* MWRA COVID Analysis on Fri Feb 04 17:16:34 2022
- input data directory: ./data
- results directory: ./results
- transcript to: ./results/mwra-covid-transcript.txt
Archival:
---------
* Archived analysis script(s) to ./results:
- ./mwra-covid-3.r
Loading datasets and constructing joint dataset:
------------------------------------------------
* Reading US county-level COVID data from ./data/us-counties.csv.gz
- Dropping 2 columns for being empty or for being state & fips: state, fips
- Differentiating cumulative cases & deaths to get daily increments
- Structure:
o 2130 rows
o 6 columns: Date, County, Cases, Deaths, Cases.New, Deaths.New
Date County Cases Deaths Cases.New Deaths.New
1 2020-03-05 Middlesex 1 0 1 0
2 2020-03-06 Middlesex 1 0 0 0
3 2020-03-07 Middlesex 5 0 4 0
4 2020-03-08 Middlesex 10 0 5 0
5 2020-03-09 Middlesex 15 0 5 0
6 2020-03-10 Middlesex 41 0 26 0
...
Date County Cases Deaths Cases.New Deaths.New
2125 2022-01-26 Suffolk 195110 2132 846 7
2126 2022-01-27 Suffolk 196144 2138 1034 6
2127 2022-01-28 Suffolk 197025 2144 881 6
2128 2022-01-29 Suffolk 197025 2144 0 0
2129 2022-01-30 Suffolk 197025 2144 0 0
2130 2022-01-31 Suffolk 198467 2156 1442 12
* Reading MWRA wastewater RNA data from ./data/MWRAData20220201-data.tsv.gz
- Structure:
o 686 rows
o 5 columns: Date, South, North, South.7, North.7
Date South North South.7 North.7
9 2020-03-09 NA 29 NA NA
10 2020-03-10 38 15 NA 21
11 2020-03-11 31 65 34 31
12 2020-03-12 25 36 31 32
13 2020-03-13 NA NA 31 32
14 2020-03-14 16 27 26 31
...
Date South North South.7 North.7
715 2022-01-26 672 904 1619 1187
716 2022-01-27 1106 1426 1503 1211
717 2022-01-28 715 821 1328 1144
718 2022-01-29 1693 1132 1276 1094
719 2022-01-30 1234 1066 1207 1050
720 2022-01-31 1388 1053 1118 1016
* Constructing joint dataset by inner join on dates
- Saved to ./results/mwra-covid-joint-data.tsv
- Structure:
o 2058 rows
o 10 columns: Date, South, North, South.7, North.7, County, Cases, Deaths, Cases.New, Deaths.New
Date South North South.7 North.7 County Cases Deaths Cases.New
1 2020-03-09 NA 29 NA NA Suffolk 10 0 1
2 2020-03-09 NA 29 NA NA Middlesex 15 0 5
3 2020-03-09 NA 29 NA NA Norfolk 10 0 3
4 2020-03-10 38 15 NA 21 Norfolk 22 0 12
5 2020-03-10 38 15 NA 21 Middlesex 41 0 26
6 2020-03-10 38 15 NA 21 Suffolk 20 0 10
Deaths.New
1 0
2 0
3 0
4 0
5 0
6 0
...
Date South North South.7 North.7 County Cases Deaths Cases.New
2053 2022-01-30 1234 1066 1207 1050 Suffolk 197025 2144 0
2054 2022-01-30 1234 1066 1207 1050 Norfolk 123471 2079 0
2055 2022-01-30 1234 1066 1207 1050 Middlesex 303054 4421 0
2056 2022-01-31 1388 1053 1118 1016 Norfolk 124407 2091 936
2057 2022-01-31 1388 1053 1118 1016 Middlesex 305536 4443 2482
2058 2022-01-31 1388 1053 1118 1016 Suffolk 198467 2156 1442
Deaths.New
2053 0
2054 0
2055 0
2056 12
2057 22
2058 12
Exploratory plots:
------------------
* Plot of north vs south RNA to ./results/plot-north-south.png
Prediction set:
---------------
* Making prediction set:
- Averaging North and South daily mRNA measurements
- For each day, summing cases and deaths over counties
- Outer joining RNA data and medical data
- Structure:
o 686 rows
o 4 columns: Date, RNA, Cases, Deaths
Date RNA Cases Deaths
1 2020-03-09 29.0 9 0
2 2020-03-10 26.5 48 0
3 2020-03-11 48.0 0 0
4 2020-03-12 30.5 12 0
5 2020-03-13 NA 15 0
6 2020-03-14 21.5 10 0
...
