Spatial clustering of leukemia and type 1 diabetes in children in Denmark

Abstract

It has been proposed that type 1 diabetes (T1D) and leukemia in children may cluster in space and time due to common spatially mediated etiologies. We investigated this hypothesis and clustering of both diseases separately in Danish children aged 0–14 years, using 1,168 leukemia cases diagnosed in the period 1980–2006, 2,443 T1D cases diagnosed 1996–2006, and population-based controls matched on age, gender, and time of diagnosis. Residential histories from birth to diagnosis were collected. For leukemia in ages 0–14 years, we found no evidence of clustering; we did find spatial clustering at time of diagnosis for children aged 2–6 years with acute lymphoblastic leukemia (ALL) (observed/expected [95% confidence interval]: 1.35 [1.15–1.54]). T1D cases showed clustering at birth for ages 0–14 years; for ages 0–4 years at diagnosis, and when the residential history was accounted for. T1D cases clustered near leukemia cases particularly in the age group 2–6 years at diagnosis. Leukemia and T1D in this age group thus may share etiological factors mediated by geographic location. This suggests common environmental risk factors, with exposure to infections as first possible candidate, geographically localized exposure to agents that compromise development and/or response of the immune system being a second, and chance being a third.

Appendices

Appendix A

Kernel density

Place a kernel at grid point i (i = 1,…,n). Each observed point location j (j = 1,…,n) is then assigned a weight according to the kernel function $k\left( {d_{ij} } \right)$, which is a function of the distance from grid point i to point location j. The intensity estimate $\hat{\lambda }_{i}$ at location i is the sum of the individual contributions mode from each observed point j: $\hat{\lambda }_{i} = \sum\nolimits_{j\left( 1 \right)}^{n} {k\left( {d_{ij} } \right)}$.

There are many possible kernel functions. We used the most common one, the quartic kernel: $k\left( {d_{ij} } \right) = {\frac{3}{{\pi \tau^{2} }}}\left( {1 - {\frac{{d_{ij}^{2} }}{{\tau^{2} }}}} \right)^{2} ;\quad d_{ij} < \tau$, where τ is the bandwidth of the kernel.

Appendix B

k-function

The k-function is a measure of the second-order characteristics of a point process. It is defined by the mean number of events within a distance h of an arbitrary event, divided by the mean number of events per unit area. The expected value of k(h) in a random pattern is equal to λπh²/λ = πh², where λ is the mean number of events per unit area. An estimate of k(h) is based on the count of number of pairs of points that are found within a distance h of one another, more formally, $\hat{k}\left( h \right) = {\frac{1}{{\hat{\lambda }^{2} R}}}\sum\nolimits_{i = 1}^{n} {\sum\nolimits_{j \ne i} {I_{ij} \left( h \right)} }$ where R is the area of the study region, n is the number of points observed in R, and I _ij (h) is an indicator function equal to one if points i and j are separated by a distance less than h.

Edge effects are incorporated by dividing the I _ij (h) term by w _ij , defined as the proportion of the circumference of a circle centered on i and passing through j that lies within the study region.

Appendix C

Cuzick–Edwards test

Cuzick–Edwards test is based on the neighboring structure in case–control data. It is the sum of the number of cases among the k-nearest neighbors of all cases, more formally,

$T_{k} = \sum\nolimits_{i = 1}^{n} {\sum\nolimits_{j = 1}^{n} {w_{ij} \delta_{i} \delta_{j} } } ,$ where δ _i is equal to one if i is a case, and zero if location i is a control. The term w _ij is equal to one if j is a k-nearest neighbor of i and zero otherwise. The choice of k determines the spatial scale at which the test is carried out.