# Presentation: 369989

## Estimation of overweight-attributable deaths

**Katherine M. Flegal, Ph.D.**

**Centers for Disease Control and Prevention**
**National Center for Health Statistics**

## Allison et al, 1999

- Allison, JAMA 1999 calculated deaths attributable to overweight and obesity in 1991,
-  using relative risks from six cohort studies
- combined with overweight and obesity prevalence from NHANES III
- and with mortality statistics for 1991.

## Actual causes of death paper, 2004

- Actual causes of death, JAMA 2004 calculated deaths attributable to overweight and obesity in 2000
-  using the same relative risks from the same six cohort studies as Allison
- combined with overweight and obesity prevalence from NHANES 1999-2000
- and with mortality statistics for 2000.

## Calculation errors in Actual Causes of Death paper

- For five of the six cohorts, the number of deaths in 1991 was used instead of the number of deaths in 2000
- For five of the six cohorts, the prevalence of BMI < 25 was taken from NHANES III but the prevalence of higher BMI categories was taken from NHANES 99-00

## Published and recalculated numbers of overweight-attributable deaths

## Mean overweight-attributable deaths over six cohorts

## Issues - 2

- Allison 1999 used a method of calculating attributable fractions – the “partially adjusted” method -  that does not fully account for confounding or effect modification

## Derivation Cohort: e.g. Framingham

- Population attributable fraction

- Total deaths

- Number of deaths attributable to obesity in target population

- Target population – the US**:**

## Derivation Cohort: e.g. Framingham

- Target population – the US:

- Population attributable fraction

- Total deaths

- Number of deaths attributable to obesity in target population

- Target population – the US**:**

## Population Attributable Fraction (PAF)

- PAF =

- P(E) * (RR-1)

- 1 + (P(E) * (RR-1))

- P(E) = prevalence of obesity

- RR = unadjusted relative risk of mortality associated with obesity

## 
Weighted sum method
“Partially-adjusted” method

- Weighted sum method
- “Partially-adjusted” method

- Calculating PAF when there is confounding of the exposure-outcome relation

## Weighted sum method

| Group | N | P(E) | RR | No. of deaths | PAF | Excess deaths |
| --- | --- | --- | --- | --- | --- | --- |
| A | 1000 | .5 | 2 | 150 | .333 | 50 |
| B | 500 | .1 | 2 | 165 | .0909 | 15 |
| Sum |  |  |  |  |  | 65 |

## “Partially adjusted” method

| Group | N | P(E) | RR | No. of deaths | PAF | Excess deaths |
| --- | --- | --- | --- | --- | --- | --- |
| A | 1000 | .5 | 2 | 150 | .333 | 50 |
| B | 500 | .1 | 2 | 165 | .0909 | 15 |
| Sum |  |  |  |  |  | 65 |
| Total | 1500 | .37 | 2 | 315 | .2683 | 84.5 |

## Rockhill et al, 1998

- 1998, Rockhill B, Newman B, Weinberg C.  Use and misuse of population attributable fractions, Am J Pub Hlth
- “..Errors in estimation are common. Probably the most common error is the use of adjusted relative risks in formula 3 [formula for unadjusted RR].  The magnitude of the bias resulting from this error will depend on the degree of confounding.”  P. 16

##        “Partially-adjusted” method	

- Annual deaths attributable to obesity in the United States. JAMA. 1999; 282:1530-8.
- A simple estimate of mortality attributable to excess weight in the European Union.  Eur J Clin Nutr. 2003;57:201-8.
- Actual causes of death in the United States, 2000. JAMA. 2004;291:1238-45
- Overweight, obesity, and mortality from cancer in a prospectively studied cohort of U.S. adults. N Engl J Med. 2003;348:1625-38.

## Benichou, 2001

- 2001, Benichou J, , A review of adjusted estimators of attributable risk, Stat Med
- “Another natural approach based on using equation (2) [formula for unadjusted RR] and plugging in a common adjusted relative risk estimate...has been advocated but it too has been shown to yield inconsistent estimates. and accordingly, severe bias was exhibited in simulations...” p. 200

##        “Partially-adjusted” method	

- Calculate adjusted relative risks
- Use a PAF formula appropriate only for unadjusted relative risks
- Treat the population as a single group (no stratification)
- In general, when there is confounding, gives biased results, but degree of bias not often quantified

## Bias arising from ignoring confounding by age and sex

- Partially adjusted method overestimated excess deaths due to obesity by 17% in this hypothetical example using published relative risks, NHANES III prevalence estimates and 1991 mortality data

## Relative risks of mortality associated with obesity decrease with age

- Source: Calle et al NEJM, 1999

## Derivation Cohort: e.g. Framingham

- Target population – the US:

- Population attributable fraction

- Total deaths

- Number of deaths attributable to obesity in target population

- Target population – the US**:**

## Bias arising from ignoring confounding and effect modification

- Partially adjusted method overestimated excess deaths by 42% in this example when the derivation cohort had 0.4% elderly (80+ y) and the target population had 3.4% elderly

## Derivation cohort and the target population 

- If there is effect modification, additional bias may result from using the ‘partially adjusted method’ when the derivation cohort differs from the target population in:
- Relative proportion of subgroups
- Probability of mortality in the non-obese
- Prevalence of obesity

## The “partially adjusted” method 

- Commonly used and intuitively appealing
- Statistical literature has already documented that the partially adjusted method gives rise to bias
- Our  hypothetical examples suggest bias upwards for deaths associated with obesity
- Even when this method shows little bias in a derivation cohort, the results may be biased when applied to a different population

## Why not  just use the weighted sum method?

- Age and sex are not the only confounders.
- The weighted sum method requires information on the number of deaths within each subgroup – information not generally available.
- An alternative PAF approach when there is confounding would require knowledge of the proportion of decedents who were obese – also information not generally available

## The “partially adjusted” method 

- Attempts to solve the problem of having relative risks from one cohort combined with exposure data from a different source
- This method has already been shown in the statistical literature to lead to bias
- A different approach is needed to account for confounding and for effect modification