class: top, left, title-slide # Lecture 3: Introduction to biostatistics ## MEDI 504 ### <span class="citation">@TiffanyTimbers</span> (UBC) ### 2021-11-08 --- ## Module learning objectives By the end of this module, students should be able to: - Identify the different types of data analysis questions and categorize a question into the correct type - Identify a suitable analysis type to answer an inferential question, given the data set at hand - Use the R programming language to carry out analysis to answer inferential question - Interpret and communicate the results of the analysis from an inferential question --- ## What is the question? <div class="figure"> <img src="img/what_is_the_question.png" alt="What is the question? by Roger Peng and Jeff Leek" width="50%" /> <p class="caption">What is the question? by Roger Peng and Jeff Leek</p> </div> --- #### 1. Descriptive One that seeks to summarize a characteristic of a set of data. No interpretation of the result itself as the result is a fact, an attribute of the data set you are working with. -- Examples: - What is the frequency of viral illnesses in a set of data collected from a group of individuals? -- - How many people live in each US state? --- #### 2. Exploratory One in which you analyze the data to see if there are patterns, trends, or relationships between variables looking for patterns that would support proposing a hypothesis to test in a future study. -- Examples: - Do diets rich in certain foods have differing frequencies of viral illnesses **in a set of data** collected from a group of individuals? -- - Does air pollution correlate with life expectancy **in a set of data** collected from groups of individuals from several regions in the United States? --- #### 3. Inferential One in which you analyze the data to see if there are patterns, trends, or relationships between variables in a representative sample. We want to quantify how much the patterns, trends, or relationships between variables is applicable to all individuals units in the population. -- Examples: - Is eating at least 5 servings a day of fresh fruit and vegetables is associated with fewer viral illnesses per year? -- - Is the gestational length of first born babies the same as that of non-first borns? --- #### 4. Predictive One where you are trying to predict measurements or labels for individuals (people or things). Less interested in what causes the predicted outcome, just what predicts it. -- Examples: - How many viral illnesses will someone have next year? -- - What political party will someone vote for in the next US election? --- #### 5. Causal Asks about whether changing one factor will change another factor, on average, in a population. Sometimes the underlying design of the data collection, by default, allows for the question that you ask to be causal (e.g., randomized experiment or trial) -- Examples: - Does eating at least 5 servings a day of fresh fruit and vegetables cause fewer viral illnesses per year? -- - Does smoking lead to cancer? --- #### 6. Mechanistic One that tries to explain the underlying mechanism of the observed patterns, trends, or relationship (how does it happen?) -- Examples: - How do changes in diet lead to a reduction in the number of viral illnesses? -- - How does how airplane wing design changes air flow over a wing, leading to decreased drag? --- ## Challenge #1 What kind of statistical question is this? #### *Is a yet undiagnosed patient's breast cancer tumor malignant or benign?* --- ## Challenge #2 What kind of statistical question is this? #### *Is inhalation of marijuana associated with lung cancer?* --- ## Challenge #2 What kind of statistical question is this? #### *Does a truncation of the BRCA2 gene cause cancer?* --- ## Challenge #4 What kind of statistical question is this? #### *Are there sub-types of ovarian tumors?* --- ### So you know the type of question, now what? .pull-left[ This helps narrow down the possibilities of the kind of analysis you might want to do! -- For example, if you have the question: **"How many viral illnesses will someone have next year?"** and you identify that it is **predictive.