Here below we will study the combined effect of vaccinations and seniority on antibody titers. We will perform analysis of covariance (ANCOVA) to discern the separate and combined effect of the two regressors. The vaccination status is treated as a categorical binary variable (vaccinated/non vaccinated), as the self-reported number of vaccinations cannot be considered a reliable estimate, while the age is a quantitative covariate.
We will perform ANCOVA estimates with the relation shot*age, meaning that the
model will try to estimate the antibody titer as a function of the vaccination
status, the age and their product. In symbols
$$
antibody = intercept + \alpha \cdot age + \beta \cdot shot + \gamma \cdot age \cdot shot
$$
which can be rewritten as
$$
antibody = intercept + \beta \cdot shot + (\gamma \cdot shot + \alpha) \cdot age.
$$
If the glm which performs robust linear regression accounting for non
constant variance (a.k.a. heteroskedasticity).
A slow-paced discussion of ANCOVA can be found in this blog post.
For H1 Brisbane, we remove first the interaction term and then also the age, concluding that only the vaccinations are contributing to the antibody titer.
##
## Call:
## glm(formula = H1_brisbane_log ~ age * shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5414 -0.4532 -0.0748 0.4620 1.6803
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.28380 0.22607 10.10 < 2e-16 ***
## age 0.00190 0.00616 0.31 0.75809
## shotVaccinated 0.99266 0.29164 3.40 0.00078 ***
## age:shotVaccinated -0.01147 0.00749 -1.53 0.12706
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.4203)
##
## Null deviance: 120.96 on 248 degrees of freedom
## Residual deviance: 102.97 on 245 degrees of freedom
## (24 observations deleted due to missingness)
## AIC: 496.8
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H1_brisbane_log ~ age + shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5023 -0.4799 -0.0828 0.4604 1.6925
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.55457 0.14119 18.09 < 2e-16 ***
## age -0.00585 0.00352 -1.66 0.097 .
## shotVaccinated 0.56757 0.08946 6.34 1.1e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.4226)
##
## Null deviance: 120.96 on 248 degrees of freedom
## Residual deviance: 103.95 on 246 degrees of freedom
## (24 observations deleted due to missingness)
## AIC: 497.1
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H1_brisbane_log ~ shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5084 -0.5121 -0.0793 0.4696 1.7541
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.3501 0.0699 33.6 < 2e-16 ***
## shotVaccinated 0.5290 0.0867 6.1 4.1e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.4256)
##
## Null deviance: 120.96 on 248 degrees of freedom
## Residual deviance: 105.12 on 247 degrees of freedom
## (24 observations deleted due to missingness)
## AIC: 497.9
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H1_PR8_log ~ age * shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.1690 -0.2956 -0.0147 0.2782 1.4335
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.83891 0.13705 20.71 <2e-16 ***
## age 0.00254 0.00369 0.69 0.49
## shotVaccinated 0.03979 0.17836 0.22 0.82
## age:shotVaccinated 0.00371 0.00453 0.82 0.41
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.1676)
##
## Null deviance: 46.370 on 258 degrees of freedom
## Residual deviance: 42.728 on 255 degrees of freedom
## (14 observations deleted due to missingness)
## AIC: 278.3
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H1_PR8_log ~ age + shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.1822 -0.2903 -0.0149 0.2716 1.4240
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.75222 0.08680 31.71 <2e-16 ***
## age 0.00499 0.00215 2.32 0.0209 *
## shotVaccinated 0.17867 0.05449 3.28 0.0012 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.1673)
##
## Null deviance: 46.37 on 258 degrees of freedom
## Residual deviance: 42.84 on 256 degrees of freedom
## (14 observations deleted due to missingness)
## AIC: 277
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H1_PR8_log ~ shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.2347 -0.2573 -0.0117 0.2701 1.3865
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.9286 0.0426 68.82 < 2e-16 ***
## shotVaccinated 0.2094 0.0533 3.93 0.00011 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.1702)
##
## Null deviance: 46.370 on 258 degrees of freedom
## Residual deviance: 43.744 on 257 degrees of freedom
## (14 observations deleted due to missingness)
## AIC: 280.4
##
## Number of Fisher Scoring iterations: 2
Although the interaction term is not very strong, removing it doesn't improve the fit, at least in terms of AIC. Removing the shot entirely leaves us with an even higher AIC. Bootstrapping 200 samples gives equivalent AIC scores for full, noint and age only. So we should choose age only.
