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Ljk.imag.frBiostatistics Primer: Part I
Brian R. Overholser and Kevin M. Sowinski The online version of this article can be found at: http://ncp.sagepub.com/cgi/content/abstract/22/6/629 can be found at:
Nutrition in Clinical Practice
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Biostatistics Primer: Part I
Brian R. Overholser, PharmD; and Kevin M. Sowinski, PharmD, BCPS, FCCPDepartment of Pharmacy Practice, Purdue University, School of Pharmacy and Pharmaceutical Sciences, WestLafayette and Indianapolis, Indiana; and the Department of Medicine, Indiana University, School of Medicine,Indianapolis, Indiana ABSTRACT: Biostatistics is the application of statistics
the scope of this review, but the importance of the to biologic data. The field of statistics can be broken down chosen sampling procedure should not be over- into 2 fundamental parts: descriptive and inferential.
Descriptive statistics are commonly used to categorize, In clinical studies, the specific individuals are display, and summarize data. Inferential statistics can be commonly patients or healthy research subjects. The used to make predictions based on a sample obtained from information collected from the subjects is referred to a population or some large body of information. It is these as variables. Variables are measurable characteris- inferences that are used to test specific research hypoth- tics or attributes of these research subjects (eg, eses. This 2-part review will outline important features of weight, age, blood pressure). The collected variables descriptive and inferential statistics as they apply to are used as estimates of the actual population char- commonly conducted research studies in the biomedical acteristics. The specific type of the variable collected literature. Part 1 in this issue will discuss fundamental is important to determine how to properly summa- topics of statistics and data analysis. Additionally, some of rize the data and to determine what type of statis- the most commonly used statistical tests found in the tical test should be used to test a specific hypothesis.
biomedical literature will be reviewed in Part 2 in theFebruary 2008 issue.
Variables can be classified as qualitative and quantitative. Qualitative variables can be furtherclassified as nominal or ordinal. Nominal variables,also referred to as categorical variables, are descrip- The Basics
tive for a name or category. For example, the sex of a research subject is a commonly collected nominalvariable (ie, male or female). Sex is an unordered Sampling is the most fundamental concept in categorical variable. Categorical variables that have both descriptive and inferential statistics. Sampling a specific order associated with them are termed is the process of randomly obtaining information ordinal. For example, nutrition studies in patients from larger bodies of information called populations.
with chronic liver disease often assess the baseline It is these samples that are used to describe or make severity of liver function using the Child-Pugh score inferences about the entire population. A sample is (class A, B, or C).2 These variables are categorical obtained from a larger population because in most and more specifically ordinal because a class A score instances, especially in the medical field, it is impos- has a better prognosis associated with it than class sible to study the entire population. Therefore, sam- ples are obtained from the selected population Quantitative variables can be continuous or dis- according to the specific research question and are crete. A variable is by definition a continuous vari- used to predict valuable information about the able if it can take on any value within a given range.
entire population. Specific sampling procedures and By this convention, a continuous variable could take methods for assurance of randomization are beyond on an infinite number of possibilities for a givenrange. For example, age is an example of a continu-ous variable. Even if the protocol of a research studyonly recruits subjects between 20 and 30 years old,age remains a continuous variable in that study.
Correspondence: Kevin M. Sowinski, PharmD, BCPS, FCCP, There are still an infinite number of values that age Purdue University, Department of Pharmacy Practice, W7555 could take, even though there is a predefined range Myers Building, WHS, 1001 West Tenth Street, Indianapolis, IN46202. Electronic mail may be sent to firstname.lastname@example.org.
for this study. Age can be reported in years, months,days, hours, seconds, and so on. Therefore, there is always a more accurate way to represent a continu- Nutrition in Clinical Practice 22:629–635, December 2007Copyright 2007 American Society for Parenteral and Enteral Nutrition ous measure, such as age, and it is dependent on the 2007 The American Society for Parenteral and Enteral Nutrition. All rights reserved. Not for commercial use or unauthorized distribution.
methods in the study. As an example, a 20-year-oldresearch subject could be classified as 19.8 years oldor as 19.76 years old, etc. There are an infinitenumber of ways to classify the age of this subject,and hence this variable fits the definition of acontinuous variable.
