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Survivors (non-survivors) whose Ps values are less than (exceed) 0.5 are identified as having statistically 'unexpected outcomes' and as being worthy of peer review. Survival/death outcome evaluation z and W statistics

Principally because of the MTOS (1982-1989) endorsed by the American College of Surgeons, z and W statistics have become standards for comparison of survival/death outcomes among patient subsets. z and W compare the actual number (A) of survivors in a patient sample with the expected number (E) based on TRISS or ASCOT norms. W measures the clinical significance and z the statistical significance of the comparison.

W represents the difference between the actual and expected numbers of survivors per 100 patients treated. For example, a W value of +2 signifies that A > E and means that there were two more survivors per 100 patients treated than would have been expected based on national data. Likewise, a W value of -2 signifies that A < E and means that there were two fewer survivors per 100 patients treated than would have been expected.

For W to be statistically different from zero, z must be greater than +1.96 or less than -1.96. If z is between -1.96 and +1.96, the difference between A and E is not statistically different from zero and thus neither is W.

The formulas for W and z are

where N is the number of patients in the sample and z = (A - E)/S

S is a scale factor that accounts for statistical variation. The following two examples illustrate why both W and z are needed. Example 1

Suppose that an institution has the same outcome results for five successive years, i.e for each year N = 500, A = 455, E = 450, and S = 1.

For each year z = 1.25 and W = 1, and neither is statistically different from zero. However, for all 2500 patients, both z = 2.80 and W = 1 are statistically different from zero. This indicates that, although the yearly outcomes were not statistically better than expected based on MTOS norms, as the sample size increased the results became significant and indicate one more survivor than expected per 100 patients treated.

If the institution had the same results for 20 years, W would still be 1 but z would increase to 10, signifying a stronger statistical certification of the results. Example 2

The z and W values for six United States trauma centers are given in T§b.!e .Z.. The results for center 5 are better than those for center 3, as N, z, and W are greater for center 5. The results for center 1 are even better than those for center 5. Although center 2 has a striking W value, the small sample size causes one to reserve judgment about its ability to sustain such a large W value as N increases. Center 6 is an example of large z and small W values. The W value of 0.58 indicates a slight improvement in survival rate over the norm; the z value of 10.23 indicates that this slight improvement is strongly statistically significant. However, the large sample size gives the potential for large z values.

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Table 7 z and W values for six trauma centers

Table 7 z and W values for six trauma centers

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