##
## Call:
## glm(formula = H2_log ~ age * shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.2207 -0.2181 0.0005 0.2011 0.9413
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.80065 0.11967 15.05 <2e-16 ***
## age 0.02016 0.00318 6.34 1e-09 ***
## shotVaccinated -0.52000 0.15825 -3.29 0.0012 **
## age:shotVaccinated 0.01082 0.00397 2.72 0.0069 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.1384)
##
## Null deviance: 65.217 on 264 degrees of freedom
## Residual deviance: 36.113 on 261 degrees of freedom
## (8 observations deleted due to missingness)
## AIC: 233.9
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H2_log ~ age + shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.181 -0.230 0.005 0.198 0.981
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.55281 0.07858 19.76 <2e-16 ***
## age 0.02709 0.00193 14.03 <2e-16 ***
## shotVaccinated -0.10996 0.04898 -2.25 0.026 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.1417)
##
## Null deviance: 65.217 on 264 degrees of freedom
## Residual deviance: 37.138 on 262 degrees of freedom
## (8 observations deleted due to missingness)
## AIC: 239.3
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H2_log ~ age, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.2099 -0.2101 0.0064 0.2264 0.9521
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.52469 0.07817 19.5 <2e-16 ***
## age 0.02608 0.00189 13.8 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.1439)
##
## Null deviance: 65.217 on 264 degrees of freedom
## Residual deviance: 37.852 on 263 degrees of freedom
## (8 observations deleted due to missingness)
## AIC: 242.3
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H3_brisbane_log ~ age * shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.3079 -0.3746 -0.0131 0.3938 1.5608
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.59135 0.20498 12.64 <2e-16 ***
## age -0.00311 0.00549 -0.57 0.57
## shotVaccinated 0.01827 0.27011 0.07 0.95
## age:shotVaccinated 0.00564 0.00685 0.82 0.41
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.3894)
##
## Null deviance: 100.005 on 251 degrees of freedom
## Residual deviance: 96.561 on 248 degrees of freedom
## (21 observations deleted due to missingness)
## AIC: 483.4
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H3_brisbane_log ~ age + shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.2774 -0.3728 -0.0023 0.4107 1.5010
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.463195 0.133186 18.49 <2e-16 ***
## age 0.000506 0.003284 0.15 0.8777
## shotVaccinated 0.229615 0.083511 2.75 0.0064 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.3889)
##
## Null deviance: 100.005 on 251 degrees of freedom
## Residual deviance: 96.824 on 249 degrees of freedom
## (21 observations deleted due to missingness)
## AIC: 482.1
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H3_brisbane_log ~ shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.2817 -0.3710 -0.0031 0.4048 1.5093
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.4811 0.0645 38.45 <2e-16 ***
## shotVaccinated 0.2325 0.0812 2.86 0.0046 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.3873)
##
## Null deviance: 100.005 on 251 degrees of freedom
## Residual deviance: 96.834 on 250 degrees of freedom
## (21 observations deleted due to missingness)
## AIC: 480.1
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H3_HK_log ~ age * shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.3715 -0.3073 -0.0317 0.3229 1.0837
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.62255 0.15191 10.68 < 2e-16 ***
## age 0.02816 0.00402 7.00 2.1e-11 ***
## shotVaccinated 0.02026 0.19995 0.10 0.92
## age:shotVaccinated -0.00082 0.00502 -0.16 0.87
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.2201)
##
## Null deviance: 87.716 on 263 degrees of freedom
## Residual deviance: 57.229 on 260 degrees of freedom
## (9 observations deleted due to missingness)
## AIC: 355.6
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H3_HK_log ~ age + shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.3745 -0.3068 -0.0309 0.3223 1.0848
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.6415 0.0981 16.73 <2e-16 ***
## age 0.0276 0.0024 11.53 <2e-16 ***
## shotVaccinated -0.0109 0.0611 -0.18 0.86
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.2193)
##
## Null deviance: 87.716 on 263 degrees of freedom
## Residual deviance: 57.235 on 261 degrees of freedom
## (9 observations deleted due to missingness)
## AIC: 353.6
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H3_HK_log ~ age, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.377 -0.304 -0.035 0.321 1.081
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.63848 0.09649 17.0 <2e-16 ***
## age 0.02754 0.00233 11.8 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.2185)
##
## Null deviance: 87.716 on 263 degrees of freedom
## Residual deviance: 57.242 on 262 degrees of freedom
## (9 observations deleted due to missingness)
## AIC: 351.6
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H4_log ~ age * shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.9014 -0.1201 -0.0077 0.1315 1.5033