Unlike continuous variables, discrete variables can only take on a limited number of values in anygiven range. For example, the Clinical Risk Indexfor Babies (CRIB) is a scoring system that takes intoconsideration several continuous and ordinal vari-ables to provide an index of initial neonatal risk. Thescoring system generates a whole number. Forinstance, the CRIB index cannot have a value of1.4.3 Therefore, the magnitude of the differencebetween a score of 2 and a 1 may not be equivalent Figure 1. Grouped frequency histogram generated from a to the difference between a score of 3 and that of a 2.
simulation of 1000 low-density lipoprotein (LDL) concen-trations. The simulated data were broken down into 10 In some cases, discrete variables may be grouped to equal class intervals. The smooth line was generated as a make them easier to handle. Ordinal variables, symmetrical bell-shaped curve overlying the histogram, which are categorical, are commonly assigned representing a normal population distribution.
numeric values, which transform them into discretevariables.
For example, low-density lipoprotein (LDL) cho- Section 1: Descriptive Statistics
lesterol concentrations were randomly generated for1000 hypothetical subjects. LDL is a continuous Descriptive statistics are used to summarize and variable because it can take on an infinite number of display raw data that are collected or generated in values in a given range. The 1000 hypothetical LDL research studies. This can be accomplished by both concentrations ranged from 50 to 150 mg/dL. The raw data were grouped into 10 equal class intervals,and observed LDL concentrations were counted in each class interval as the frequency on the y axis of Trends and patterns can be uncovered by the the histogram. Figure 1 displays the grouped fre- visual display of raw data. This provides a structure quency histogram developed from the generated that can be used to choose the appropriate methods to summarize the data and choose the most appro- Histograms, such as the one in Figure 1, provide priate statistical analysis. There are countless a starting point for researchers to classify data for approaches to visually represent data, and it is further analyses. For example, the frequency distri- beyond the scope of this review to give specific bution in Figure 1 displays a trend in the data that examples of graphic representation found in the is observed for many biologic and physiologic vari- biomedical literature.4 However, this section will ables. The distribution is approximately bell shaped, briefly discuss a simple way to visually inspect raw as demonstrated by the smooth line overlying the data that helps determine its underlying distribu- histogram. This smooth line is symmetrical, with tion and, hence, select the proper statistical either half being a mirror image of the other. These approach. Subsequently, this section will introduce are the characteristics of a normal distribution (also the most commonly encountered distribution of con- called Gaussian distribution). As the sample size in tinuous data (ie, the normal or Gaussian distribu- this example is increased from n ϭ 1000 to the size tion) and set the foundation for the most commonly of the entire population, assuming the data are from used summarization methods and statistical tests a normal distribution, the histogram will more closely approach the smooth line in Figure 1. Data The histogram is a commonly used and relatively that follow a normal distribution can be appropri- simple method to quickly assess the underlying ately summarized and analyzed by powerful statis- distribution of variables collected in research stud- tical methods. A recurring error in the medical ies. A histogram is a graph used to display the literature is reporting results for data that are frequency distribution of data. The frequency distri- clearly skewed by using statistical analyses that are bution is an ordered list of possible values that a only valid for normally distributed data or for which variable can assume in a research study, along with the variable is not continuous. These data should be the frequency that the value occurred in the study.
analyzed by an alternative statistical method or Because continuous variables can take on an infinite transformed to approximate a normal distribution.1 number of possibilities for any given study, the Although data transformation is beyond the scope of frequencies are generally grouped into class inter- this review, alternative statistical methods for non- normally distributed data will be discussed under 2007 The American Society for Parenteral and Enteral Nutrition. All rights reserved. Not for commercial use or unauthorized distribution.
the descriptions of specific statistical tests in Part 2 The absolute range of any dataset is simply the of this review, to be published in February 2008.