** You could narrow down that some kind of statistical or machine learning model might help you answer that. -- Then you need to go a step deeper and look at the data that you have, and see which kind of statistical or machine learning model is most suitable for your data. ] .pull-right[ <img src="https://scikit-learn.org/stable/_static/ml_map.png" width=700> Source: [scikit-learn algorithm cheat sheet](https://scikit-learn.org/stable/tutorial/machine_learning_map/index.html) ] --- ## Another example .pull-left[ For example, if you have the question: "Is the gestational length of first born babies the same as that of non-first borns?" and you identify that it is inferential. You could narrow down that some kind of statistical inference approach might help you answer that. -- Then again, you need to go a step deeper and look at the data that you have, and see which kind of statistical inference approach is most suitable for your data. ] .pull-right[ <img src="https://onishlab.colostate.edu/wp-content/uploads/2019/07/which_test_flowchart.png" width=700> Source: https://onishlab.colostate.edu/summer-statistics-workshop-2019/ Or for another, see this website: http://www.biostathandbook.com/testchoice.html ] --- ## Practice --- ### Case 1 Question: *Is a yet undiagnosed patient's breast cancer tumor malignant or benign?* Data: | ID| Radius| Texture| Perimeter| Area| Smoothness|Class | |------:|----------:|---------:|----------:|----------:|----------:|:-----| | 926125| 1.9275296| 1.3485941| 2.1001278| 1.9667039| 0.9627130|M | | 926424| 2.1091388| 0.7208383| 2.0589739| 2.3417954| 1.0409262|M | | 926682| 1.7033556| 2.0833009| 1.6145108| 1.7223261| 0.1023682|M | | 926954| 0.7016669| 2.0437755| 0.6720844| 0.5774446| -0.8397450|M | | 927241| 1.8367249| 2.3344032| 1.9807813| 1.7336925| 1.5244257|M | | 92751| -1.8068114| 1.2207179| -1.8127934| -1.3466044| -3.1093489|B | Data reference: https://archive-beta.ics.uci.edu/ml/datasets/breast+cancer+wisconsin+diagnostic --- ### Case 2 Question: *Is inhalation of marijuana associated with lung cancer?* Data: | ID|sex |gender | age| smoker|marijuana_use | bmi| lung_cancer| |-----:|:------|:------|---:|------:|:-------------|----:|-----------:| | 50841|male |fluid | 35| 1|never | 22.3| 0| | 54135|male |male | 43| 0|frequent | 18.0| 0| | 53176|male |male | 29| 0|sometimes | 32.5| 1| | 59343|female |female | 54| 0|frequent | 20.0| 0| | 50495|female |female | 37| 0|never | 26.1| 0| | 52159|male |male | 51| 0|never | 29.8| 1| *Note: this is simulated data.* --- ### Case 3 Question: *Does a truncation of the BRCA2 gene cause cancer?* Data: | ID|sex |gender | age| smoker| bmi| brca2_truncation| cancer| |-----:|:------|:------|---:|------:|----:|----------------:|------:| | 27443|male |fluid | 35| 1| 22.3| 1| 1| | 28942|male |male | 43| 0| 18.0| 0| 0| | 26022|male |male | 29| 0| 32.5| 1| 1| | 22547|female |female | 54| 0| 20.0| 0| 0| | 29040|female |female | 37| 0| 26.1| 0| 0| | 22119|male |male | 51| 0| 29.8| 0| 1| *Note: this is simulated data.* --- ### Case 4 Question: *Are there sub-types of ovarian tumors?* Data: | ID| Radius| Texture| Perimeter| Area| Smoothness| |------:|----------:|---------:|----------:|----------:|----------:| | 926125| 1.9275296| 1.3485941| 2.1001278| 1.9667039| 0.9627130| | 926424| 2.1091388| 0.7208383| 2.0589739| 2.3417954| 1.0409262| | 926682| 1.7033556| 2.0833009| 1.6145108| 1.7223261| 0.1023682| | 926954| 0.7016669| 2.0437755| 0.6720844| 0.5774446| -0.8397450| | 927241| 1.8367249| 2.3344032| 1.9807813| 1.7336925| 1.5244257| | 92751| -1.8068114| 1.2207179| -1.8127934| -1.3466044| -3.1093489| *Note: this is simulated data.* --- ## Some key notes: - identifying whether there even is a response variable is important! - the kind of response variable/target is critical for narrowing down the method - the explanatory variables/predictors/features are also important, but I consider these after the response variabe --- ## A question for you! Write down one statistical question you are trying to answer with your research. Identify the type of question it is. --- ## The statistical landscape in R Common packages include: <img src="img/stat-landscape.png" width="80%" /> --- ## Example of an inferential analysis in R Question: *Does sexual activity effect the longevity of male fruit flies?* -- What kind of question is this? --- ## Data Fruitflies were divided randomly into groups of 25 each. The response was the longevity of the fruitfly in days. One group was kept solitary, while another was given 8 virgin females per day. ```r library(tidyverse) fruitfly_2_groups <- read_csv("data/fruitfly_2_groups.csv") fruitfly_2_groups ``` ``` ## # A tibble: 50 x 2 ## longevity sexually_active ## <dbl> <chr> ## 1 40 No ## 2 37 No ## 3 44 No ## 4 47 No ## 5 47 No ## 6 47 No ## 7 68 No ## 8 47 No ## 9 54 No ## 10 61 No ## # … with 40 more rows ``` *Note: this is a modification of the original data set where we only considered two of the groups from the original experiment.* *Original data source: [`faraway` R package](https://cran.r-project.org/web/packages/faraway/faraway.pdf).