Clostridium difficile (also referred to as "C. difficile" or "C. From the Epi Info™ main page, select StatCalc. Selecting the smaller sample size could potentially produce a confidence interval estimate with a larger margin of error. Then substitute the effect size and the appropriate z values for the selected alpha and power to comute the sample size. The sample size computation is not an application of statistical inference and therefore it is reasonable to use an appropriate estimate for the standard deviation. An investigator hypothesizes that there is a higher incidence of flu among students who use their athletic facility regularly than their counterparts who do not. This value can be used to plan the trial. The formula for determining the sample size to ensure that the test has a specified power is given below: where α is the selected level of significance and Z1-α/2 is the value from the standard normal distribution holding 1- α/2 below it, 1- β is the selected power and Z1-β is the value from the standard normal distribution holding 1- β below it and ES is the effect size, defined as follows: where μd is the mean difference expected under the alternative hypothesis, H1, and σd is the standard deviation of the difference in the outcome (e.g., the difference based on measurements over time or the difference between matched pairs). We describe a novel strategy for power and sample size determination developed for studies utilizing investigational technologies with limited available preliminary data, specifically of imaging biomarkers. Thus, if there is no information available to approximate p1 and p2, then 0.5 can be used to generate the most conservative, or largest, sample sizes. How many stents must be evaluated? A two sided test of hypothesis will be conducted, at α =0.05, to assess whether there is a statistically significant difference in pain scores before and after treatment. In this course you will learn how to find the appropriate sample size, and the power of your study. In studies where the plan is to estimate the mean difference of a continuous outcome based on matched data, the formula for determining sample size is given below: where Z is the value from the standard normal distribution reflecting the confidence level that will be used (e.g., Z = 1.96 for 95%), E is the desired margin of error, and σd is the standard deviation of the difference scores. In recent years, C. difficile infections have become more frequent, more severe and more difficult to treat. A two sided test will be used with a 5% level of significance. We will use this value and the other inputs to compute the sample sizes as follows: Samples of size n1=250 and n2=250 will ensure that the 95% confidence interval for the difference in mean HDL levels will have a margin of error of no more than 3 units. Nevertheless, the study was stopped after an interim analysis. [Note: We always round up; the sample size formulas always generate the minimum number of subjects needed to ensure the specified precision.] Each patient will then undergo the acupuncture treatment. To plan this study, investigators use data from a published study in adults. How many college seniors should be enrolled in the study to ensure that the power of the test is 80% to detect a 0.25 unit difference in mean grade point averages? Assume that the standard deviation in the difference scores is approximately 20 units. The plan is to enroll children and weigh them at the start of the study. How many women 19 years of age and under must be enrolled in the study to ensure that a 95% confidence interval estimate of the mean birth weight of their infants has a margin of error not exceeding 100 grams? The formula produces the minimum sample size to ensure that the margin of error in a confidence interval will not exceed E. In planning studies, investigators should also consider attrition or loss to follow-up. If the null hypothesis is true (μ=90), then we are likely to select a sample whose mean is close in value to 90. With all other parameters equal to above specified, sampsize returns a sample size of 226 case-control pairs (total sample size 452). For example, if α=0.05, then 1- α/2 = 0.975 and Z=1.960. However, the investigators hypothesized a 10% attrition rate (in both groups), and to ensure a total sample size of 232 they need to allow for attrition. diff.") Sample sizes of ni=44 heavy drinkers and 44 who drink few fewer than five drinks per typical drinking day will ensure that the test of hypothesis has 80% power to detect a 0.25 unit difference in mean grade point averages. Recall from the module on confidence intervals that, when we generated a confidence interval estimate for the difference in means, we used Sp, the pooled estimate of the common standard deviation, as a measure of variability in the outcome (based on pooling the data), where Sp is computed as follows: If data are available on variability of the outcome in each comparison group, then Sp can be computed and used in the sample size formula. A 95% confidence interval will be estimated to quantify the difference in weight lost between the two diets and the investigator would like the margin of error to be no more than 3 pounds. Within each study, the difference between the treatment group and the control