maximum value minus the minimum value. Theinterquartile range is the difference in the value atthe 75th percentile from the value at the 25th Numerical: Measures of Central Tendency and percentile. The value located at the 50th percentile of any dataset is, by definition, the median. This is The histogram is a powerful tool to sort and generally more useful than the absolute range organize data, but it does not provide a simple because extreme outliers do not influence the inter- summary indicating where the data are centered or the variability in the dataset. This information is The variance associated with a mean can be reported using a measure of central tendency that described as a measure of dispersion using the describes the center of the distribution of the standard deviation, which is the square root of the observed values and a corresponding measure to variance. The absolute and interquartile ranges are represent the variability or degree of dispersion in limited because they are calculated from only 2 the dataset. The population measures of central values in any given dataset. On the other hand, the tendency and variability are referred to as popula- standard deviation is calculated using all of the data tion parameters, whereas in a sample they are in a sample and provides a more complete picture of commonly referred to as statistics. The following variability. The standard deviation is not appropri- notations for size, measures of central tendency, and ate, however, to describe the variability of a non- normal distribution. Furthermore, the standard deviation (SD) provides the most valuable informa- tion for data that follow a normal distribution, as stated by the empirical rule.5 The empirical rule states that 68% of all values will be Ϯ1 SD away from the mean in a given dataset that is normally distributed. Furthermore, 95% of all values will be It is important to note that the population pa- rameters, population mean (), and population stan- The data presented in Table 1 have been repro- dard deviation (⌽) will not be known in almost all duced from a clinical study3 to provide examples of instances. Therefore, the sample mean (X) and sam- measures of central tendency and variability among ple standard deviation (s) are used to estimate the other examples that will be discussed in Part 1 of population parameters and are the basis for com- this review. The investigators were assessing poten- monly used methods of statistical estimation and tial mechanisms for a lower infection rate in very- low-birth-weight (VLBW) infants receiving glu- The 2 most frequently used measures of central tamine-enriched enteral nutrition. Table 1 displays tendency are the mean and median. The mean is the baseline characteristics of infants assigned the simply the average of the data, whereas the median glutamine-enriched enteral nutrition and those is the midpoint of the variables when they are placed assigned the control diet. It is important to note that in order of value. Although the calculations of theseare fairly intuitive, there are certain types of data in the CRIB is a discrete variable and has been appro- which one is preferred over the other. Choosing the priately presented as the median and absolute range correct measure of central tendency depends on in this table. The measure of central tendency and several factors, most importantly the distribution of variability for the continuous variable (birth weight) the data. The most accurate measure of central is reported using the mean and standard deviation.
tendency for data that do not follow a normal distri- The baseline birth weight in the glutamine-enriched bution is generally the median (eg, data with outli- enteral nutrition group is reported as 1.18 Ϯ 0.4 kg ers). Unlike the median, the mean is affected by in Table 1. By applying the empirical rule and extreme outliers and will trend toward the tails of assuming a normal distribution, approximately 95% skewed distributions (ie, the end of the dataset that of all babies in this study weighed between 1.10 and has extreme outliers). Biologic and physiologic data 1.26 kg (ie, Ϯ2 SD from the mean) in the glutamine- are generally skewed in the positive direction, which means that the extreme values are in the positive The standard error of the mean (SEM) is also direction. In these cases, the mean would overesti- commonly reported in the literature. The SEM is mate the central tendency of the data.
used to construct confidence intervals for the popu- The mean is useful to indicate the center of the distribution for a given dataset. The median Although a detailed description of the SEM is describes the middle value of a set of data. However, beyond the scope of this review, it is important to measures of central tendency alone do not provide mention here because it has been used incorrectly in any indication about the variability of the dataset.
the literature.5 SEM is calculated as the sample SD The variability associated with the median is gener- divided by the square root of the sample size. The ally reported by the absolute or interquartile range.
SEM will therefore always be smaller than the 2007 The American Society for Parenteral and Enteral Nutrition. All rights reserved. Not for commercial use or unauthorized distribution.
Table 1Baseline and nutrition characteristics (modified with permission from van den Berg A et al3) Values are mean Ϯ SD, median (range), or number (%).
