From b6edcf4f311ef4a5f58a21903041070e6322c219 Mon Sep 17 00:00:00 2001
From: AHsu98 <34590951+AHsu98@users.noreply.github.com>
Date: Sun, 29 Jan 2023 09:57:15 -0800
Subject: [PATCH] changed prev to rate in readme

---
 readme.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/readme.md b/readme.md
index adb56a4..4ec8774 100644
--- a/readme.md
+++ b/readme.md
@@ -5,7 +5,7 @@ The most basic functionality is to perform disaggregation under the rate multipl
 
 The setup is as follows: 
 
-Let $D_{1,...,k}$ be an aggregated measurement across groups ${g_1,...,g_k}$, where the population of each is $p_i,...,p_k$. Let $f_1,...,f_k$ be the baseline pattern of the prevalence across groups, which could have potentially been estimated on a larger dataset or a population in which have higher quality data on. Using this data, we generate estimates for $D_i$, the number of events in group $g_i$ and $\hat{f_{i}}$, the prevalence in each group in the population of interest by combining $D_{1,...,k}$ with $f_1,...,f_k$ to make the estimates self consistent. 
+Let $D_{1,...,k}$ be an aggregated measurement across groups ${g_1,...,g_k}$, where the population of each is $p_i,...,p_k$. Let $f_1,...,f_k$ be the baseline pattern of the rates across groups, which could have potentially been estimated on a larger dataset or a population in which have higher quality data on. Using this data, we generate estimates for $D_i$, the number of events in group $g_i$ and $\hat{f_{i}}$, the rate in each group in the population of interest by combining $D_{1,...,k}$ with $f_1,...,f_k$ to make the estimates self consistent. 
 
 Mathematically, in the simpler rate multiplicative model, we find $\beta$ such that 
 $$D_{1,...,k} = \sum_{i=1}^{k}\hat{f}_i \cdot p_i $$
@@ -15,11 +15,11 @@ $$\hat{f_i} = T^{-1}(\beta + T(f_i)) $$
 This yields the estimates for the per-group event count, 
 
 $$D_i = \hat f_i \cdot p_i $$
-For the current models in use, T is just a logarithm, and this assumes that each prevalence is some constant multiple muliplied by the overall global or baseline prevalence level. Allowing a more general transformation T, such as a log-odds transformation, assumes multiplicativity in the prevalence odds, rather than the prevalence rate, and can produce better estimates statistically (potentially being a more realistic assumption in some cases) and practically, restricting the estimated prevalences to lie within a reasonable interval. 
+For the current models in use, T is just a logarithm, and this assumes that each rate is some constant muliplied by the overall rate pattern level. Allowing a more general transformation T, such as a log-odds transformation, assumes multiplicativity in the associated odds, rather than the rate, and can produce better estimates statistically (potentially being a more realistic assumption in some cases) and practically, restricting the estimated rates to lie within a reasonable interval. 
 
 ## Current Package Capabilities and Models
 Currently, the multiplicative-in-rate model RateMultiplicativeModel with $T(x)=\log(x)$ and the Log Modified Odds model LMO_model(m) with $T(x)=\log(\frac{x}{1-x^{m}})$ are implemented. Note that the LMO_model with m=1 gives a multiplicative in odds model.
 
 A useful (but slightly wrong) analogy is that the multiplicative-in-rate is to the multiplicative-in-odds model as ordinary least squares is to logistic regression in terms of the relationship between covariates and output (not in terms of anything like the likelihood)
 
-Increasing in the model LMO_model(m) gives results that are more similar to the multiplicative-in-rate model currently in use, while preserving the property that prevalence estimates are bounded by 1. 
\ No newline at end of file
+Increasing m in the model LMO_model(m) gives results that are more similar to the multiplicative-in-rate model currently in use, while preserving the property that rate estimates are bounded by 1. 
\ No newline at end of file