Date RNA Cases Deaths
681 2022-01-26 788.0 3414 31
682 2022-01-27 1266.0 3432 31
683 2022-01-28 768.0 2891 34
684 2022-01-29 1412.5 0 0
685 2022-01-30 1150.0 0 0
686 2022-01-31 1220.5 4860 46
- Saved to ./results/mwra-covid-joint-data-prediction-set.tsv.
Correlation plots:
------------------
* Correlation time courses plotted to ./results/plot-med-loads-vs-RNA-1.png
* Correlation chart plotted to ./results/plot-med-loads-vs-RNA-2.png
Lagged regressions:
-------------------
* Regressing medical vars on RNA at various lags to test predictive power
* Scatterplotting significance & strength vs RNA lag
- ./results/plot-RNA-Cases-lags.png
- ./results/plot-RNA-Deaths-lags.png
* Optimal lags for each medical variable:
MedVar Lag p Adj.R2
1 Cases 7 6.511943e-93 0.49721375
2 Deaths 18 8.273442e-09 0.05265426
Final regressions:
------------------
* Trying some regressions at the optimal lag for each variable:
- Regressing Cases on RNA at lag 7 days:
Call:
lm(formula = as.formula(sprintf("%s ~ RNA", mv)), data = transform(predictionSet,
RNA = lagVector(predictionSet[, "RNA"], lag)))
Residuals:
Min 1Q Median 3Q Max
-11250.8 -280.8 -121.6 214.0 19470.9
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 317.09647 68.33327 4.64 4.26e-06 ***
RNA 1.03859 0.04232 24.54 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1552 on 607 degrees of freedom
(77 observations deleted due to missingness)
Multiple R-squared: 0.498, Adjusted R-squared: 0.4972
F-statistic: 602.3 on 1 and 607 DF, p-value: < 2.2e-16
2.5 % 97.5 %
(Intercept) 182.8981252 451.294808
RNA 0.9554764 1.121701
o Plot to ./results/plot-RNA-Cases-regression.png
- Regressing Deaths on RNA at lag 18 days:
Call:
lm(formula = as.formula(sprintf("%s ~ RNA", mv)), data = transform(predictionSet,
RNA = lagVector(predictionSet[, "RNA"], lag)))
Residuals:
Min 1Q Median 3Q Max
-32.118 -7.998 -4.014 3.870 85.089
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 8.9882052 0.5803964 15.486 < 2e-16 ***
RNA 0.0021169 0.0003621 5.847 8.27e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 13.14 on 596 degrees of freedom
(88 observations deleted due to missingness)
Multiple R-squared: 0.05424, Adjusted R-squared: 0.05265
F-statistic: 34.18 on 1 and 596 DF, p-value: 8.273e-09
2.5 % 97.5 %
(Intercept) 7.848334454 10.128075989
RNA 0.001405821 0.002828059
o Plot to ./results/plot-RNA-Deaths-regression.png
MedVar Wave Lag.Days p AdjR2Pct Intercept InterceptCL Slope
1 Cases All 7 6.5e-93 50 320 +182.90 - +451.29 1.0000
2 Deaths All 18 8.3e-09 5 9 +7.85 - +10.13 0.0021
SlopeCL
1 +0.96 - +1.12
2 +0.00 - +0.00
[1] "Wave1"
* Scatterplotting significance & strength vs RNA lag
- ./results/Wave1/Wave1-plot-RNA-Cases-lags.png
- ./results/Wave1/Wave1-plot-RNA-Deaths-lags.png
* Optimal lags for each medical variable:
MedVar Lag p Adj.R2
1 Cases 10 3.31171e-15 0.6354045
2 Deaths 15 7.84316e-16 0.6836086
* Trying some regressions at the optimal lag for each variable:
- Regressing Cases on RNA at lag 10 days:
Call:
lm(formula = as.formula(sprintf("%s ~ RNA", mv)), data = transform(predictionSet,
RNA = lagVector(predictionSet[, "RNA"], lag)))
Residuals:
Min 1Q Median 3Q Max
-852.62 -117.09 -43.26 69.57 1128.18
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 45.9176 47.7420 0.962 0.34
RNA 2.7311 0.2615 10.443 3.31e-15 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 274.2 on 61 degrees of freedom
(44 observations deleted due to missingness)
Multiple R-squared: 0.6413, Adjusted R-squared: 0.6354
F-statistic: 109.1 on 1 and 61 DF, p-value: 3.312e-15
2.5 % 97.5 %
(Intercept) -49.54841 141.383570
RNA 2.20810 3.254006