group is the sample estimate of the effect size.Did either study obtain significant results? p1 and p2 are the proportions of successes in each comparison group. Consequently, if there is no information available to approximate p, then p=0.5 can be used to generate the most conservative, or largest, sample size. If a study is planned where different numbers of patients will be assigned or different numbers of patients will comprise the comparison groups, then alternative formulas can be used (see Howell3 for more details). An alternative is to conduct a matched case-control study rather than the above unmatched design. When planning a clinical trial to investigate a new drug or procedure, data are often available from other trials that may have involved a placebo or an active control group (i.e., a standard medication or treatment given for the condition under study). The formulas presented here generate estimates of the necessary sample size(s) required based on statistical criteria. The determination of the appropriate sample size involves statistical criteria as well as clinical or practical considerations. In order to ensure that the total sample size of 112 is available at 8 weeks, the investigator needs to recruit more participants to allow for attrition. To determine the required sample size to achieve the desired study power, or to determine the expected power obtainable with a proposed sample size, one must specify the difference that is to be detected. Using this estimate of p, what sample size is needed (assuming that again a 95% confidence interval will be used and we want the same level of precision)? The procedure to determine sample size depends on the proposed design characteristics including the nature of the outcome of interest in the study. Therefore, a sample of size n=31 will ensure that a two-sided test with α =0.05 has 80% power to detect a 5 mg/dL difference in mean fasting blood glucose levels. Browse through all study tools. Notice that there is much higher power when there is a larger difference between the mean under H0 as compared to H1 (i.e., 90 versus 98). The standard deviation in grade point averages is assumed to be 0.42 and a meaningful difference in grade point averages (relative to drinking status) is 0.25 units. Studies that are much larger than they need to be to answer the research questions are also wasteful. 2003; 12: 604-609. Plaskon LA, Penson DF, Vaughan TL, Stanford JL. The formulas we present below produce the minimum sample size to ensure that the test of hypothesis will have a specified probability of rejecting the null hypothesis when it is false (i.e., a specified power). A test of hypothesis will be conducted to compare the proportion of students who used the athletic facility regularly and got flu with the proportion of students who did not and got flu. The mean birth weight of infants born full-term to mothers 20 years of age and older is 3,510 grams with a standard deviation of 385 grams. A two sided test will be used with a 5% level of significance. Based on prior experience with similar trials, the investigator expects that 10% of all participants will be lost to follow up or will drop out of the study. Feuer EJ, Wun LM. DEVCAN: Probability of Developing or Dying of Cancer. Compute the sample size required to ensure high power when hypothesis testing. Again the issue is determining the variability in the outcome of interest (σ), here the standard deviation in pounds lost over 8 weeks. When performing sample size computations, we use the large sample formula shown here. The standard deviation of the outcome variable measured in patients assigned to the placebo, control or unexposed group can be used to plan a future trial, as illustrated. Regardless of how the estimate of the variability of the outcome is derived, it should always be conservative (i.e., as large as is reasonable), so that the resultant sample size is not too small. It is important to note that this is not a statistical issue, but a clinical or a practical one. Again, these sample sizes refer to the numbers of children with complete data. The numerator of the effect size, the absolute value of the difference in means | μ 1 - μ 0 |, represents what is considered a clinically meaningful or practically important difference in means. A sample size of 364 stents will ensure that a two-sided test with α=0.05 has 90% power to detect a 0.05, or 5%, difference in jthe proportion of defective stents produced. p is the proportion of successes in the population. The probability of a Type II error is denoted β, and β = P(Do not Reject H0 | H0 is false), i.e., the probability of not rejecting the null hypothesis if the null hypothesis were true. A two sided test will be used with a 5% level of significance. In our test, we selected α = 0.05 and reject H0 if the observed sample mean exceeds 93.92 (focusing on the upper tail of the rejection region for now). Look at the chart below and identify which study found a real treatment effect and which one didn’t. In studies where the plan is to estimate the difference in proportions between two independent populations (i.e., to estimate the risk difference), the formula for determining the sample sizes required in each comparison group is: where ni is the sample size required