Presentation of data & statistical tests

class: title-slide, left, middle
# Presentation of data & statistical tests
----
<br> 
.right[
### Ghana Medical Journal Workshop
### August 1, 2023
Dr Samuel Blay Nguah .title-t[FWACP FGCPS]
]

---
class: inverse middle center
# No conflict of interest to declare.
----

---
# Outline
----
- Determinants of appropriate analysis
- Common pitfalls in analysis
- Descriptive vs Inferential statistics
- Parametric vs Non-parametric tests
- Analysis and presentation
    - Continuous variables
    - Categorical variables
    - Time to event analysis
- Confounding & Interaction

---
# Determinants of appropriate statistical analysis
----
- What is the research question(s) 
- What is/are the objective(s)?
- What type of variables were collected?
    - Relate variables required for each objective
- What is the study methodology?
- What is the sample size?
- How many .red[**missing variables**]?
- How do you intend to deal with missing?

---
# Common pitfalls

----

.pull-left[
## Statistical analysis
- Poorly written
- Does not conform to analysis done
- Wrong statistical tests applied
- Wrongful dichotomization
- Assumption of test not evaluated
- Missing data: How much was present and how they were dealt with.
- Analysis does not conform to basis for the sample size determination
]

.pull-right[
## Reporting
- P-value not reported as exact (NS)
- Wrong interpretation of P-value (Especially combo p-values)
- Data dredging (p-hacking)
- Ignoring confounders and effect modifiers
- Obvious bias: "Almost significant"
- Transcription errors.
]

---
# An example statistical analysis

> Data Analysis: Statistical analysis was done with the Statistical Package for Social Sciences version 21.0 (Chicago Ill, IBM). Qualitative variables were summarized as frequencies (percentages), while quantitative variables were summarized as means (standard deviation). Student’s t-test, analysis of variance, or Chi-square test was used, as appropriate, to determine the statistical significance of the difference between the two groups. P <0.05 was taken as statistically significant.

---
# What is the research question?

----
Some study questions may appear "the same" but are very different!

.pull-left[
.red[Is there a difference in height between male and female residents?] 
]

.pull-right[
.red[Requires a **two-side** test.]
]

.pull-left[
.green[Are female residents taller than male residents?] 
]

.pull-right[
.green[Requires a **one-side** test.]
]

.pull-left[
.blue[Are male residents taller than female residents?] 
]

.pull-right[
.blue[Requires a **one-side** test.]
]

---
# What are the variables required?

----
- **Dependent** vs. **Independent** variables

.pull-left[
## Categorical 
- Nominal 
- Binary
- Ordinal
- Are some data missing?
- Are the groups balanced?
- What  are the proportions of the outcome and predictors?
]

.pull-right[
##Interval or ratio
- Continuous 
- Discrete
- What is the distribution, normal or non-normal?
- Are there outliers?
]

---
# Methodology

.panelset[

.panel[
.panel-name[Descriptive]
.pull-left[
##Scenario
- Describe what pertains 
- **What is the prevalence of hypertension among staff of the Komfo Anokye Teaching Hospital?**
]

.pull-right[
##Descriptive Analysis
###Categorical 
- Frequency, percentages

###Numeric
- Mean(SD)
- Median(IQR,Range)
- Percentiles
]
]

.panel[
.panel-name[Predictive]
## Scenario
- What is the relationship between two or more variables
- Can one variable predict the other

>**E.g.: What is the relationship between age and incidence of arthritis?**

##Method of Analysis
.pull-left[
- Agreement
- Correlation
]
.pull-right[
- Regression
- Survival 
]
]

.panel[
.panel-name[Comparative]
## Scenario
- Look for differences between groups
> **Is the prevalence of low back pain higher among Surgeons compared to Physicians**

## Analysis
.pull-left[
###Compare averages
- T-test,
- ANOVA
- etc
]

.pull-right[
###Compare proportions
- Chi-square test
- etc...
]
]
]

