On some osteoporosis analyses

Abstract

The articles by Reginster et al. [1] and Bhattoa et al. [2] are flawed, because the analysis of variance and the twosample t -tests or variations to it are inappropriate. The Central Limit Theorem justifies the normality assumed by these methods for mean inferences. The problem is that the two above methods also assume that the unknown variances of the groups of interest are equal. Since unknown variances need not be equal, both the analysis of variance and the two-sample t -tests are not generally applicable to comparing means. Futilely [3] testing for the equality of variances does not remove this problem. Nor does avoiding normality with nonparametric rank tests such as the KruskalWallis test. Being a comparison of distributions, the latter says nothing about the means or any specific moment of the distributions if significant, and is biased to one side [4] in a two-sided test. Tsakok [5] has solved this Behrens-Fisher problem of exactly comparing the means of normal distributions from samples in its generalized form, simultaneously showing that it is more effective in detecting significant mean differences, even with unknown equal variances. Its exposition [6] is available. The software GSP implements the Tsakok technique. Applying it to compare means at .02 (one significant figure) significance level per comparison, GSP finds significant differences in calcium of Table 5 [1] between placebo and the strontium ranelate (SR) 1 g/day group at M12 and M24. For Table 3 [1], GSP finds significant differences of BMD percentage change in femoral neck between placebo and SR 125 mg/day, in femoral neck between placebo and SR 500 mg/day and in total hip between placebo and SR 500 mg/day. For Table 3 [2], GSP finds significant differences in the intention-to-treat C4 between estradiol and placebo at months 3, 6, 9 and 12. For on-treatment total complement activity (CH50/ml) estradiol of Table 3 [2], there are significant differences between baseline and months 9 and 12. For on-treatment C3 estradiol (Table 3 [2]), there are also significant differences between baseline and months 9 and 12. These were overlooked. The care acquiring the data means that they deserve correct analysis. The article by Tsakok [7] on constructing exact, unconditional uniformly most powerful unbiased tests extends the Tsakok technique to the nonparametric problem of comparing samples, superseding rank tests, the chi-squared test or the Fisher’s ‘‘exact’’ test (it is neither exact nor unconditional). There is an indication [8] that the Tsakok technique applies to dependent samples. The Tsakok articles are reprinted [9] with further results.