o Plot to ./results/Wave1/Wave1-plot-RNA-Cases-regression.png
- Regressing Deaths on RNA at lag 15 days:
Call:
lm(formula = as.formula(sprintf("%s ~ RNA", mv)), data = transform(predictionSet,
RNA = lagVector(predictionSet[, "RNA"], lag)))
Residuals:
Min 1Q Median 3Q Max
-55.840 -6.621 0.138 6.148 42.636
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.82182 3.31232 0.55 0.584
RNA 0.19408 0.01742 11.14 7.84e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 17.75 on 56 degrees of freedom
(49 observations deleted due to missingness)
Multiple R-squared: 0.6892, Adjusted R-squared: 0.6836
F-statistic: 124.2 on 1 and 56 DF, p-value: 7.843e-16
2.5 % 97.5 %
(Intercept) -4.8135620 8.457199
RNA 0.1591918 0.228978
o Plot to ./results/Wave1/Wave1-plot-RNA-Deaths-regression.png
[1] "Wave2"
* Scatterplotting significance & strength vs RNA lag
- ./results/Wave2/Wave2-plot-RNA-Cases-lags.png
- ./results/Wave2/Wave2-plot-RNA-Deaths-lags.png
* Optimal lags for each medical variable:
MedVar Lag p Adj.R2
1 Cases 0 8.395252e-50 0.6119030
2 Deaths 16 2.567886e-30 0.4527565
* Trying some regressions at the optimal lag for each variable:
- Regressing Cases on RNA at lag 0 days:
Call:
lm(formula = as.formula(sprintf("%s ~ RNA", mv)), data = transform(predictionSet,
RNA = lagVector(predictionSet[, "RNA"], lag)))
Residuals:
Min 1Q Median 3Q Max
-2073.87 -199.75 -21.41 159.73 2201.38
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 286.95294 44.01463 6.519 4.36e-10 ***
RNA 1.50575 0.07845 19.193 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 437.8 on 232 degrees of freedom
(10 observations deleted due to missingness)
Multiple R-squared: 0.6136, Adjusted R-squared: 0.6119
F-statistic: 368.4 on 1 and 232 DF, p-value: < 2.2e-16
2.5 % 97.5 %
(Intercept) 200.233468 373.672420
RNA 1.351179 1.660325
o Plot to ./results/Wave2/Wave2-plot-RNA-Cases-regression.png
- Regressing Deaths on RNA at lag 16 days:
Call:
lm(formula = as.formula(sprintf("%s ~ RNA", mv)), data = transform(predictionSet,
RNA = lagVector(predictionSet[, "RNA"], lag)))
Residuals:
Min 1Q Median 3Q Max
-21.1525 -5.3180 -0.3423 4.6747 22.6715
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.95681 0.77875 6.365 1.15e-09 ***
RNA 0.01801 0.00134 13.436 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 7.162 on 216 degrees of freedom
(26 observations deleted due to missingness)
Multiple R-squared: 0.4553, Adjusted R-squared: 0.4528
F-statistic: 180.5 on 1 and 216 DF, p-value: < 2.2e-16
2.5 % 97.5 %
(Intercept) 3.42188132 6.49173131
RNA 0.01536397 0.02064646
o Plot to ./results/Wave2/Wave2-plot-RNA-Deaths-regression.png
[1] "Wave2.5"
* Scatterplotting significance & strength vs RNA lag
- ./results/Wave2.5/Wave2.5-plot-RNA-Cases-lags.png
- ./results/Wave2.5/Wave2.5-plot-RNA-Deaths-lags.png
* Optimal lags for each medical variable:
MedVar Lag p Adj.R2
1 Cases 2 2.011629e-10 0.2319787
2 Deaths 17 2.233901e-07 0.1746985
* Trying some regressions at the optimal lag for each variable:
- Regressing Cases on RNA at lag 2 days:
Call:
lm(formula = as.formula(sprintf("%s ~ RNA", mv)), data = transform(predictionSet,
RNA = lagVector(predictionSet[, "RNA"], lag)))
Residuals:
Min 1Q Median 3Q Max
-701.17 -146.73 -35.91 90.90 1479.29
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 51.5808 50.6711 1.018 0.31
RNA 1.2737 0.1866 6.827 2.01e-10 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 359.8 on 150 degrees of freedom
(2 observations deleted due to missingness)
Multiple R-squared: 0.2371, Adjusted R-squared: 0.232
F-statistic: 46.61 on 1 and 150 DF, p-value: 2.012e-10