*Student’s t-test, Mann-Whitney U test, 2 test, and log rank test for continuous normally distributed data, nonparametric continuous data, dichotomous data, and time-dependent data, respectively.
sample SD and can make sample data seem to have for the population mean (). As displayed in Fig- less variability. It is frequently used in figures to ure 2, the confidence interval is constructed from the increase the clarity of the figure by providing error product of the SEM and the predetermined level bars that are shorter than they would be by using of confidence chosen to estimate the population the SD. The SEM does not illustrate the variability of the actual population and should be interpreted In the medical literature, 95% confidence inter- vals (95% CIs) are the most commonly reported.
Although not entirely technically correct, thisimplies that 95% of the time the true population Section 2: Inferential Statistics
mean will fall within the given range in the CI. In An educated statement about an unknown popu- some cases, 90% or 99% CIs are reported. As an lation is commonly referred to in statistics as an example, refer to the baseline birth weight in the inference. A statistical inference can be made by glutamine-enriched enteral nutrition group with a (1) estimation or (2) hypothesis testing. This section mean Ϯ SD of 1.18 Ϯ 0.4 kg, as reported in Table 1.
will provide a brief description of these fundamental Using the sample size, mean, and SD and assuming statistical inferences. The following sections will a normal distribution, the 95% CI is calculated to be provide examples of common statistical applications 1.07–1.29. Essentially, this states that there is 95% certainty that the true mean of the entire populationstudied will have a mean weight between 1.07 and 1.29 kg. The 90% CI for this sample has beencalculated to be 1.09 –1.27. It is important to note Estimation is a method that can be used to make that the 95% CI will always be wider (have a larger an inference about a population parameter. Confi- range) than the 90% CI for any given sample.
dence intervals are commonly reported as a way to Therefore, the wider the CI, the more likely it is to estimate a continuous population parameter. Confi- dence intervals are developed by first obtaining a As noted above, CIs can be constructed for a random sample from the population of interest and single continuous variable with a normal distribu- then calculating the sample statistics (ie, mean and tion, but they can also be used to estimate the SD). Of note, in almost all instances the sample difference between an intervention or proportions mean will not be identical to the true population such as odds ratios and relative risks. The differ- mean. This phenomenon is due to sampling errorand will be described in detail later in this review.
Therefore, confidence intervals provide a range ofvalues that are likely to encompass the true popu-lation mean with a certain level of confidence.
The first step in estimating a population param- eter is to obtain a point estimate from the sample, asdisplayed in the Figure 2 schematic. The point Figure 2. Schematic representing the fundamental ele- estimate should be unbiased and the best available ments needed to construct confidence intervals for estima- estimate of the population parameter of interest.
tion of the unknown population parameter () from a For continuous, normally distributed data, the sam- ple mean (X) is commonly used as the point estimate 2007 The American Society for Parenteral and Enteral Nutrition. All rights reserved. Not for commercial use or unauthorized distribution.
ences between the SD, SEM, and CIs should be (Step 2) Set the significance level and gener-
noted when interpreting the literature because they ate a decision rule. A decision rule needs to be
are often used interchangeably. Although it is a developed after the research question has been common misconception for CIs to be confused with stated in the form of a null hypothesis. The decision SDs, the information that each provides is quite rule is used to determine the level of acceptable different and needs to be assessed correctly.
sampling error, more commonly referred to as thelevel of significance. Therefore, the decision rule isgenerated according to an acceptable error rate (␣ The types of error associated with statistical tests Hypothesis testing is used to answer specific are discussed in detail in the sections “Power and research questions by making inferences about 1 or Statistical Error” and “Interpreting the p Value.” In more populations. More specifically, hypothesis test- most instances, the acceptable ␣ error rate is set at ing is used to make a prediction or inference about 5% or ␣ ϭ .05 in the medical literature.
