diff --git a/test_example/expected_titers_for_test.csv b/test_example/expected_titers_for_test.csv
index 5a0d76d..ea05991 100644
--- a/test_example/expected_titers_for_test.csv
+++ b/test_example/expected_titers_for_test.csv
@@ -1,195 +1,194 @@
-group,serum,virus,n_replicates,titer_bound,titer
-pilot,A23038d0_r32_75K,A/Bangkok/P3599/2023,2,interpolated,1863
-pilot,A23038d0_r32_75K,A/Bangkok/P3755/2023,3,interpolated,851.5
-pilot,A23038d0_r32_75K,A/Bhutan/0006/2023,3,interpolated,611.9
-pilot,A23038d0_r32_75K,A/Bhutan/FLU-BTG-00988/2022,3,interpolated,552
-pilot,A23038d0_r32_75K,A/Brisbane/429/2023,2,interpolated,1534
-pilot,A23038d0_r32_75K,A/Busan/1301/2023,2,interpolated,773.6
-pilot,A23038d0_r32_75K,A/California/81/2023,2,interpolated,1454
-pilot,A23038d0_r32_75K,A/Cambodia/e0826360/2020_egg,3,interpolated,8843
-pilot,A23038d0_r32_75K,A/Catalonia/2041146NS/2023,2,interpolated,747
-pilot,A23038d0_r32_75K,A/Catalonia/NSVH102124476/2023,3,interpolated,655.3
-pilot,A23038d0_r32_75K,A/Chipata/15-NIC-001/2023,3,interpolated,1137
-pilot,A23038d0_r32_75K,A/EHIME/50/2023,3,interpolated,1167
-pilot,A23038d0_r32_75K,A/Georgia/40/2023,3,interpolated,1123
-pilot,A23038d0_r32_75K,A/Hong_Kong/2671/2019,3,interpolated,8785
-pilot,A23038d0_r32_75K,A/Hong_Kong/45/2019,3,interpolated,1040
-pilot,A23038d0_r32_75K,A/Hong_Kong/4801/2014,2,interpolated,5075
-pilot,A23038d0_r32_75K,A/Hong_Kong/4801/2014_(15/192),3,lower,1.28e+04
-pilot,A23038d0_r32_75K,A/Jeju/1047/2023,2,interpolated,1049
-pilot,A23038d0_r32_75K,A/Kansas/14/2017,2,interpolated,4041
-pilot,A23038d0_r32_75K,A/Krabi/THIS050/2023,2,interpolated,3116
-pilot,A23038d0_r32_75K,A/Malaysia/IMR-SARI1989/2023,2,interpolated,1422
-pilot,A23038d0_r32_75K,A/Massachusets/18/2022,2,interpolated,1241
-pilot,A23038d0_r32_75K,A/Netherlands/01685/2023,2,interpolated,1424
-pilot,A23038d0_r32_75K,A/Netherlands/01760/2023,3,interpolated,1764
-pilot,A23038d0_r32_75K,A/Ontario/RV00796/2023,3,interpolated,1238
-pilot,A23038d0_r32_75K,A/SOUTH_AFRICA/R07876/202023,3,interpolated,797.5
-pilot,A23038d0_r32_75K,A/Saint-Petersburg/RII-MH144113/2023,3,interpolated,1685
-pilot,A23038d0_r32_75K,A/Saskatchewan/SKFLU317847/2023,2,interpolated,2104
-pilot,A23038d0_r32_75K,A/Schleswig-Holstein/4/2023,3,interpolated,1451
-pilot,A23038d0_r32_75K,A/Singapore/INFIMH-16-0019/2016,3,interpolated,3345
-pilot,A23038d0_r32_75K,A/Singapore/INFIMH-16-0019/2016_X-307A,3,lower,1.28e+04
-pilot,A23038d0_r32_75K,A/SouthAfrica/PET28931/2023,3,interpolated,1104
-pilot,A23038d0_r32_75K,A/SouthSudan/631/2023,3,interpolated,721.3
-pilot,A23038d0_r32_75K,A/South_Africa/K056872/2023,2,interpolated,1115
-pilot,A23038d0_r32_75K,A/South_Africa/R05384/2023,3,interpolated,448.6
-pilot,A23038d0_r32_75K,A/South_Africa/R05510/2023,2,interpolated,3338
-pilot,A23038d0_r32_75K,A/South_Africa/R06240/2023,2,interpolated,1397
-pilot,A23038d0_r32_75K,A/South_Africa/R06359/2023,2,interpolated,558.4
