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In this section, we apply our method to the whole-genome sequencing time series data of influenza A H1N1 (IVA) strain. The data were collected from multiple passages with total two biological replicates (E1 \& E2) in the presence and absence of an inhibitor of neuraminidase, oseltamivir (see Figure \ref{fig:flow_flu1}). At the end of each passage, whole-genome high throughput sequencing data were collected. The read counts are unbalanced between the two experiments, as the first replicate, E1, consistently had more reads than the second one.
The IVA strain consists of 8 segments: PB2 (2313 nucleotides (nts)), PB1 (2301 nts), PA (2303 nts), HA (1775 nts), NP (1396 nts), NA (1426 nts), M1/2 (1005 nts), and NS1/2 (869 nts). To reduce computational intensity, we examine each segment per replicate separately. Within each duplicate, we analyze the control and treatment groups over selected time points simultaneously. In particular, we choose five time points: 1, 3, 9, 12, and the end (13 and 18 for the Ruplicates I and II, respectively). Since the first three passages were shared across groups,
there were we analyze total
of 8 time-samples, three of which were treated, for each biological replicate. Denote the 8 collection times as $t_1, t_2, t_3, t_4, t_5, t_{3D}, t_{4D}, t_{5D}$. The summary statistics are then formulated as
\begin{equation}
Ht(D_i) = \min\{ Ht(\pi_i^{t_1},\pi_i^{t_{5D}}), Ht(\pi_i^{t_2},\pi_i^{t_{5D}}), \}
\label{eq:HtFluDi}
\end{equation}
\begin{equation}
Ht(N_i) = \max\{ Ht(\pi_i^{t_1},\pi_i^{t_2}), Ht(\pi_i^{t_1},\pi_i^{t_j}), Ht(\pi_i^{t_2},\pi_i^{t_j}), \; j=3,4,5 \},
\label{eq:HtFluNi}
\end{equation}
The Tto allow additional response time for the drug, the comparisons to $t_{3D}$ and $t_{4D}$
were are not directly included in
$Ht(D_i)$ to allow additional response time for the drug. $Ht(D_i)$. However, the information obtained at time $t_{3D}$ and $t_{4D}$
was are utilized for borrowing information across time.
Figure \ref{fig:H1N1Ct_seg67} shows the zoom-in view of the
trajectories of the set size number of
elements in $S_1^d, S_2^d, S_3^d$
as a function of threshold $d$ for segment 6 and 7. The top panels are based on Replicate I while the bottom two based on Replicate II. The dashed vertical lines are the thresholds
$d_0$. $d_0$ obtained using our method. At each
threshold $d_0$, panels Seg6E1, Seg6E2, and Seg7E1 each has one site identified as signal. There is no signal in Seg7E2 at $d_0 = 8.864$.