2.5 % 97.5 %
(Intercept) -48.5405115 151.702090
RNA 0.9050617 1.642332
o Plot to ./results/Wave2.5/Wave2.5-plot-RNA-Cases-regression.png
- Regressing Deaths on RNA at lag 17 days:
Call:
lm(formula = as.formula(sprintf("%s ~ RNA", mv)), data = transform(predictionSet,
RNA = lagVector(predictionSet[, "RNA"], lag)))
Residuals:
Min 1Q Median 3Q Max
-3.9597 -1.7906 -0.1524 1.3540 8.9683
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.762701 0.318866 2.392 0.0181 *
RNA 0.006605 0.001210 5.458 2.23e-07 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.223 on 135 degrees of freedom
(17 observations deleted due to missingness)
Multiple R-squared: 0.1808, Adjusted R-squared: 0.1747
F-statistic: 29.79 on 1 and 135 DF, p-value: 2.234e-07
2.5 % 97.5 %
(Intercept) 0.132081980 1.393319918
RNA 0.004211881 0.008998891
o Plot to ./results/Wave2.5/Wave2.5-plot-RNA-Deaths-regression.png
[1] "Wave3"
* Scatterplotting significance & strength vs RNA lag
- ./results/Wave3/Wave3-plot-RNA-Cases-lags.png
- ./results/Wave3/Wave3-plot-RNA-Deaths-lags.png
* Optimal lags for each medical variable:
MedVar Lag p Adj.R2
1 Cases 7 9.857586e-10 0.3563977
2 Deaths 19 4.962621e-05 0.1970670
* Trying some regressions at the optimal lag for each variable:
- Regressing Cases on RNA at lag 7 days:
Call:
lm(formula = as.formula(sprintf("%s ~ RNA", mv)), data = transform(predictionSet,
RNA = lagVector(predictionSet[, "RNA"], lag)))
Residuals:
Min 1Q Median 3Q Max
-10827.9 -1389.3 -25.4 973.1 19378.0
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 728.2772 584.7717 1.245 0.216
RNA 0.9594 0.1392 6.893 9.86e-10 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3982 on 83 degrees of freedom
(7 observations deleted due to missingness)
Multiple R-squared: 0.3641, Adjusted R-squared: 0.3564
F-statistic: 47.52 on 1 and 83 DF, p-value: 9.858e-10
2.5 % 97.5 %
(Intercept) -434.8102110 1891.36460
RNA 0.6825411 1.23617
o Plot to ./results/Wave3/Wave3-plot-RNA-Cases-regression.png
- Regressing Deaths on RNA at lag 19 days:
Call:
lm(formula = as.formula(sprintf("%s ~ RNA", mv)), data = transform(predictionSet,
RNA = lagVector(predictionSet[, "RNA"], lag)))
Residuals:
Min 1Q Median 3Q Max
-30.732 -7.480 -1.815 5.894 47.980
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.5129524 2.1138904 3.081 0.00293 **
RNA 0.0020578 0.0004762 4.321 4.96e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 13.51 on 71 degrees of freedom
(19 observations deleted due to missingness)
Multiple R-squared: 0.2082, Adjusted R-squared: 0.1971
F-statistic: 18.67 on 1 and 71 DF, p-value: 4.963e-05
2.5 % 97.5 %
(Intercept) 2.297974625 10.72793016
RNA 0.001108245 0.00300743
o Plot to ./results/Wave3/Wave3-plot-RNA-Deaths-regression.png
MedVar Wave Lag.Days p AdjR2Pct Intercept InterceptCL Slope
1 Cases All 7 6.5e-93 50 320.00 +182.90 - +451.29 1.0000
3 Cases Wave1 10 3.3e-15 60 46.00 -49.55 - +141.38 2.7000
5 Cases Wave2 0 8.4e-50 60 290.00 +200.23 - +373.67 1.5000
7 Cases Wave2.5 2 2.0e-10 20 52.00 -48.54 - +151.70 1.3000
9 Cases Wave3 7 9.9e-10 40 730.00 -434.81 - +1891.36 0.9600
2 Deaths All 18 8.3e-09 5 9.00 +7.85 - +10.13 0.0021
4 Deaths Wave1 15 7.8e-16 70 1.80 -4.81 - +8.46 0.1900
6 Deaths Wave2 16 2.6e-30 50 5.00 +3.42 - +6.49 0.0180
8 Deaths Wave2.5 17 2.2e-07 20 0.76 +0.13 - +1.39 0.0066
10 Deaths Wave3 19 5.0e-05 20 6.50 +2.30 - +10.73 0.0021
SlopeCL
1 +0.96 - +1.12
3 +2.21 - +3.25
5 +1.35 - +1.66
7 +0.91 - +1.64
9 +0.68 - +1.24
2 +0.00 - +0.00
4 +0.16 - +0.23
6 +0.02 - +0.02
8 +0.00 - +0.01
10 +0.00 - +0.00
* MWRA COVID Analysis completed Fri Feb 04 17:16:51 2022 (17.2 sec elapsed).