It is our primary focus to study the spatial distribution of disease incidence at different geographical levels. Often, spatial data are available in the form of aggregation at multiple scale levels such as census tract, county, state, and so on. When data are aggregated from a fine (e.g. county) to a coarse (e.g. state) geographical level, there will be loss of information. The problem is more challenging when excessive zeros are available at the fine level. After data aggregation, the excessive zeros at the fine level will be reduced at the coarse level. If we ignore the zero inflation and the aggregation effect, we could get inconsistent risk estimates at the fine and coarse levels. Hence, in this paper, we address those problems using zero inflated multiscale models that jointly describe the risk variations at different geographical levels. For the excessive zeros at the fine level, we use a zero inflated convolution model, whereas we consider a regular convolution model for the smoothed data at the coarse level. These methods provide a consistent risk estimate at the fine and coarse levels when high percentages of structural zeros are present in the data.

中文翻译：

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聚合小区域健康数据的零膨胀多尺度模型

研究不同地理层面疾病发病率的空间分布是我们的主要重点。通常，空间数据以多尺度级别（例如人口普查区、县、州等）的聚合形式提供。当数据从精细（例如县）到粗糙（例如州）地理级别聚合时，将会丢失信息。当在精细级别可用过多零时，该问题更具挑战性。数据聚合后，细化层过多的零将在粗化层减少。如果我们忽略零通胀和聚合效应，我们可能会在精细和粗略级别上得到不一致的风险估计。因此，在本文中，我们使用零膨胀多尺度模型来解决这些问题，这些模型共同描述了不同地理级别的风险变化。对于精细级别的过多零，我们使用零膨胀卷积模型，而我们在粗略级别考虑平滑数据的常规卷积模型。当数据中存在高百分比的结构零时，这些方法在精细和粗略级别提供一致的风险估计。