an observed difference in the measure of interest The 5% error rate (␣ ϭ .05), can be converted to a between 1, 2, or more experimental groups. In critical value that is specific for any given statistical almost all situations, it is expected that a difference test. Once the data are collected, a test statistic is will be observed between the sample means of 2 calculated using the chosen statistical test. The test groups due to random sampling. For example, if 2 statistic can be directly compared with the critical random samples of n ϭ 25 are obtained from the value to determine if statistical significance was same population (N ϳ ϱ), the sample means and achieved. Statistical significance is achieved when a SDs may be quite different, and neither may be a likely difference exists in the populations and the good representation of the unknown population differences in sample means were likely not due to parameters. This is referred to as sampling error and is the basis of hypothesis testing. Sampling The calculated test statistics and a priori critical error is the difference between the parameter esti- values are rarely reported in clinical studies. This is mate based on the sample and the actual population due to the fact that each individual statistical test parameter. Therefore, regardless of the scrutiny put will have a different critical value associated with an into the design and implementation of a clinical ␣ ϭ .05, and most statistical software packages will trial, there will always be a certain amount of convert the test statistic directly to a p value. There- chance to make an incorrect inference due to sam- fore, in the medical literature the test statistic is reported as a p value and compared directly to the Hypothesis testing involves 4 sequential steps.
predetermined ␣. The p value is the probability that (Step 1) Set up the hypothesis to be tested. The
you obtain a result at least as extreme as you primary hypothesis to be tested should always be observed if the null hypothesis were true. A detailed defined a priori. If this is not defined before the discussion of the p value and its meaning, includingcommon misconceptions, can be found in the “Inter- study initiation, the inferences and study conclu- preting the p Value” section.
sions cannot be properly evaluated. The hypothesis (Step 3) Perform the experiment and com-
to be tested should initially be set up in the form of pute the test statistic. This step is individualized,
a null hypothesis (H ). The null hypothesis states depending on the design of the study and chosen that there is no difference in the outcomes tested. If statistical analysis. Experimental design is beyond the null hypothesis is rejected by hypothesis testing, the scope of this review.6 The methods for computing then the conclusion will be based on the alternative test statistics for individual statistical tests are hypothesis. The alternative hypothesis (H ) is usu- described in “Section 3: Commonly Used Statistical ally the opposite of the null hypothesis and states that there is a difference in the outcomes. Null and (Step 4) Make an inference. Once the experi-
alternative hypotheses will be written differently, ment has been completed, and data have been col- depending on the study design and the type of lected and analyzed, an inference will be made. The inference is a prediction based on the sample An example of a null hypothesis can be easily obtained from the large body of information, the imagined using the continuous variable of weight of population. It is on this inference that the conclu- VLBW infants receiving a glutamine-enriched diet sions of the study will be based. The inference is vs those receiving a control diet. The null hypoth- based on the predetermined critical value and cal- esis could be stated as follows: the mean weight culated test statistic or, more commonly, the prede- termined acceptable error rate and the calculated p enriched diets is equal to the weight ( value. The inference is made by rejecting or failing VLBW infants receiving control diet. Note that the to reject the null hypothesis. If the p value is population mean () is used to state the null hypoth- calculated to be less than the predetermined ␣, the esis. Additional examples of null hypotheses for the null hypothesis will be rejected. If the p value is calculated to be greater than the predetermined ␣, throughout Parts 1 and 2 of this review.
there will be a failure to reject the null hypothesis. A 2007 The American Society for Parenteral and Enteral Nutrition. All rights reserved. Not for commercial use or unauthorized distribution.
failure to reject the null hypothesis is not the same (decrease type II error) without increasing the type as accepting the null hypothesis as true. It simply I error rate is to increase the sample size.
indicates that there was not enough evidence to A statistical power analysis should be performed support the rejection of the null hypothesis.
