Inappropriate use of statistical power.

INTRODUCTION: We are pleased to add this typescript, Inappropriate use of statistical power by Raphael Fraser to the BONE MARROW TRANSPLANTATION Statistics Series. The authour discusses how we sometimes misuse statistical analyses after a study is completed and analyzed to explain the results. The most egregious example is post hoc power calculations.When the conclusion of an observational study or clinical trial is negative, namely, the data observed (or more extreme data) fail to reject the null hypothesis, people often argue for calculating the observed statistical power. This is especially true of clinical trialists believing in a new therapy who wished and hoped for a favorable outcome (rejecting the null hypothesis). One is reminded of the saying from Benjamin Franklin: A man convinced against his will is of the same opinion still.As the authour notes, when we face a negative conclusion of a clinical trial there are two possibilities: (1) there is no treatment effect; or (2) we made a mistake. By calculating the observed power after the study, people (incorrectly) believe if the observed power is high there is strong support for the null hypothesis. However, the problem is usually the opposite: if the observed power is low, the null hypothesis was not rejected because there were too few subjects. This is usually couched in terms such as: there was a trend towards… or we failed to detect a benefit because we had too few subjects or the like. Observed power should not be used to interpret results of a negative study. Put more strongly, observed power should not be calculated after a study is completed and analyzed. The power of the study to reject or not the null hypothesis is already incorporated in the calculation of the p value.The authour use interesting analogies to make important points about hypothesis testing. Testing the null hypothesis is like a jury trial. The jury can find the plaintiff guilty or not guilty. They cannot find him innocent. It is always important to recall failure to reject the null hypothesis does not mean the null hypothesis is true, simply there are insufficient evidence (data) to reject it. As the author notes: In a sense, hypothesis testing is like world championship boxing where the null hypothesis is the champion until defeated by the challenger, the alternative hypothesis, to become the new world champion.The authour include a discussion of what is a p-value, a topic we discussed before in this series and elsewhere [1, 2]. Finally, there is a nice discussion of confidence intervals (frequentist) and credibility limits (Bayesian). A frequentist interpretation views probability as the limit of the relative frequency of an event after many trials. In contrast, a Bayesian interpretation views probability in the context of a degree of belief in an event . This belief could be based on prior knowledge such as the results of previous trials, biological plausibility or personal beliefs (my drug is better than your drug). The important point is the common mis-interpretation of confidence intervals. For example, many researchers interpret a 95 percent confidence interval to mean there is a 95 percent chance this interval contains the parameter value. This is wrong. It means, if we repeat the identical study many times 95 percent of the intervals will contain the true but unknown parameter in the population. This will seem strange to many people because we are interested only in the study we are analyzing, not in repeating the same study-design many times.We hope readers will enjoy this well-written summary of common statistical errors, especially post hoc calculations of observed power. Going forth we hope to ban statements like there was a trend towards… or we failed to detect a benefit because we had too few subjects from the Journal. Reviewers have been advised. Proceed at your own risk. Robert Peter Gale MD, PhD, DSc(hc), FACP, FRCP, FRCPI(hon), FRSM, Imperial College London, Mei-Jie Zhang PhD, Medical College of Wisconsin.

A note on median regression for complex surveys.

There is a great need for statistical methods for analyzing skewed responses in complex sample surveys. Quantile regression is a logical option in addressing this problem but is often accompanied by incorrect variance estimation. We show how the variance can be estimated correctly by including the survey design in the variance estimation process. In a simulation study, we illustrate that the variance of the median regression estimator has a very small relative bias with appropriate coverage probability. The motivation for our work stems from the National Health and Nutrition Examination Survey where we demonstrate the impact of our results on iodine deficiency in females compared with males adjusting for other covariates.

The effect of earlier puberty on cardiometabolic risk factors in Afro-Caribbean children.

An earlier onset of puberty is associated with increased cardiometabolic risk. We investigated whether this relation was independent of faster childhood growth or current size in an Afro-Caribbean birth cohort (n=259). Anthropometry was measured at birth and then 6-monthly. Tanner staging started at age 8 years. Cardiometabolic risk factors were measured at mean age 11.5 years. In boys, pubarchal stage and testicular size were associated with lower high-density lipoprotein cholesterol, higher systolic blood pressure, and higher homeostasis model assessment of insulin resistance score, but not after adjusting for current body mass index (BMI) or rate of growth (up to age 8 years). In girls, earlier menarche and greater breast development were associated with higher fasting glucose even after adjusting for current BMI or prior growth. Pubarchal stage was associated with systolic blood pressure, even after adjusting for current BMI and prior growth. We concluded that earlier puberty is independently associated with cardiometabolic risk in girls but not in boys.

Higher rates of hemolysis are not associated with albuminuria in Jamaicans with sickle cell disease.

