evaluating weight loss directly. For this setting, both collider bias and heterogeneity of disease bias are mathematically possible, and have therefore been widely discussed as plausible explanations for the obesity paradox; however, each bias emerges only under specific causal scenarios which may not be common. The plausibility of bias-inducing scenarios differs between cancer types, and it is therefore important that researchers understand and evaluate these assumptions on a case by case basis. We aim to illustrate an approach to evaluating these two non-causal explanations for the obesity paradox.

Materials and Methods

Figures 1 and 2 illustrate the collider-stratification and heterogeneity in disease explanations for the obesity paradox in cancer. Given recent attention to heterogeneity in disease as a potential explanation for the obesity paradox in renal cancer,(9) we use renal cancer as the example in our simulations. Collider-stratification bias(10) is a non-causal association induced between an exposure and an outcome that can arise when analyzing data from only one, highly restricted, subgroup of people, such as renal cancer patients. In the case of the obesity paradox in renal cancer, this bias might occur if an unmeasured risk factor or group of risk factors influences both cancer incidence and post-diagnosis mortality (Figure 1). Heterogeneity in disease is a distinct source of bias (Figure 2), which may be of increasing relevance as molecular phenotyping demonstrates heterogeneity within malignancies previously considered similar.(9) This scenario is relevant because cancer diagnoses are often non-specific and could include any of multiple underlying neoplastic conditions, some of which are more aggressive than others. For example, heterogeneity in disease bias might occur if obesity causes an indolent type of renal cancer with excellent survival rates, but obesity has no effect on incidence of a much more aggressive type of renal cancer with low survival rates. If analyses do not separately evaluate survival of patients with indolent and aggressive cancer types, obesity could spuriously be associated with better survival. Both of these scenarios could create a spurious beneficial association between overweight or obesity and better survival of cancer patients, even if weight status had no beneficial effect on post-diagnosis survival. The same biases could, at least in theory, offset a harmful effect of obesity. Collider-stratification bias or heterogeneity in disease bias could be in the opposite direction and larger than any actual causal effect of obesity, creating a spurious protective net association between obesity and mortality in cancer patients.

Figure 1.

Collider-stratification bias scenario: obesity and unmeasured risk factors “A” increase renal cancer risk, but A only increases renal cancer risk for people who are not obese. Renal cancer increases mortality risk. Both obesity and A increase mortality risk in renal cancer patients. The box around “renal cancer” indicates that analyses are conducted among people with renal cancer. Restricting analyses to renal cancer patients could create a spurious association between obesity and A, and thereby make obesity appear to protect against mortality among renal cancer patients even though the causal effect of obesity is to increase mortality. The diagram would be equivalent for overweight.

Figure 2.

Heterogeneity in disease bias scenario: obesity increases risk of a relatively indolent form of renal cancer, which does not increase mortality risk, but obesity has no effect on an aggressive form of renal cancer, which increases mortality risk. Conducting analyses among all renal cancer patients, without distinguishing between indolent and aggressive cancer types, could make obesity look protective against mortality, even though the causal effect of obesity is to increase mortality. The diagram would be equivalent for overweight.

Both biases are mathematically possible, but are they likely? Both Figures 1 and 2 include a variable (or group of variables) that is unmeasured. For collider-stratification bias, the unmeasured variable is a patient characteristic (or set of characteristics) that influences both risk of cancer and post-diagnosis mortality. For example, unmeasured variables might include an unmeasured genetic risk variant, lifetime exposure to cigarette smoking, or a harmful occupational exposure. For heterogeneity in disease bias, the unmeasured variable is whether the diagnosed case is an indolent or aggressive form of cancer. The plausibility of these scenarios must depend on researchers’ judgement about these unknowns, but simulation models can provide a basis for such evaluations.(7, 11) Simulations allow us to say: given what we know about each type of cancer, is it plausible that overweight or obesity might appear harmless or protective when they are actually harmful for post-diagnosis survival?

We conducted simulations to assess the plausibility of collider-stratification bias and heterogeneity in disease bias explanations for the obesity paradox in cancer. These are simplified simulations created with the goal of illustrating the assumptions that researchers need to make in order to evaluate artifactual explanations for the obesity paradox. We consider a hypothetical cohort of 100,000 people without renal cancer, with equal numbers of normal weight, overweight, and obese people at baseline. Over the hypothetical study period, we specify cumulative incidence of renal cancer and a five-year risk of mortality among people with and people without renal cancer. Table 1 and Table 2 describe the specific values we assigned for these assumptions in our illustrative example, and we explain below.