for every study a priori to determine the appropriate As an example, refer to the previously stated null sample size in order to decrease the potential for a type II error. The acceptable type II error rate is infants receiving glutamine-enriched diets is equal generally 0.10 or 0.20, depending on the study, and corresponds to 0.90 and 0.80 study power, respec- control diet. Following this study, if a p value were tively. Given the acceptable type II error rate, a calculated to be less than .05, the null hypothesis difference in the outcomes of interest that would be would be rejected and the conclusion would be that considered clinically significant, the expected vari- the mean weight of VLBW infants receiving glu- ability in the measure, and the type I error rate, an tamine-enriched diets is not equal to the weight of appropriate sample size can be calculated. The sam- VLBW infants receiving control diet. Of course when ple size calculation is an important step to properly evaluating this conclusion, the reader will have to conducting clinical research. If the power of a study ensure the study was designed appropriately to is not indicated for an investigation that failed toreject null hypothesis, the occurrence of a type II minimize bias, that the study was designed for this error should be considered. Furthermore, for studies specific hypothesis, and that the correct statistical in which the null hypothesis is not rejected, a power test was chosen, given the variable of interest, the calculation can be recalculated using the actual distribution, and other factors that are discussed in observed difference in the sample means and the observed variability in that study. This informationcan then be used to determine the number of sub- jects needed to detect a difference in the populations It has become a convention to set the ␣ of a study of interest if the study were to be repeated or at .05, and therefore if the calculated p value is less than .05, statistical significance is said to beachieved. However, just because a p value is reported to be less than .05, it does not definitivelytell us that there is an actual difference between the An inference is made according to obtaining 1 or populations sampled. By definition, this states that, more samples and the calculation of the p value. The assuming proper study design and analysis, there conclusion of most research reports will rely heavily was less than a 5% chance to observe the difference on the fact that statistical significance has or has not in the sample means if they came from the same been achieved. In several cases, this statement may population. In other words, 5% of the time a come down to the calculation of a single p value. It is researcher will conclude there is a statistically sig- therefore important that the calculation of this p nificant difference when one does not exist. This is value be done correctly and that the study be prop- one form of statistical error and is referred to as type erly designed for that specific research question. It isalso important that the reader have knowledge of I or ␣-error; ␣ is the probability of a type I error. On the meaning of the p value and thus how to accu- the other hand, it is possible a conclusion could be made that there is not a statistically significant As previously stated, the p value is the probabil- difference when one does exist. This is referred to as ity of obtaining results at least as extreme as type II or ␤-error; ␤ is the probability of a type II observed if the null hypothesis were true. In other error. Type I (␣) error will be described in detail in words, if 2 independent samples were randomly the section “Interpreting the p Value” of this review.
obtained from the same population, the p value is The power of a study is the ability to detect a the probability of the magnitude of the observed difference between study groups if one actually difference in the 2 sample means. Therefore, 5% of exists. Study power is indirectly related to the like- the time, 2 sample means from the same population lihood of making a ␤-error; power is ϭ 1 Ϫ ␤.
will be different enough that one would incorrectly Therefore, as study power increases, the likelihood conclude that they were different or from different of concluding that there is not a difference when populations with an ␣ ϭ .05. In almost all cases, it there is one will decrease. The power of a study is will never be known if the null hypothesis is actually dependent on (1) sample size, (2) the actual differ- true because the entire population cannot be stud- ence between the outcomes of interest (eg, difference ied. Therefore, an erroneous conclusion suggesting between the actual population means and ), (3) that differences exist will occur 5 times out of 100.
the variability around each outcome, and (4) the An example illustrating the concept of sampling predetermined significance level (␣). Because the error and associated p values can be described by differences between the population means and the evaluating the reported p values in Table 1. This population variance cannot be influenced by the table was originally intended to demonstrate the investigator, the only way to increase study power similarities in the baseline characteristics of the 2007 The American Society for Parenteral and Enteral Nutrition. All rights reserved. Not for commercial use or unauthorized distribution.
study participants before the nutrition interven- of hormone replacement therapy have demonstrated tion. Therefore, these subjects were theoretically an LDL-lowering ability, but when clinical outcomes sampled from the same population (ie, infants such as mortality for cardiovascular disease were with a gestational age Ͻ32 weeks or birth weight evaluated, hormone replacement therapy was not Ͻ1.5 kg admitted to a neonatal intensive care unit).