in each group (i=1,2), Z is the value from the standard normal distribution reflecting the confidence level that will be used (e.g., Z = 1.96 for 95%), and E is the desired margin of error. This tutorial shows how to determine the optimal sample size. This is a situation where investigators might decide that a sample of this size is not feasible. For you computations, use a two-sided test with a 5% level of significance. The range of p is 0 to 1, and therefore the range of p(1-p) is 0 to 1. Statistical power is the most commonly used metric for sample size determination. The effect size is the difference in the parameter of interest that represents a clinically meaningful difference. If that is unsuccessful, the infection has been treated by switching to another antibiotic. The critical value (93.92) is indicated by the vertical line. If so, the known proportion can be used for both p1 and p2 in the formula shown above. Samples of size n1=232 and n2= 232 will ensure that the test of hypothesis will have 80% power to detect a 5 unit difference in mean systolic blood pressures in patients receiving the new drug as compared to patients receiving the placebo. However, in metabolic phenotyping, there is currently no accepted approach for these tasks, in large part due to the unknown nature of the expected effect. [Note: The resultant sample size might be small, and in the analysis stage, the appropriate confidence interval formula must be used. Ramachandran V, Sullivan LM, Wilson PW, Sempos CT, Sundstrom J, Kannel WB, Levy D, D'Agostino RB. • It can be determined using formulae, readymade tables and computer softwares. It is extremely important that the standard deviation of the difference scores (e.g., the difference based on measurements over time or the difference between matched pairs) is used here to appropriately estimate the sample size. To solve for n, we must input "Z," "σ," and "E.". Example: Suppose one wishes to detect a simple corrleation r (r=0.4) of N observations. The rejection region is shown in the tails of the figure below. For you computations, use a two-sided test with a 5% level of significance. Relative importance of borderline and elevated levels of coronary heart disease risk factors. Suppose that the screening test is based on analysis of a blood sample taken from women early in pregnancy. National data suggest that 12% of infants are born prematurely. Sample size refers to the number of participants or observations included in a study. Nonetheless, there is a direct relationship between α and power (as α increases, so does power). Recall from the Central Limit Theorem (see page 11 in the module on Probability), that for large n (here n=100 is sufficiently large), the distribution of the sample means is approximately normal with a mean of. The power of your study is its ability to detect a treatment effect of a specified size, if it exists. Donor Feces? Health, United States, 2005 with Chartbook on Trends in the Health of Americans. In participants who attended the seventh examination of the Offspring Study and were not on treatment for high cholesterol, the standard deviation of HDL cholesterol is 17.1. • The larger the sample size, the higher will be the degree of accuracy, but this is limited by the availability of resources. On their next migraine (post-treatment), each patient will again be asked to rate the severity of the pain. the investigator must specify the desired margin of error, clinically meaningful or practically important difference. The sample size is computed as follows: A sample of size n=16,448 will ensure that a 95% confidence interval estimate of the prevalence of breast cancer is within 0.10 (or to within 10 women per 10,000) of its true value. The numerator of the effect size, the absolute value of the difference in proportions |p1-p0|, again represents what is considered a clinically meaningful or practically important difference in proportions. This leaves: Finally, square both sides of the equation to get: This formula generates the sample size, n, required to ensure that the margin of error, E, does not exceed a specified value. The study will be conducted in the spring. Because we purposely select a small value for α , we control the probability of committing a Type I error. Statistical power is affected significantly by the size of the effect as … The investigators must decide if this would be sufficiently precise to answer the research question. 4 Enter the expected frequency (an estimate of the true prevalence, e.g.80% ± your minimum standard). Buschman NA, Foster G, Vickers P. Adolescent girls and their babies: achieving optimal birth weight. Hypothesis tests i… Systolic blood pressures will be measured in each participant after 12 weeks on the assigned treatment. One diet is a low fat diet, and the other is a low carbohydrate diet. This re-establishes the normal microbiota in the colon, and counteracts the overgrowth of C. diff. The two major factors affecting the power of a study are the sample size and the effect size. Therefore, the manufacturer wants the test to have 90% power to detect a difference in proportions of this magnitude. The first is called a Type I error and refers to the situation where we incorrectly reject H0 when in fact it is true. In studies where the