---
# Descriptive statistics
----
.pull-left[
## Categorical variable
- Frequency tables – univariate
- Contingency tables – bivariate
    - Row percentage
    - Column percentage
- Graphical representations
    - Bar chart
    - Pie Chart
    - Others
- Odds & Odds Ratio
- Risk & Risk Ratio
]

.pull-right[
## Continuous Variable
- Measures of central tendency
    - Mean
        - Arithmetic Mean
        - Geometric mean
        - Harmonic mean
    - Median
    - Mode
- Measures of dispersion
    - Standard deviation
    - Variance
    - Interquartile range
    - Range
]

---
#Inferential statistics
----
## Statistical tests
- p-value

##Estimates
- Point estimates
- Interval estimates
    - Confidence interval

> The 95% confidence interval is the interval that is likely to contain the population  parameter 95% of the time.

---
# Paramatric vs. Non-parametric test?

.panelset[
.panel[.panel-name[Outline]
.pull-left[
##Parametric
- Must be interval data
- Approximately normally distributed
- Approximately normally distributed on transformation
- Enough sample size?

E.g: T-test, ANOVA, etc
]
.pull-right[
##Non-parametric
- Alternative to parametric
- Does not require a specific distribution 
- Can handle low samples sizes
- Interpretation can be difficult
]
]

.panel[.panel-name[Assumption]
- Statistical tests have assumptions
- More stringent in parametric tests
- These should be evaluated for before using the test
- E.g.: For a Student's T-test:
    1. Independence of observations
    2. Normality of data
    3. Homogeneity of Variances
    4. Random Sampling methodology
    5. Adequacy of sample size
]
]

---
# Analysis - Single categorical

.panelset[

.panel[.panel-name[Descriptive]
.pull-left[
Example: **What is the proportion of workers with diabetes mellitus in my study**

##Presentation 
- Frequency/Count
- Proportion
- Percentages
]

.pull-right[
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<table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
  <caption class='gt_caption'><strong>Table 1</strong>: Univariate categorical table</caption>
  <thead>
    
    <tr class="gt_col_headings">
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="<strong>Characteristic</strong>"><strong>Characteristic</strong></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>N = 50</strong>"><strong>N = 50</strong></th>
    </tr>
  </thead>
  <tbody class="gt_table_body">
    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Sex, n (%)</td>
<td headers="stat_0" class="gt_row gt_center"></td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Female</td>
<td headers="stat_0" class="gt_row gt_center">26 (52.0)</td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Male</td>
<td headers="stat_0" class="gt_row gt_center">24 (48.0)</td></tr>
    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Age Grouping, n (%)</td>
<td headers="stat_0" class="gt_row gt_center"></td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Middle age</td>
<td headers="stat_0" class="gt_row gt_center">17 (34.0)</td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Elderly</td>
<td headers="stat_0" class="gt_row gt_center">33 (66.0)</td></tr>
  </tbody>
  
  
</table>
</div>
]
]

.panel[.panel-name[Inferential]
.pull-left[
Example: **What is the proportion of workers with diabetes mellitus in Ghana**

##Presenation 
- Frequency/Count
- Proportion
- Percentages
- Confidence intervals (Binomial)
]

.pull-right[
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<table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
  <caption class='gt_caption'><strong>Table 1</strong>: Univariate categorical table</caption>
  <thead>
    
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      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="<strong>Characteristic</strong>"><strong>Characteristic</strong></th>
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<td headers="stat_0" class="gt_row gt_center"></td>
<td headers="ci_stat_0" class="gt_row gt_center"></td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Female</td>
<td headers="stat_0" class="gt_row gt_center">26 (52.0)</td>
<td headers="ci_stat_0" class="gt_row gt_center">38%, 66%</td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Male</td>
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    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Age Grouping, n (%)</td>
<td headers="stat_0" class="gt_row gt_center"></td>
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    <tr><td headers="label" class="gt_row gt_left">    Middle age</td>
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    <tr><td headers="label" class="gt_row gt_left">    Elderly</td>
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      <td class="gt_footnote" colspan="3"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span> CI = Confidence Interval</td>
    </tr>
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</table>
</div>
]
]
]