-pilot,A23038d0_r32_75K,A/South_Africa/R06477/2023,2,interpolated,1876
-pilot,A23038d0_r32_75K,A/South_Africa/R06506/2023,3,interpolated,1036
-pilot,A23038d0_r32_75K,A/South_Africa/R07188/2023,2,interpolated,1987
-pilot,A23038d0_r32_75K,A/Switzerland/9715293/2013,2,interpolated,4503
-pilot,A23038d0_r32_75K,A/Switzerland/9715293/2013_NIB-88,2,interpolated,6760
-pilot,A23038d0_r32_75K,A/Sydney/332/2023,3,interpolated,1350
-pilot,A23038d0_r32_75K,A/Sydney/710/2023,3,interpolated,805.1
-pilot,A23038d0_r32_75K,A/Sydney/715/2023,2,interpolated,1176
-pilot,A23038d0_r32_75K,A/Sydney/749/2023,3,interpolated,1952
-pilot,A23038d0_r32_75K,A/TECPAN/017FLU/2023,3,interpolated,756
-pilot,A23038d0_r32_75K,A/Texas/50/2012,3,lower,1.28e+04
-pilot,A23038d0_r32_75K,A/Townsville/68/2023,3,interpolated,780
-pilot,A23038d0_r32_75K,A/Victoria/1033/2023,2,interpolated,1089
-pilot,A23038d0_r32_75K,A/Wisconsin/27/2023,2,interpolated,2235
-serum,M099d0,A/Bangladesh/2221/2021,6,interpolated,280.5
-serum,M099d0,A/Bangladesh/3210810034/2021,4,interpolated,227.6
-serum,M099d0,A/Bangladesh/8002/2021,6,interpolated,294.7
-serum,M099d0,A/Bangladesh/8036/2021,6,interpolated,313.6
-serum,M099d0,A/Belgium/H0017/2022,6,interpolated,670.2
-serum,M099d0,A/Belgium/H0038/2022,6,interpolated,905.3
-serum,M099d0,A/Brisbane/02/2018,8,interpolated,752.6
-serum,M099d0,A/Brisbane/48/2022,6,interpolated,271.7
-serum,M099d0,A/California/07/2009,8,interpolated,845
-serum,M099d0,A/Chester/5355/2022,6,interpolated,420.2
-serum,M099d0,A/Cote_DIvoire/1448/2021,6,interpolated,756
-serum,M099d0,A/England/220200318/2022,6,interpolated,802.8
-serum,M099d0,A/Ghana/138/2020,6,interpolated,758.8
-serum,M099d0,A/Ghana/2080/2020,6,interpolated,710.5
-serum,M099d0,A/Hawaii/70/2019,8,interpolated,782.1
-serum,M099d0,A/India-PUN-NIV328484/2021,6,interpolated,310.8
-serum,M099d0,A/India-Pune-Nivcov2221170/2022,4,interpolated,205.1
-serum,M099d0,A/India/Pun-NIV312851/2021,6,interpolated,293.1
-serum,M099d0,A/Michigan/19/2021,6,interpolated,392.9
-serum,M099d0,A/Michigan/45/2015,8,interpolated,854.6
-serum,M099d0,A/Newcastle/2/2022,6,interpolated,303.7
-serum,M099d0,A/Niger/10217/2021,6,interpolated,757.7
-serum,M099d0,A/Nimes/871/2021,6,interpolated,924.1
-serum,M099d0,A/Paris/30353/2021,6,interpolated,769.6
-serum,M099d0,A/Paris/31196/2021,6,interpolated,879
-serum,M099d0,A/Perth/1/2022,6,interpolated,341.2
-serum,M099d0,A/SouthAfrica/R14850/2021,6,interpolated,432.7
-serum,M099d0,A/SouthAfrica/R16462/2021,6,interpolated,866.5
-serum,M099d0,A/Sydney/43/2022,6,interpolated,279.3
-serum,M099d0,A/Togo/0274/2021,6,interpolated,770.9
-serum,M099d0,A/Togo/0304/2021,6,interpolated,958.9
-serum,M099d0,A/Togo/845/2020,6,interpolated,852.5
-serum,M099d0,A/Utah/27/2022,6,interpolated,251.2
-serum,M099d0,A/Washington/23/2020,6,interpolated,398.2
-serum,M099d0,A/Wisconsin/588/2019,5,interpolated,297
-serum,M099d30,A/Bangladesh/2221/2021,6,interpolated,1491