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.99426 0.09597 20.78 <2e-16 ***
## age -0.00139 0.00252 -0.55 0.58
## shotVaccinated -0.06722 0.12629 -0.53 0.60
## age:shotVaccinated 0.00263 0.00314 0.84 0.40
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.07996)
##
## Null deviance: 19.480 on 245 degrees of freedom
## Residual deviance: 19.351 on 242 degrees of freedom
## (27 observations deleted due to missingness)
## AIC: 82.65
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H4_log ~ age + shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.8842 -0.1194 -0.0032 0.1335 1.4996
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.933157 0.062110 31.12 <2e-16 ***
## age 0.000296 0.001507 0.20 0.84
## shotVaccinated 0.033313 0.038292 0.87 0.39
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.07986)
##
## Null deviance: 19.480 on 245 degrees of freedom
## Residual deviance: 19.407 on 243 degrees of freedom
## (27 observations deleted due to missingness)
## AIC: 81.35
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H4_log ~ shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.8872 -0.1174 -0.0046 0.1340 1.4985
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.9439 0.0296 65.75 <2e-16 ***
## shotVaccinated 0.0350 0.0372 0.94 0.35
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.07955)
##
## Null deviance: 19.48 on 245 degrees of freedom
## Residual deviance: 19.41 on 244 degrees of freedom
## (27 observations deleted due to missingness)
## AIC: 79.39
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H5_1st_dil_percent ~ age * shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -21.40 -4.40 -0.92 3.00 69.18
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.5799 3.3600 -0.17 0.86
## age 0.0565 0.0900 0.63 0.53
## shotVaccinated 5.2465 4.4561 1.18 0.24
## age:shotVaccinated -0.0494 0.1127 -0.44 0.66
##
## (Dispersion parameter for gaussian family taken to be 113.9)
##
## Null deviance: 31494 on 272 degrees of freedom
## Residual deviance: 30644 on 269 degrees of freedom
## AIC: 2073
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H5_1st_dil_percent ~ age + shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -21.25 -4.20 -0.89 2.78 69.53
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.5393 2.1835 0.25 0.805
## age 0.0249 0.0541 0.46 0.645
## shotVaccinated 3.3861 1.3672 2.48 0.014 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 113.6)
##
## Null deviance: 31494 on 272 degrees of freedom
## Residual deviance: 30665 on 270 degrees of freedom
## AIC: 2072
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H5_1st_dil_percent ~ shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -21.46 -4.46 -0.92 2.58 69.04
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.42 1.04 1.36 0.1738
## shotVaccinated 3.54 1.33 2.67 0.0081 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 113.2)
##
## Null deviance: 31494 on 272 degrees of freedom
## Residual deviance: 30690 on 271 degrees of freedom
## AIC: 2070
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H7_1st_dil_percent ~ age * shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -21.66 -9.63 -1.90 7.43 43.20
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.3386 3.8048 3.51 0.00053 ***
## age 0.0315 0.1020 0.31 0.75736
## shotVaccinated -6.9838 5.0459 -1.38 0.16749
## age:shotVaccinated 0.1474 0.1276 1.16 0.24910
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 146.1)
##
## Null deviance: 40131 on 272 degrees of freedom
## Residual deviance: 39293 on 269 degrees of freedom
## AIC: 2141
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H7_1st_dil_percent ~ age + shot, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -22.66 -9.22 -1.83 7.33 43.65
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.0020 2.4778 4.04 7.1e-05 ***
## age 0.1256 0.0614 2.05 0.042 *
## shotVaccinated -1.4375 1.5514 -0.93 0.355
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 146.3)
##
## Null deviance: 40131 on 272 degrees of freedom
## Residual deviance: 39488 on 270 degrees of freedom
## AIC: 2141
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H7_1st_dil_percent ~ age, data = ic_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -21.48 -8.95 -1.62 7.89 43.25
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.6399 2.4462 3.94 0.0001 ***
## age 0.1121 0.0596 1.88 0.0609 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 146.2)
##
## Null deviance: 40131 on 272 degrees of freedom
## Residual deviance: 39613 on 271 degrees of freedom
## AIC: 2140
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H1_pdm09_log ~ age * shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.7359 -0.2104 0.0016 0.1937 0.7995
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.28347 0.10002 12.83 <2e-16 ***