---
# Analysis - Two categorical

.panelset[

.panel[.panel-name[Descriptive]
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Example: **What is the proportion of males who have DM in my study**

##Presenation 
- Frequency/Count
- Proportion
- Percentages - Row vs. Column
- Contingency table
]

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<table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
  <caption class='gt_caption'>**Bivariate categorical table</caption>
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]
]

.panel[.panel-name[Inferential]
.pull-left[
Example: **Is having diabetes related to sex in Ghana?**

##Presenation 
- Confidence intervals
- p-value from appropriate statistical test
    - Chi-square test
    - Fisher's test
    - Etc
]

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<td headers="stat_1" class="gt_row gt_center"></td>
<td headers="stat_2" class="gt_row gt_center"></td>
<td headers="p.value" class="gt_row gt_center">0.924</td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Middle age</td>
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<td headers="stat_2" class="gt_row gt_center">8 (33.3)</td>
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    <tr><td headers="label" class="gt_row gt_left">    Old Drug</td>
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<td headers="stat_2" class="gt_row gt_center">11 (45.8)</td>
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    <tr><td headers="label" class="gt_row gt_left">    New Drug</td>
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<td headers="stat_2" class="gt_row gt_center">13 (54.2)</td>
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      <td class="gt_footnote" colspan="4"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span> Pearson’s Chi-squared test</td>
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</div>
]

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  border-left-width: 1px;
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  border-right-style: none;
  border-right-width: 1px;
  border-right-color: #D3D3D3;
  vertical-align: middle;
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}

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  font-size: 100%;
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#gxonvjzloh .gt_from_md > :last-child {
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#gxonvjzloh .gt_row {
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  padding-bottom: 8px;
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  padding-right: 5px;
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  border-right-style: none;
  border-right-width: 1px;
  border-right-color: #D3D3D3;
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#gxonvjzloh .gt_row_group_first th {
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#gxonvjzloh .gt_first_summary_row.thick {
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  border-right-width: 2px;
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  <thead>
    
    <tr class="gt_col_headings">
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="<strong>Characteristic</strong>"><strong>Characteristic</strong></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>Female</strong>, N = 26<span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span>"><strong>Female</strong>, N = 26<span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>Male</strong>, N = 24<span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span>"><strong>Male</strong>, N = 24<span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>Odds Ratio</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>2</sup></span>"><strong>Odds Ratio</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>2</sup></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>95% CI</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>2,3</sup></span>"><strong>95% CI</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>2,3</sup></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>p-value</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>2</sup></span>"><strong>p-value</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>2</sup></span></th>
    </tr>
  </thead>
  <tbody class="gt_table_body">
    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Treatment Type</td>
<td headers="stat_1" class="gt_row gt_center"></td>
<td headers="stat_2" class="gt_row gt_center"></td>
<td headers="estimate" class="gt_row gt_center">0.87</td>
<td headers="ci" class="gt_row gt_center">0.25, 3.06</td>
<td headers="p.value" class="gt_row gt_center">>0.999</td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Old Drug</td>
<td headers="stat_1" class="gt_row gt_center">11 / 26 (42%)</td>
<td headers="stat_2" class="gt_row gt_center">11 / 24 (46%)</td>
<td headers="estimate" class="gt_row gt_center"></td>
<td headers="ci" class="gt_row gt_center"></td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
    <tr><td headers="label" class="gt_row gt_left">    New Drug</td>
<td headers="stat_1" class="gt_row gt_center">15 / 26 (58%)</td>
<td headers="stat_2" class="gt_row gt_center">13 / 24 (54%)</td>
<td headers="estimate" class="gt_row gt_center"></td>
<td headers="ci" class="gt_row gt_center"></td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Age Grouping</td>
<td headers="stat_1" class="gt_row gt_center"></td>
<td headers="stat_2" class="gt_row gt_center"></td>
<td headers="estimate" class="gt_row gt_center">1.06</td>
<td headers="ci" class="gt_row gt_center">0.28, 4.03</td>
<td headers="p.value" class="gt_row gt_center">>0.999</td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Middle age</td>
<td headers="stat_1" class="gt_row gt_center">9 / 26 (35%)</td>
<td headers="stat_2" class="gt_row gt_center">8 / 24 (33%)</td>
<td headers="estimate" class="gt_row gt_center"></td>
<td headers="ci" class="gt_row gt_center"></td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Elderly</td>
<td headers="stat_1" class="gt_row gt_center">17 / 26 (65%)</td>
<td headers="stat_2" class="gt_row gt_center">16 / 24 (67%)</td>
<td headers="estimate" class="gt_row gt_center"></td>
<td headers="ci" class="gt_row gt_center"></td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
  </tbody>
  
