Clinical Epidemiology I - Sampling Design and Sample Size Determination PDF

CLINICAL EPIDEMIOLOGY I SAMPLING DESIGN AND SAMPLE SIZE DETERMINATION TERM 1 | SHIFT 2 | November 11 & 15, 2024 | Dr. Aquino ​ The population that you TABLE OF...

CLINICAL EPIDEMIOLOGY I SAMPLING DESIGN AND SAMPLE SIZE DETERMINATION TERM 1 | SHIFT 2 | November 11 & 15, 2024 | Dr. Aquino ​ The population that you TABLE OF CONTENTS conceptualize for your study. ​ The universe; group from which 1.​ Sampling representative information is 1.1.​ Why Sample? desired and to which inference will 1.2.​ Why Compute For Sample Size? be made. 2.​ Types of Sampling Designs 2.1.​ Probability Sampling Accessible ​ The portion of the target population 2.2.​ Non-Probability Sampling Population that is accessible to the 2.3.​ Considerations When Selecting A Sample researcher 3.​ Computing Sample Size ​ Operational definition of the 3.1.​ Data Needed For Computing Sample Size target population 3.2.​ Calculating Sample Size ​ Just a portion of your target 4.​ Considerations In Determining Sample Size population that is accessible to you 4.1.​ Dropouts ​ e.g. A study that generalizes to 4.2.​ Categorical Variables young adults about drinking 4.3.​ Survival Analysis behavior 4.4.​ Matching ○​ All adults in the whole world is 4.5.​ Multivariate Adjustment and Other Special the target population. Statistical Analyses ○​ Realistically, the accessible 4.6.​ When Is A Sample Size FIxed? population is young adults in UST. ​ In reality, it is impossible to fully LEGEND 📚 Book 🗣​ Verbatim identify all the characteristics of the 📖​​ Reference ⭐​ Take Note / Important Info target population. Since it is not Previous Trans tangible, we need to rely on the accessible population. Section A - Blue Section C - Orange Section B - Purple Section D - Green Sample A group of individuals taken from a larger population and used to find something about the population. 1. SAMPLING KGCG, RFFA, EJC, CLAP, SCC Sampling ​ Comprehensive list of ALL Definition of Terms frame members of target population from which sample will be drawn Population Any collection of individuals which ​ First step in sampling we may be interested where these ​ Similar to Accessible Population individuals may be anything, and ○​ May not accurately represent the number of individuals may be the target population finite or infinite. ​ Operational definition of Target ​ entire group of individuals or items Population of interest in the study (people ​ Based on registries or databases medical records, biological vectors, ​ Problems with lists: “noncoverage” rural health units, houses, etc) bias ​ Defined as the bigger collection of ○​ Bias from incomplete records individuals further categorized as ​ Ex: not everyone in Manila target population and accessible is a registered voter population ○​ May fail to take into account ​ All your tweets in twitter is a some patients population. Countries can be a ○​ May result from clerical errors population. ​ Population may be finite or infinite. Sampling ​ Ultimate unit or individual from Element whom information will be collected. Target Population to whom the results of the ○​ Level of sampling Population study is intended to be beneficial/to be generalized to Page 1 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 ​ Should be clearly specified city, instution or country, and “just a (individuals, entire households, study”. 🗣 institutions) ​ Usually in our setting and in surveys it is individual Sampling Frame Operational definition of the target population ○​ Complex sampling designs - successive stages Who will be Registry of Filipino patients 20-50 y/o ​ Region ➡ City ➡ Institution ➡ included? with Graves disease Patient Where can Consulting at USTH-OPD they be Example No. 1 located? Among Filipinos with Graves’ disease between 20-50 Sampling A list of all Filipinos aged 20-50 with years old, is the health-related quality of life different Frame Grave’s disease at the hospital or for those who have been cured by radioiodine therapy (Sec C) clinics who have been treated with controlled by anti-thyroid drugs? either radioiodine therapy or anti-thyroid drugs. Target 20-50 year old Filipinos with Graves’ population disease This is just the list where you will gather your sample. Accessible Filipino patients with Graves’ disease population in UST Sampling This is the list of who will be sampled Frame to make the collection of data easier. This is part of the target population but (Sec B) may not be representative of the entire Question is: Are they accessible? Who Filipinos with Graves’ disease. We are they? Where are they located? may need to expand the accessible population and include other hospitals. Sample frame can also be established. ​ Ex. Registry or sign up sheet Ensure that by choosing an accessible ○​ with contact information that population, it is not just accessible to will be used for sampling you but it is a representative of the frame. target population. If not, you cannot ​ Census or hospital list can be generalize the results to the target used. population. ​ Roster of enrollees 🗣​ Don’t just conceptualize the target population (leads to difficulty with Example No. 2 🗣​ feasibility) Decide on a population that will be the most practical in terms of What is the average number of hours of sleep per night among medical students in the Philippines? access. Target All medical students in the Philippines. Sampling A group of Filipinos aged 20-50 with population This includes students enrolled in any Unit Graves’ disease who actually medical school across the country. participated in the study. Accessible Medical students from five selected Sampling Each patient aged 20-50 with Graves’ population medical schools across the Element Disease who is on the list and eligible Philippines. for selection. Sample A group of 200 randomly selected Actual patient included in the sampling students from these five schools. frame This is the biggest differentiation Example No. 3 between an ecological study, where the sampling size is bigger such as Dr. Y, the municipal health officer, is trying to Page 2 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 determine the prevalence of ascariasis among credibility of the result that we will children 6 to 12 yrs old in the municipality of get from the sample/accessible Sampaloc. He conducted