-serum,M099d30,A/Bangladesh/3210810034/2021,4,interpolated,1378
-serum,M099d30,A/Bangladesh/8002/2021,6,interpolated,1526
-serum,M099d30,A/Bangladesh/8036/2021,6,interpolated,1721
-serum,M099d30,A/Belgium/H0017/2022,6,interpolated,2830
-serum,M099d30,A/Belgium/H0038/2022,6,interpolated,2932
-serum,M099d30,A/Brisbane/02/2018,8,interpolated,4975
-serum,M099d30,A/Brisbane/48/2022,6,interpolated,1257
-serum,M099d30,A/California/07/2009,8,interpolated,4498
-serum,M099d30,A/Chester/5355/2022,6,interpolated,1416
-serum,M099d30,A/Cote_DIvoire/1448/2021,6,interpolated,3649
-serum,M099d30,A/England/220200318/2022,6,interpolated,2973
-serum,M099d30,A/Ghana/138/2020,6,interpolated,2261
-serum,M099d30,A/Ghana/2080/2020,6,interpolated,3078
-serum,M099d30,A/Hawaii/70/2019,8,interpolated,2861
-serum,M099d30,A/India-PUN-NIV328484/2021,6,interpolated,2532
-serum,M099d30,A/India-Pune-Nivcov2221170/2022,4,interpolated,1005
-serum,M099d30,A/India/Pun-NIV312851/2021,6,interpolated,1621
-serum,M099d30,A/Michigan/19/2021,6,interpolated,1795
-serum,M099d30,A/Michigan/45/2015,8,interpolated,5004
-serum,M099d30,A/Newcastle/2/2022,6,interpolated,1462
-serum,M099d30,A/Niger/10217/2021,6,interpolated,1984
-serum,M099d30,A/Nimes/871/2021,6,interpolated,3136
-serum,M099d30,A/Norway/25089/2022,5,interpolated,826.4
-serum,M099d30,A/Paris/30353/2021,6,interpolated,1799
-serum,M099d30,A/Paris/31196/2021,6,interpolated,3247
-serum,M099d30,A/Perth/1/2022,6,interpolated,1797
-serum,M099d30,A/SouthAfrica/R14850/2021,6,interpolated,1124
-serum,M099d30,A/SouthAfrica/R16462/2021,6,interpolated,2627
-serum,M099d30,A/Sydney/43/2022,6,interpolated,1107
-serum,M099d30,A/Togo/0274/2021,6,interpolated,2629
-serum,M099d30,A/Togo/0304/2021,6,interpolated,1988
-serum,M099d30,A/Togo/845/2020,6,interpolated,2076
-serum,M099d30,A/Utah/27/2022,6,interpolated,1388
-serum,M099d30,A/Wisconsin/588/2019,6,interpolated,2318
-serum,Y044d30,A/Bangladesh/2221/2021,3,interpolated,2083
-serum,Y044d30,A/Bangladesh/3210810034/2021,2,interpolated,516.4
-serum,Y044d30,A/Bangladesh/8002/2021,3,interpolated,1606
-serum,Y044d30,A/Bangladesh/8036/2021,3,interpolated,1620
-serum,Y044d30,A/Belgium/H0017/2022,3,interpolated,1.396e+04
-serum,Y044d30,A/Belgium/H0038/2022,3,interpolated,1.441e+04
-serum,Y044d30,A/Brisbane/02/2018,4,interpolated,1.326e+04
-serum,Y044d30,A/Brisbane/48/2022,3,interpolated,1525
-serum,Y044d30,A/California/07/2009,4,interpolated,8685
-serum,Y044d30,A/Chester/5355/2022,3,interpolated,1402
-serum,Y044d30,A/Cote_DIvoire/1448/2021,3,interpolated,1.962e+04
-serum,Y044d30,A/England/220200318/2022,3,interpolated,1.96e+04
-serum,Y044d30,A/Ghana/138/2020,3,interpolated,2.031e+04
-serum,Y044d30,A/Ghana/2080/2020,3,interpolated,1.858e+04
-serum,Y044d30,A/Hawaii/70/2019,4,interpolated,1.534e+04
-serum,Y044d30,A/India-PUN-NIV328484/2021,3,interpolated,1588
-serum,Y044d30,A/India-Pune-Nivcov2221170/2022,2,interpolated,1617