## age 0.00235 0.00267 0.88 0.38
## shotVaccinated 0.00857 0.13216 0.06 0.95
## age:shotVaccinated 0.00432 0.00334 1.30 0.20
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.09922)
##
## Null deviance: 30.372 on 271 degrees of freedom
## Residual deviance: 26.590 on 268 degrees of freedom
## (1 observation deleted due to missingness)
## AIC: 149.4
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H1_pdm09_log ~ age + shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.7925 -0.2195 -0.0021 0.1831 0.8261
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.18484 0.06496 18.24 < 2e-16 ***
## age 0.00512 0.00160 3.19 0.0016 **
## shotVaccinated 0.17157 0.04053 4.23 3.2e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.09947)
##
## Null deviance: 30.372 on 271 degrees of freedom
## Residual deviance: 26.757 on 269 degrees of freedom
## (1 observation deleted due to missingness)
## AIC: 149.1
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H1_pdm09_log ~ shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.7163 -0.2021 -0.0101 0.1949 0.8134
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.3670 0.0316 43.26 <2e-16 ***
## shotVaccinated 0.2016 0.0401 5.03 9e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.1029)
##
## Null deviance: 30.372 on 271 degrees of freedom
## Residual deviance: 27.770 on 270 degrees of freedom
## (1 observation deleted due to missingness)
## AIC: 157.2
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H1_PR8_log ~ age * shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.9297 -0.2093 0.0053 0.1873 1.0806
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.771087 0.102209 17.33 <2e-16 ***
## age 0.008895 0.002739 3.25 0.0013 **
## shotVaccinated 0.367045 0.135550 2.71 0.0072 **
## age:shotVaccinated -0.000979 0.003428 -0.29 0.7754
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.1054)
##
## Null deviance: 40.307 on 272 degrees of freedom
## Residual deviance: 28.355 on 269 degrees of freedom
## AIC: 166.5
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H1_PR8_log ~ age + shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.9375 -0.2090 0.0032 0.1881 1.0747
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.79325 0.06641 27.00 < 2e-16 ***
## age 0.00827 0.00164 5.03 9.0e-07 ***
## shotVaccinated 0.33021 0.04158 7.94 5.4e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.1051)
##
## Null deviance: 40.307 on 272 degrees of freedom
## Residual deviance: 28.364 on 270 degrees of freedom
## AIC: 164.6
##
## Number of Fisher Scoring iterations: 2
Bootstrapping and looking at the AIC there is no reason to include the shots, and the age alone explain everything equally well. Last fit forces the intercept to zero.
##
## Call:
## glm(formula = H2_log ~ age * shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8669 -0.2943 -0.0111 0.3151 1.6909
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.13879 0.16619 0.84 0.404
## age 0.02446 0.00443 5.52 8.1e-08 ***
## shotVaccinated -0.43695 0.21926 -1.99 0.047 *
## age:shotVaccinated 0.01166 0.00553 2.11 0.036 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.272)
##
## Null deviance: 115.19 on 269 degrees of freedom
## Residual deviance: 72.35 on 266 degrees of freedom
## (3 observations deleted due to missingness)
## AIC: 420.7
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H2_log ~ age + shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9225 -0.2863 -0.0036 0.3022 1.7351
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.12781 0.10846 -1.18 0.24
## age 0.03194 0.00267 11.96 <2e-16 ***
## shotVaccinated 0.00287 0.06767 0.04 0.97
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.2755)
##
## Null deviance: 115.185 on 269 degrees of freedom
## Residual deviance: 73.558 on 267 degrees of freedom
## (3 observations deleted due to missingness)
## AIC: 423.1
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H2_log ~ age, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9245 -0.2866 -0.0023 0.3026 1.7359
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.1270 0.1067 -1.19 0.23
## age 0.0320 0.0026 12.32 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.2745)
##
## Null deviance: 115.185 on 269 degrees of freedom
## Residual deviance: 73.558 on 268 degrees of freedom
## (3 observations deleted due to missingness)
## AIC: 421.1
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H2_log ~ 0 + age, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9188 -0.3131 -0.0235 0.3035 1.7622
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## age 0.029016 0.000776 37.4 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.2749)
##
## Null deviance: 458.294 on 270 degrees of freedom
## Residual deviance: 73.947 on 269 degrees of freedom
## (3 observations deleted due to missingness)
## AIC: 420.6
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H3_log ~ age * shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.2192 -0.3243 -0.0402 0.3013 1.3745