the survey among school population. children aged 6 to 12 years attending elementary ○​ However, if the situation is similar schools in the municipality. to the previous example—where your accessible population Sampling Frame No. of enrollees in school consists only of patients in UST, yet you aim to generalize findings Sampling Unit School to all Filipinos with Graves' disease—this may not accurately Elementary Unit Child represent the target population. Can we fund ○​ A bulk of the funding is spent on 1.1. Why Sample? RFA this? participation alone; all this must PRACTICALITY 🗣 be budgeted beforehand. ​ From the materials needed for allocation treatment or capturing ​ Conducting research on the entire target data and compensating them for population will be very costly ​ Researchers would rather run an experiment on a small portion of the accessible population where 🗣 their time. ​ Estimate and compute how much you're going to spend per patient costs will be more permissive ○​ Example: For a sample size of ​ Results observed in the parts will be observed in 1,500, we need to account for the whole, given that the part has the same funding each individual, including characteristics of the whole transportation, participation, and ​ The idea is you will get a representation of the all aspects of data collection. whole population by getting a group of individuals within that population 1.3. Characteristics of Good Sampling ALPP ○​ With the characteristics of those in the sample being representative of the entire population Characteristics of Good Sampling RFA 1.2. Why Compute For Sample Size? Represent ​ It should protect both ative characteristics and variability of the FEASIBILITY ASSESSMENT population. 🗣​ Sample size computation is the first tests for feasibility assessment. It will help us answer the Adequate ​ Sample size should be large to ferment reliable generalization 🗣​ following questions. Sample size can somehow determine whether you will be able to do this study within the time frame Practical about the whole population. ​ The sampling design should be 🗣​ that you have. Compute for the sample size after establishing how the researchers will measure the and Feasible sufficiently straightforward. simple and Intervention/Exposure, Comparison, & Outcome Smallest ​ The economy and efficiency should Cost also be considered. Can we ​ Allows the researchers to better sustain this plan their recruitment techniques 2. TYPES OF SAMPLING DESIGNS ALPP study for the and study implementation, in ​ A sampling design is basically a fundamental part whole length order to meet the sample size of your data collection for deciding whether your of the within the time limit hypothesis is correct or not, or valid. observation? ​ A well-developed sampling design plays a critical role in ensuring that the data are sufficient. Can we get ○​ In cases where the accessible ​ Non-probability and probability sampling differ in credible population is so small that it terms of how you show the participants, or, and the results from matches the sample, this is likelihood of each member of the population to be this? 🗣 acceptable. ​ We will be able to gauge the selected. Page 3 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 Non-probability Probability samples samples relies on human judgment relies on laws of chance ​ Convenience ​ Simple Random ​ Snowball ​ Systematic Random ​ Quota ​ Stratified ​ Theoretical ​ Multi-stage Cluster 2.1. Probability Sampling EYG Figure 1. Simple random sampling ​ Utilizes some form of random selection ​ Set up some process that assures that the different units in your population have equal probabilities of 🗣​ Simplest but first needs a complete sampling frame or a list where you can get the entire accessible being chosen ​ We know the probability that we have represented the population well 🗣​ population Missing sampling frame → cannot do simple random ​ Gives the best chance of meeting assumptions 🗣​ sampling For example, you may obtain a list from incomplete 🗣 needed for statistical inferences ​ Random error is easier to pinpoint than a systematic records such as the voter’s list of Manila. However this list only contains the population that can read or 🗣 error. ​ It uses a set up that has equal probability among the write, and the ones who can’t are not included in this particular list. Therefore, you cannot capture the true 🗣 samples. ​ All probability sampling techniques need a sampling frame. You cannot forgo a sampling frame. 🗣 population of that area. ​ Thus if it is incomplete, using simple random sampling in that particular area is not doable ​ We can determine the probability of each person because you are not including the entire population. being selected. ​ Key point to remember is that the probability of selection is both equal and known for all members of Steps to Simple Random Sampling the population. ​ To give you an overview, probability in the statistics part, we use probability sampling if you know you 1. Identify the 🗣​ For instance, let’s say that we have a list of all the people in the room have a normal distribution bell curve, but if the curve sampling and then all those who were able to is skewed - presence of outliers, we use the frame sign the attendance would have a non-probability statistics as it is not normally random number assigned. 🗣 distributed. ​ All of them have ⅛ of a chane of being selwcted. Their selsction is not based on their capability, age ○​ From the student number, I will generate random numbers from a randomizer such as or ethnicity. We know the probability of random.org. representative of the population when we do ○​ In the olden days, theyll have a probability sampling. This gives us the best chances random number table usually for making the assumptions that we need for when found in all statistics book to we do statistical inferences that uses parametric generate sequences or tests. randomization. ○​ After you get the list of random numbers, whoever has the 🗣 2.1.1. Simple Random Sampling ​ Most basic of all the probability sampling designs same numbers generated in ​ Select sample through random drawing of numbers such that every element in the population has a 🗣 that list would be the sample. ​ Take not that you cannot have a sampling frame arranged or known, nonzero, and equal chance of being included ​ Requires a