# Forecasting US deaths per-day from Covid-19

Time Series are a common task in data science. The possibilities for applying time series analysis to real world situations are endless. Think of all the different aspects of your life or business and the chances are if you think of them in terms of time, or occuring over a period of time, that they could be turned into data and analyzed with a time series analysis. Time series analysis, however can be challenging: making predictings into the future is difficult because no one can exactly predict the future. For one, unforeseen events or events with unpredictable outcomes may occur that could effect the dependent variable we are intersted in predicting.

Another way we can look at this is to ask, “what would have happened if X did not take place?”. One such example of this in the real world involves the novel Covid-19 virus. With the fairly comprehensive amount of testing and hospital record collection that ocurred in the United States through the early stages of the pandemic, we have a high quality dataset with which to ask questions about the pandemic in the US and abroad. Here, I perform an exploratory data analysis of the global covid-19 daily death count data, and then conduct a time series analysis on the daily death count data in the US. The goal of the analysis is to forecast daily death counts if the mRNA vaccines and boosters had not been administered.

The approach I took was to break the US data into logical segments and analyze each segment independently. For example, the first segment I delineated, spanned the time from the first recorded covid case to the release of the first booster. With the first segment, the training and testing data were split on the date of the realease of the first vaccine. I then forecasted daily death rates for the testing dataset based on the training data (the data before the vaccine was released) so the model would not take into account the impact of the vaccine on death rates. I repeated this process for the booster.

Time series analysis has a number of components that are somewhat unique to time series data. These are: trend, seasonality, cyclicality, and irregularity. There is also a concept called ‘stationarity’ which basically means the data is free of the trend, seasonality, etc. The steps for performing time series analysis are first to preprocess the data, perform exploratory data analysis, split the data into train and test sets, check for stationarity (Augmented Dickey-Fuller Test), remove stationarity (differencing, detrending, deseasoning and or log transformation), build models (AR, MA, ARMA, ARIMA), and forecast.

After download the John’s Hopkins global Covid-19 death count dataset from kaggle (https://www.kaggle.com/datasets/antgoldbloom/covid19-data-from-john-hopkins-university), I began by checking for missing data.

```
--------number of single country records, and number of provincial records---------
False 201
True 88
dtype: int64
--------number of records per country---------
Country/Region
Australia 8
Canada 16
China 34
Denmark 3
France 12
Netherlands 5
New Zealand 3
United Kingdom 15
dtype: int64
```

What is clear from the table above is that the data recorded for some countries has state/province information, but for other countries there is none. I am not interested in the states provincial feature at this time so I will drop it. Next I group the data by country using the pandas dataframe groupby() method and plot a correlation heatmap of death counts for the top 20 countries with the highest death counts.

One important thing to note about the covid 19 data is that not all countries followed the same reporting standards for infections or deaths. Therefor it is important to keep in mind that some countries that may not be in the top 20 in this dataset may have had underinflated death count data. Interestingly, in the correlation heatmap we can see that there are some lighter groups of blocks indicating correlation between the daily death counts between some countries. For example Brazil and India, or Columbia, and Argentina,a nd finally the UK, Italy, Germany, and France. The latter two groups make perfect sense as these countries are geographically, culturally, and economically more closely related. Next, I extracted the US data from the global dataset. The remainder of the analysis will focus just on the US dataset.

### US Covid 19 daily death rate analysis

plotting the cummulative US death counts from the start of the pandemic, we can see there are changes in the death rate over time:

To get a better picture of the these changes in death rate, I transformed the data into non-cumulative data using the built in pandas shift() method to the subtract the previous day from each days death count.

### convert US to non-cummulative daily death counts

Here is the resulting non-cumulative data plotted from the start of the pandemic, with significant vaccination developments included as vertical dashed lines:

The vaccination events appear to be correlated with unpredictable drops in the covid death rate. To explore this further, I break the dataset into smaller windows of analysis. The first window is from the start of the pandemic to the release of the 1st booster. The training and testing data are split based on the date of the release of the 1st vaccines. I will then forecast the predicted death rate of the testing dataset with an ARIMA model.