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.78978 0.15099 25.10 < 2e-16 ***
## age -0.01563 0.00405 -3.86 0.00014 ***
## shotVaccinated -0.11842 0.20024 -0.59 0.55477
## age:shotVaccinated 0.00895 0.00506 1.77 0.07836 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.23)
##
## Null deviance: 68.041 on 272 degrees of freedom
## Residual deviance: 61.877 on 269 degrees of freedom
## AIC: 379.5
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H3_log ~ age + shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.2531 -0.3219 -0.0404 0.2933 1.3818
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.58723 0.09865 36.36 < 2e-16 ***
## age -0.00992 0.00244 -4.06 6.4e-05 ***
## shotVaccinated 0.21829 0.06177 3.53 0.00048 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.2318)
##
## Null deviance: 68.041 on 272 degrees of freedom
## Residual deviance: 62.595 on 270 degrees of freedom
## AIC: 380.7
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H4_log ~ age * shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4648 -0.3277 0.0514 0.3390 2.4037
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.32850 0.21074 6.30 1.2e-09 ***
## age 0.00498 0.00564 0.88 0.38
## shotVaccinated 0.26120 0.28051 0.93 0.35
## age:shotVaccinated -0.00353 0.00707 -0.50 0.62
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.4445)
##
## Null deviance: 118.61 on 266 degrees of freedom
## Residual deviance: 116.89 on 263 degrees of freedom
## (6 observations deleted due to missingness)
## AIC: 547.2
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H4_log ~ age + shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4718 -0.3204 0.0446 0.3473 2.4212
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.40817 0.13752 10.24 <2e-16 ***
## age 0.00274 0.00340 0.81 0.42
## shotVaccinated 0.12791 0.08616 1.48 0.14
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.4432)
##
## Null deviance: 118.61 on 266 degrees of freedom
## Residual deviance: 117.00 on 264 degrees of freedom
## (6 observations deleted due to missingness)
## AIC: 545.4
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H4_log ~ shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4569 -0.3145 0.0414 0.3445 2.3840
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.5056 0.0656 22.97 <2e-16 ***
## shotVaccinated 0.1444 0.0836 1.73 0.085 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.4426)
##
## Null deviance: 118.61 on 266 degrees of freedom
## Residual deviance: 117.29 on 265 degrees of freedom
## (6 observations deleted due to missingness)
## AIC: 544.1
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H4_log ~ age, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4318 -0.3291 0.0495 0.3279 2.4840
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.43970 0.13618 10.57 <2e-16 ***
## age 0.00394 0.00331 1.19 0.24
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.4452)
##
## Null deviance: 118.61 on 266 degrees of freedom
## Residual deviance: 117.98 on 265 degrees of freedom
## (6 observations deleted due to missingness)
## AIC: 545.6
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H5_log ~ age * shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.2326 -0.3418 -0.0208 0.2794 1.3767
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.08812 0.15153 7.18 6.8e-12 ***
## age 0.00872 0.00406 2.15 0.033 *
## shotVaccinated 0.00520 0.20097 0.03 0.979
## age:shotVaccinated 0.00703 0.00508 1.38 0.168
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.2317)
##
## Null deviance: 77.389 on 272 degrees of freedom
## Residual deviance: 62.326 on 269 degrees of freedom
## AIC: 381.5
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H5_log ~ age + shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.3085 -0.3280 -0.0335 0.2644 1.3831
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.92891 0.09879 9.40 < 2e-16 ***
## age 0.01321 0.00245 5.40 1.5e-07 ***
## shotVaccinated 0.26984 0.06185 4.36 1.8e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.2325)
##
## Null deviance: 77.389 on 272 degrees of freedom
## Residual deviance: 62.770 on 270 degrees of freedom
## AIC: 381.4
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H7_log ~ age * shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5249 -0.1917 -0.0046 0.1854 1.0107
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.761111 0.088516 19.90 <2e-16 ***
## age -0.003045 0.002372 -1.28 0.20
## shotVaccinated 0.005758 0.117391 0.05 0.96
## age:shotVaccinated -0.000311 0.002969 -0.10 0.92
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.07906)
##
## Null deviance: 21.718 on 272 degrees of freedom
## Residual deviance: 21.267 on 269 degrees of freedom
## AIC: 87.95
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H7_log ~ age + shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5232 -0.1912 -0.0003 0.1847 1.0092
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.76816 0.05750 30.75 <2e-16 ***