complete sampling frame numbered alphabetically. Because if it is like that, then that would 🗣 ​ Use Lottery, random numbers table ​ You can use either lottery, random numbers table or computer based generation of random numbers mean that the selection would be connected to the chance that they are related to something else. 2. Number the sampling elements in the sampling Page 4 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 frame 3. Generate random numbers (random.org) 4. Select numbered 🗣​ More sampling size, there’s a higher chance to capture normal elements trend, as supposed to a smaller that were sampling size, it may not represent included in the random 🗣 the target population. ​ From the list, you will get random samples using your sampling Figure 2. Systematic random sampling number frame. Steps to Systematic Random Sampling generation 1. Select a random 🗣​ Thats why its important that when you have a list you still assign them EXAMPLE number random numbers and you which will rearrange them according to that Dr. Mercado inputs the list of class numbers of the students in CE1-B into random.org, and generates four be known as k 🗣 random number. ​ For example, you want to sample 20, arrange them into 5 rows and random numbers. random.org spits out 2, 5, 8, and 10. Thus students 2, 5, 8, and 10 are chosen as part of the then roll the dice to know where to sample. 🗣 start. ​ If its a random number we start at 4, and then every 5th number is 2.1.2. Systematic Random Sampling going to be invited to join the study. ​ There is a system on how the numbers are chosen ​ The numbers must not be arranged in any kind of 2. Get a list of people (sampling frame) or observe ○​ ✅ systematic rhythm Arranging names randomly before choosing a flow of people (e.g pedestrian on a corner) ○​ ❌ every kth sample Arranging names alphabetically before choosing every kth sample 3. Select every kth person thereafter 4. Select ​ There should be no systematic ​ Determine the Sample Interval ○​ Compute by dividing using the ratio of your population over sample size numbered elements that were 🗣️ rhythm to the flow or list of people Flow or rhythm should be eliminated within the list ​ ALWAYS USE A SAMPLING FRAME ​ For example: ○​ Identify sampling frame: 1st year section 1D included in the random ​ 🗣️ Figure 2 Explanation: ○​ N=100 (total number of sampling ○​ Determine the number of sampling frame: 120 number frame) (assign each individual with a number) generation ○​ n=20 (preferred number of ○​ Generate number via fishbowl or random participants) order.net ○​ N/n = 5 ○​ Select the population through the assigned ○​ From 1-5, you select random 🗣 number ​ Important to break the flow/systematic rhythm of the list. number ○​ In the example, they chose 4 ○​ Start with 4 and take every 5th ○​ For example, for every section, students are unit assigned alphabetically. You need to change the order, like arranging the list from oldest to 2.1.3. Stratified Random Sampling JBMP youngest. You need to mix the list first before proceeding with this type of sampling. ​ Separate the population into groups or “strata” and ○​ 🗣️ sample from each stratum Base the group on a known confounder (e.g. age, gender, or severity of the condition (mild, moderate, severe)) ​ If there are few members of the group or “strata” of interest in the population, stratified random sampling ○​ 🗣️ is better Identify crucial strata to be included Page 5 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 ○​ 🗣️ E.g., Household Income (high income, low income, etc.) ​ Ensures that cases from ALL the groups of interest will be included ​ When an investigator wants to control the effect of a 🗣 known confounder ​ This is the best sampling design if there are a few members of the group or strata of interest in the 🗣 population. ​ Ex.: Stratification of groups among Caucasians, African-Americans, & Hispanic-Americans Step 3: Sample within the strata The residents within each stratum are randomly ○​ Given the concept of “access to care in the U.S. sampled. Random samples from each stratum are by the target population”. selected using either proportionate or disproportionate ○​ Since the U.S. is multicultural, the population sampling. 🗣 can be stratified. ​ Before you apply the random sample, you arrange them based on their characteristics. You want to Subtypes of Stratified Random Sampling make sure that certain characteristics are equally PROPORTIONATE DISPROPORTIONATE distributed in the study. ○​ That may mean that they are not in exact The number of elements stratified sampling procedure proportion as they occur in the population. That allocated is proportional to where the number of is okay, sometimes your study design would be their representation in the elements sampled from each best done in the extremes of that population and target population stratum is not proportional you want to oversample those extremes. to their representation in the ○​ Sometimes you have confounders that we want total population to make sure that distribution is equal to Reflects the same Varies the proportion across proportions as they occur in strata. 🗣 eliminate systematic bias in each group. ​ For instance, older age group tend to perform badly in reaction time experiments and so we don't want 📚 reality Sample size of each 📚 Sample size of each them to be distributed more in one group more than stratum is stratum is EQUAL the other. PROPORTIONAL to the irrespective of the ○​ It can also happen in random sampling, population size of the population size of the because it may happen that per chance, when stratum. stratum you did your randomization, there were more older generation in that group. And for that not to happen, you may exert more control by stratifying first and then randomly sampling thru the strata. Steps to Stratified Random Sampling Figure 3. Proportionate vs Disproportionate Sampling Step 1: Identify the sampling frame Sampling frame: The residents of Brgy. 007 Step 2: Identify the groups/strata Each stratum is determined by age group Figure 4. Proportionate vs Disproportionate Sampling 2.1.4. Cluster Sampling JBMP Page 6 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 ​ Divide the population into clusters and then 🗣 randomly sample the clusters. ​ Usually the clusters are divided into regions, 🗣️Typically geographic location (e.g., national