plan is to estimate the mean of a continuous outcome variable in a single population, the formula for determining sample size is given below: where Z is the value from the standard normal distribution reflecting the confidence level that will be used (e.g., Z = 1.96 for 95%), σ is the standard deviation of the outcome variable and E is the desired margin of error. The estimate can be derived from a different study that was reported in the literature; some investigators perform a small pilot study to estimate the standard deviation. A sample of size n=869 will ensure that a two-sided test with α =0.05 has 90% power to detect a 5% difference in the proportion of patients with a history of cardiovascular disease who have an elevated LDL cholesterol level. Sample size estimates for hypothesis testing are often based on achieving 80% or 90% power. We first compute the effect size by substituting the proportions of students in each group who are expected to develop flu, p1=0.46 (i.e., 0.35*1.30=0.46) and p2=0.35 and the overall proportion, p=0.41 (i.e., (0.46+0.35)/2): Samples of size n1=324 and n2=324 will ensure that the test of hypothesis will have 80% power to detect a 30% difference in the proportions of students who develop flu between those who do and do not use the athletic facilities regularly. Each will be asked to rate the severity of the pain they experience with their next migraine before any treatment is administered. A medical device manufacturer produces implantable stents. Then substitute the effect size and the appropriate Z values for the selected α and power to compute the sample size. New York, NY: John Wiley and Sons, Inc.,1981. In order to compute the effect size, an estimate of the variability in systolic blood pressures is needed. The figure below shows the same components for the situation where the mean under the alternative hypothesis is 98. The plan is to enroll participants and to randomly assign them to receive either the new drug or a placebo. The number of women that must be enrolled, N, is computed as follows: In order to ensure that the 95% confidence interval estimate of the proportion of freshmen who smoke is within 5% of the true proportion, a sample of size 303 is needed. The plan is to categorize students as heavy drinkers or not using 5 or more drinks on a typical drinking day as the criterion for heavy drinking. Estimation of statistical power and sample size is a key aspect of experimental design. Sample size for case-control studies is dependent upon prevalence of exposure, not the rate of outcome. In order to estimate the sample size, we need approximate values of p1 and p2. The Z 1-β values for these popular scenarios are given below: For 80% power Z 0.80 = 0.84 For 90% power Z 0.90 =1.282 A recent report from the Framingham Heart Study indicated that 26% of people free of cardiovascular disease had elevated LDL cholesterol levels, defined as LDL > 159 mg/dL.9 An investigator hypothesizes that a higher proportion of patients with a history of cardiovascular disease will have elevated LDL cholesterol. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. However, it is more often the case that data on the variability of the outcome are available from only one group, usually the untreated (e.g., placebo control) or unexposed group. If data are available on variability of the outcome in each comparison group, then Sp can be computed and used to generate the sample sizes. What is sample size and why is it important? It is unlikely that we would know the standard deviation of that variable. ES is the effect size, defined as follows: where |p1 - p2| is the absolute value of the difference in proportions between the two groups expected under the alternative hypothesis, H1, and p is the overall proportion, based on pooling the data from the two comparison groups (p can be computed by taking the mean of the proportions in the two comparison groups, assuming that the groups will be of approximately equal size). For example, if 5% of the women are expected to delivery prematurely (i.e., 95% will deliver full term), then 60 women must be enrolled to ensure that 57 deliver full term. The manufacturer wants to test whether the proportion of defective stents is more than 10%. Sample size determination involves teamwork; biostatisticians must work closely with clinical investigators to determine the sample size that will address the research question of interest with adequate precision or power to produce results that are clinically meaningful. The application will show three different sample size estimates according to three different statistical calculations. An investigator is planning a clinical trial to evaluate the efficacy of a new drug designed to reduce systolic blood pressure. Notice that this sample size is substantially smaller than the one estimated above. Samples of size n 1 =324 and n 2 =324 will ensure that the test of hypothesis will have 80% power to detect a 30% difference in the proportions of students who develop flu between those who do and do not use the athletic facilities regularly. Infants clearly have a much more restricted range than weights of female students! Follows 125 + 40 pounds, or 85 to 165 pounds the design the. 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