## age -0.00324 0.00142 -2.28 0.024 *
## shotVaccinated -0.00596 0.03600 -0.17 0.869
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.07877)
##
## Null deviance: 21.718 on 272 degrees of freedom
## Residual deviance: 21.267 on 270 degrees of freedom
## AIC: 85.96
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H7_log ~ age, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5192 -0.1936 0.0016 0.1841 1.0078
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.76666 0.05668 31.17 <2e-16 ***
## age -0.00330 0.00138 -2.39 0.018 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.07849)
##
## Null deviance: 21.718 on 272 degrees of freedom
## Residual deviance: 21.270 on 271 degrees of freedom
## AIC: 83.99
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H7_vir_log ~ age * shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.1668 -0.1605 0.0079 0.1750 0.5868
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.27681 0.08618 14.82 <2e-16 ***
## age 0.00116 0.00231 0.50 0.62
## shotVaccinated -0.06398 0.11429 -0.56 0.58
## age:shotVaccinated -0.00027 0.00289 -0.09 0.93
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.07494)
##
## Null deviance: 20.497 on 272 degrees of freedom
## Residual deviance: 20.158 on 269 degrees of freedom
## AIC: 73.34
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H7_vir_log ~ age + shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.1679 -0.1594 0.0075 0.1745 0.5854
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.282920 0.055985 22.92 <2e-16 ***
## age 0.000989 0.001386 0.71 0.476
## shotVaccinated -0.074131 0.035054 -2.11 0.035 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.07466)
##
## Null deviance: 20.497 on 272 degrees of freedom
## Residual deviance: 20.159 on 270 degrees of freedom
## AIC: 71.35
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H7_vir_log ~ shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.1743 -0.1590 0.0132 0.1742 0.5772
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.3180 0.0268 49.2 <2e-16 ***
## shotVaccinated -0.0682 0.0340 -2.0 0.046 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.07453)
##
## Null deviance: 20.497 on 272 degrees of freedom
## Residual deviance: 20.197 on 271 degrees of freedom
## AIC: 69.87
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H7_vir_log ~ age, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.1291 -0.1625 -0.0041 0.1879 0.6228
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.264250 0.055637 22.72 <2e-16 ***
## age 0.000294 0.001355 0.22 0.83
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.07562)
##
## Null deviance: 20.497 on 272 degrees of freedom
## Residual deviance: 20.493 on 271 degrees of freedom
## AIC: 73.84
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H12_log ~ age * shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.0532 -0.3413 -0.0355 0.2635 1.5024
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.50951 0.14358 17.48 <2e-16 ***
## age -0.00938 0.00385 -2.44 0.015 *
## shotVaccinated -0.11583 0.19042 -0.61 0.543
## age:shotVaccinated 0.00653 0.00482 1.36 0.177
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.208)
##
## Null deviance: 58.020 on 272 degrees of freedom
## Residual deviance: 55.957 on 269 degrees of freedom
## AIC: 352.1
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H12_log ~ age + shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.0513 -0.3413 -0.0318 0.2798 1.5178
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.36180 0.09359 25.23 <2e-16 ***
## age -0.00521 0.00232 -2.25 0.025 *
## shotVaccinated 0.12971 0.05860 2.21 0.028 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.2087)
##
## Null deviance: 58.020 on 272 degrees of freedom
## Residual deviance: 56.339 on 270 degrees of freedom
## AIC: 351.9
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H12_log ~ age, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.1265 -0.3375 -0.0435 0.2885 1.5565
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.39447 0.09308 25.72 <2e-16 ***
## age -0.00400 0.00227 -1.76 0.079 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.2117)
##
## Null deviance: 58.020 on 272 degrees of freedom
## Residual deviance: 57.362 on 271 degrees of freedom
## AIC: 354.8
##
## Number of Fisher Scoring iterations: 2
##
## Call:
## glm(formula = H12_log ~ shot, data = ec_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.1179 -0.3343 -0.0283 0.2697 1.4837
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.1769 0.0451 48.24 <2e-16 ***
## shotVaccinated 0.0985 0.0574 1.72 0.087 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.2118)
##
## Null deviance: 58.020 on 272 degrees of freedom
## Residual deviance: 57.396 on 271 degrees of freedom
## AIC: 355
##
## Number of Fisher Scoring iterations: 2
## [1] "EC50; H4"
## [1] "1.625 +/- 0.682"
## [1] "EC50; H7"
## [1] "1.645 +/- 0.362"
## [1] "EC50; H7_vir"
## [1] "1.273 +/- 0.352"
## [1] "EC50; H12"
## [1] "2.215 +/- 0.619"
## [1] "IC50; H7_1st_dil_percent"
## [1] "11.500 +/- 17.500"