surveys) locations, or geographic areas Steps to Cluster Sampling ​ Measure all units within sampled clusters ​ Be sure to differentiate the sampling unit from the Step 1: Identify accessible population cluster. ○​ Example: Randomly sample private hospitals, but measure all patients within that hospital ​ Sampling unit: patients ​ Cluster: hospitals ​ Primary purpose: ○​ maximize dispersion of the sample throughout 🗣​ Clusters should be ideally relatively homogenous within themselves but heterogeneous across the the community so as to fully represent the diversity that exists while minimizing costs and visits 🗣​ population. The elements or participants within the particular 🗣️ ​ Used in national surveys (e.g. Election Polls) cluster are sort of the same but the clusters ​ Another example: Let’s say you want to study the should be different from each other so the entire prevalence of a certain disease in a large country. Instead of creating a list of the entire country (very 🗣 population can be captured. ​ Randomly select which cluster one will get and then sample the entire cluster (not just one difficult), you can divide the population of the country into regions so that would be your clusters, and you individual in that cluster). randomly select the regions or the cluster. ​ Issues: Step 2: Define the clusters ○​ Difficult to compute sample size ○​ Possibility of more heterogeneity between than within clusters, which leads to higher sampling ​ ✅ errors. All clusters have relatively similar ​ ❌ variability Some clusters have a higher population of x individuals, which may lead to errors in Identify how the population clusters together ​ (i.e. location) ​ 🗣 generalizability The individuals within the clusters are not very similar to each other which can lead Step 3: Randomly sample the clusters ​ 🗣 to a higher sampling error. If you have a higher sampling error, the sample mean will not be a good representation of the true population and The clusters in red were selected for sampling. there can be an increased variability that can lead to a wider confidence interval and a less precise estimate. Stratified Random vs. Cluster Sampling ​ Things to consider: STRATIFIED RANDOM CLUSTER SAMPLING ○​ What defines our clusters? SAMPLING ○​ Is the variability in the clusters similar to the Select individuals within a Select entire subgroups population? subgroup (strata). (clusters) 📚 📚 ○​ Will we sample the whole cluster or just a few individuals within the clusters or a combination Select some units of all Randomly select entire of both? groups and include them in groups and include all ​ Think of M&M bags. They are already a good-mixed your sample. units of each group in your bag; every bag contains the same characteristics. sample Kahit anong M&M bag ang kunin mo, you will get roughly the same number of colors. Figure 5. Cluster Sampling Page 7 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 ​ When to use non-probability sampling : ○​ Exploratory research ○​ Qualitative research ○​ When the target population is difficult to access or identify Types of non-probability sampling Convenience Find some people that are easy to Figure 6. Stratified Random vs Cluster Sampling / Accidental/ find *not part of the lecture but included to clarify concepts Haphazard Sampling Participation based on availability 2.2. Non-Probability Sampling ALPP and accessibility; meant to be ​ Sampling for proportionality is not the primary convenient for the researcher concern ​ The chance of an individual being chosen can’t be (e.g. Interview first 30 patients who empirically estimated consulted in the ER; first 100 people ​ Possible to UNINTENTIONALLY over- or who walked into a mall; first 50 undersample students who passed by the pavillion) Advantages Weaknesses Purposive Select people who serve a certain Sampling purpose ​ Cost-effective (less expensive than probability sampling) ​ One is likely to overweight subgroups in the 🗣️ Relies on the judgment of the researcher when choosing who to ask ​ Time-efficient, quicker population that are to participate; participants are selected to do (vs. probability more readily based on a certain criteria sampling) ​ Good for exploratory research accessible ​ Results are generalizable not (e.g. 🗣️ The participants have the characteristics which makes you want ​ Good for studying a “Knowledge and to choose/include them in your study very rare disease Attitudes about aside from being just part of the (only few participants skincare products” population/inclusion or exclusion for that particular and you posted the criteria condition) advertisement on social media. But you Focus Group Discussions; Based on cannot really capture the level of cooperation of people and those who do not use a specific purpose social media, hence it is not generalizable. 🗣️ (e.g. Interviewing specific people about a new policy in school – may ​ Useful in early stages of a study design in need participation from specific people developing and testing questions and procedures such as faculty, students, support staff) ​ The probability of an element of a population to be chosen (selection probability) is difficult to determine or cannot be specified 🗣️ There has been a lot of discussion about the definition of purposive ​ Best utilized for descriptive purposes sampling, a lot of research disciplines ​ Not for making generalizations or inferences about define this differently. The CE the target population because it is prone to department agreed that having an ​ 🗣️ volunteer bias. This sampling technique is where the selection sample is based on researcher’s subjective inclusion and exclusion criteria does not mean that your study is purposive. The inclusion and exclusion criteria is judgment rather than random selection. This means the operational definition for your that not every member of the population has an population. It is also important to take equal chance of being selected unlike random note that inclusion and exclusion sampling where there is an equal chance of being criteria are not antonyms of each other, selected. Here (non-probability sampling), each they have to be additive. You only member of the population does not have that chance to be selected. Page 8 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 apply the criteria on individuals that pass the inclusion. 