effective and actually may have been deleterious.7,8 Although this table is reporting baseline charac- The problems encountered with hormone replace- teristics, a p value has been reported to indicate ment therapy are probably not due to the fact that whether there were statistically significant differ- LDL is a poor clinical marker for cardiovascular ences between the 2 study groups. Statistical tests disease. More likely, the negative clinical outcomes were performed on these selected variables to indi- were due to the fact that the negative actions of cate that the sampling error did not alter the con- hormone replacement therapy outweighed the ben- clusions after the assigned interventions. The p efits of lowering LDL. Therefore, additional consid- values are all reported to be greater than .05 and, erations to assess clinical significance include the therefore, it is concluded that the 2 study groups had risks vs benefits of the treatments being evaluated, which are often not assessed in clinical studies by As a hypothetical example after the intervention statistical methods. If clinical effectiveness is dem- in the study on glutamine-enriched enteral nutrition onstrated for any given intervention, the p value vs control, imagine that glutamine had absolutely no alone will not give guidance into the risks, discom- physiologic effect (in reality this would be unknown).
fort, time consumption, or economic burdens of the Therefore, when the primary outcome is analyzed, intervention. These are all issues that must be (ie, intestinal permeability in this study), the same considered when evaluating the biomedical litera- population would be assessed because no physiologic ture for clinical significance, even when statistical difference would have occurred. Therefore, if the study were repeated 100 times, 5 of them would Nutrition practitioners will benefit from under- standing the basics of statistics. Part 2 of this article enteral nutrition altered the measure of intestinal appearing in the February 2008 issue of Nutrition in permeability due to sampling error alone.
Clinical Practice will expand on this topic and fur-ther address inferential statistics.
Statistical Significance vs Clinical Significance References
As discussed, several important issues should be taken into consideration when evaluating p values 1. DeMuth JE. t-Tests. In: DeMuth JE, ed. Basic Statistics and Pharmaceutical Statistical Applications. Boca Raton, FL: Chap- and hence conclusions of research reports. One recurring issue is that statistical significance does 2. Albers I, Hartmann H, Bircher J, Creuztfeld W. Superiority of the not always relate to clinical significance. When Child-Pugh classification to quantitative liver function tests for assessing the clinical significance of an observed assessing prognosis of liver cirrhosis. Scand J Gastroenterol.
outcome, considerations should be assessed such as 3. van den Berg A, Fetter WP, Westerbeek EA, van der Vegt IM, van the study design and variable chosen as the out- der Molen HR, van Elburg RM. The effect of glutamine-enriched come. Studies that assess a true clinical outcome, enteral nutrition on intestinal permeability in very-low-birth- such as mortality, may have more clinical signifi- weight infants: a randomized controlled trial. JPEN J Parenter cance than one assessing the change in a clinical or Enteral Nutr. 2006;30:408 – 414.
4. Larson MG. Descriptive statistics and graphical displays. Circu- surrogate marker, such as blood pressure. Further- more, the general acceptance of the marker relating 5. D’Agostino RB, Sullivan LM, Beiser AS. Introductory Applied to true clinical events should be evaluated. That is, Biostatistics. Belmont, CA: Thomson Higher Education; 2006.
there are substantial data to suggest that lowering 6. Stanley K. Design of randomized controlled trials. Circulation. blood pressure below a certain cutoff will decrease 7. Anderson GL, Limacher M, Assaf AR, et al. Effects of conjugated mortality; however, such a cutoff may not exist for equine estrogen in postmenopausal women with hysterectomy: the Women’s Health Initiative randomized controlled trial.
Even using an accepted marker to assess a clini- cal outcome should be interpreted cautiously. An 8. Rossouw JE, Anderson GL, Prentice RL, et al. Risks and benefits of estrogen plus progestin in healthy postmenopausal women: example is the case with hormone replacement ther- principal results from the Women’s Health Initiative randomized apy and its effect on LDL cholesterol. Investigations controlled trial. JAMA. 2002;288:321–333.
2007 The American Society for Parenteral and Enteral Nutrition. All rights reserved. Not for commercial use or unauthorized distribution.
W ater & Atmospher e 17(1) 2009 Water Quality Nutrient trading to improve and preserve water quality Kit Rutherford and Tim Cox are modelling a market where the currency is nitrogen exports and the commodity is clean water. Trading in a watery market • Regions are setting limits (‘caps’) on how much here’s a lot in the news about