  <tfoot class="gt_footnotes">
    <tr>
      <td class="gt_footnote" colspan="6"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span> n / N (%)</td>
    </tr>
    <tr>
      <td class="gt_footnote" colspan="6"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>2</sup></span> Fisher’s Exact Test for Count Data</td>
    </tr>
    <tr>
      <td class="gt_footnote" colspan="6"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>3</sup></span> CI = Confidence Interval</td>
    </tr>
  </tfoot>
</table>
</div>

]
]
]

---
# Analysis: Single numeric

.panelset[

.panel[.panel-name[Descriptive]

.pull-left[
Example: **What is the average hemoglobin of doctors in Kath**
##Presenation 
- Mean(SD)
- Median(IQR), 
- Median(Range)
]

.pull-right[
<div id="xojenyfkdz" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
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  background-color: #FFFFFF;
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  padding-top: 8px;
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  padding-top: 8px;
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  padding-left: 5px;
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  <caption class='gt_caption'>**Table **: Univariate numeric table</caption>
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<td headers="stat_0" class="gt_row gt_center">98.3 (5.2)</td></tr>
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<td headers="stat_0" class="gt_row gt_center">88.2 (6.9)</td></tr>
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</table>
</div>

]
]

.panel[.panel-name[Inferential]
.pull-left[
Example: **What is the average Hemoglobin of Ghanaians?**

##Presenation 
- Mean(SD)
- Median(IQR), 
- Median(Range)
- Confidence interval
]

.pull-right[
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<table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
  <caption class='gt_caption'><strong>Table 1</strong>: Univariate continuous</caption>
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      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="<strong>Characteristic</strong>"><strong>Characteristic</strong></th>
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    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Age in years, Median (Minimum,Maximum)</td>
<td headers="stat_0" class="gt_row gt_center">63 (45,75)</td>
<td headers="ci_stat_0" class="gt_row gt_center">60, 63</td></tr>
    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Initial blood pressure (mmHg), Mean (SD)</td>
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<td headers="ci_stat_0" class="gt_row gt_center">97, 100</td></tr>
    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Blood Pressure after treatment, Median (IQR)</td>
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<td headers="ci_stat_0" class="gt_row gt_center">87, 90</td></tr>
  </tbody>
  
  <tfoot class="gt_footnotes">
    <tr>
      <td class="gt_footnote" colspan="3"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span> CI = Confidence Interval</td>
    </tr>
  </tfoot>
</table>
</div>
]
]
]

---
# Analysis: Two continuous
.panelset[

.panel[
.panel-name[Difference]

Example: **What is the difference in weight between males and females?**

.pull-left[
## Tests - Unpaired
- Parametric: 
    - T-test (Unequal variance)
    - T-test (Equal variance)
- Non-parametric: 
    - Mann-Whitney U test
]

.pull-right[

## Test - Paired
- Parametric
    - Paired T-test
- Non-parametric
    - Wilcoxon-Signed rank test

]
]

.panel[
.panel-name[Difference 2]
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<table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
  <caption class='gt_caption'><strong>Table</strong>: Bivariate continuous</caption>
  <thead>
    