🗣️ Based on demographic a specific location or Quota Select people non-randomly according Sampling to some fixed quota Modal Sampling the most frequent or the 🗣️ Population sub-groups is based divided on into specific Instance Sampling “typical” case Informal public opinion polls characteristics (age, gender, or race) then a predetermined number of participants is selected from each 🗣️ In UST, the majority of students are science students. When you do the sub-group survey, you want to choose science 🗣️ Differs from stratified random students as they represent the majority of the population sampling (needs sampling frame and stratifications from which participants are randomly selected) 🗣️ Usually used study cases when you want to that are most ​ Quota sets a cap and does NOT representative of the characteristic entail randomization within the within the group (e.g. public opinion particular sub-group posts) (e.g. An Interviewer might be told to go 2.3. Considerations When Selecting A Sample into a voting center and interview 50 women and 50 men who had just 2.3.1. Based on Study Type voted) 🗣️ Quota sampling is like stratified sampling but doesn’t have a sampling Qualitative Quantitative Main consideration: Main consideration: frame. It’s conveniently sampled but ​ “How many” isn't the ​ Can you safely you have cut off values. issue. Do you generalize to the understand the population? Snowball Find a few people/initial participants phenomenon? ​ Have you Sampling that are relevant to your topic, ask ​ Have you learned systematically them to refer you to more potential enough? excluded anyone? participants ​ You want deep ​ Seek statistical validity understanding ​ Usually employ Useful for populations that are hard ​ Initial stages of probability sampling to find (e.g. homeless, illicit drug research. You do a users, prostitutes); also used for rare probability sampling diseases, conditions often ​ Study the stigmatized (e.g. HIV, leprosy); A phenomenon that more recent example would be the cannot be answered individuals against the use/take of by numbers. vaccines.They may be ostracized which makes it harder to find them. Sample at data saturation* to obtain a deep Prone to selection bias understanding Chunk Group of people who happen to be *Data saturation: the point in a research process where |enough data has been collected to draw necessary conclusions, and any further Sampling available at the time of the study data collection will not produce value-added insights. 🗣️ Survey a particular group, with a more deliberate selection process 2.3.2. Based on Study Design as opposed to convenience sampling Cross-section Need to look at whether the 🗣️ (e.g. Interview faculty from the Department of Clinical Epidemiology al designs designated time period for identifying the population represents the population over time or at a specified regarding a particular policy) point in time Page 9 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 🗣​ For example, if you want to study about students’ experience ✂ HYPOTHESIS TESTING (LEAPMed Trans: [RES] 07 Sampling Methods and during covid, participants would Data Analysis on Experimental Research v.1) be students from 2019-2022 as they have more insights about Null ○​ No difference or no relationship the topic compared to students hypothesis between the independent and now. (HO) dependent variables ○​ “Independent variable has no Case control Careful attention to ensure that the effect on dependent variable.” or group groups are being compared are ​ e.g. Tai Chi will not improve comparison systematically and adequately balance in older adults. designs included in the sampling plan ​ e.g. Drug A has no effect on the blood pressure of hypertensive Ensure exchangeability adults. ​ Control - absence of disease ​ Cases - presence of disease Alternative ○​ Stating the expected relationship hypothesis between independent and Longitudinal designs Must anticipate issues of whether the same or different people will be followed up and what additional steps (HA) ○​ 🗣️ dependent variables How it will be stated depends on the researcher, for example: will need to be taken to ensure ​ One-way/direction: Tai Chi can compatibility of data gathered over improve balance control in older 🗣 time ​ If the study requires several years to get the results, must adults. ⇒​ clearly states desired effect, i.e., positive effect have certain measures like ​ Two-way/direction: Drug A will following up every 6 months to have an effect on the blood ensure that particular participants pressure of hypertensive adults. will stay for the duration of the ⇒​ “play safe”; did not clearly 🗣 study. ​ Enroll 20% more of the participants to be able to cover state what effect does the treatment have ​ Determining whether the HA is for the dropouts. one-way or two-way is important in sample size calculation ⇒​ e.g., in Gpower app, the user 3. CONCEPTUALIZATION OF RESEARCHES MPGP is asked to select whether the ​ A statistician should always be included in the HA is one-way or two-way conceptualization of a research ○​ To define the dependent and independent (exposure) variables of the study ○​ For determination of sample size 🗣️ Think of hypothesis as the representation of our answer to your clinical question. You need to state both ○​ For planning of data management and analysis of your hypotheses. Having no change in the result of your study, it can still be considered as a positive result. 3. COMPUTING SAMPLE SIZE 3.1. Data Needed For Computing Sample Size Choosing the type of hypothesis What data should we know before we compute sample size? Two-Sided ​ Preferred 1.​ Null hypothesis and the sided-ness of the alternative Hypothesis ​ Test for difference hypothesis ​ Drug A is different from drug B. ​ Whether there is no effect or no difference ​ No drug is more effective than the ​ Clearly define what you’re testing other 2.​ Planned statistical analysis ​ Any difference whether greater or 3.​ Effect size and variability lesser 4.​ Alpha and Beta ​ More conservative 5.