-serum,Y044d30,A/India/Pun-NIV312851/2021,3,interpolated,1391
-serum,Y044d30,A/Michigan/19/2021,3,interpolated,1472
-serum,Y044d30,A/Michigan/45/2015,4,interpolated,1.274e+04
-serum,Y044d30,A/Newcastle/2/2022,3,interpolated,1398
-serum,Y044d30,A/Niger/10217/2021,3,interpolated,1.169e+04
-serum,Y044d30,A/Nimes/871/2021,3,interpolated,1.706e+04
-serum,Y044d30,A/Norway/25089/2022,3,interpolated,929.4
-serum,Y044d30,A/Paris/30353/2021,3,interpolated,1.003e+04
-serum,Y044d30,A/Paris/31196/2021,3,interpolated,1.299e+04
-serum,Y044d30,A/Perth/1/2022,3,interpolated,1423
-serum,Y044d30,A/SouthAfrica/R14850/2021,3,interpolated,548.7
-serum,Y044d30,A/SouthAfrica/R16462/2021,3,interpolated,1.717e+04
-serum,Y044d30,A/Sydney/43/2022,3,interpolated,1620
-serum,Y044d30,A/Togo/0274/2021,3,interpolated,2.312e+04
-serum,Y044d30,A/Togo/0304/2021,3,interpolated,8907
-serum,Y044d30,A/Togo/845/2020,3,interpolated,1.969e+04
-serum,Y044d30,A/Utah/27/2022,3,interpolated,1595
-serum,Y044d30,A/Washington/23/2020,3,interpolated,3396
-serum,Y044d30,A/Wisconsin/588/2019,3,interpolated,1501
-serum,Y154d182,A/Bangladesh/2221/2021,3,interpolated,199.3
-serum,Y154d182,A/Bangladesh/3210810034/2021,2,interpolated,244.8
-serum,Y154d182,A/Bangladesh/8002/2021,3,interpolated,273.8
-serum,Y154d182,A/Bangladesh/8036/2021,3,interpolated,259.2
-serum,Y154d182,A/Belgium/H0017/2022,3,interpolated,1978
-serum,Y154d182,A/Belgium/H0038/2022,3,interpolated,3448
-serum,Y154d182,A/Brisbane/02/2018,4,interpolated,4279
-serum,Y154d182,A/Brisbane/48/2022,3,interpolated,251.4
-serum,Y154d182,A/California/07/2009,4,interpolated,4355
-serum,Y154d182,A/Chester/5355/2022,3,interpolated,236.8
-serum,Y154d182,A/Cote_DIvoire/1448/2021,3,interpolated,3436
-serum,Y154d182,A/England/220200318/2022,3,interpolated,2487
-serum,Y154d182,A/Ghana/138/2020,3,interpolated,2912
-serum,Y154d182,A/Ghana/2080/2020,3,interpolated,2655
-serum,Y154d182,A/Hawaii/70/2019,4,interpolated,3705
-serum,Y154d182,A/India-PUN-NIV328484/2021,3,interpolated,272.8
-serum,Y154d182,A/India-Pune-Nivcov2221170/2022,2,interpolated,165.5
-serum,Y154d182,A/India/Pun-NIV312851/2021,3,interpolated,285.9
-serum,Y154d182,A/Michigan/19/2021,3,interpolated,248.5
-serum,Y154d182,A/Michigan/45/2015,4,interpolated,6216
-serum,Y154d182,A/Newcastle/2/2022,3,interpolated,272.6
-serum,Y154d182,A/Niger/10217/2021,3,interpolated,2855
-serum,Y154d182,A/Nimes/871/2021,3,interpolated,3384
-serum,Y154d182,A/Norway/25089/2022,3,interpolated,215.8
-serum,Y154d182,A/Paris/30353/2021,3,interpolated,2317
-serum,Y154d182,A/Paris/31196/2021,3,interpolated,4817
-serum,Y154d182,A/Perth/1/2022,3,interpolated,292.4
-serum,Y154d182,A/SouthAfrica/R14850/2021,3,interpolated,226.7
-serum,Y154d182,A/SouthAfrica/R16462/2021,3,interpolated,3079
-serum,Y154d182,A/Sydney/43/2022,3,interpolated,248.9
-serum,Y154d182,A/Togo/0274/2021,3,interpolated,3440
-serum,Y154d182,A/Togo/0304/2021,3,interpolated,3511