Table 1.

Collider-stratification bias scenario simulation input parameters and observed association between obesity and mortality among renal cancer patients.

	Normal weight	Overweight	Obese
Input parameters based on published data
Prevalence of weight status in the populationa	0.333	0.333	0.333
Lifetime cancer riskb	0.012	0.016	0.021
Effect of weight status on cancer incidencec	ref	OR=1.50	OR=2.00
Input parameters based on expert opinion
Effect of unmeasured risk factor A on cancer riskd	OR=1.50	OR=1.00	OR=1.00
Effect of A on death of cancer patientsd	OR=2.00	OR=2.00	OR=2.00
Causal compared with observed association between weight status and mortality among renal cancer patients
Causal odds ratio for weight status and mortality among cancer patientse	ref	OR=1.10	OR=1.30
Observed odds ratio for weight status and mortality among cancer patients	ref	OR=0.86	OR=1.00

We assumed 5-year survival among cancer-free people of 0.93 (estimated based on US life tables for 65-year-olds(14)) and 5-year survival among cancer patients of 0.74 (based on SEER statistics(15)). OR=odds ratio. Results based on 1,000 replications.

^aApproximate prevalence of overweight and obesity in U.S. adult population.(16) Conceptually, our simulations assume that each individual’s weight status is stable throughout the period they are at risk for developing renal cancer.

^bLifetime cancer risk estimates by weight status are estimated to be consistent with SEER report of lifetime risk of kidney and renal pelvic cancers (0.016).(15)

^cEstimate of effects of weight status on renal cancer incidence from a large US cohort.(17)

^dDistribution of unmeasured risk factor “A” mean=0.0 and SD=1.0 for all weight status groups. A may represent a single risk factor or the combined effects of multiple risk factors operating in concert; examples of possible “A” variables might include an unmeasured genetic risk variant, lifetime exposure to cigarette smoking, or a harmful occupational exposure.

^eThe causal odds ratio for weight status and mortality among cancer patients assumes that the true causal OR for weight status on mortality is the same in cancer patients as in the general population of US adults. We assumed the ORs of 1.10 and 1.30 for overweight and obesity on mortality (estimates based on Berrington de Gonzaez et al(18)).

Table 2.

Heterogeneity in disease scenario simulation input parameters and observed association between obesity and mortality among renal cancer patients.

	Normal weight	Overweight	Obesity
Input parameters
Prevalence of weight status in the populationa	0.333	0.333	0.333
Lifetime indolent cancer riskb	0.010	0.016	0.018
Lifetime aggressive cancer riskb	0.001	0.001	0.001
Effect of weight status on indolent cancer incidencec	ref	OR=1.50	OR=2.00
Effect of weight status on aggressive cancer incidencec	ref	OR=1.00	OR=1.00
Causal compared with observed association between weight status and mortality among renal cancer patients
Causal odds ratio for weight status and mortality among cancer patientsd	ref	OR=1.10	OR=1.30
Observed odds ratio for weight status and mortality among cancer patients	ref	OR=0.94	OR=1.00

We assumed 5-year survival among cancer-free adults of 0.93 (based on US life tables for 65-year-olds(14)) and 5-year survival of 0.80 among patients with indolent cancer type and 0.08 among patients with aggressive cancer type (based on SEER estimate of 5-year survival for renal cancer (all stages)(15) and American Cancer Society survival estimates for renal cancer by stage(19)). OR=odds ratio. Results based on 1,000 replications.

^aEstimate of effects of weight status on renal cancer incidence from a large US cohort.(16) Conceptually, our simulations assume that each individual’s weight status is stable throughout the period they are at risk for developing renal cancer.

^bEstimated based on SEER report of lifetime risk of kidney and renal pelvic cancers (0.016),(15) and assuming 9% of renal cancer cases are an “aggressive” type and 91% are a relatively “indolent” type. As a proxy to estimate frequency of aggressive cancer type, we used stage 4 at diagnosis from Hakimi and Furberg et al.(20)

^cWe assumed that weight status has no effect on aggressive cancer incidence and that the effect of weight status on indolent cancer incidence is approximated by the effect of weight status on renal cancer overall because the vast majority of renal cancer is assumed to be of the indolent form.