​ Program or calculator to be used for computation ​ In a two-sided hypothesis, the area of rejection and acceptance, the 3.1.1. Null Hypothesis and the Sidedness Of The alpha value or the probability that Alternative Hypothesis Page 10 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 you are going to commit a type 1 ​ s: standard deviation error is split into 2. ​ n: sample size One-Sided ​ Less preferred;Reviewers and grant t-Test For Unpaired Samples/ Independent Samples Hypothesis approvers review this very critically ​ Example, test if drug A is more 𝑥1−𝑥2 effective than the gold standard 𝑡= 1 1 drug 𝑠 𝑛1 +𝑛 2 ​ In a one-sided hypothesis, the 0.5 percent is on one side. The cut for ​ t: significant difference between population means this hypothesis is larger. ​ x1: mean value of group 1 ​ In general, we don’t use this type of ​ x2: mean value of group 2 hypothesis. In order to do a ​ s: standard deviation one-sided hypothesis, you need a ​ n1: size of group 1 lot more proof that the opposite ​ n2: size of group 2 side of the alternative will not happen. (ex. You claim that the efficacy of a certain drug will just go up and there is no way it will go down. Therefore, you need a magnanimous amount of literature to proved that.) Effect on sample size: two-sided hypotheses give bigger sample sizes than one-sided hypotheses ​ ☛ Last to be manipulated to lessen sample size ​ ☛ Use one sided hypothesis IF there is Figure 7. Statistics decision tree: when is this statistical overwhelming evidence that one-sided test appropriate? hypothesis will be more fitting Retrieved from KwikFixSkills ​ For one-sided hypothesis, since you already *not part of lecture but included to clarify concepts know the direction of the study of this particular relationship, you don’t need a big sample size. 3.1.2. Planned Statistical Analysis ​ Depends on type of data to be analyzed ​ Sample size computation is heavily reliant on the formula of the statistical analysis to be used ○​ Treat like an algebra problem: How many samples do I need to get this t test result with this difference and this variability? ○​ For example, mean change in quality of life, can use a t-test, if comparing 2 groups. ​ Must be planned carefully because there are different formulas for different types of data (see table below) Comparing t-test formulas t-Test For Paired Samples/ Dependent Samples 𝑑 𝑡= 𝑠𝑑 𝑛 ​ t: significant difference between the population mean and a hypothesized value ​ d: sample mean of the differences Page 11 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 Figure 8. Types of statistical tests the drug’s effect is really big (ex: Retrieved from Towards Data Science amlodipine: good way of lowering *not part of lecture but included to clarify concepts blood pressure), then you only need to sample a small group to 3.1.3. Effect Size and Variability see that effect ​ If effect is small, then you won’t Where to get effect size and variability estimates? know if the effect is just due to the variability in sphygmomanometer or ​ Information from literature blood pressure, sample size should ​ Estimates from national census be more ​ Clinically relevant values 🗣 Where can you get your effect size? Usually from literature. If you are repeating a study, the results of ✂ EFFECT SIZE (LEAPMed Trans: [RES] 7 Sampling Methods and Data that study will be your effect size (if having the same Analysis on Experimental Research v.1) population as your study). If you have a different population, you may look for estimates in our census. Effect size: a statistical expression of the magnitude of If you can’t find a census, you may have to ask your difference between group means 🗣 content adviser for the clinically relevant values. Ex. A lot of quality of life studies have been done 🗣 ​ indicates the degree of separation between groups Measures the strength of relationships between two variables ​ E.g. in Amsterdam, first world nations with a lot of Western individuals living there ○​ Because they have universal healthcare ​ Small effect size ○​ It’s easy to find all of them (they’re just in ○​ Not perceptible to the human eye; When not databases) under good experimental control ​ Usually we don’t have quality of life bases ○​ Equivalent to 20% of a standard deviation (cannot be found in literatures or census) ○​ Cohen’s d = 0.2 and below ​ Solution: just ask your content adviser ○​ “Doc, ito yung nakita namin sa study na ito. 🗣 o​ Cohen’s d – used for effect size Needs greater sample size to observe the effect Do you think the number that they said in their study would mimic ours? Or meron po ​ Medium effect size bang cutoff? ○​ visible to the naked eye ○​ one would be aware of the change with normal deviation Effect on sample size on: ○​ 50% of a standard deviation ○​ Cohen’s d = 0.5 Effect size ​ the bigger the effect size, the ○​ When your findings are very believable and you smaller the sample size are confident that the IV is the reason for ○​ Greater effect size ➡ less change in DV difference between samples ➡ less 🗣 samples needed to observe trends ​ Large effect size Pag mas malaki yung effect ○​ great degree of separation (obvious na obvious na sya), ○​ very little overlap kailangan mo pa ba ng mas ○​ with large samples and good experimental maraming sample, ehh obvious na control nga sya? ○​ here, you are certain that their difference is because of the intervention given Variability ​ the bigger the variability, the bigger ○​ 80% of standard deviation (ito yung basis kung the sample size bakit gusto mong 80% yung power) ​ Greater variability ➡ greater difference ➡ more samples needed 🗣 🗣 ○​ Cohen’s d = 0.8 Needs smaller sample size to observe the effect 🗣 to observe trends More substantial difference = easier to detect than Spread of data/deviation from the smaller effect size mean ​ Difference that you expect to say 3.1.4. Alpha and Beta that there’s significance ​ If effect size is big (effect of intervention is more obvious) or if ✂ TYPES OF ERRORS Page 12 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 (LEAPMed Trans: [RES] 7 Sampling Methods and Data ○​ Also known as level of statistical Analysis on Experimental Research v.1) significance ○​ Flip side: level of confidence ​ Type I error (α) ​ 1 - α = level of confidence o​ An incorrect decision to reject the null hypothesis, concluding that a relationship 🗣 ​ 95% confidence = 5% alpha α = 0.05 (0.05% chance of rejecting exists when in fact it does not o​ Risk willing to commit in saying that the observations being compared are different 🗣 null hypothesis) Increase sample size to reduce errors. when, in truth they are not o​ False positive ​ Type II error (ß) o​ An incorrect decision to accept