* --- ## So how should we analyze this data? - What is our response variable? What kind of data is it? - What is our explanatory variable? What kind of data is it? --- ## So how should we analyze this data? - a t-test is suitable here (as would be a permutation test for difference of means, or a Mann Whitney U Test) - to perform this, we need to parameterize null ($H_0$) and alternative hypotheses ($H_A$): *$H_0$: There **is no** difference in mean longevity of sexually active and non-sexually active male fruitflies.* *$H_A$: There **is** difference in mean longevity of sexually active and non-sexually active male fruitflies.* --- ## Always start with a visualization - The visualization should be related to your question! - It should complement your statistical method(s) -- - We are interested in the mean - the population mean however! -- - **So here, we should visualize our estimates of the population means, as well as our uncertainty about them!** --- ## Visualizing estimates and their uncertainty 1. Calculate estimates & uncertainty 2. Visualize estimates and uncertainty, communicating as much about the underlying sample data as possible! --- ## Calculate estimates & uncertainty Here we calculate the sample means and 95% confidence interval for a mean using the t-distribution, assuming independence and the central limit theorem. ```r fruitfly_2_estimates <- fruitfly_2_groups %>% group_by(sexually_active) %>% summarise(mean = mean(longevity), n = n(), se = sd(longevity) / sqrt(n()), df = n - 1, t_star = qt(0.975, df), lower = mean - t_star * se, upper = mean + t_star * se) fruitfly_2_estimates ``` ``` ## # A tibble: 2 x 8 ## sexually_active mean n se df t_star lower upper ## <chr> <dbl> <int> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 No 63.6 25 3.29 24 2.06 56.8 70.4 ## 2 Yes 38.7 25 2.42 24 2.06 33.7 43.7 ``` --- ## Final visualization ```r # plot raw data points for each group as a transparent grey/black point # overlay mean as a red diamond fruitfly_2_estimates_viz <- ggplot(fruitfly_2_groups, aes(x = sexually_active, y = longevity)) + geom_jitter(width = 0.1, size = 2, alpha = 0.2) + stat_summary(fun = mean, geom = "point", shape = 18, size = 4, color = "blue") + geom_errorbar(data = fruitfly_2_estimates, mapping = aes(x = sexually_active, y = mean, ymin = lower, ymax = upper), width = 0.15, colour = "blue", size = 1) + ylim(c(0, 100)) + ylab("Longevity (days)") + xlab("Sexual activity") + theme_bw() + theme(text = element_text(size=20)) ``` --- class: center ```r fruitfly_2_estimates_viz ``` <!-- --> -- What do we think so far? Are we likely to reject the null hypothesis? --- ## Example of t-test ```r fruitfly_2_ttest <- t.test(longevity ~ sexually_active, data = fruitfly_2_groups) fruitfly_2_ttest ``` ``` ## ## Welch Two Sample t-test ## ## data: longevity by sexually_active ## t = 6.0811, df = 44.09, p-value = 2.545e-07 ## alternative hypothesis: true difference in means between group No and group Yes is not equal to 0 ## 95 percent confidence interval: ## 16.60817 33.07183 ## sample estimates: ## mean in group No mean in group Yes ## 63.56 38.72 ``` -- How do we parse this output? --- ## Using base R ```r fruitfly_2_ttest$p.value ``` ``` ## [1] 2.545463e-07 ``` ```r fruitfly_2_ttest$statistic ``` ``` ## t ## 6.081128 ``` --- ## Using `broom` ```r library(broom) fruitfly_2_ttest_tidy <- tidy(fruitfly_2_ttest) ``` ```r fruitfly_2_ttest_pval <- fruitfly_2_ttest_tidy %>% select(p.value) %>% pull() fruitfly_2_ttest_pval ``` ``` ## [1] 2.545463e-07 ``` --- ## What are our conclusions? -- The male fruitflys which were not sexually active were observed to have an increased lifespan (they lived 24.84 days longer). Specifically, the male fruitflys which were not sexually active had a mean lifespan of 64 (95% confidence interval was 57, 70) days, while male fruitflys which were sexually active had a mean lifespan of 39 (95% confidence interval was 34, 44) days. Carrying out a t-test (assuming independence and the central limit theorem) with alpha set to 0.05, indicated that we have enough statistical evidence to reject our null hypothesis, `\(H_0\)`, as our p-value was much smaller than alpha (p = 2.5454628\times 10^{-7}). We can suggest the alternative hypothesis, `\(H_1\)`, may be more favourable. Specifically, that there is a difference in the male fruitfly lifespan when males are sexually active compared to when they are not. Due to the randomized experimental design, we can also suggest that this effect of sexual activity is causal on the change in lifespan. Specifically, sexual activity in male fruitflys decreases lifespan. --- ## Summary 1. Identify the kind of question 2. Look at the data 3. Identify a **suitable** statistical method for your question and data 4. Create a visualization 5. Apply your statistical method 6. (maybe create another visualization) 7. Interpret and communicate your assumptions and results --- ## Questions?