    <tr class="gt_col_headings">
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="<strong>Characteristic</strong>"><strong>Characteristic</strong></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>Old Drug</strong>, N = 22"><strong>Old Drug</strong>, N = 22</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>New Drug</strong>, N = 28"><strong>New Drug</strong>, N = 28</th>
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      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>95% CI</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1,2</sup></span>"><strong>95% CI</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1,2</sup></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>p-value</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span>"><strong>p-value</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span></th>
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    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Age in years, Mean (SD)</td>
<td headers="stat_1" class="gt_row gt_center">62 (7)</td>
<td headers="stat_2" class="gt_row gt_center">61 (7)</td>
<td headers="estimate" class="gt_row gt_center">1.1</td>
<td headers="ci" class="gt_row gt_center">-2.7, 4.9</td>
<td headers="p.value" class="gt_row gt_center">0.562</td></tr>
    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Initial blood pressure (mmHg), Mean (SD)</td>
<td headers="stat_1" class="gt_row gt_center">97.1 (3.6)</td>
<td headers="stat_2" class="gt_row gt_center">99.2 (6.0)</td>
<td headers="estimate" class="gt_row gt_center">-2.1</td>
<td headers="ci" class="gt_row gt_center">-4.9, 0.68</td>
<td headers="p.value" class="gt_row gt_center">0.135</td></tr>
    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Blood Pressure after treatment, Mean (SD)</td>
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<td headers="stat_2" class="gt_row gt_center">85.8 (3.3)</td>
<td headers="estimate" class="gt_row gt_center">6.4</td>
<td headers="ci" class="gt_row gt_center">4.5, 8.3</td>
<td headers="p.value" class="gt_row gt_center"><0.001</td></tr>
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      <td class="gt_footnote" colspan="6"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span> Welch Two Sample t-test</td>
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      <td class="gt_footnote" colspan="6"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>2</sup></span> CI = Confidence Interval</td>
    </tr>
  </tfoot>
</table>
</div>
]

.panel[
.panel-name[Correlation]
Example: **Does the serum lactate in children with severe malaria correlate with their hemoglobin concentration?**

.pull-left[
##Parametric
- Pearson correlation coefficient
- Confidence interval
- p-value

]
.pull-right[
## Non-parametric
- Spearman correlation coefficient
- Kendal's tau
- Confidence interval
- p-value
]
]

.panel[.panel-name[Relationship]
Example: **What is the relationship between age and mean blood pressure?**

.pull-left[
##Parametric
- Linear regression
]
.pull-right[
##Non-parametric 
- Non-linear regression
- Quantile regression
]
]
]

---
# Regression

.panelset[

.panel[.panel-name[Confounding]
.pull-left[
#Confounder
- Extraneous or nuisance pathway that the investigator hopes to rule out
- If present, it has to be adjusted for

>E.g: Relationship between Birth order, maternal age and Down Syndrome
]

.pull-right[
#Effect modifier
- The effect differs for the various groups
- Simply put! it depends.
- If present, the groups will have to be reported separately

>E.g: Salt intake, hypertension and age.
]
]

.panel[.panel-name[Linear]
.pull-left[

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    <tr><td headers="label" class="gt_row gt_left">    Female</td>
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<td headers="estimate" class="gt_row gt_center">—</td>
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      <td class="gt_footnote" colspan="5"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span> CI = Confidence Interval</td>
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    <tr><td headers="label" class="gt_row gt_left">    Female</td>
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      <td class="gt_footnote" colspan="4"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span> CI = Confidence Interval</td>
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  <caption class='gt_caption'>Univariate Logistic regression</caption>
  <thead>
    