the null Beta (ß) Error 🗣 ○​ Probability of making a Type II error There is no significant difference when in reality there is. hypothesis, concluding that no relationship ○​ Flip side: power exists when in fact it does ​ 1 - ß = power o​ The risk willing to commit in saying that the observations being compared are the same Effect on ​ Smaller α/ß ➡ Less tolerant to when in truth, they are different sample errors ➡ bigger sample size o​ False negative size needed ​ Same on the flipside: ○​ Bigger confidence interval = smaller α ○​ Bigger confidence level / power = smaller sample size Fig 2. Depiction of Types of Errors Summary of the sample sizes of different (Source: instructor’s slide) components Component Bigger Sample Smaller Sample HO: The patient is not pregnant. Size Size HO is TRUE HO is FALSE Hypothesis Two-sided One-sided sidedness Type I error (False positive) Type of data Nominal data Continuous data Concluding that the (differences in (differences of Reject Correct outcome man is pregnant proportions) mean) HO (True positive) (i.e., rejecting the Ho) when in fact he Effect size Smaller effect Bigger effect size is not. size Type II error (False Variability Bigger variability Smaller variability negative) Fail to Concluding that the Alpha and Smaller alpha and Bigger alpha and Correct outcome reject woman is NOT Beta beta beta (True negative) HO pregnant (i.e., not rejecting the Ho) when in fact she is. 3.2. Calculating Sample Size 3.2.1. Calculating The Sample Size When Comparing The Means of Treatment Groups Alpha and Beta ✂ t-TEST Alpha (α) Error 🗣 ○​ Probability of making a Type I error Rejected null, accepted alternative (There is a significant difference (LEAPMed Trans: [RES] 07 Sampling Methods and Data Analysis on Experimental Research v.1) when in reality there isn’t.) t- Test Page 13 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 ​ Also called Student’s t-test Alternative Mean FEV1 after 2 weeks of treatment ​ Statistical procedure used to compare two means, hypothesis is different in asthmatic patients i.e., two groups, which can either be: (two-sided) treated with albuterol as in those o​ one treatment group and one control group treated with ipratropium o​ one group and its pre-test and post-test are compared Effect size 0.2L (10% x 2.0L) ​ Unpaired t-test or Independent t-test “The investigator would like to be able o​ Used when the means of two independent to detect a difference of 10% or more in groups of subjects are compared mean FEV1 between the two treatment o​ E.g., comparing means of intervention group groups.” and control group for a primary or a secondary outcome Standard 1.0L ​ Paired t-test or Correlated t-test deviation of o​ Used when comparing means from correlated FEV1 samples or repeated measures o​ E.g., comparing pre-test value mean to post-test Standard = 𝑒𝑓𝑓𝑒𝑐𝑡 𝑠𝑖𝑧𝑒 𝑆𝐷 value mean of the effect size 0.2𝐿 = 1.0𝐿 = 0.2 EXAMPLE Alpha 0.05 The research question is whether there is a difference (two-sided) in the efficacy of albuterol and ipratropium bromide for the treatment of asthma. Beta = 1 - 0.8 The investigator plans a randomized trial of the effect of = 0.2 the drugs on FEV1 (forced expiratory volume in 1 Power = 1 – beta second) after 2 weeks of treatment. Computation (using sample-size.net) A previous study has reported that the mean FEV1 in persons with treated asthma was 2.0 liters, with a standard deviation of 1.0 liter. The investigator would like to be able to detect a difference of 10% or more in mean FEV1 between the two treatment groups. How many patients are required in each group (albuterol and ipratropium) at alpha (two-sided) =0.05 and power = 0.80? 🗣 So for this one, ang nahanap lang nila sa literature is like for all patients treated for asthma. So that just 🗣 means control group. They want to detect a 10% difference. So wala silang nakita in literature for whatever man yung drug 🗣 nila. So, 1 is from census and the other portion, kasi wala silang mahanap for the second group, ang tinanong nila is ano yung clinically relevant value Null Mean FEV1 after 2 weeks of treatment hypothesis is the same in asthmatic patients treated with albuterol as in those treated with ipratropium Page 14 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 Sample Size 785 Alpha 0.05 Needed *Always uses the normal approximation (two-sided) 🗣 🗣 Liters = continuous data q1 and q0 refers to allocation ratio Beta = 1 - 0.8 = 0.2 ○​ If you want it 1:1, keep it at 0.5 Power = 1 – beta ○​ If you want a bigger allocation ratio for 1 group, change it Computation (using sample-size.net) o​ 2:1 = one would be 0.75 and the other one is 🗣 🗣 0.25 E = effect size | S = standard deviation If we increase the power to 90%, that would result to a data of 0.1, that would balloon your sample to 1,052. 3.2.2. Calculating The Sample Size When Comparing The Relationship Between Two Variables Calculating Sample Size When Using The Chi-Squared Test EXAMPLE The research question is whether subjects who practice Tai Chi have a lower risk of developing back pain than those who jog for exercise. A review of the literature suggests that the 2-year risk of back pain is about 0.30 in joggers. The investigator hopes to be able to show that Tai Chi reduces that risk by at least 0.10. At alpha (two-sided)=0.05 and power=0.8, how many subjects will need to be studied to determine whether the 2-year incidence of developing back pain is 0.2 (or less) in those who do Tai Chi? Chi-Squared Test 🗣 usually used when you want risk ratio, odds ratio, difference in Sample Size 626 (with continuity correction) ​ Needed or 586 (without continuity correction) 🗣 Inferential test proportion (50% more or 55% less) Calculating Sample Size When Using The Pearson Null The incidence of back pains is the Correlation Coefficient Test hypothesis same in those who jog and those who EXAMPLE practice Tai Chi. The research question is whether urinary cotinine levels Alternative The incidence of back pains differs in (a measure of the intensity of current cigarette smoking) hypothesis those who jog and those who practice are correlated with none density in smokers. (two-sided) Tai Chi. A previous study found a modest correlation (r=-0.3) P1 ​ Incidence in those who practice Tai between reported smoking (in cigarettes per day) and Chi bone density (in g/cm3). ​ 0.20 The investigator anticipates