BACKGROUND: Albuminuria is a marker of glomerular damage in Sickle Cell Disease (SCD). In this study, we sought to determine the possible predictors of albuminuria in the two more prevalent genotypes of SCD among the Jamaica Sickle Cell Cohort Study participants. METHODS: An age-matched cohort of 122 patients with HbSS or HbSC genotypes had measurements of their morning urine albumin concentration, blood pressure, body mass index, haematology and certain biochemistry parameters done. Associations of albuminuria with possible predictors including hematological parameters, reticulocyte counts, aspartate aminotransferase (AST) and lactate dehydrogenase (LDH) levels were examined using multiple regression models. RESULTS: A total of 122 participants were recruited (mean age 28.6 years ±2.5 years; 85 HbSS, 37 HbSC). 25.9% with HbSS and 10.8% with HbSC disease had microalbuminuria (urine albumin/creatinine ratio  =  30-300 mg/g of creatinine) whereas 16.5% of HbSS and 2.7% of HbSC disease had macroalbuminuria (urine albumin/creatinine ratio>300 mg/g of creatinine). Mean arterial pressure, hemoglobin levels, serum creatinine, reticulocyte counts and white blood cell counts were statistically significant predictors of albuminuria in HbSS, whereas white blood cell counts and serum creatinine predicted albuminuria in HbSC disease. Both markers of chronic hemolysis, i.e. AST and LDH levels, showed no associations with albuminuria in either genotype. CONCLUSIONS: Renal disease, as evidenced by excretion of increased amounts of albumin in urine due to a glomerulopathy, is a common end-organ complication in SCD. It is shown to be more severe in those with HbSS disease than in HbSC disease. Rising blood pressure, lower hemoglobin levels and higher white blood cell counts are hints to the clinician of impending renal disease, whereas higher rates of hemolysis do not appear to play a role in this complication of SCD.

Hb S-ß-thalassemia: molecular, hematological and clinical comparisons.

Clinical and hematological features are presented for 261 patients with identified ß-thalassemia (ß-thal) mutations. Mutations causing Hb S [ß6(A3)Glu→Val]-ß(0)-thal were IVS-II-849 (A>G) in 44%, frameshift codon (FSC) 6 (-A) in 14%, Hb Monroe [ß30(B12)Arg→Thr] in 14%, and IVS-II-1 (G>A) in 10%. Mutations causing Hb S-ß(+)-thal with 14-25% Hb A (type III) were -29 (A>G) mutation in 60%, -88 (C>T) in 22% and the polyadenylation signal site (polyA) (T>C) mutation in 14%, and in Hb S-ß(+)-thal with 1-7% Hb A (type I), all had the IVS-I-5 (G>C) mutation. Hematologically, only minor differences occurred between the four Hb S-ß(0)-thal mutations, but among the three mutations causing Hb S-ß(+)-thal type III, levels of Hb A(2), Hb F, hemoglobin (Hb), MCV and MCH were highest in the -88 and lowest in the polyA mutations. Clinically, Hb S-ß(0)-thal and Hb S-ß(+)-thal type I were generally severe, and Hb S-ß(+)-thal type III disease with the -88 mutation was milder than that caused by the polyA mutation.

Developmental origins of cardiovascular risk in Jamaican children: the Vulnerable Windows Cohort study.

Both intra-uterine and early childhood development contribute to the risk of developing CVD in adult life. We therefore evaluated the maternal, placental, fetal, birth, infant and childhood determinants of cardiovascular risk in a cohort of Afro-Jamaican children. The Vulnerable Windows Cohort is a longitudinal survey of 569 mothers and their offspring recruited from the first trimester. The offspring's anthropometry was measured at birth, at 6 weeks, every 3 months to 1 year and then every 6 months. At mean age 11.5 years, fasting blood was sampled for glucose, insulin and lipids. Analyses were confined to 296 women and their offspring who had complete data. Waist circumference (WC) was related to maternal weight and BMI, placental weight and to the size of the offspring in utero, at birth and the rate of growth in childhood (P < 0.05). Total cholesterol, TAG and glucose concentrations were unrelated to maternal, placental, fetal, neonatal and childhood measurements. Fasting insulin and homeostasis model assessment of insulin resistance were related to maternal weight and BMI (P < 0.05), but not after adjusting for WC. HDL-cholesterol was inversely related to placental and birth weight, and inversely related to weight and BMI throughout childhood (P < 0.001), but not after adjusting for WC. Systolic blood pressure was directly related to maternal weight, child's height, weight and BMI (P < 0.05), but not after adjustment for WC. Systolic blood pressure and fasting glucose concentration were inversely related to birth weight in boys but directly associated in girls. We concluded that maternal anthropometry during pregnancy, fetal size, and childhood growth rate contribute to cardiovascular risk factors in childhood.

Growth, body composition, and the onset of puberty: longitudinal observations in Afro-Caribbean children.

CONTEXT: Childhood growth and body composition may influence the onset of puberty. OBJECTIVE: We examined the effects of birth size, growth rates throughout childhood, and body composition on the onset of puberty in Afro-Caribbean children. DESIGN AND SETTING: This was a longitudinal birth cohort study (the Vulnerable Windows Cohort Study) in Jamaica. SUBJECTS AND MEASUREMENTS: The anthropometry (weight, height, skinfold measurements, and waist circumference) of 259 children was measured at birth, at 6 wk, every 3 months to 2 yr, and then every 6 months. Tanner staging for puberty and orchidometry were performed every 6 months starting at approximately age 8 yr. Bioelectrical impedance was done at age 11 yr. RESULTS: In the girls, thelarche, pubarche, and menarche occurred at median ages of 8.8, 9.9, and 12.0 yr, respectively. Pubarche in boys occurred at a median age of 11.3 yr when the median testicular volume was 2.8 ml. Faster weight gain during infancy (age 0-6 months) and childhood, but not birth size, was associated with more advanced puberty (P values <0.05). Fat mass at age 8 yr was associated with more advanced puberty (P values <0.001) in both sexes. At age 11 yr, lean mass, but not fat mass, was associated with more advanced puberty (P values <0.001). CONCLUSION: These data support the hypothesis that faster growth throughout childhood, especially with fat mass accretion, is associated with more advanced puberty apart from menarche. With the onset of puberty, lean mass accretion significantly increases.