HLTH 4200 Week 7 Confounding Write-Up Example

Why Hospital A Looks Worse and Is Not: Surgical Deaths at Two Composite Hospitals Split by Admission Type, and How the Third Variable Reverses the Comparison

Student Name

Walden University

HLTH 4200: Principles of Epidemiology

Instructor Name

Month Day, Year

Why Hospital A Looks Worse and Is Not: Surgical Deaths at Two Composite Hospitals Split by Admission Type, and How the Third Variable Reverses the Comparison

The Crude Comparison

A county health report, composite for this exercise, compares 30-day surgical death rates at its two hospitals for one year. Hospital A had 66 deaths after 1,000 operations, a rate of 6.6%. Hospital B had 32 deaths after 1,000 operations, a rate of 3.2%. Read on its face, the crude comparison suggests that patients at Hospital A were about twice as likely to die after surgery, a crude risk ratio of 6.6 ÷ 3.2 = 2.06.

The two hospitals, however, do different work. Hospital A, near the interstate, takes most of the county's emergency operations: trauma, ruptured appendixes, bowel obstructions. Hospital B mainly performs scheduled operations, such as joint replacements and planned hernia repairs. Emergency surgery carries a much higher risk of death than scheduled surgery, whatever the hospital.

The Comparison Split by Admission Type

Within emergency operations, Hospital A's death rate, 8.0%, is lower than Hospital B's, 10.0%. Within scheduled operations, Hospital A's rate, 1.0%, is again lower than Hospital B's, 1.5%. Hospital A fares better in every group, yet worse overall. This reversal is known as Simpson's paradox (Julious & Mullee, 1994).

Table 1

Surgical Deaths by Hospital and Admission Type

Within each admission type, Hospital A has the lower death rate; only the combined rate favors Hospital B.

Why the Reversal Happens

Admission type is a confounder: it is associated with the exposure, which hospital a patient used, and independently with the outcome, death after surgery, and it is not a step on the path between them (Centers for Disease Control and Prevention, 2012). Eighty percent of Hospital A's operations were emergencies, compared with 20% of Hospital B's. Because emergency operations carry death rates many times those of scheduled ones, Hospital A's overall rate is pulled up by its case mix. The crude comparison is not a comparison of hospital quality; it is mostly a comparison of how many emergency patients each hospital treated.

The same pattern has appeared in real clinical data. In a widely cited comparison of treatments for kidney stones, one treatment had a higher success rate for both small and large stones, yet a lower success rate overall, because it was used more often for large stones, which are harder to treat (Charig et al., 1986). Julious and Mullee (1994) used those data to show how a confounder can reverse an association when groups differ in their mix.

Adjusting for Admission Type

Two methods remove the influence of case mix.

Direct Standardization

Apply each hospital's admission-type-specific rates to a single standard population, here the two hospitals' combined operations: 1,000 emergency and 1,000 scheduled.

On a common case mix, Hospital A's standardized rate is 4.5% and Hospital B's is 5.75%. The standardized risk ratio is 4.5 ÷ 5.75 = 0.78.

Table 2

Directly Standardized Death Rates

With the same case mix, Hospital A's expected death rate is lower than Hospital B's.

Mantel-Haenszel Risk Ratio

The Mantel-Haenszel method combines the stratum-specific comparisons into one summary, weighting each stratum by its size. For each stratum, the numerator term is Hospital A's deaths multiplied by Hospital B's operations, divided by the stratum total, and the denominator term is Hospital B's deaths multiplied by Hospital A's operations, divided by the stratum total.

Emergency: numerator 64 × 200 ÷ 1,000 = 12.8; denominator 20 × 800 ÷ 1,000 = 16.0.

Scheduled: numerator 2 × 800 ÷ 1,000 = 1.6; denominator 12 × 200 ÷ 1,000 = 2.4.

Summary risk ratio = (12.8 + 1.6) ÷ (16.0 + 2.4) = 14.4 ÷ 18.4 = 0.78.

Both methods give an adjusted risk ratio of about 0.78: after accounting for admission type, patients at Hospital A had about 22% lower risk of death than comparable patients at Hospital B. The crude ratio of 2.06 and the adjusted ratio of 0.78 point in opposite directions.

Checking Whether Adjustment Is Appropriate

Adjustment combines strata into one summary, which is sensible only when the comparison is similar across strata. Here, Hospital A's risk relative to Hospital B is 0.80 for emergency operations (8.0 ÷ 10.0) and 0.67 for scheduled operations (1.0 ÷ 1.5). The two stratum-specific ratios point the same way and are reasonably close, so a single adjusted ratio is a fair summary. If Hospital A had been better for emergencies but worse for scheduled operations, a single summary would hide a real difference, and the stratum-specific results should be reported instead.

What the Adjusted Figure Does and Does Not Show

The adjusted comparison removes the effect of admission type. It does not remove other differences between the hospitals' patients. Within emergency surgery, Hospital A may treat more trauma and Hospital B more elderly patients with bowel obstruction; within scheduled surgery, patients may differ in age and illness. Each of these could confound the comparison further, and a full analysis would adjust for them, typically with a measure of patient severity. Adjustment can only remove confounding by variables that were measured, and it cannot rescue a comparison from differences no one recorded.

The write-up also shows a reporting lesson. A report that published only the crude rates would have directed patients, payers or regulators away from the hospital that performed better within every type of surgery.

Conclusion

Crude surgical death rates made Hospital A look twice as dangerous as Hospital B. Splitting by admission type showed that Hospital A had lower death rates for both emergency and scheduled operations, and that its higher crude rate reflected its much larger share of emergency surgery. Adjusted by standardization or by the Mantel-Haenszel method, the risk ratio was about 0.78, favoring Hospital A. Admission type confounded the crude comparison and reversed its direction.

References

Centers for Disease Control and Prevention. (2012). Principles of epidemiology in public health practice: An introduction to applied epidemiology and biostatistics (3rd ed.). U.S. Department of Health and Human Services. https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/index.html

Charig, C. R., Webb, D. R., Payne, S. R., & Wickham, J. E. (1986). Comparison of treatment of renal calculi by open surgery, percutaneous nephrolithotomy, and extracorporeal shockwave lithotripsy. BMJ, 292(6524), 879-882. https://doi.org/10.1136/bmj.292.6524.879

Julious, S. A., & Mullee, M. A. (1994). Confounding and Simpson's paradox. BMJ, 309(6967), 1480-1481. https://doi.org/10.1136/bmj.309.6967.1480