-serum,Y154d182,A/Togo/845/2020,3,interpolated,2327
-serum,Y154d182,A/Utah/27/2022,3,interpolated,275.3
-serum,Y154d182,A/Washington/23/2020,3,interpolated,835.2
-serum,Y154d182,A/Wisconsin/588/2019,3,interpolated,1094
+group,serum,virus,titer,titer_bound,titer_sem,n_replicates,titer_as
+pilot,A23038d0_r32_75K,A/Bangkok/P3599/2023,1863,interpolated,25.05,2,midpoint
+pilot,A23038d0_r32_75K,A/Bangkok/P3755/2023,851.5,interpolated,540.5,3,midpoint
+pilot,A23038d0_r32_75K,A/Bhutan/0006/2023,611.9,interpolated,86.66,3,midpoint
+pilot,A23038d0_r32_75K,A/Bhutan/FLU-BTG-00988/2022,552,interpolated,183.8,3,midpoint
+pilot,A23038d0_r32_75K,A/Brisbane/429/2023,1534,interpolated,331.1,2,midpoint
+pilot,A23038d0_r32_75K,A/Busan/1301/2023,773.6,interpolated,57.66,2,midpoint
+pilot,A23038d0_r32_75K,A/California/81/2023,1454,interpolated,901.2,2,midpoint
+pilot,A23038d0_r32_75K,A/Cambodia/e0826360/2020_egg,8843,interpolated,1407,3,midpoint
+pilot,A23038d0_r32_75K,A/Catalonia/2041146NS/2023,747,interpolated,136.9,2,midpoint
+pilot,A23038d0_r32_75K,A/Catalonia/NSVH102124476/2023,655.3,interpolated,119.3,3,midpoint
+pilot,A23038d0_r32_75K,A/Chipata/15-NIC-001/2023,1137,interpolated,639.8,3,midpoint
+pilot,A23038d0_r32_75K,A/EHIME/50/2023,1167,interpolated,285.7,3,midpoint
+pilot,A23038d0_r32_75K,A/Georgia/40/2023,1123,interpolated,345,3,midpoint
+pilot,A23038d0_r32_75K,A/Hong_Kong/2671/2019,8621,interpolated,1408,3,midpoint
+pilot,A23038d0_r32_75K,A/Hong_Kong/45/2019,1040,interpolated,12.96,3,midpoint
+pilot,A23038d0_r32_75K,A/Hong_Kong/4801/2014,5075,interpolated,2410,2,midpoint
+pilot,A23038d0_r32_75K,A/Hong_Kong/4801/2014_(15/192),1.28e+04,lower,437.4,3,midpoint
+pilot,A23038d0_r32_75K,A/Jeju/1047/2023,1039,interpolated,515,2,midpoint
+pilot,A23038d0_r32_75K,A/Kansas/14/2017,4041,interpolated,2384,2,midpoint
+pilot,A23038d0_r32_75K,A/Krabi/THIS050/2023,3116,interpolated,2069,2,midpoint
+pilot,A23038d0_r32_75K,A/Malaysia/IMR-SARI1989/2023,1422,interpolated,3.266,2,midpoint
+pilot,A23038d0_r32_75K,A/Massachusets/18/2022,1241,interpolated,202.4,2,midpoint
+pilot,A23038d0_r32_75K,A/Netherlands/01685/2023,1424,interpolated,19.06,2,midpoint
+pilot,A23038d0_r32_75K,A/Netherlands/01760/2023,1764,interpolated,228.9,3,midpoint
+pilot,A23038d0_r32_75K,A/Ontario/RV00796/2023,1238,interpolated,385.7,3,midpoint
+pilot,A23038d0_r32_75K,A/SOUTH_AFRICA/R07876/202023,797.5,interpolated,83.49,3,midpoint
+pilot,A23038d0_r32_75K,A/Saint-Petersburg/RII-MH144113/2023,1685,interpolated,222.5,3,midpoint
+pilot,A23038d0_r32_75K,A/Saskatchewan/SKFLU317847/2023,2104,interpolated,432.1,2,midpoint
+pilot,A23038d0_r32_75K,A/Schleswig-Holstein/4/2023,1451,interpolated,332.6,3,midpoint
+pilot,A23038d0_r32_75K,A/Singapore/INFIMH-16-0019/2016,3274,interpolated,754.6,3,midpoint
+pilot,A23038d0_r32_75K,A/Singapore/INFIMH-16-0019/2016_X-307A,1.28e+04,lower,0,3,midpoint
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