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      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="<strong>Characteristic</strong>"><strong>Characteristic</strong></th>
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      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>p-value</strong>"><strong>p-value</strong></th>
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<td headers="stat_n" class="gt_row gt_center">50</td>
<td headers="estimate" class="gt_row gt_center"></td>
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    <tr><td headers="label" class="gt_row gt_left">    Female</td>
<td headers="stat_n" class="gt_row gt_center"></td>
<td headers="estimate" class="gt_row gt_center">—</td>
<td headers="ci" class="gt_row gt_center">—</td>
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      <td class="gt_footnote" colspan="5"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span> CI = Confidence Interval</td>
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    <tr><td headers="label" class="gt_row gt_left">    Female</td>
<td headers="estimate" class="gt_row gt_center">—</td>
<td headers="ci" class="gt_row gt_center">—</td>
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      <td class="gt_footnote" colspan="4"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span> OR = Odds Ratio, CI = Confidence Interval</td>
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]
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  <caption class='gt_caption'>Multivariate Linear regression - Interaction</caption>
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    <tr><td headers="label" class="gt_row gt_left">    Female</td>
<td headers="estimate" class="gt_row gt_center">—</td>
<td headers="ci" class="gt_row gt_center">—</td>
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      <td class="gt_footnote" colspan="4"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span> CI = Confidence Interval</td>
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<table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
  <caption class='gt_caption'>Multivariate logistic regression - interaction</caption>
  <thead>
    
    <tr class="gt_col_headings">
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="<strong>Characteristic</strong>"><strong>Characteristic</strong></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>OR</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span>"><strong>OR</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>95% CI</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span>"><strong>95% CI</strong><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>p-value</strong>"><strong>p-value</strong></th>
    </tr>
  </thead>
  <tbody class="gt_table_body">
    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Sex</td>
<td headers="estimate" class="gt_row gt_center"></td>
<td headers="ci" class="gt_row gt_center"></td>
<td headers="p.value" class="gt_row gt_center">0.815</td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Female</td>
<td headers="estimate" class="gt_row gt_center">—</td>
<td headers="ci" class="gt_row gt_center">—</td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Male</td>
<td headers="estimate" class="gt_row gt_center">0.27</td>
<td headers="ci" class="gt_row gt_center">0.00, 21,466</td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Age in years</td>
<td headers="estimate" class="gt_row gt_center">0.94</td>
<td headers="ci" class="gt_row gt_center">0.81, 1.07</td>
<td headers="p.value" class="gt_row gt_center">0.347</td></tr>
    <tr><td headers="label" class="gt_row gt_left" style="font-weight: bold;">Sex * Age in years</td>
<td headers="estimate" class="gt_row gt_center"></td>
<td headers="ci" class="gt_row gt_center"></td>
<td headers="p.value" class="gt_row gt_center">0.761</td></tr>
    <tr><td headers="label" class="gt_row gt_left">    Male * Age in years</td>
<td headers="estimate" class="gt_row gt_center">1.03</td>
<td headers="ci" class="gt_row gt_center">0.86, 1.24</td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
  </tbody>
  
  <tfoot class="gt_footnotes">
    <tr>
      <td class="gt_footnote" colspan="4"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;"><sup>1</sup></span> OR = Odds Ratio, CI = Confidence Interval</td>
    </tr>
  </tfoot>
</table>
</div>
]
]
.panel[.panel-name[Cox's]
<img src="Images/cox-regression.jpg" style="width: 70%" />
]
]

---
class: inverse 
#Summary of tests: Categorical

.footnote[https://www.researchgate.net/figure/Common-statistical-tests-to-compare-categorical-data-for-difference_fig1_305213637]

---
class: inverse
#Summary of tests: Numeric

.footnote[https://www.slideshare.net/ShefaliJain74/overview-of-different-statistical-tests-used-in-epidemiological]

---
# Summary
----
- Determinants of appropriate analysis
- Common pitfalls in analysis
- Descriptive vs Inferential statistics
- Parametric vs Non-parametric tests
- Analysis and presentation
    - Continuous variables
    - Categorical variables
    - Time to event analysis
- Confounding & Interaction

---
background-image: url("Images/take_home_message.jpg")
background-position: bottom right
background-size: 35%, 35%
# Take home ...
>Good results from a study comes from planning, appropriate sample size, application of the right statistical techniques and appropriate presentation of the data.

---
class: inverse middle center
<style>
.bye{
    font-size: 3em;
    font-weight: bold;
    /*font-style: italic;*/
    color: white;
}
</style>

.bye[
    Thank you!!!
]