back-pain.qmd

---
title: "Back pain: four outcomes"
author: "Ty and Kaja"
format: 
  pdf:
    toc: true
    highlight-style: atom-one
    number-sections: true
editor: source
---


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```{R}
#| include: false
knitr::read_chunk('back-pain.R')
```

\newpage

# Approach 

For each outcome, the simplest model that has appropriate fit will be sought. Models have been classified in rough ordering from "simplest" below using A, B, C, or D with A representing the common/easily understood models

<!-- thanks to https://www.tablesgenerator.com/markdown_tables -->

| **Outcome variable**/*Model* | *Multiple linear regression* (A) | *Ordinal logistic regression* (B${}^{*}$) | *Logistic regression* (B) | *Poisson/negative binomial regression* (C) | *Beta regression* (D) | 
|---|---|---|---|---|---|
| **Binary** | - | - | + | - | - | 
|   |   |   |   |   |   |
| **Ordinal** | - | + | + (if outcome made binary) | - | - | 
|   |   |   |   |   |   |
| **Values from 0 to 100** | + (outcome potentially transformed) | - (if outcome made ordinal but bad option) | + (if outcome made binary) | + | + |  


${}^{*}$Probably "C" not "B" but is basically multiple logistic regressions performed with different dichotomisations of the order levels in the outcome 


\newpage

# Set up

## Packages


```{R, libs}

```

## Constants


```{R, consts}

```


\newpage


# Data wrangling

## Read data


```{R, read}

```

## Tidy data


```{R, tidy}

```


## Impute missing values in compositions

This code is thanks to Kaja! 

Missing data is assumed to be below detectable threshold and imputed.

```{R, impute}

```


## Compositions transformation to *ilr*s

The below function will allow us to automatically add ilrs to a dataset

```{R, ilr_create}

```


\newpage


# Exploratory analysis

## Missing/`NA` value summaries



```{R, explore1}
#| warning: false
#| fig-height: 4
#| fig-width: 8


```


## Pairwise plots between *ilr*s and outcome variables


```{R, explore2}
#| warning: false
#| fig-height: 15
#| fig-width: 15


```


\newpage


# Statistical analysis

## Outcome 0: binary outcome of `Pain = "yes"`

### Model fit

```{R, outcome0}
```


### Model diagnostics

```{R, outcome0_diag}

```

### Model predictions

```{R, outcome0_pred}
#| fig-height: 8
#| fig-width: 8
```


\newpage

## Note for outcomes 1 to 2

The dataset for the remain outcomes will be limited to people who responded:



```{R, update_data}
```

\newpage


## Outcome 1: `LBP_frequency_year`

### Model fit

```{R, outcome1}
```

Ordinal logistic regression has fit the model:

<!-- logit (\hat{P}(Y \le \texttt{0days})) & =   \hat{\beta}_{0,\texttt{0days|1-7days}} –  \hat{\beta}_1 (age == \texttt{2\_middle}) – \ldots –  \hat{\beta}_p {\times} \texttt{ilr(..+-)} \\ -->

$$
\begin{aligned}
logit (\hat{P}(Y \le \texttt{1-7days})) & =   \hat{\beta}_{0,\texttt{1-7days|8-30days}} –  \hat{\beta}_1 {\times}(age ) – \ldots –  \hat{\beta}_p {\times} \texttt{ilr(..+-)} \\
logit (\hat{P}(Y \le \texttt{8-30days})) & =   \hat{\beta}_{0,\texttt{8-30days|31-90days }} –  \hat{\beta}_1 {\times}(age ) – \ldots –  \hat{\beta}_p {\times} \texttt{ilr(..+-)} \\
logit (\hat{P}(Y \le \texttt{31-90days})) & =   \hat{\beta}_{0,\texttt{31-90days|91+\_not\_evday}} –  \hat{\beta}_1 {\times}(age) – \ldots –  \hat{\beta}_p {\times} \texttt{ilr(..+-)} \\
logit (\hat{P}(Y \le \texttt{91+\_not\_evday})) & =   \hat{\beta}_{0,\texttt{91+\_not\_evday|everyday}} –  \hat{\beta}_1 (age == \texttt{2\_middle}) – \ldots –  \hat{\beta}_p {\times} \texttt{ilr(..+-)} \\
\end{aligned}
$$



### Model diagnostics

```{R, outcome1_diag}
```

### Model predictions

```{R, outcome1_pred_a}
#| fig-height: 10
#| fig-width: 10
```


```{R, outcome1_pred_b}
#| fig-height: 10
#| fig-width: 10
```


\newpage

## Outcome 2: `LBP_intensity_year`

### Model fit

```{R, outcome2}
#| fig-height: 6
#| fig-width: 6
```

### Model diagnostics

```{R, outcome2_diag}
#| fig-height: 12
#| fig-width: 8
```

### Model predictions

```{R, outcome2_pred_a}
#| fig-height: 8
#| fig-width: 8
```


\newpage

#### Absolute scale

```{R, outcome2_pred_b_abs}
#| fig-height: 8
#| fig-width: 8
```


\newpage

#### Ratio scale

```{R, outcome2_pred_b_rat}
#| fig-height: 8
#| fig-width: 8
```



\newpage

# Session information


```{R}
format(Sys.time(), '%d %b %Y')
sessionInfo()
```