that the urinary cotinine P2 ​ Incidence in those who jog levels will be at least as well correlated. ​ 0.30 How many smokers will need to be enrolled, at alpha P1-P2 0.10 Page 15 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 ○​ Point estimate: use of sample data to calculate (two-sided)=0.05 and beta=0.01? a single value which is to serve as a "best 🗣️ Rarely done. For associations: odds ratio, risks ratio, guess" or "best estimate" of an unknown population parameter 🗣️ and differences for two groups were used. Both independent and dependent variables MUST be CONTINUOUS VARIABLES. We look at the slope of ​ RR or OR ○​ Standard deviation of the variable of interest (for continuous outcomes): average amount of 🗣️ the line for the relationship. If the line is 45 degree angle (in relative to x-axis) variability in your dataset ○​ Width of the confidence interval: if the interval is 🗣️ means very good correlation coefficient (perfect). We just always remember the value of the ‘r” to wider (e.g. 0.60 to 0.93) the uncertainty is greater 🗣️ interpret. Unless the value of “r” may be found from literatures, we tend to set it at conservative/modest value since ○​ Confidence level: probability that a population parameter will fall between a set of values for a certain proportion of times there is no such thing as “perfect correlation or r = 1.0.” Calculating Sample Size for a Descriptive Study of a Null There is no correlation between Continuous Variable hypothesis urinary cotinine level and bone density in smokers. EXAMPLE Alternative There is a correlation between urinary The investigator seeks to determine the mean hypothesis cotinine level and bone density in hemoglobin level among third graders in an urban area (two-sided) smokers. with a 95% confidence interval of ±0.3 g/dL. Effect size = |-0.3| Previous study found that the standard deviation of (r) =0.3 hemoglobin in a similar city was 1g/dL. Alpha 0.05 Standard deviation 1 g/dL (two-sided) of variable (SD) Beta = 0.1 Total width of 0.6 g/dL interval ​ 0.3 g/dL above and 0.3 g/dL Computation (using sample-size.net) below Standardization = 𝑡𝑜𝑡𝑎𝑙 𝑤𝑖𝑑𝑡ℎ 𝑆𝐷 width of interval 0.6 = 1.0 =0.6 Confidence level 95% Computation (using sample-size.net) Sample Size Needed: 85 3.2.3. Calculating The Sample Size For Descriptive Studies General advice ​ ☛ This can be tricky because sometimes there’s too many factors to consider ​ Determine if there is a comparison between groups Sample Size Needed: 43 that may be a more important goal to find out within the study ​ Otherwise, determine the following: Page 16 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 Calculating Sample Size for a Descriptive Study of a ​ Significance: estimated drop out Dichotomous Variable number cannot exceed 0.2 EXAMPLE ○​ the border of tolerance per dropout is 20% The investigator wishes to determine the sensitivity of a new diagnostic test for pancreatic cancer. Categorical ​ Data from ordinal variables may Variables sometimes be treated as Based on a pilot study, she expects that 80% of patients continuous if: with pancreatic cancer will have positive tests. ○​ There are a lot of categories (≥10 is continuous) How many such patients will be required to estimate a ○​ Averaging values of the 95% confidence interval for the test’s sensitivity of variables make sense 0.80 ± 0.05? ​ How to do the computation if it cannot be treated as continuous? Expected 0.20 ○​ Dichotomize the data proportion Because sample size is more than (categorize data into a 2x2 half, the sample size estimated from table) the proportion is expected a falsely negative result Survival ​ Although outcome say months of Analysis survival, what is being assessed is not time but the proportion of Total width of 0.10 g/dL subjects still alive at each point in interval ​ 0.05 above and 0.05 below time ​ Just estimate the proportion Confidence 95% expected to EVER have the level outcome ​ IF the outcome is expected to Computation (using sample-size.net) occur in most of the subject, then estimate sample size based on the proportions of subjects in each group who are expected to have the outcome at a point during follow-up when about half of the total outcomes have occurred Multivariate ​ Analysis for studies whose goals Adjustment are to establish causation, mediation, or interaction ​ They could also be for studies that aim to establish attribution only but want to eliminate any influence Sample Size Needed: 53 from known confounders ​ The goal of this study is to prove the null hypothesis 4. CONSIDERATIONS IN DETERMINING SAMPLE ○​ Equivalence is the rejection of SIZE the two-sided alternative ○​ Non-inferiority is rejection of Dropouts ​ Subjects who are enrolled in a the one-sided alternative study but in whom outcome status cannot be ascertained Things to consider ​ Usually computed as ○​ Computed sample size + ​ Prevalence of the confounder (computed sample size * ​ Strength of the association estimated drop out) between and confounder ○​ Computed sample size + ​ Strength of association confounder 1 and outcome 1−𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛 𝑜𝑓 𝑑𝑟𝑜𝑝𝑜𝑢𝑡 What to do? Page 17 of 18 VALIDITY AND THREATS TO VALIDITY CLINICAL EPIDEMIOLOGY I LESSON 4 ​ Compute as if you are computing ​ Nominal scale: only provides categories or for a simpler study classifications of each observation, but unable to be ​ Employ a statistician if you are ranked applying for a big grant ○​ E.g. male or female ○​ Dichotomous: considered as nominal with only How to tell if you have enough two categories without consulting a statistician? ​ Ordinal scale: categories are ranked based on a defined characteristic or property ​ A good shorthand rule is for every ○​ E.g. fever parameters: (Afebrile, confounder you add to your model, ○​ Feverish, Highly febrile) you should ensure at least 10 participants Continuous (Quantitative) ​ Therefore: study with 3 ​ Data collected have numerical sense and can be confounders needs at least a directly used for mathematical operations. sample size of 30 to be able to adjust for the effect of the confounders ✂ MATCHING ([EPI] 04: Validity and Threats to Validity) Ways to compute for sample size: Matching ​ Confounder: Disease severity ​ Find the smallest clinical significant ○​ two samples differ in disease severity effect size and compute the sample from there ​ Proc