^dThe causal odds ratio for weight status and mortality among cancer patients assumes that the true causal OR for weight status on mortality is the same in cancer patients as in the general population of US adults. We assumed the ORs of 1.10 and 1.30 for overweight and obesity on mortality (estimates based on Berrington de Gonzaez et al(18)).

Results

For the collider-stratification bias scenario, we assume that overweight and obesity increase odds of cancer by 50% and 100%, respectively. Each unit increase in the unmeasured risk factor “A” increases odds of renal cancer by 50% among normal weight people, but has no effect on odds of renal cancer among overweight or obese people. We incorporated interaction between weight status and risk factor A on odds of cancer. Prior work demonstrates that the magnitude of bias arising from collider-stratification bias is substantially larger if such an interaction is present.(7, 11–13) The unmeasured factor A doubles odds of mortality after cancer diagnosis regardless of weight status. We assume five-year survival for renal cancer patients is 74%. With these assumptions, overweight and obese people with renal cancer are less likely to have high levels of risk factor A than normal weight people with renal cancer (which was not the case in the cancer-free population). Because A has larger effects on mortality than do overweight or obesity, the net association of overweight and obesity with survival among renal cancer patients is beneficial. Under the input parameters we chose (which would differ by cancer type), we found that although overweight and obesity were assumed to have harmful causal ORs for mortality (1.10 and 1.30, respectively), the observed ORs for the association between overweight and obesity on mortality among renal cancer patients were biased downwards from the casual effects (to 0.86 and 1.00, respectively) (Table 1).

To evaluate the heterogeneity in disease scenario, we assume there are two types of renal cancer, a common, relatively indolent version with 5-year survival of 80%, and a rarer, aggressive type with 5-year survival of 8%. We assume overweight and obesity increase odds of the indolent form of renal cancer by 50% and 100%, respectively, but have no effects on incidence of the aggressive form. In this setting, among people with renal cancer, overweight and obesity are correlated with having the indolent form of cancer, whereas normal weight patients are more likely to have the aggressive form of cancer. Under the input parameters we chose (which would differ by cancer type), we found that although overweight and obesity were assumed to have harmful causal ORs for mortality (1.10 and 1.30, respectively), the observed ORs for the association between overweight and obesity on mortality among renal cancer patients were biased downwards from the casual effects, with ORs of 0.94 and 1.00, respectively (Table 2).

Discussion

Using simulations, we examined two artifactual explanations for the obesity paradox in cancer and how to approach evaluating these non-causal explanations. Collider-stratification bias or heterogeneous disease bias could induce spurious, protective associations of overweight and obesity with mortality in cancer patients, even if overweight and obesity truly have modestly harmful causal effects on mortality. An especially influential and uncertain assumption in the collider-stratification bias scenario is the large interaction between weight status and risk factor A on cancer risk.(7, 11–13) Subject matter experts must consider whether such an interaction is plausible. Advances in molecular phenotyping(9) will strengthen evidence for reasonable input parameters for the heterogeneity in disease scenario.

The magnitude of the spurious association of overweight and obesity with mortality in renal cancer patients from each of these phenomena depends on unknown parameters. Scientific experts will need to evaluate whether these parameters are plausibly large enough to account for the observed associations in each type of cancer. Because both artifactual and causal phenomena may account for the obesity paradox, a case by case examination of the links between obesity and mortality for each cancer type is necessary. Over the long run, other approaches, such as randomized trials or quasi-experiments, can help evaluate whether these associations are causal, but researchers, clinicians, and patients need to know the best available evidence in the short term. The three articles in this issue of the Journal provide vital preliminary evidence. We described the assumptions under which two important artifactual explanations may lead to underestimation of harmful effects of overweight and obesity, and provided a simulation tool to estimate the magnitude of bias for alternative cancer types (Supplemental Material). The next step is for topical experts to evaluate whether these assumptions, or more extreme values, are plausible for various cancer types. If better cancer survival among overweight or obese patients cannot be explained with an artifact, we must seriously consider the possibility that excess weight has health benefits (or at least no health harms) for cancer patients and incorporate this evidence into clinical care.