### Forecasting the predicted covid deaths ‘hypothetically without first vaccine’

First, lets take a look at the trend and seasonlity of the training set…

There is a clear upward trend, but there is also some unpredictability still in the trend line. There is also some ‘seasonality’ to the data, this is likely the affect of when data were collected and released on a weekly basis. Next I perform an augmented Dickey-Fuller (ADF) test after applying a single shift to the data to check for continued non-stationarity. In the adfuller method from the statsmodels package in python, we test the alternative hypothesis (Ha) that the data are stationary, against teh null hypothesis (H0) that the data are non-stationary.

```
Dickey-Fuller Test:
Test Statistic -3.232943
p-value 0.018155
Lags Used 13.000000
No. of Observations 294.000000
Critical Value (1%) -3.452790
Critical Value (5%) -2.871422
Critical Value (10%) -2.572035
dtype: float64
```

According to the ADF test, after shifting the data a single period the p-value is .018 meaning that we reject the null hypothesis, the data are stationary and dont need further differencing or transformation. Next I fit an ARIMA model. ARIMA stands for Auto-Regressive Integrated Moving Average and takes three hyperparameters: lag (p), degree of differencing (d), and the order of the moving average (q). using the auto-arima method from the pmdarima package, first I fit an ARIMA model to the undifferenced training data:

```
Performing stepwise search to minimize aic
ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=4823.159, Time=0.43 sec
ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=5005.576, Time=0.01 sec
ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=5003.219, Time=0.02 sec
ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=4996.994, Time=0.07 sec
ARIMA(0,1,0)(0,0,0)[0] : AIC=5003.693, Time=0.01 sec
ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=4921.755, Time=0.29 sec
ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=4893.048, Time=0.19 sec
ARIMA(3,1,2)(0,0,0)[0] intercept : AIC=inf, Time=0.38 sec
ARIMA(2,1,3)(0,0,0)[0] intercept : AIC=4801.726, Time=0.42 sec
ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=4910.872, Time=0.33 sec
ARIMA(3,1,3)(0,0,0)[0] intercept : AIC=4825.775, Time=0.46 sec
ARIMA(2,1,4)(0,0,0)[0] intercept : AIC=4803.279, Time=0.51 sec
ARIMA(1,1,4)(0,0,0)[0] intercept : AIC=4865.388, Time=0.40 sec
ARIMA(3,1,4)(0,0,0)[0] intercept : AIC=4799.294, Time=0.50 sec
ARIMA(4,1,4)(0,0,0)[0] intercept : AIC=4686.396, Time=0.60 sec
ARIMA(4,1,3)(0,0,0)[0] intercept : AIC=4741.888, Time=0.49 sec
ARIMA(5,1,4)(0,0,0)[0] intercept : AIC=4662.236, Time=0.63 sec
ARIMA(5,1,3)(0,0,0)[0] intercept : AIC=4716.051, Time=0.61 sec
ARIMA(5,1,5)(0,0,0)[0] intercept : AIC=4660.664, Time=0.79 sec
ARIMA(4,1,5)(0,0,0)[0] intercept : AIC=4660.880, Time=0.74 sec
ARIMA(5,1,5)(0,0,0)[0] : AIC=4662.059, Time=0.57 sec
Best model: ARIMA(5,1,5)(0,0,0)[0] intercept
Total fit time: 8.480 seconds
```

The best model according the method’s evaluation of AIC is p=5, d=1, q=5. The Root mean squared error of the predictions made with this model are:

```
RMSE: 2847.6034508083358
```

This is rather high, and likely do to the fact that the model is overfittig by fitting to the ‘seasonal’ fluctuations and noise in the data, mimicing the pattern with which hospitals released data. Finally, I plot the forecast for the daily covid death rate on the testing data:

According to the ARIMA model, the death rate would have continued to increase in 2021 given the training data prior to 01-01-2021. From an epedemiological standpoint, this model does not take into account other confounding variables that may have had an effect of the death rates in early 2021 that could have lead to the sharp decrease we see in the testing dataset. One possible cause of the decrease in actual deaths we see in early 2021 could have been due to the realse of the mRNA vaccines. This brief time series analysis of the covid-19 death data in the US is one approach for forecasting what could have happened had the vaccines not been released.